B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) I
123456
123456
Supporting Early NumeracyBC Early Numeracy Project (K-1)
Ministry of Education
Supporting Early NumeracyBC Early Numeracy Project (K-1)
S U P P O R T I N G E A R L Y N U M E R A C Yii
N AT I O N A L L I B R A RY O F C A N A D I A N C ATA L O G U I N G I N P U B L I C AT I O N D ATAMain entry under title:Supporting early numeracy : BC Early Numeracy Project (K-1)
“Developed by the British Columbia Early NumeracyProject to complement Assessing early numeracy.”—Introd.
ISBN 0-7726-5134-5
1. Arithmetic - Study and teaching (Elementary) -British Columbia. 2.Arithmetic - Study and teaching(Preschool) - British Columbia. I. British Columbia.Ministry of Education. II. British Columbia. EarlyNumeracy Project. III. Title: Assessing early numeracy.
QA135.6.S96 2004 372.7’2044 C2004-960017-6
© 2003 Ministry of Education, Province of British Columbia.
C O P Y R I G H T N OT I C E
No part of this document may be reproduced in any form or by any means,including electronic storage, reproduction, execution or transmissionwithout the prior written consent of the Province.
P R O P R I E TA RY N OT I C E
This document contains information that is proprietary and confidential to theProvince. Any reproduction, disclosure or other use of this document is expresslyprohibited except as the Province may authorize in writing.
Permission to copy and use this publication in part, or in its entirety, for non-profiteducational purposes within British Columbia and the Yukon, is granted to all staffof BC school board trustees, including teachers and administrators; organizationscomprising the Educational Advisory Council as identified by Ministerial Order; andother parties providing direct or indirect education programs to entitled students asidentified by the School Act.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) iii
Table of ContentsTable of Contents
Introduction . . . 1
Introducing Supporting Early Numeracy . . . 1
Connecting Assessment and Instruction . . . 2
Using Assessment Results to Inform Instruction . . . 4
Fostering Numeracy Development . . . 5
Framework for Number Development . . . 7
Numeracy Experiences in K-1 Classrooms . . . 10
Quick Tour of This Resource . . . 13
Small-Group Intervention . . . 15
Surprise Box . . . 15
Focused Instruction for the Classroom . . . 27
Estimation . . . 27
Pattern . . . 47
Counting and Numeral Recognition . . . 59
Visual-Spatial Pattern Recognition . . . 78
Math Playground . . . 91
Masters
Master 1: Sorting Boards . . . 101
Master 2: Two-column Bar Graph . . . 102
Master 3: Comparison Strips . . . 103
Master 4: Ladybug Mat . . . 104
Master 5: Ten-frame Mat . . . 105
Master 6: Dice Game Record Sheet . . . 106
S U P P O R T I N G E A R L Y N U M E R A C Yiv
Master 7: Dice Pattern Cards . . . 107
Master 8: Numeral Cards 0–9 . . . 108
Master 9: 100 Chart . . . 109
Master 10: Number Lines . . . 110
Master 11: Record Sheet 1 . . . 111
Master 12: Record Sheet 2 . . . 112
Master 13: 5-Way Sorting Mat . . . 113
Master 14: 100 Chart Grid . . . 114
Master 15: Coin Cut-outs . . . 115
Master 16: Dice Mat . . . 116
Master 17: Domino Mat . . . 117
Master 18: Dot Pattern Cards . . . 118
Master 19a: Domino Cards . . . 119
Master 19b: Domino Cards . . . 120
Master 20: Ten-frame Cards . . . 121
Master 21: Ladybug Cards . . . 122
Master 22: Ten-frame Mats . . . 123
Master 23: Double Ten-frame Cards . . . 124
Master 24: Pattern Cards . . . 125
Master 25: Pattern Game Board . . . 126
Master 26: Small 100 Charts . . . 127
Master 27: Geoboards . . . 128
Master 28: Bingo Cards . . . 129
Master 29: Cover the Blocks 1 . . . 130
Master 30: Cover the Blocks 2 . . . 131
Master 31: Cover the Blocks 3 . . . 132
Master 32: Cover and Copy . . . 133
Master 33: Pattern Block Challenge . . . 134
Master 34: Combinations 1 . . . 135
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) v
Master 35: Combinations 2 . . . 136
Master 36: Combinations 3 . . . 137
Master 37: How Many Triangles? 1 . . . 138
Master 38: How Many Triangles? 2 . . . 139
Master 39: How Many Triangles? 3 . . . 140
Master 40: How Many Triangles? 4 . . . 141
Master 41: How Many Triangles? 5 . . . 142
Master 42: Tangram Matching . . . 143
Master 43: Tangram Cover-up 1 . . . 144
Master 44: Tangram Cover-up 2 . . . 145
Master 45: Tangram Cover-up 3 . . . 146
Master 46: Tangram Cover-up 4 . . . 147
Master 47: Tangram Cover-up 5 . . . 148
Master 48: Tangram Cover-up 6 . . . 149
Master 49: Tangram Cover-up 7 . . . 150
Master 50: Surprise Box Record Sheet . . . 151
Master 51: Large Triangles for Triangle Challenge . . . 152
Master 52: Squared Paper . . . 153
Master 53: Triangle Paper . . . 154
Master 54: Assessment Class Compilation . . . 155
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 1
Introduction
“There is a bigchange for mein terms ofhow I assess.… a lot of kidsjust aren’t ableto share theirthinking in awritten formator even inpictorial form. ”
Introduction
Introducing Supporting Early Numeracy
Supporting Early Numeracy was developed by the British Columbia
Early Numeracy Project to complement Assessing Early Numeracy.
● Assessing Early Numeracy helps teachers determine which
children would benefit from support in grade one and identifies
the aspects on which to focus.
● Supporting Early Numeracy is an instructional resource to
support grade one students who are at risk of falling behind
because they lack basic numeracy concepts, skills and attitudes.
Children who would benefit from using these materials include
those who:
– need explicit and structured support
– hesitate to ask for assistance
– avoid taking risks
– do not demonstrate growth or progress over time
– might respond to an alternative approach
Supporting Early Numeracy provides teaching suggestions to follow
up the K-1 assessment. An overall focus of the resource is to develop
positive math attitudes or dispositions. The content focuses on
number sense (Estimation, pages 27–46; Pattern, pages 47–58;
Counting and Numeral Recognition, pages 59–77) and spatial
thinking (Visual-Spatial Pattern Recognition, pages 78–90; Math
Playground, pages 91–100).
S U P P O R T I N G E A R L Y N U M E R A C Y2
Connecting Assessment and Instruction
When used at the end of kindergarten or early in grade one, the K-1
Early Numeracy Assessment can help you determine which
students might benefit most from the activities in this resource.
Once you have completed the assessment, the Learner Profiles
you compile provide an overview of each child’s strengths and
weaknesses. This information can be used to determine
appropriate follow-up instruction for individuals, small groups
or the whole class.
Supporting Early Numeracy was informed by the Framework
for Number Development described on pages 7 to 9.
The developmental progression (Emergent,
Early, Developing, Expanding and Established)
is noted in the directions for each activity (with the exception of
those in Surprise Box and Math Playground). These levels are
approximate and are meant to be used only as a guideline.
❍ ❍ ❍ ❍ ❍
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 3
Counting, Visual- MathEstimation Pattern Numerals Spatial Playground
1 Mathematical Awareness
2 Recognizing Dot Patterns
3 Matching Numerals and Sets
4 Ordering Numerals 0-9
5 Counting Forward
6 Counting Backwards
7 Estimate and Check
8 Invariance and Counting On
9 Build and Change
10 Pattern Items
11 Problem Solving
12 Squares Puzzle
13 Reading Numerals
14 Printing Numerals
15 Coin Sets •
16 Cube Building •
17 100 Chart •
• optional items
Table 1: Linking Assessing Early Numeracy withSupporting Early Numeracy
The following table shows how Supporting Early Numeracy
connects to the different assessment items in Assessing Early
Numeracy. A dark screen indicates a major relationship, a light
screen indicates a minor relationship, and no screen indicates
no relationship.
S U P P O R T I N G E A R L Y N U M E R A C Y4
Using Assessment Results to Inform
Instruction
S U P P O R T I N G E A R LY N U M E R AC Y
Supporting Early Numeracy offers instructional suggestions for
follow-up to the assessment:
S M A L L - G R O U P I N T E RV E N T I O N
You may find children who struggled with most or all of the items
on the assessment. These children likely would benefit most from
additional support working in a small-group setting outside the
classroom to build or consolidate kindergarten-level early numeracy
skills. The section designed with these children in mind is Surprise
Box, a small-group intervention program for children at risk.
F O C U S E D I N S T RU C T I O N F O R T H E C L A S S R O O M
Some children perform strongly on some assessment items and
struggle with others. The chart on page 31 can help to determine
which parts of this resource to use for working on specific concepts
and skills. The Focused Instruction for the Classroom section
contains skill-specific activities that are designed to be used in
small groups (or with the whole class if appropriate).
W E B S I T E R E S O U R C E S
The Ministry of Education website (http://www.bced.gov.bc.ca/
primary_program/) also provides access to Math for Families –
Supporting Numeracy at Home, which provides suggestions for
ways that families can continue to support children’s numeracy
development through at home activities. Please encourage parents
to use the ideas in Math for Families – Supporting Numeracy at
Home on the website. You are also invited to duplicate the parts you
would like to share with families in newsletters, conferences or
family mathematics sessions.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 5
Fostering Numeracy Development
Supporting Early Numeracy balances spatial and number content to
encourage alternative paths to success. The lessons and activities
described in this resource develop numeracy skills in ways that are
active and fun.
● Number sense involves number skills, number concepts and a
positive mathematical disposition.
● Spatial activities involving hands-on experiences provide the
sensory input that helps to develop mental imagery.
● Attitude is key. Children who see themselves as capable math
thinkers and problem solvers are on the road to mathematical
success.
● The focus is on meaning, with skills used in context. The more
connections children can make, the better.
● Visual cues and formats support learning.
● Building mental imagery expands children’s ability to think in
flexible ways.
● Bridges are built to new learning by first reviewing what the children
know and then connecting their knowledge to new goals.
● Emphasis is gradually put on making written records of the
activities that can be used for reinforcement in the classroom
and at home.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 7
Framework for Number Development
K
Grade 1
Grade 2
Grade 3
Table 2: Typical Number Concept DevelopmentPatterns for K-3
In Assessing Early Numeracy a research-based developmental
scheme is used as a frame of reference to consider children’s
understanding of number. This frame of reference is not tied to ages
or grades. Rather, it highlights growth in number reasoning and
understanding. Table 2 includes a graphic representation of the
scheme’s levels. This graphic is included with the activity directions
in Supporting Early Numeracy to provide you with “at a glance”
information about each activity’s level.
❍ ❍ ❍ ❍ ❍
Emergent Early Developing Expanding Established
K
Grade 1
Grade 2
Grade 3
The following framework for the development of number is based
on extensive research. This framework is concerned first with the
underlying conceptual development that provides the foundation
for children’s understanding of number. Though the rate and nature
of growth in number understanding varies for every child, growth
generally follows the described sequence from emergent to
established number.
The following chart summarizes the characteristics of the develop-
mental scheme. These stages or levels of understanding are perhaps
the most important aspect of a child’s grasp of number, and have
important implications for the development of early numeracy.
S U P P O R T I N G E A R L Y N U M E R A C Y8
Emergent Number
Children at this stage rely on
visual perception to make
estimates. They are starting to
use the language of quantity
but are not yet counting
systematically (e.g., they can
tell you which of two piles
contains more by “eyeballing”
them and seeing that one is
bigger, but they can’t count
the groups).
Children’s thinking at this pre-
counting stage typically
demonstrates:
● reliance on intuitive
reasoning
● unsystematic means of
counting (e.g., 1, 2, 3, 5,
8, 9…)
● visual-spatial strengths,
with perception used as
the basis for judgments
● multisensory
dependence (i.e., need
to see, hear, feel/touch)
● the ability to recognize
visual-spatial groupings
(e.g., dice patterns)
without counting
Early Number
Once children have
established a reliable one-to-
one counting scheme, they are
able to work systematically
with quantities of gradually
increasing size. At this stage,
for example, given an
established set of 10, when 2
more are added, they will
count from 1 to 12.
Children’s thinking at this
stage typically demonstrates:
● a systematic counting
chain to at least 10
● counting by 1s from 1.
This is called “Count All.”
● one-to-one
correspondence at least
for small quantities
● dependence on the use
of materials to support
thinking
● an ordinal view of
number (e.g., 3 means
number 3 in the row)
● a lack of invariance or
conservation of
number; perception still
dominates
Framework for the Development of Number
SNAPSHOT
CHILDREN’STHINKING
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 9
Expanding Number
Counting is no longer limited to
1s. Children can use mental chunks
as part of the quantifying process
(e.g., asked for the sum of 5+6, they
will use the known fact of 5+5 and
add 1 more to 10). This is the
early basis of place value reasoning
and multiplicative thinking.
Children’s thinking at this stage
typically demonstrates:
● a preference for using mental
reasoning, drawing on known
facts and relationships
● an ability to think in chunks
rather than counting by 1s
(shifting to many-to-one
correspondence)
● a grasp of place value, which
extends their number range
● an understanding of
reversibility and part-whole
thinking
Developing Number
Children are now able to
mentally represent a quantity
and count on or back (e.g., given
an established set of 10, when 2
more are added, they will count
11, 12). Children at this stage
conceptualize 10 as a unit and
group and count objects in
10s, but often revert to counting
by 1s.
Children’s thinking at this stage
typically demonstrates:
● reliance on counting by 1s
including counting on or
back from a starting set
(e.g., 5+3…5…6, 7, 8)
● the ability to count on or
back with tally (double
count—e.g., put out
fingers to show 1, 2, 3 but
count on 12, 13, 14)
● a cardinal view of number:
- inclusion relation
(e.g., sees 3 as part of 5)
- conservation of
number
● the ability to mentally
represent number
● reliance on fingers,
touching or head nods to
support counting
Established Number
This stage represents a shift from
additive thinking to multiplicative
reasoning. Children have moved from
relying on counting by 1s to relying
on more powerful groupings and
relationships (e.g., asked for the sum
of 27 and 35, they can mentally
decompose the numbers into 10s and
1s and recompose the groupings).
Children’s thinking at this stage
typically demonstrates:
● efficient use of facts,
relationships, strategies
● extensive mental
representation
● the ability to keep track of
several operations at once
● fully operational grouping
structures—i.e., can
meaningfully shift place values;
rename metric measures (e.g.,
2␣ m = 200 cm); and recognize
equivalent fractional parts (e.g.,
2 whole pies = 4 half pies)
S U P P O R T I N G E A R L Y N U M E R A C Y10
Numeracy Experiences in K-1 Classrooms
A rich mathematical environment is important for all kindergarten
children. Children benefit from early exposure to a wide range of
mathematical concepts, skills and attitudes, and the opportunity to
learn from these experiences. The following list provides examples
of kindergarten experiences typical of a rich mathematical
environment. The Integrated Resource Package (IRP) was used as
the starting point for this list; however, some elaboration has been
provided on particular aspects. It is important to keep in mind that
this list involves exposure or “the opportunity to learn” in
kindergarten. It is not a list of expectations for all children.
In order for this assessment to be fair, it is important that
kindergarten children have had the opportunity to learn the
concepts and skills assessed. The following overview describes
learning opportunities that kindergarten students might experience
as part of a rich mathematical literacy program.
N U M B E R C O N C E P T S A N D O PE R AT I O N S
● using a wide variety of concrete, hands-on manipulatives for
counting
● comparing more or less
● counting and comparing how many students are here today
(number of boys/girls/in all)
● ordering/sequencing sets, pictures and numbers from least to
greatest
● counting forward and backwards to and from 20
● using counting rhymes and finger play
● estimating and checking guesses for objects, actions, times, and
so on
● counting beyond 20—people, things, actions, days (e.g.,
celebrate the 100th day of school)
● solving problems involving joining, separating, grouping and
sharing, drawn from real-life situations
● being exposed to numbers from 0 to 100, including the use of
number lines and 100 charts
● using calendar activities to count forward and backwards to
specific days or events (e.g., someone’s birthday)
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 11
● recognizing, identifying and printing numerals from 1 to 10
(minimum)
● matching objects and numerals to 10 (minimum)
● using numbers on the computer keyboard
● counting by 2s, 5s and 10s and connecting counting to the
number line and 100 chart using colour coding
● grouping using counting sticks or straws and bundling quantities
by 2s, 5s, 10s and 100s
● cutting snacks (e.g., apples) into equal parts to share
● understanding half as part of a whole
● playing games using dice and playing cards to reinforce increase/
decrease skills (e.g., Box Cars and One-Eyed Jacks)
● being exposed to part/whole relationships (e.g., using two-sided
counters: 3 red, 2 white, 5 in all)
P AT T E R N S
● creating, identifying, reproducing and extending patterns using a
variety of hands-on manipulatives (e.g., Unifix cubes, pattern
blocks, buttons)
● creating, identifying, reproducing and extending patterns using
different body actions (e.g., clapping, snapping, stomping,
patting) and pictures or diagrams
● using words to describe the pattern (e.g., red, red, blue, red, red,
blue or a, a, b, a, a, b)
● being exposed to and experiencing patterns using the Calendar
● looking for patterns on the 100 chart
● experiencing dot patterns through the use of dice and dominoes
games
● identifying patterns in the environment or surroundings
M E A S U R E M E N T
● experiencing non-standard units (e.g., estimate and check how
many paper clips or Unifix cubes are needed to make the length
of the chalk brush)
● ordering objects by size, length, height and/or weight; identifying
which object is bigger/smaller, longer/shorter, taller/shorter,
heavier/lighter
● reading the thermometer and identifying the temperature through
daily calendar activities; using the terms hotter, colder or warmer
S U P P O R T I N G E A R L Y N U M E R A C Y12
● being exposed to units of time through daily calendar activities
(e.g., days of the week/times of the day/seasons)
● being exposed to the names and values of different Canadian
coins (penny, nickel, dime, quarter, loonie, toonie) through
informal activities (e.g., set up a store or restaurant with a cash
register)
● comparing different-size containers on the water table; using the
terms empty, full, half-full
S H A PE S
● recognizing, identifying and creating basic shapes (square, circle,
triangle, rectangle, oval, diamond)
● making body shapes in the gym
● identifying basic shapes in the environment or in their
surroundings (e.g., going on a Shape Walk to identify shapes: tires
are circles; the door is a rectangle; and so on)
● sorting and classifying objects by shapes
● tracing and drawing different shapes
● patterning with shapes (e.g., using pattern blocks: diamond,
square; diamond, square)
● experimenting and constructing using foam or wooden blocks
V I S UA L - S PAT I A L
● being exposed to tangram shapes, geometric puzzles.
● using tangram or pattern block pieces to re-create a picture or
build on top of a picture
● using geoboards and geobands
● being exposed to dice and domino patterns
● being exposed to simple symmetry using mirrors and pattern
blocks
S TAT I S T I C S A N D P R O B A B I L I T Y / D ATA A N A LY S I S
● collecting, organizing and comparing data using appropriate
language (e.g., more/less)
● conducting surveys (e.g., surveying their classmates)
● graphing information and interpreting data
● using many different types of graphs to record information in a
variety of ways
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 13
● being exposed to concepts such as always, sometimes, and never
● being exposed to probability through dice activities (e.g., Box
Cars) and other fun, hands-on activities (e.g., How many red
candies do you think are in this box?)
Quick Tour of This Resource
Supporting Early Numeracy is divided into two sections:
● Small-Group Intervention
● Focused Instruction for the Classroom
The blackline masters for both sections are located on pages 101–151.
S M A L L - G R O U P I N T E RV E N T I O N
Surprise Box—an instructional sequence for working with at-risk
grade one children in a small-group setting outside of the
classroom. The Surprise Box resource is designed to develop
positive attitudes and kindergarten-level concepts and skills in a
supportive environment.
S U P P O R T I N G E A R L Y N U M E R A C Y22
Surprise Box Part 4Surprise Box Part 4
W H AT D O YO U N E E D ?
● Two-Column Bar Graph (Master 2)
● Comparison Strips (Master 3)
● Numeral Cards for 7 and 8 (Master 8; use
only if child is secure in recognizing
numerals up to 6)
W H A T ’ S I N T H E B O X ?
● Each box contains up to 15 Unifix cubes of
two colours (e.g., 7+8 or 6+9).
● Have extra cubes available for patterning,
but put the same number back in the boxes.
W H AT D O YO U D O ?
● Count objects as they come out of the boxes
and go back into the boxes.
● Count backwards as you return one cube at
a time to the box (e.g., “3 red cubes, 2 red
cubes, 1 red cube, 0 red cubes. All the red
ones are in the box—3, 2, 1, 0. Now let’s do
our blue cubes—4 in all, and so on.”) Use
subsets of one colour at a time, increasing
the number gradually.
● Sort and count, using comparative language.
● Work on recognizing parts of a set and the
whole set (e.g., 3 red, 5 blue, 8 cubes in all).
● Work on creating and reading patterns,
making sounds and actions to match.
L A N G UAG E TO M O D E L A N D E N C O U R AG E
● part/whole language (e.g., some, all, none)
● the language of addition and subtraction
(when items are put into and taken out of
the boxes)
● pattern words (e.g., repeat, same, change,
different)
P R O C E S S E S T O M O D E L A N D E N C O U R AG E
● representing patterns and collections in
various ways
D I S P O S I T I O N S TO E N C O U R A G E
● positive attitude: Patterning is fun; I can
continue patterns; I can count and compare
groups.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 23
Surprise Box Part 5Surprise Box Part 5
W H AT D O YO U N E E D ?
● part/whole mat, such as Ladybug Mat
(Master 4)
● 10-Frame Mats (Master 5)
● dice
● Dice Game Record Sheet (Master 6)
W H A T ’ S I N T H E B O X ?
● Each box has up to 20 objects, 6 round
counters as one set, 10 and 4 as the others.
W H AT D O YO U D O ?
● Count to 20 for all objects in the box; count
back from 10 using subsets.
● Name parts and wholes for sets to 6 using
part/whole mats.
● Make sets of 10 on 10-frames, matching to
fingers.
● Part/Whole Game:
5 little ants in all.
Some are hiding under the rock.
4 are on the rock.
How many are hidden?
Let’s check:
4 on the rock.
1 under the rock.
5 in all.
This time 2 are on the rock….
L A N G UA G E TO M O D E L A N D E N C O U R A G E
● words for pulling apart and putting back
together (e.g., separate, join, subtract, add)
● names for numbers, naming parts of wholes
(e.g., 4 and 2 is a name for 6; 3 and 3 is
another name for 6)
P R O C E S S E S TO M O D E L A N D E N C O U R A G E
● building sets of 10
● recognizing numerals
● printing numerals
● using number rhymes to remember numerals
D I S P O S I T I O N S T O E N C O U R AG E
● positive self-concept: I can take sets apart and
rejoin them; I can name parts and wholes.
S U P P O R T I N G E A R L Y N U M E R A C Y14
S U P P O R T I N G E A R L Y N U M E R A C Y72
Find and Read Two-Digit NumbersFind and Read Two-Digit Numbers
Math Focus: Two-Digit Numbers❍ ● ● ❍ ❍
W H AT D O YO U N E E D ?
◗ wall-size 100 Chart
◗ wall calendar
◗ individual sets of Numeral Cards 0-9 (Master 8)
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
◗ count to 100?
◗ give the number that comes after, to 100?
◗ give the number that comes before, to 100?
◗ give the number that comes between two
other two-digit numbers?
◗ find given two-digit numbers on the 100
chart and number line?
◗ print or use cards to show given two-digit-
numbers?
◗ find two-digit numbers on the calendar, 100
chart or number line?
◗ recognize and name numerals to 100?
The ability to recognize and read two-digit
numbers can support children’s early
understanding of place value. Similarly,
knowing that 12 is “twelve” in the counting
sequence precedes recognizing 12 as 10 and 2.
W H AT M I G H T YO U T RY ?
◗ Introduce the 100 chart (the wall chart may
already have been noticed). Focus on the 10s
column, and count together. Ask the children
what patterns they can see on the chart. Ask
them to show the patterns they see. Do this
on a regular basis. Your most adept math
students will find patterns that the other
children will gradually be able to see.
◗ Practise counting daily on the wall 100 chart.
◗ On the calendar, focus on reading 20 to 31.
Then look at the 100 chart and practise
reading 20 to 100.
◗ Play I Spy: “Can you find 75? What row will it
be in on the 100 chart? Point to it.” Model
analytical thinking, and have the children
explain how they knew where the numbers
would be found.
◗ Use individual numeral cards to show two-
digit numbers. Point to 36, for example, on
the number line, and ask the students to
make that number with their cards. At first
this will be a simple matching task. Later, try
it from memory.
◗ Continue to work with extending the children’s
counting chains up to 100. Emphasize the
decade shifts with your expression. Build
rhythm into the counting. Connect this
counting to the Estimation work.
◗ Connect this counting to work the children
are doing in the Visual-Spatial section,
particularly with 10-frames.
◗ Practise naming the number before, after or
between, using the 100 chart and number
line as a reference at first, then working
toward doing it with eyes closed. Different
children will develop the mental imagery at
different times.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 73
Teen NumbersTeen Numbers
Math Focus: Teen Numbers
W H AT D O YO U N E E D ?
◗ number line
◗ 100 Chart
◗ baggies and small counters
◗ Unifix cubes
◗ dimes and pennies
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
◗ count verbally from 1 into the 20s or 30s?
◗ give the next number when given a teen
number?
◗ give the number that comes before when
given a teen number?
◗ describe 14 as 10 and 4 when given a 10 and
1s model?
◗ find teen numbers in a random collection of
numerals?
◗ read teen numbers accurately and match
them to the 100 chart?
The teen numbers can be challenging for young
children because of their conflicting number
names (i.e., seventeen suggests 7teen and is
often written as 71). There are also auditory
challenges due to the similar sounding number
names of teens with multiples of 10 (i.e., thirty
sounds like thirteen and can cause confusion if
not addressed).
W H AT M I G H T YO U T RY ?
◗ Ensure the students have a grasp of number
above 20 for counting, reading and even writing
before going back and re-emphasizing teens.
◗ Ensure the students are familiar with the 100
chart before focusing on teens, so they can
place them within the counting framework.
◗ Clearly articulate and focus on the verbal
difference between teens and the decades
(i.e., 30, 40, 50). This is especially important
for ESL students.
◗ Use the number line and 100 chart to show
13 vs. 30, 15 vs. 50, and so on.
◗ Introduce a new way to read the teen numbers
by building up from 10, saying 10 and 1, 11 in
all; 10 and 2, 12 in all; 10 and 3, and so on.
Sometimes this verbal pattern can help to
establish both the correct printing pattern for
teens and an intuitive understanding of the
place value that underlies our system.
◗ Bag and label sets of 10 so that you can practise
counting together 10 and 1, 10 and 2, and so on.
◗ Provide Unifix cubes for building 5s in one
colour. Use these to build 10-sticks in two
colours. Use the 10-sticks with 1s to build
teen numbers.
◗ Introduce the dime as 10 cents, and use
dimes and pennies to practise teens. (This is
useful even for children who don’t count on.
Familiarity will help connect the conceptual
and procedural when it makes sense.)
❍ ● ● ❍ ❍
F O C U S E D I N S T RU C T I O N F O R T H E C L A S S R O O M
This section includes two sets of structured activities and three
“idea files” that can all be used in small groups (or whole groups as
appropriate). The five skill-specific sections include:
● Estimation—a collection of structured activities that help
children learn a variety of strategies to assist with estimation and
recognize when it is appropriate to estimate.
● Pattern—a sequence of patterning activities that moves from
simple hands-on, active pattern tasks to more complex number
patterns. This section combines number concepts and spatial
thinking.
● Counting and Numeral Recognition—an idea file for children
who need more time and systematic reinforcement to reach
proficiency in counting and numeral recognition.
● Visual-Spatial Pattern Recognition—a sequential set of five-
minute teacher-led activities aimed at developing mental
imagery to support number sense.
● Math Playground—a resource file of hands-on spatial
explorations for independent centre work, either in the
classroom or for small-group work outside the classroom.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 15
Small-Group InterventionSmall-Group Intervention
Children who struggle with learning have few opportunities to feel
successful and safe working at their level of understanding. This
small-group intervention strategy provides a chance for these
children to shine. It is designed to be active and fun and to provide
something special for the at-risk student. Most importantly, it is
designed to build in success through careful sequencing of key
numeracy concepts and skills.
Surprise Box
Surprise Box is an activity that children can look forward to—
coming to the resource room to get their shoebox of surprises,
opening it and sorting the objects in it, then working with the
teacher to use the contents of the box. The teacher changes the
contents on a regular basis so there is an element of surprise. The
materials used can be any kind of small objects good for counting,
sorting, comparing and manipulating: Unifix cubes, pennies,
wrapped candies, buttons, shells and ribbons. Finding things that
are not usually found in the classroom adds to the “special” aspect.
Be creative!
Surprise Box activities let children practise:
● counting forward and backwards
● counting and building sets of objects
● multiple counting
● counting on
● visual-spatial quantifying
● matching and sorting
● comparing and ordering
● recognizing numerals
● interrelating concrete, verbal and symbolic
● recognizing a quantity despite perceptual changes (invariance)
● recognizing parts of wholes (e.g., seeing 3 as part of 5 without
having to recount from 1)
S U P P O R T I N G E A R L Y N U M E R A C Y16
● increasing and decreasing
● combining and separating sets
● seeing different ways to name the parts of a whole
● problem solving through modeling and recording
The numeracy intervention sessions should develop the following:
● active engagement
● numeracy concepts and skills
● vocabulary/language
● time on task
● organizational skills
● thinking and reasoning
● positive dispositions
● confidence
Using the Surprise Box Small-Group
Intervention Resource
The Surprise Box resource is divided into seven parts. Each part will
take approximately a week. By changing the objects in the boxes,
you can repeat the same focus over several days as necessary.
Repeating tasks over a series of days and with a variety of materials
provides a chance for children to become secure in their
understanding of concepts and to become competent and
confident with the skills involved. Move on to the next part only
when students have a firm grasp of the content goals.
P A R T S O F T H E R E S O U R C E
The Surprise Box activity is intended to be the first part of a 25-to-
30-minute intervention session. Each session includes three
elements:
Su r p r i s e B o x ( 1 0 - 1 5 m i n u t e s )
The children arrive and immediately get their personal “Surprise
Box.” Have each child decorate a shoebox on the first day. Fill them
with “surprises” every week (or more often). The starting set of
surprises might include three ribbons, five buttons and two of
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 17
something else (different items for each child). Have the children
take their boxes and lay the contents out on the rug or table, sorting
the materials any way they like. Ask them to count, compare, order,
describe, build and change, or pattern in progressively more
complex ways each day and week, always with the intent of
developing key number concepts connected with counting skills
and organizational strategies. As you work through the lessons,
gradually increase the number of objects and sets as well as the
complexity of ideas and language.
Sp e c i a l Sk i l l ( 5 - 1 0 m i n u t e s )
Depending on the needs of your group, choose a focus from the
skill-specific sections of the Supporting Early Numeracy resource.
For example, you may choose to focus on Estimation or Counting or
to use the Visual-Spatial sequence to build systematic patterns for
number.
W i n d - u p E x p l o r a t i o n ( 5 - 1 0 m i n u t e s )
For a fun and active wind-up, choose one of the Math Playground
activities for the children to use independently while you record
progress, informally assess or make notes for the next session.
S U R P R I S E B OX F O R M AT
Each of the seven parts of the Surprise Box resource includes the
following headings:
● What do you need?
● What’s in the box?
● What do you do?
Parts 2 through 6 also offer suggestions for:
● language to model and encourage
● processes to model and encourage
● dispositions to encourage
S U P P O R T I N G E A R L Y N U M E R A C Y18
Surprise Box Part 1Surprise Box Part 1
Day 1 Welcome and decorate
boxes.
W H AT D O YO U N E E D ?
● shoeboxes, one per child
● paper, stickers, glitter, paint, feathers or
other materials to decorate the boxes
● glue, felts, scissors, tape
W H AT D O YO U D O ?
This is a day to get to know the children and to
provide them with their boxes and decorating
materials, such as stickers, pictures, felts and
glitter. They can add things to the outside of the
boxes as they go along. They change the
outside, but you change the surprises inside.
Before the children leave, build some
excitement for the next session by having them
predict what might be in the boxes and how
many items there might be. On a chart or
chalkboard, record at least one idea from each
child. Read the list together before the children
return to their classes.
Day 2 Introduce the format
for using the Surprise Boxes.
W H AT D O YO U N E E D ?
● Before the children arrive on Day 2, put a
starting set of objects into each box. Make
each box the same to begin (e.g., 3 ribbons,
5 buttons, 2 stickers).
W H AT ’ S I N T H E B OX ?
● Three types of objects in groups of 2, 3 and 5,
for a total of 10.
● Aim for variety and novelty in your choice of
objects.
W H AT D O YO U D O ?
● Have the children find their boxes, empty out
the contents carefully and sort the contents
in some way (children’s choice).
● Ask questions to elicit sorting concepts and
vocabulary. Build on the children’s language,
connecting to more accurate labels and
reinforcing sorting vocabulary.
“How have you sorted the things in your
Surprise Box? Can you explain it to me?”
(Accept anything the students do, and
describe it in your language.)
“Jan has (model how to move as you
count so that the organization is clear) 1,
2, 3 ribbons (move and count), 1, 2, 3, 4, 5
buttons, 1, 2 stickers.”
“How many do you think she has in all?”
(Hear ideas, then count to check.)
“Do the groups of surprises have the same
number of objects? How many do you
think you have in all?”
“Matt’s things are grouped by colour. Let’s
count his groupings. Do you think he will
have the same number in all? How do you
know?”
● Repeat for each child. Look for positives to
highlight (e.g., creative sortings, verbal
descriptions, careful counting, reasonable
estimating, organized groupings).
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 19
● Explain the format for putting the objects
away:
“How many here? Let’s count as we put
them away…1, 2, 3.” (In Part 4, students
begin to count backwards as they put the
materials away.)
Day 3 Use the basic format as
above, but with the following
changes:
W H AT D O YO U N E E D ?
● Objects as described above.
W H AT ’ S I N T H E B OX ?
● Alter each child’s box so the subsets are
different but the total is still 10.
W H AT D O YO U D O ?
● Greet the children as they come in and
ensure they follow the previous day’s
routine.
● Discuss same and different in comparison to
the previous session’s collections. Use more
and most as you discuss the box contents
(e.g., more stickers, more than the number
of ribbons, “Which has more?” “Which has
the most?”)
● Help the children recognize that it is
sometimes hard to remember from day to
day. You want them to realize that it can help
to write down amounts. This can be an
introduction to using numerals and making
a permanent record. Model the use of
numerals from this point on.
“Which row has the most?”
“How many are red? Let’s count.”
“What about the rest? What do you have
the most of today?”
“Is that different from yesterday?”
“How many __ do you have today?”
“Can you put your groups in order from
the least to the greatest number of
things?”
Day 4
If you need another day to establish the routine,
repeat the previous day’s plan. If the children
are ready, continue on to Part 2, using the
established format.
S U P P O R T I N G E A R L Y N U M E R A C Y20
Surprise Box Part 2Surprise Box Part 2
W H AT D O YO U N E E D ?
● Sorting Boards (enlarge Master 1)
W H AT ’ S I N T H E B OX ?
● Everyone’s boxes hold the same: three types
of objects, groups of 2, 3 and 5 objects.
W H AT D O YO U D O ?
S o r t i n g
● Encourage the children to sort the objects in
their box any way they like.
“How did you sort your objects? John
sorted his by ___ (e.g., shape, colour).”
Name the characteristic.
● Gradually introduce the students to sorting
boards, or different ways to separate their
materials. (See Master 1.)
C o m p a r i n g
● Ask: “What is the same about the things in
this group? What is different about these two
groups?”
“Let’s match or count to find which
groups have the same amount (have the
same/equal, have more/fewer, have the
most/least).”
“Let’s count to see how many we have
altogether.”
C o u n t i n g
“Can you count your group of ___?” (sets
to 10)
“How many in this part? That part? In all?”
“Count to find which group has one
more/one less.”
L A N G UA G E TO M O D E L A N D E N C O U R A G E
● the language of sorting processes, categories
and characteristics (e.g., sort, organize, same,
different, group by colour, by shape, by size)
● the language of comparison (e.g., bigger/
biggest, more/most, fewer/fewest)
● counting words to 10
P R O C E S S E S TO M O D E L A N D E N C O U R A G E
● helpful ways to organize materials
● moving and counting vs. pointing and counting
to ensure clarity of what has been counted
D I S P O S I T I O N S T O E N C O U R AG E
● positive self-concept: I can do it; I am smart;
I can learn it.
● positive view of math: This is fun; this is
something I enjoy doing.
Good thinking!That is a differentidea for sorting!
How manybuttons do wehave altogether?
Let’s count as weput them back inour boxes!
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 21
Surprise Box Part 3Surprise Box Part 3
W H AT D O YO U N E E D ?
● Numeral Cards to match to groupings
(Master 8)
● Sorting Boards for sorting (Master 1)
● Dice Pattern Cards to connect to quantities
(Master 7)
W H A T ’ S I N T H E B O X ?
● Each child’s box holds different numbers of
objects, total to 10, three types maximum.
W H AT D O YO U D O ?
Build on what you introduced the first week by
adding the following:
S o r t i n g
● Use the sorting boards to sort materials. This
is a pre-bar graph activity—encourage the
children to sort in rows, one object per box,
then ask comparison questions (e.g., more/
less, in all). This helps children start to line
up objects for one-to-one comparisons.
Comment on how rows make comparing
easy.
● Ask: “Can you use the sorting board to
separate your groups?”
C o m p a r i n g a n d c o u n t i n g s e t s t o 1 0
● Continue counting and comparing, finding
parts and finding the whole or total.
● Compare different collections, different ways
to get 10 in all.
● As appropriate, introduce numeral cards to
6, practise reading numerals, and match
numerals to sets. (Adjust to correspond to
the child’s progress in reading numerals.)
● As appropriate, introduce dice pattern cards:
match objects to dice patterns and to
numerals.
L A N G UAG E TO M O D E L A N D E N C O U R A G E
● full sentences
● reinforce number names, part/whole
language and comparative language (e.g.,
more/less, most/least)
P R O C E S S E S TO M O D E L A N D E N C O U R A G E
● naming, counting, comparing
D I S P O S I T I O N S T O E N C O U R A G E
● curiosity: I wonder what is in here; I wonder
how many.
● independence
S U P P O R T I N G E A R L Y N U M E R A C Y22
Surprise Box Part 4Surprise Box Part 4
W H AT D O YO U N E E D ?
● Two-Column Bar Graph (Master 2)
● Comparison Strips (Master 3)
● Numeral Cards for 7 and 8 (Master 8; use
only if child is secure in recognizing
numerals up to 6)
W H A T ’ S I N T H E B O X ?
● Each box contains up to 15 Unifix cubes of
two colours (e.g., 7+8 or 6+9).
● Have extra cubes available for patterning,
but put the same number back in the boxes.
W H AT D O YO U D O ?
● Count objects as they come out of the boxes
and go back into the boxes.
● Count backwards as you return one cube at
a time to the box (e.g., “3 red cubes, 2 red
cubes, 1 red cube, 0 red cubes. All the red
ones are in the box—3, 2, 1, 0. Now let’s do
our blue cubes—4 in all, and so on.”) Use
subsets of one colour at a time, increasing
the number gradually.
● Sort and count, using comparative language.
● Work on recognizing parts of a set and the
whole set (e.g., 3 red, 5 blue, 8 cubes in all).
● Work on creating and reading patterns,
making sounds and actions to match.
L A N G UAG E TO M O D E L A N D E N C O U R AG E
● part/whole language (e.g., some, all, none)
● the language of addition and subtraction
(when items are put into and taken out of
the boxes)
● pattern words (e.g., repeat, same, change,
different)
P R O C E S S E S TO M O D E L A N D E N C O U R A G E
● representing patterns and collections in
various ways
D I S P O S I T I O N S T O E N C O U R AG E
● positive attitude: Patterning is fun; I can
continue patterns; I can count and compare
groups.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 23
Surprise Box Part 5Surprise Box Part 5
W H AT D O YO U N E E D ?
● part/whole mat, such as Ladybug Mat
(Master 4)
● 10-Frame Mats (Master 5)
● dice
● Dice Game Record Sheet (Master 6)
W H A T ’ S I N T H E B O X ?
● Each box has up to 20 objects, 6 round
counters as one set, 10 and 4 as the others.
W H AT D O YO U D O ?
● Count to 20 for all objects in the box; count
back from 10 using subsets.
● Name parts and wholes for sets to 6 using
part/whole mats.
● Make sets of 10 on 10-frames, matching to
fingers.
● Part/Whole Game:
5 little ants in all.
Some are hiding under the rock.
4 are on the rock.
How many are hidden?
Let’s check:
4 on the rock.
1 under the rock.
5 in all.
This time 2 are on the rock….
L A N G UA G E TO M O D E L A N D E N C O U R AG E
● words for pulling apart and putting back
together (e.g., separate, join, subtract, add)
● names for numbers, naming parts of wholes
(e.g., 4 and 2 is a name for 6; 3 and 3 is
another name for 6)
P R O C E S S E S TO M O D E L A N D E N C O U R A G E
● building sets of 10
● recognizing numerals
● printing numerals
● using number rhymes to remember numerals
D I S P O S I T I O N S T O E N C O U R A G E
● positive self-concept: I can take sets apart and
rejoin them; I can name parts and wholes.
S U P P O R T I N G E A R L Y N U M E R A C Y24
Surprise Box Part 6Surprise Box Part 6
W H AT D O YO U N E E D ?
● Dice Pattern Cards (Master 7)
● 10-Frame Mats (Master 5)
● Numeral Cards 0-9 (Master 8)
W H AT ’ S I N T H E B OX ?
● Each box has a total of 20 objects.
● Make one subset something fun and silly, a
real surprise (perhaps something edible).
W H AT D O YO U D O ?
● Follow the previous format, making
adjustments to suit the pace of your group.
● Order (multiple comparisons); organize box
subsets from least to greatest.
● Order numeral cards (to highest number
introduced).
● Work on recognizing one more/one less,
finding subsets. (e.g., I have 5; Who has one
more than 5?)
● Play Build and Change game for recognizing
increase/decrease, decompose/recompose.
● Build and Change game:
Show me 5.
Now change it to 3.
What did you do?
Now change it to 6.
What did you do?
What do you have to do to change it to 4? 5?
2? (Use dice or numeral cards to show
change.)
L A N G UAG E TO M O D E L A N D E N C O U R AG E
● the language of order (e.g., more/most,
higher/highest, in order)
P R O C E S S E S TO M O D E L A N D E N C O U R A G E
● matching, comparing, ordering, counting,
increasing and decreasing
● printing numerals
● rolling dice
D I S P O S I T I O N S T O E N C O U R AG E
● positive self-concept: I can count; I can
understand more and less; I can graph
numbers.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 25
Surprise Box Part 7Surprise Box Part 7
W H AT D O YO U N E E D ?
● All materials used to date (e.g., counters,
numeral cards, 10-frames)
● Master 50 to record results (Surprise Box
Record Sheet).
W H A T ’ S I N T H E B O X ?
● Each box contains up to 25 objects that are
suitable for patterning (e.g., buttons, shells,
macaroni).
W H AT D O YO U D O ?
Over the next few days, students can use
independent tasks from the Pattern section
while you assess the following and record the
results on the record sheet:
● Counts sets to ___.
● Counts backwards from ___.
● Recognizes numerals to ___.
● Compares and orders sets to ___.
● Matches numerals and sets to ___.
● Compares sets to ___.
● Compares numerals to ___.
● Orders sets and numerals to ___.
● Builds and changes to ___.
● Counts on verbally (e.g., start at 6) to ___.
● Counts on with materials (e.g., sees 3 as part
of 5 and counts on to 3 to make 5) to ___.
● Recognizes parts and wholes to ___.
● Decomposes/recomposes (names for
numbers) to ___.
● Finds a missing part to ___.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 27
Focused Instruction forthe ClassroomFocused Instruction forthe Classroom
The Learner Profiles you compiled when you completed the Early
Numeracy Assessment indicate each child’s strengths and
weaknesses. This section of the resource is intended to help you
target specific areas where children need extra instruction. The
activities in this section can be used in small groups or with the
whole class. The section is divided into five parts:
● Estimation—a collection of structured activities that help
children recognize when it is appropriate to estimate and learn a
variety of strategies to assist with estimation.
● Pattern—a sequence of patterning activities that moves from
simple hands-on, active pattern tasks to more complex number
patterns. This section combines number concepts and spatial
thinking.
● Counting and Numeral Recognition—an idea file for children
who need more time and systematic reinforcement to reach
proficiency in counting and numeral recognition.
● Visual-Spatial Pattern Recognition—a sequential set of five-
minute teacher-led activities aimed at developing mental
imagery to support number sense.
● Math Playground—a resource file of hands-on spatial
explorations for independent centre work, either in the
classroom or for small-group work outside the classroom.
Estimation
A B O U T T H E E S T I M AT I O N A C T I V I T I E S
In this section the term estimation is broadly interpreted to include
estimating, predicting and checking. Estimation is a sense-making
process rather than discrete skills arranged developmentally.
Throughout the development of number sense, children need to
have experiences that require them to estimate increasingly greater
amounts in a variety of contexts. Developing the ability to make
reasonable estimates depends on:
S U P P O R T I N G E A R L Y N U M E R A C Y28
● the extent of the child’s meaningful number range
● their inclination to use what they know to figure out a reasonable
estimate
● their ability to use both numerical and spatial information in the
process
● their personal store of relevant benchmarks, which involves both
experience and memory (e.g., I am 110cm tall, so you must be
about ___)
● their willingness to risk an incorrect answer
● their experience with the estimation process and with strategies
for refining estimates
W h y a r e e s t i m a t i o n s k i l l s i m p o r t a n t ?
Estimation is an important process for helping children make sense
of number. The process encourages children to create a personal
frame of reference that can be used in similar situations in the
future. Children need to experience estimation activities in a variety
of situations throughout the early years so that:
● their estimates become more refined
● they learn when it is appropriate to estimate
● they learn a variety of strategies to assist with estimation
C O N N E C T I O N TO T H E K - 1 E A R LY N U M E R A C Y A S S E S S M E N T
The estimation activities in this section are appropriate for all
children, especially those who lack confidence or competence with
number. This section is especially valuable for students who had
difficulty with the following items in the Early Numeracy
Assessment:
Item 2—Recognizing Dot Patterns
Item 5—Counting Forward
Item 6—Counting Back
Item 7—Estimate and Check
Item 8—Counting on and Invariance of Number
Item 9—Build and Change
Item 11—Problem Solving
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 29
U S I N G T H E E S T I M AT I O N A C T I V I T I E S
This section includes 10 activities that use a variety of strategies to
help children refine their ability to estimate. The strategies may be
used in any order you prefer, but if the student’s sense of number is
at a very early level, you may wish to introduce the set comparison
strategy first. The estimation strategies include:
● set comparisons
● number comparisons
● spatial clues
● samplings
● finding differences
Each of the 10 activities include the following:
● What do you need?
● What are you looking for?
● What do you do?
● How might you adapt this activity?
● How might you extend this activity?
At the end of each activity description, ideas are provided for
adapting and extending the activity to meet the needs of a diverse
group of learners. The activities can be adapted and extended in
several ways by changing the collections. You can do this by:
● changing the quantity in the collections
● changing the complexity of the collections
● varying the materials or level of representation of the collection
Also, at the end of the set of 10 activities, there is a Quick Tasks
section that gives further ideas for incorporating these strategies
into the classroom routine.
G u i d e l i n e s f o r t e a c h i n g e s t i m a t i o n
● Choose relevant, varied and motivating contexts.
● Encourage children to take risks.
● Limit quantities to within the reach of the estimators. (i.e.,
Children who count to only 5 or 10 will not be able to make a
reasonable estimate of 50. To them, 50 looks like a million.)
● Make constant use of reference points (e.g., “There are 5 in here.
S U P P O R T I N G E A R L Y N U M E R A C Y30
Can that help us figure out how many are in the bigger pile?”
“John has 8. Do we have more or less?”
● Focus on improving estimates, not on right or wrong. Look at the
range where most of the estimates fall, not at the “way out there”
estimates. Emphasize reasonable estimates. Encourage children
to ask: “Does this make sense?”
● Provide opportunities to revise estimates based on new
information. Recognize good thinking for using that new
information.
● Focus on developing estimation skill in a range of contexts (e.g.,
height, number, area). Remember that appropriate estimates
always depend on the context.
C o l l e c t i o n s ( l e v e l s o f r e p re s e n t a t i o n )
The collections of items provided for estimating need to include:
● a variety of concrete, pictorial and symbolic items
● items that are sometimes arranged randomly and other times in
order
● both two- and three-dimensional collections
The activities described in this section should be repeated with
different types of collections, which may alter the difficulty of the
estimation activity. Types of collections may include:
● like objects/people
● like objects of different sizes
● unlike objects
● items presented on an overhead
● pictures of collections
● items in containers (e.g., jelly beans in a jar)
● items in existing groupings (e.g., pages in a book)
R e c o rd i n g
As soon as the children are able to identify specific numerals, they
can use numeral cards to record their estimates or say them orally.
Their inability to write numerals should not prevent children from
engaging in estimation activities. Once children learn to print
numerals, recording should be an integral part of the activities.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 31
Estimation Activities
Activity Stage/Level Math Focus Page
Musical Chairs Set Comparisons 32
Make a Graph Set Comparisons 33
One for Me? Number Comparisons 34
How Much Time? Number Comparisons 36
Taking Up Space Spatial Clues 37
How Many Beans, Jack? Spatial Clues 38
Let Me Guess Samplings 40
Estimate Before You Eat Samplings 42
Targets Finding Differences 44
How Long Is It? Finding Differences 45
Quick Tasks 46
● ● ● ❍ ❍
● ● ● ❍ ❍
● ● ● ❍ ❍
❍ ● ● ● ❍
● ● ● ❍ ❍
● ● ● ❍ ❍
● ● ● ❍ ❍
● ● ● ❍ ❍
● ● ● ❍ ❍
● ● ● ❍ ❍
S U P P O R T I N G E A R L Y N U M E R A C Y32
Musical ChairsMusical Chairs
Math Focus: Set Comparisons
W H AT D O YO U N E E D ?
● a collection of chairs or mats for the children
to sit on
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● understand the language used?
● willingly make a guess?
● make an estimate without being concerned
about being correct?
● give reasonable answers to questions within
their range of number understanding?
● independently answer the questions?
● estimate without counting the collections
from 1?
● use spatial clues to estimate?
● share their thinking about the estimates?
W H AT D O YO U D O ?
● Set up more/less/the same number of chairs
as there are children.
● Introduce the term estimate to mean making
a good guess or prediction.
● Ask a variety of questions to compare the
quantity of the collection to the quantity of
children.
“Do we have enough chairs for everyone?”
“Do we have too many chairs for everyone?”
“Will there be somebody who does not get a
chair?”
● ● ● ❍ ❍
“Why do you think there are enough/too
many?”
“Do we have more or less chairs than
children? Do we have the the same number
of chairs as children?”
● Have the children sit on chairs.
● Encourage the children to make concluding
statements. Emphasize matching to check
predictions.
“We had less/more chairs than children.”
“We had less/more children than chairs.”
“We had just enough chairs for everyone.”
“We had the same number of chairs as
children.”
“There are some chairs/children left over.”
“There are not enough chairs/children.”
H OW M I G H T YO U A D A P T T H I S A C T I V I T Y ?
● Reduce the size of the group and work with
small groups (e.g., four children) if children
have difficulty with understanding number
to 5.
H OW M I G H T YO U E X T E N D T H I S A C T I V I T Y ?
● Use name cards for the students and picture
cards of hats. Spread each group out
separately. Ask if there are enough “hats” for
all of the names.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 33
Make a GraphMake a Graph
Math Focus: Set Comparisons● ● ● ❍ ❍
W H AT D O YO U N E E D ?
● two collections of items with different
quantities (e.g., plastic spiders and snakes)
● graphing floor mat with two columns of
eight boxes for sorting
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● understand the language used?
● willingly make a guess?
● independently answer the questions?
● estimate without counting the collections
from 1?
● use spatial clues to estimate?
● share their thinking about the estimates?
W H AT D O YO U D O ?
● Show the two collections to the children.
● Ask the children to estimate/predict which
collection has more, which has less or
whether the sets are the same. Ask the
children to explain their predictions.
● Discuss different ideas for deciding which
collection has more/less/the same (e.g.,
separating and sorting sets, organizing sets
in a line or in groups of 2).
● After the discussion ask the children to
estimate and predict again.
● Focus on matching as a way to check and
compare. Have children put the items on a
graphing mat and match them one-to-one.
The items can be placed on the mat in pairs
to highlight the matching.
● Compare the collections by asking these
questions:
“Do we have more spiders or snakes?”
“How many more/less do we have?”
“How do you know there are more/less?”
● Help children make concluding statements.
“We had less/more spiders than snakes.”
“It is easier to see how many more/less we
have when we match them and put them on
a graphing mat.”
H OW M I G H T YO U A D A P T T H I S A C T I V I T Y ?
● Use real people for the two sets (e.g., male
and female students, 5- and 6-year-olds).
After estimating, match the students in lines
by putting one child from each group side by
side.
H OW M I G H T YO U E X T E N D T H I S A C T I V I T Y ?
● Place two sets of items on the overhead
projector for estimating. Then place a two-
column bar graph (Master 2) on the overhead
to do the matching.
S U P P O R T I N G E A R L Y N U M E R A C Y34
One for Me?One for Me?
Math Focus: Number Comparisons
W H AT D O YO U N E E D ?
● a collection of items to distribute (e.g.,
lollipops)
● chart paper and markers
● individual Number Lines (Master 10)
● math journals and pencils
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● understand the language used?
● make an estimate without being concerned
about being correct?
● give reasonable answers to questions within
their range of number understanding?
● estimate without counting the collections
from 1?
● use spatial clues to estimate?
● share their thinking about the estimates?
● record their thinking?
W H AT D O YO U D O ?
● Ask a variety of questions to compare the
quantity of the collection to the quantity of
children. Start the discussion with
comparative terms (e.g., more, less) and
then discuss numbers.
“Do we have enough lollipops for everyone?
What can we do to find out?”
“Why do you think there are enough/too
many?”
● ● ● ❍ ❍
“Will there be somebody who does not get a
lollipop? What can we do to find out?”
● Discuss the strategy of matching the two sets.
● Ask the children to estimate and state the
number of lollipops. Record these numbers
on a chart.
● Pick a child to distribute the lollipops to the
others, and help the children make
concluding statements. Discuss matching as
a way of checking predictions.
● Have the group count children and lollipops.
Discuss counting as a way of checking
predictions.
“We had less/more lollipops than children.”
“We had less/more children than lollipops.”
“We had just enough lollipops for everyone.”
“There are ___ lollipops/children left over.”
“There are ___ more lollipops/children.”
“There are ___ lollipops, and there are ____
children.”
“___ (number of lollipops) is more/less than
___ (number of children).”
● Compare the actual number to the estimates.
Use a number line and locate both numbers
for the comparison. It is important to focus
on the reasonableness of the answers rather
than the correctness.
● Have the students record their thinking in
their math journals.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 35
H OW M I G H T YO U A D A P T T H I S AC T I V I T Y ?
● Work with a smaller group of students and
use a collection of items that the children
can physically put on (e.g., hats or old
shirts). If the children are not yet able to
print numerals, they can make their
estimates, choose the corresponding
numeral card and place it in front of them.
When the actual number is determined, they
can then choose that numeral card and
compare the two numbers. Have them find
the numbers on a number line to help with
the comparison. Dot pattern cards can also
be used instead of numeral cards.
H OW M I G H T YO U E X T E N D T H I S AC T I V I T Y ?
● Use pairs of items for estimating (e.g.,
mittens). Lead the students to discuss how
the number of students relates to the pairs
of mittens rather than to the total number
of mittens.
● Use a collection of items for estimating that
have several pieces per person (e.g., a table
place setting with plate, cup, fork, knife and
spoon).
S U P P O R T I N G E A R L Y N U M E R A C Y36
How Much Time?
Math Focus: Number Comparisons
W H AT D O YO U N E E D ?
● chart paper and markers
● percussion instrument (e.g., drum or triangle)
● Record Sheet 1 (Master 11) and/or journal
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● understand the language used?
● willingly make a guess?
● make an estimate without being concerned
about being correct?
● give reasonable answers to questions within
their range of number understanding?
● independently answer the questions?
● use references (e.g., benchmarks, visual
patterns, samplings) to estimate?
● share their thinking about the estimates?
● record their thinking?
W H AT D O YO U D O ?
● Have the children perform a number of
activities (e.g., walk across the classroom, tie
shoes, walk across the gym, walk to the
playground and back, print their name).
● Time each activity by counting beats on the
percussion instrument.
● Ask the children to estimate the number of
beats before each activity and record their
estimates on the chart.
● Have the children predict which activities
will need the fewest beats and which will
need the most.
● Check by comparing the actual to the estimates.
Focus on the reasonableness of the answers.
● Compare the number of beats for different
activities. Put the activities in order from
shortest to longest amount of time.
“Which took the longest/shortest amount
of time?”
“Are there any activities which took the same
amount of time?”
“Can you think of another activity which
might take the same amount of time as one
of the activities we already did?”
● Have the students test their predictions and
compare the results.
● Ask the students to record their thinking in
their math journals.
H OW M I G H T YO U A D A P T T H I S A C T I V I T Y ?
● Choose activities that are quick, active and
easily manageable by the children (e.g., 10
jumping jacks). Predict and compare after
each activity.
H OW M I G H T YO U E X T E N D T H I S A C T I V I T Y ?
● Time the activity with a stopwatch. Estimate
the amount of time it takes to perform in
seconds/minutes.
● Ask the students to suggest three new activities.
Estimate the amount of time each activity
will take and rank the activities from shortest
to longest amount of time before starting.
Have the children do the activities and
compare their estimates to the actual times.
❍ ● ● ● ❍
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 37
Taking Up SpaceTaking Up Space
Math Focus: Spatial Clues
W H AT D O YO U N E E D ?
● a collection of macaroni
● math journals and pencils
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● understand the language used?
● willingly make a guess?
● independently answer the questions?
● use spatial clues to estimate?
● use references (e.g., benchmarks, visual
patterns, samplings) to estimate?
● share their thinking about the estimates?
● record their thinking?
W H AT D O YO U D O ?
● Place 2 pieces of macaroni in front of each
child.
● Look at the space that the macaroni pieces
take up (spatial clue).
● Ask the children to draw in their math
journals the smallest rectangle that they
think would hold 10 pieces of macaroni.
● Test with macaroni.
● Draw a rectangle around the 10 pieces of
macaroni.
● Compare the two rectangles.
● Discuss how looking at the space taken up
by two pieces can help estimate the space
needed for 10 pieces.
H OW M I G H T YO U A D A P T T H I S A C T I V I T Y ?
● Have the students place 2 pencils end to end.
Ask them to draw a line that they think would
be 4 pencils long. Test with the pencils and
discuss the results.
H OW M I G H T YO U E X T E N D T H I S A C T I V I T Y ?
● Place 2 pattern blocks so that they touch
each other on one side. Ask the children to
draw the smallest square that would hold 10
pieces. Have them test with the pattern
blocks and draw the square around the
blocks. Compare the two squares.
● Choose a different pattern block and repeat
the activity.
“Are there other ways to orient the pieces to
make a smaller square?”
● ● ● ❍ ❍
S U P P O R T I N G E A R L Y N U M E R A C Y38
How Many Beans, Jack?How Many Beans, Jack?
Math Focus: Spatial Clues
W H AT D O YO U N E E D ?
● a collection of beans
● a copy of Jack and the Beanstalk
● individual chalk boards or math journals
and pencils
● chart paper and markers
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● make an estimate without being concerned
about being correct?
● give reasonable answers to questions within
their range of number understanding?
● independently answer the questions?
● use spatial clues to estimate?
● use references (e.g., benchmarks, visual
patterns, samplings) to estimate?
● share their thinking about the estimates?
● record their thinking?
W H AT D O YO U D O ?
● Read Jack and the Beanstalk aloud. Remind
the children that Jack received only a few
beans for the cow.
“How many beans do you think Jack would
have if he had received a whole handful
instead of just a few?”
● Have the children record their estimates on
their chalk boards and then say “1, 2, 3 show
me.”
● The teacher can take a range of estimates by
asking someone to share their estimates.
“Does anyone have a number larger than
what (the first student) said?”
● Find the largest estimate in the class, and
then ask if anyone has a smaller estimate
than the first estimate shared.
● Discuss the range of estimates made by the
children.
“How many beans do you think you can
hold in a handful?”
● Have the children record their estimates.
“How did you make your estimate?”
“What were you thinking?”
“Did anyone do it a different way?”
● Have the children work in pairs to take
handfuls of beans and then compare their
estimates and actual counts.
H OW M I G H T YO U A D A P T T H I S A C T I V I T Y ?
● Show a handful of beans to the class for five
seconds, and then ask the students to
estimate how many beans.
● Do the activity in small groups with adult
direction, using extra-large lima beans.
H OW M I G H T YO U E X T E N D T H I S A C T I V I T Y ?
● Pour out a collection of beans that fills a jar.
● Use a 500ml scoop instead of handfuls and
estimate the total number of beans as well as
the number of scoops needed to refill the jar.
Fill the scoop with beans, and have the
students revise their estimates.
● ● ● ❍ ❍
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 39
“Are there enough beans to fill the scoop
again?”
● Count the beans in the scoop. Have the
students revise their estimates of the total
number of beans.
S U P P O R T I N G E A R L Y N U M E R A C Y40
Let Me GuessLet Me Guess
Math Focus: Samplings● ● ● ❍ ❍
W H AT D O YO U N E E D ?
● a collection of similar counters (e.g., bugs,
dinosaurs)—total number should be a
multiple of 5
● Five-Way Sorting Mats (Master 13)
● overhead projector
● overhead copy of a Five-Way Sorting Mat
(Master 13)
● math journals and pencils
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● give reasonable answers to questions within
their range of number understanding?
● independently answer the questions?
● use spatial clues to estimate?
● use references (e.g., benchmarks, visual
patterns, samplings) to estimate?
● share their thinking about the estimates?
● record their thinking?
W H AT D O YO U D O ?
● Pour out the collection of items on the
overhead projector. (Use a collection size
appropriate for the counting abilities of the
group.)
● Give the students five seconds to estimate
how many objects. Ask them to record their
estimates.
● Ask for a volunteer to state his or her estimate.
“Who has a lower guess?”
● Keep asking until you get the lowest guess.
Repeat to find the highest guess.
● State the range of guesses (e.g., the range is
20 to 100).
● Next, show the sorting mat on the overhead.
Count the five sections.
● Ask a child to put the items from the
collection on the mat. Then ask:
“How many mats do we need altogether so
that all the items are on a mat?”
“How many items are there in the collection?”
● Discuss and record the revised estimates.
● Begin to match the items on the mat with the
children.
“How many groups of 5s do we have so far?”
“How many more groups of 5s do we need?”
● When about half of the collection has been
placed on the mats, have the children
estimate again how many mats are needed
and the total of the collection. Compare all
their estimates.
● Finish matching the objects on the mats and
then count the number of mats.
● Count the total number of items by 5s.
● Compare the estimates to the actual numbers.
● Discuss how the set of 5 on the mat helped to
estimate the total collection.
● Repeat the activity with partners or in small
groups using a variety of materials. Have the
students place the objects on their own
sorting mats.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 41
H OW M I G H T YO U A D A P T T H I S AC T I V I T Y ?
● Use mats that have only two sections and
use groupings of two to help estimate the
number of the objects.
H OW M I G H T YO U E X T E N D T H I S AC T I V I T Y ?
● Show a 10-frame for 5 or a domino pattern for
5. Then show a collection of coloured disks.
“How many groups of 5?”
“How many altogether?”
● Use mats with 10 sections. Increase the size
of the collection.
“How many groups of 10?”
“How many altogether?”
S U P P O R T I N G E A R L Y N U M E R A C Y42
Estimate Before You EatEstimate Before You Eat
Math Focus: Samplings● ● ● ❍ ❍
W H AT D O YO U N E E D ?
● a collection of coloured candies
● small paper cups for counting sets of 10
● a copy of More m & m’s Math by Barbieri
McGrath (optional)
● Record Sheet 2 (Master 12)
● index cards
● crayons to match the candy colours
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● give reasonable answers to questions within
their range of number understanding?
● use spatial clues to estimate?
● use references (e.g., benchmarks, visual
patterns, samplings) to estimate?
● share their thinking about the estimates?
● record their thinking?
W H AT D O YO U D O ?
● Fill the cups with 10 candies of different
colours before starting the activity. The total
number of candies and cups needed will
vary, depending on the size of the collection
the children are able to work with.
● Make colour cards for each candy colour.
Print the colour word on an index card with
the matching crayon colour.
● If you have the book, read the first 12 pages
of More m & m’s Math as motivation.
● Explain that the children are going to use
cups with groups of 10 candies in each to
help them sort the candy.
● Distribute the cups so that each child has a
cup of multicoloured candies.
● Have the students estimate the total number
of candies (some may immediately see how
to figure out the actual number based on
counting by 10s).
● Ask the children to sort their set of candies by
colour. Have each child place his or her
candies near the appropriate colour cards.
● Discuss which colour appears to have the
most or the least.
“Are there any colours which have the same
amount?”
● Then focus on one colour at a time. Ask the
children to estimate how many candies there
are. Have them record their estimates for
each colour on their record sheets, or record
them on a large chart.
● Ask the children to estimate how many
counting cups with 10 candies would be
needed for that colour.
● To check, have the children put 10 candies of
one colour in a cup. Keep filling the cups
with groups of 10. Discuss and record how
many cups of candies and how many
remaining candies. Have the students
determine the totals for the different colours.
Discuss and record the actual number, and
compare to the estimates on the recording
sheets or chart.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 43
● Compare and discuss the results for all the
colours.
● Count the total number of candies by 10s
and 1s. Compare to the original estimates.
● At the end of the activity, let the students eat
one candy of each colour.
H OW M I G H T YO U A D A P T T H I S AC T I V I T Y ?
● Use only two different colours of candies.
● Place a smaller number of candies in the
cups (e.g., groups of 2s or 5s).
● Use buckets and coloured balls (or other
large containers and objects) for the activity.
H OW M I G H T YO U E X T E N D T H I S AC T I V I T Y ?
● Record each colour with tallies on the record
sheet.
● Create a bar graph for each colour to record
the results.
S U P P O R T I N G E A R L Y N U M E R A C Y44
TargetsTargets
Math Focus: Finding Differences● ● ● ❍ ❍
W H AT D O YO U N E E D ?
● Numeral Cards 0-9 (Master 8)
● Number Lines (Master 10)
● math journal and pencils
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● give reasonable answers to questions within
their range of number understanding?
● independently answer the questions?
● estimate without counting the collections
from 1?
● use spatial clues to estimate?
● use references (e.g., benchmarks, visual
patterns, samplings) to estimate?
● share their thinking about the estimates?
● record their thinking?
W H AT D O YO U D O ?
● Shuffle the cards and turn over the top card.
● Mark this number on the number line. It is
the target number.
● Have each child pick a card from the pack
and show it to the group.
● Ask the children to predict whose number is
closest to the target number. Encourage the
children to think about where his or her
number is on the number line.
“Whose numbers are close to the target?”
“Whose numbers are farther away?”
“Roughly how much would you have to add
(or subtract) to your number to get to the
target number?”
“Is the target number closer to 0 or to 10 (or
100)?”
● Check and mark each number on the number
line using visual clues (such as circling). Com-
pare the differences between the estimates
and the targets.
“How many places away from each other are
the numbers?”
● Have the children state whether their number
or the target number is closer to 0 or 10.
● Assign students to groups of four and have
them repeat the activity in the small groups.
They can record their predictions on their
own number lines and record their thinking
in their math journals.
H OW M I G H T YO U A D A P T T H I S A C T I V I T Y ?
● Use dot pattern cards (Master 18) instead of
numeral cards. Before having the students
pick a card, order the dot pattern cards from
the smallest to the largest. Pick the target
card, and ask the children to help find it in
the ordered cards. Place it below the ordered
lines. Have the children pick dot pattern
cards and predict whose is closest or farthest
away. Ask them to place the cards under the
ordered cards in the correct location, and
discuss the predictions.
H OW M I G H T YO U E X T E N D T H I S A C T I V I T Y ?
● Use a number line higher than 10, or use a
100 chart.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 45
How Long Is It?How Long Is It?
Math Focus: Finding Differences
W H AT D O YO U N E E D ?
● items to be measured (e.g., tracings of the
children’s feet)
● non-standard units of different sizes (e.g.,
paper clips, toothpicks, Unifix cubes)
● paper and pencils
● scissors
● Record Sheet 2 (Master 12)
● math journals
● calculators
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● independently answer the questions?
● use spatial clues to estimate?
● use references (e.g., benchmarks, visual
patterns, samplings) to estimate?
● share their thinking about the estimates?
● record their thinking?
W H AT D O YO U D O ?
● Show the children how to measure objects
by placing units end to end.
● Have the children work in pairs to trace
around one foot and then cut out the
footprints.
● Each pair of students chooses a unit for
measuring and records it on the record sheet
under the heading “What is it?”
● Have the students estimate and record how
many of the unit will be needed to measure
the length of their own footprint.
● ● ● ❍ ❍
● Now have the students use the unit to
measure the footprint.
● Record the actual number of units it takes.
● Repeat the activity with other units. Then
compare the results of the units.
“Which units gave the lowest number? The
highest number? Why?”
● Compare the actual measurements to the
estimates by calculating the differences on a
calculator.
● Have the students record their thinking and
the calculations in their math journals.
H OW M I G H T YO U A D A P T T H I S A C T I V I T Y ?
● Make several copies of your own footprint,
and use a variety of units to measure it. Do
many examples together as a class before
assigning partners.
H OW M I G H T YO U E X T E N D T H I S A C T I V I T Y ?
● Ask the students to find out a way to see who
has the largest foot in the class and who has
the smallest. “How will you estimate?”
S U P P O R T I N G E A R L Y N U M E R A C Y46
Quick TasksQuick Tasks
● Have the students look at a piece of wrapping
paper with repeating pictures of the same
object, and ask them to estimate how many.
● Hold a small collection in your hand, and ask
the children to estimate how many there are.
● At the beginning of the week, fill a jar with a
collection of objects (e.g., jelly beans), and
leave it in the math centre. Over the week,
have the students record their estimates and
strategies. Determine the actual number at
the end of the week. Change the items weekly.
● Leave sets of pictures in the math centre
(e.g., paper dolls and hats, houses and doors,
frogs and lily pads). Ask the children to
predict whether there are enough of one
item to match the other item. Have the
students record more/less/the same.
● Ask the children to estimate how much
money is in a coin purse or a piggy bank. Use
one type of coin or many types of coins.
● If the class is having a party, show the
children party items (e.g., hats, plates,
spoons), and have them estimate and then
check whether there are enough.
● Estimate how many words are on a page.
● Estimate how many books are on a shelf.
● Show a collection of objects. Have the
students estimate within a given range.
● Show a collection of objects in a square on
the overhead. Show for 10 seconds, and have
the students estimate. Organize the guesses
from least to greatest.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 47
The Pattern Activities include
the following:
● What do you need?
● What are you looking for?
● What do you do?
● How might you adapt
this activity?
● How might you extend
this activity?
Pattern
A B O U T T H E P AT T E R N A C T I V I T I E S
The Pattern section is a sequence of activities that moves from simple
hands-on, active pattern tasks to more complex number patterns.
Each of the tasks can be used as often as necessary. Many of the
required materials can be stored with directions in a zip-lock bag.
W h y a r e p a t t e r n s k i l l s i m p o r t a n t ?
Patterns are everywhere. As children become aware of patterns in a
variety of contexts, they learn to use analytical skills. They also learn
to look for similarities and differences that can help them to make
sense of the world. For young children, working with visual,
auditory, tactile, concrete and verbal patterns provides the intuitive
foundation for working with symbolic patterns, such as our base
10 number system. Regardless of when you use these lessons, be
sure to model and highlight patterns in everything you do in class
(e.g., borders around class charts, newsletters going home, covers
for journals, stickers on the weather graph).
C O N N E C T I O N TO T H E K - 1 E A R LYN U M E R AC Y A S S E S S M E N T
Children who are just beginning to reflect and analyze situations
before responding would benefit from practice with the analytical
skills developed in this section. The Pattern section
is especially valuable for children who had difficulty with the
pattern task (Item 10) in the K-1 Early Numeracy Assessment.
U S I N G T H E P AT T E R N A C T I V I T I E S
Nine pattern tasks are included here, and each can be used as often
as you see fit. Having the children record the patterns can extend
the difficulty of any one task.
S U P P O R T I N G E A R L Y N U M E R A C Y48
Pattern Activities
Activity Stage/Level Math Focus Page
People Patterns and Action Recognizing Patterns 49
Patterns
Linking Pattern Trains Making Patterns with Objects 50
What’s My Pattern? #1 Object and Size Patterns 51
Keep the Pattern Going! Extending Patterns 52
A Pattern to Follow Creating and Extending Patterns 53
Checkerboard Patterns Creating and Extending Patterns 54
What’s My Pattern? #2 Size and Shape Patterns 55
100 Chart Patterns Number Patterns 56
Guess My Pattern Mathematical Thinking Strategies 57
Action Pattern Quick Tasks 58
Number Pattern Quick Tasks 58
● ● ❍ ❍ ❍
● ● ❍ ❍ ❍
● ● ❍ ❍ ❍
❍ ● ● ❍ ❍
❍ ● ● ● ❍
❍ ● ● ● ❍
❍ ● ● ● ●
❍ ● ● ● ❍
❍ ● ● ● ❍
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 49
People Patterns and Action PatternsPeople Patterns and Action Patterns
Math Focus: Recognizing Patterns● ● ❍ ❍ ❍
W H AT D O YO U N E E D ?
No special materials are required, but pattern
cards or pattern picture cards may be used to
adapt the activity.
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● join in the activity?
● predict or tell what comes next in a pattern?
● create their own pattern for others to follow?
W H AT D O YO U D O ?
● Have the children sit or stand in a circle so they
can watch as the pattern emerges. Start with a
simple pattern (e.g., stand, sit, stand, sit).
● Assign positions to the first few children to
establish the pattern. Say the pattern aloud
as the children move to their positions.
● Encourage the children to predict the
positions as soon as they recognize the
pattern.
H OW M I G H T YO U A D A P T T H I S AC T I V I T Y ?
● Repeat as needed, with the teacher or all
students saying the pattern aloud while the
students make the appropriate action
(especially for language minority children).
● If a child seems to know the next action, ask
them: “What comes next?” This will alert the
other children to think about what they
will do.
H OW M I G H T YO U E X T E N D T H I S A C T I V I T Y ?
● As children become more familiar with
patterns, change the complexity:
- Expand the pattern to three components
(e.g., stand up, stand on knees, sit cross-
legged; or stand up, stand up, sit down).
- Use action patterns (e.g., clap, snap, clap,
snap). Begin the pattern, and encourage
the children to join in when they feel they
know the pattern.
- Extend these to verbal patterns, using
words related to the motions, letters (e.g.,
ABAB) or silly sounds (e.g., boink, ding).
- Use picture cards so the children can create
their own patterns (e.g., clap, snap, pat).
● Make books with action pictures (e.g., clap,
snap, pat) for a variety of patterns. Have the
children read through them, doing the
actions and extending the patterns.
S U P P O R T I N G E A R L Y N U M E R A C Y50
Linking Pattern TrainsLinking Pattern Trains
Math Focus: Making Patterns with Objects
W H AT D O YO U N E E D ?
● Unifix cubes (each student will need five
each of two colours)
● repeat this activity with a variety of materials
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● make a pattern that continues?
● explain their pattern using descriptive words
or letters?
● predict what comes next in their pattern? In
someone else’s pattern?
● extend a modeled pattern?
● create their own pattern with their own
materials?
● recognize what it is that keeps repeating?
W H AT D O YO U D O ?
● Have all or some students say their patterns
out loud as they point to the cubes.
● Ask: “How can we make the pattern longer?
What would come next?”
● Work with a pattern, such as AB, using
actions to establish the pattern.
● Show students your AB pattern (red, blue,
red, blue...).
● Have students make their own AB pattern
(do this for AAB, ABB, AABB, ABC...).
● Make sure the children discuss what they did
with the others.
H OW M I G H T YO U A D A P T T H I S A C T I V I T Y ?
● Use a smaller number of cubes, 3 of each
colour.
● Have the students use the same colours you
do and copy your pattern.
● Say the colours out loud while they are
making their pattern.
● Use actions for their patterns. (They may
need more active practice.)
H OW M I G H T YO U E X T E N D T H I S A C T I V I T Y ?
● Increase the complexity of the pattern.
● Put a pile of blocks on the carpet, and ask:
“Can you make our action pattern using
Unifix cubes?”
● Say the patterns using alphabet letters (e.g.,
ABABAB...).
● To provide variety and allow for additional
levels of complexity, supply pattern blocks in
place of the Unifix cubes.
● Using collections (containers of materials
such as paper clips, bread tags, buttons or
money) is the most challenging. (See next
activity for ideas.)
● Have the children create patterns using
manipulatives of only one colour. This will
force them to think about ways to make
patterns that do not rely on colour.
● Record the patterns using drawings to
provide challenge for all pattern activities.
● ● ❍ ❍ ❍
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 51
What’s My Pattern? #1What’s My Pattern? #1
Math Focus: Object and Size Patterns
W H AT D O YO U N E E D ?
● “Pattern Baggies” with materials of different
colours and sizes appropriate for patterning
(e.g., rocks, keys, shells, buttons, coloured
pasta or cereal)
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● recognize what feature is creating the
pattern (e.g., size, colour)?
● extend a modeled pattern?
● create their own patterns rather than use the
objects randomly?
● reproduce the patterns in their math journals?
W H AT D O YO U D O ?
● Create a pattern, using size as the pattern
feature.
● “Read” the pattern with the children and
ask: “Is this a pattern? How do you know?”
● Have the children take turns adding on a
next piece.
● Talk about what actions might represent
each piece and do the actions.
● Give the children their own “Pattern Baggie”
and ask them to create a size pattern.
● After a few minutes, visit each pattern and
ask questions about each. (e.g., “Is this a
pattern? How do you know? What would
come next? How do you know?”)
● ● ❍ ❍ ❍
H OW M I G H T YO U A D A P T O R E X T E N D T H I SAC T I V I T Y ?
● Take a pattern walk in the school, and look
for patterns.
● Ask the children to look for patterns at home
and report on what they find. Have them
reproduce the patterns on paper.
● Take a long, narrow piece of newsprint, and
ask: “How could we show Davinder’s pattern
on this paper?” Encourage the children to
experiment. Share and discuss.
● Change back to a colour pattern, and see if
the children can identify what type of pattern
you have.
● Use a jewelry box with lots of costume
jewelry, some with patterns and some
without. Have the children separate
patterned from non-patterned.
● Make a pattern necklace using coloured
cereal or pasta and string.
“What do you notice about these materials?”
(e.g., colour, size, shape)
“How could we make a pattern necklace?
Make yourself a pattern necklace.”
“‘Read’ your necklace. Is this a pattern? Why
or why not?”
S U P P O R T I N G E A R L Y N U M E R A C Y52
Keep the Pattern Going!Keep the Pattern Going!
Math Focus: Extending Patterns
W H AT D O YO U N E E D ?
● Pattern Cards (use Master 24 to make cards
with a variety of patterns and empty spaces
at the ends)
● long, blank pieces of newsprint
● wrapping paper with repeating patterns
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● relate the abstract picture to real materials?
● recognize the pattern?
● extend the pattern using real materials?
● verbalize what they are doing?
W H AT D O YO U D O ?
● Take out a set of cards you have made with
different patterns and empty spaces at the
end of the cards.
● “Read” the card with the children. When you
get to the end, ask:
“What would come next? How do you know?
Next? Next?”
● Give each child a different card.
“Can you keep the pattern going using the
materials on the table?”
● Have each student “read” their card while
others determine whether they kept the
pattern going.
H OW M I G H T YO U A D A P T O R E X T E N D T H I SA C T I V I T Y ?
● Bring in patterned wrapping paper. Discuss
how to extend the pattern and keep it going.
● Cut strips of patterned wrapping paper into
small pieces. Ask the children to find the
other piece(s) that extend their pattern and
glue it/them onto a long strip of newsprint.
● Invite the children to look at home for
patterned paper and materials and bring
them to school. Create a class “Patterns from
Home” book.
❍ ● ● ❍ ❍
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 53
A Pattern To FollowA Pattern To Follow
Math Focus: Creating and Extending Patterns
W H AT D O YO U N E E D ?
● Pattern Game Boards (Master 25)
● blocks or tiles
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● create a pattern that “travels” horizontally
and vertically?
● recognize someone else’s pattern?
● extend the pattern?
● verbalize what they are doing?
W H AT D O YO U D O ?
Model the game for the class. The teacher
(Partner 1) creates a pattern on the game board
with blocks or tiles. Partner 2 watches. About
halfway through, Partner 1 stops building the
pattern, and Partner 2 continues it. Switch at
the end so that Partner 2 creates a pattern and
Partner 1 gets to finish it.
How might you adapt or extend thisactivity?● Place this activity in a math centre for the
children to use during free time.
● Invite the children to make up other game
boards and travelling patterns.
❍ ● ● ● ❍
S U P P O R T I N G E A R L Y N U M E R A C Y54
Checkerboard PatternsCheckerboard Patterns
Math Focus: Creating and Extending Patterns❍ ● ● ● ❍
W H AT D O YO U N E E D ?
● a real checkerboard
● 100 Chart Grids (Master 14)
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● create a pattern in a row or column?
● “see” the repeating feature of the columns or
rows?
● verbalize what they are doing?
W H AT D O YO U D O ?
● Show a real checkerboard to the group, and
ask what they notice (i.e., black-red pattern
alternates up and down and across).
● Experiment with tiles to create checkerboard
patterns.
● Record a checkerboard pattern on a 100
chart grid.
How might you adapt or extend thisactivity?● Use the 100 chart grid to record a pattern
made with tiles, or experiment with making
tile patterns right on the 100 chart grid.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 55
What’s My Pattern? #2What’s My Pattern? #2
Math Focus: Size and Shape Patterns
W H AT D O YO U N E E D ?
● attribute blocks in baggies (a few sets, if
possible)
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● see the various orientations possible and
how they can create patterns?
W H AT D O YO U D O ?
● Present a problem: choose one shape only
and make a pattern.
“How can you create a pattern using only
one shape?”
● When someone discovers the orientation of
the shapes as a pattern, comment on their
discovery and “read” their pattern together.
● Ask: “Is there another way of doing it?” (e.g.,
using thickness or size)
How might you adapt or extendthis activity?● Have the children sort the attribute blocks
by size and shape. Ask them which sets
could be used to “tile” an area (i.e., to
completely cover it, with no space showing
between blocks). Use this activity as an
introduction to tessellations, and place it in
the math centre. Encourage the children to
discover many designs.
❍ ● ● ● ●
● Use sets of dominoes in baggies. Do the
children see relationships and patterns
within the dominoes?
● Experiment with making domino patterns.
Discuss what the children discover and any
insights they uncover.
● Extend the work with domino patterns into
noticing patterns about numbers.
“Look at all the dominoes with blank spaces.
What happens when you add a zero to a
number?”
“Do this a few times. Is there a pattern?”
● If the children are ready, extend the activity
by asking them what happens when they add
one to a number, and so on.
S U P P O R T I N G E A R L Y N U M E R A C Y56
100 Chart Patterns100 Chart Patterns
Math Focus: Number Patterns
W H AT D O YO U N E E D ?
● 100 Charts (Master 9)
● overhead projector
● transparency of 100 Chart (Master 9)
● overhead pens
● 100 Charts, cut apart (Master 9)
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● find patterns on the 100 chart when
identified? Independently?
● put the 100 chart together?
● share their thinking about how they put the
100 chart together?
W H AT D O YO U D O ?
● Give each child a 100 chart.
● Assign tasks (e.g., Circle all the numbers that
end in 0 or 5 or…).
● Ask the children to see if they can find any
other patterns.
● Encourage the children to share their
discoveries.
● Put a transparency of the 100 chart on the
overhead, and ask the students to tell you
about it.
● Record their observations on a sheet of chart
paper.
● Have the students colour in some of the
patterns that are brought up in the
discussion.
❍ ● ● ● ❍
“What do you notice about the numbers in
the last column?”
“Where are all of the numbers with a 3 in the
1s place? Where are all the 0s? How many 0s
are there?”
● After the class has talked about the 100 chart
and has identified various patterns, divide
the students into pairs or small groups and
give each group a 100 chart that has been cut
apart. (Or have the students cut the charts.)
● Challenge the teams to reassemble their
charts without looking at a completed chart.
● Discuss how the students reassembled their
charts. What strategies did they use?
● Encourage the children to share their thinking.
H OW M I G H T YO U A D A P T T H I S A C T I V I T Y ?
● Cut apart less of the 100 chart (i.e., to 20, 25,
50, depending on the level).
H OW M I G H T YO U E X T E N D T H I S A C T I V I T Y ?
● To make this activity more challenging,
colour in a pattern on the 100 chart
transparency. Ask the students to guess what
rule was used to colour in that pattern.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 57
Guess My PatternGuess My Pattern
Math Focus: Mathematical Thinking Strategies
W H AT D O YO U N E E D ?
● 100 Charts (Master 9)
● individual chalk boards
● pencil or chalk and eraser
● overhead projector and pens
● transparency of 100 Chart (Master 9)
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● share their thinking in a clear and articulate
manner?
● come up with more than one answer?
● see relationships between numbers?
● create their own patterns?
W H AT D O YO U D O ?
● Colour in a pattern on the 100 chart (e.g., 11,
22, 33, 44, 55, 66, 77, 88, 99).
● Ask the students to describe the pattern.
“What might the rule be?”
● As the children suggest rules, ask them to
share their thinking strategies.
“How did you come up with that rule?”
“How did you figure that out?”
“Are there any other rules?”
“Has anyone else come up with a different
answer?” Discuss their suggestions.
● Encourage students to come up with various
answers (e.g., multiple of 11, skip counting
by 11, add 11, no difference in digits).
● Colour in another pattern on the 100 chart
and ask the students to guess what the
pattern is and what the rule might be. Ask
them to share their responses and thinking
strategies.
● Record some number patterns on the
overhead (e.g., 4, 8, 12, 16), and ask the
students to predict which three numbers
would come next.
● Have the students share their thoughts on
what they think the pattern might be.
Encourage them to come up with more than
one answer.
H OW M I G H T YO U A D A P T T H I S A C T I V I T Y ?
● Use very simple patterns (e.g., 5, 10, 15, 20 or
10, 20, 30, 40).
● Include fewer numbers in the pattern, and
keep the numbers and pattern simple.
H OW M I G H T YO U E X T E N D T H I S A C T I V I T Y ?
● Give students patterns that involve more
than one step or operation (e.g., 4, 3, 6, 5, 8, 7,
10...).
● Encourage the children to come up with their
own challenging patterns and have the
others guess what the pattern is.
❍ ● ● ● ❍
S U P P O R T I N G E A R L Y N U M E R A C Y58
Number Pattern Quick Tasks
Action Pattern Quick TasksAction Pattern Quick Tasks
Action patterning channels a child’s natural
need to move into constructive activities.
Patterning activities can be used often
throughout the day—during circle time, while
waiting in line, for getting students’ attention
after transitions or as part of music and PE
lessons.
● Have the children watch for patterns
everywhere they go for a day.
● Choose stories and songs with patterns.
● Have a “Pattern Day” when everyone tries to
wear something that has a pattern.
● Give each child a clipboard for “Pattern
Discoveries” to record what they find.
Number Pattern Quick Tasks
● Whenever you have a few minutes, ask for
volunteers to come up to the 100 chart and
use a pointer to share any patterns or
interesting facts they notice about the 100
chart.
● Play Guess My Number: describe a number
on the 100 chart, and ask the students to
guess the number. (e.g., My number has a 2
in the 10s place, is an even number, is in the
same column as 13.)
● Place the cut up 100 chart pieces in zip-lock
bags, and leave them in the math centre for
the children to play with whenever they have
extra time.
● Give a short pattern, and ask the students to
fill in the next three numbers. (This can be
done whenever you have two minutes.)
● Discuss the types of number patterns found
in a storybook.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 59
Counting and Numeral Recognition
A B O U T T H E C O U N T I N G A N D N U M E R A LR E C O G N I T I O N A C T I V I T I E S
This part of the resource is designed to provide focused practice in
specific counting and numeral recognition skills for children who
need more time and systematic reinforcement. Making connections
between words and symbols, number names and numerals is a skill
that requires varying degrees of practice for different children. The
activities in this section provide practice opportunities to
supplement the contextualized counting practice in your regular
mathematics program. Look for natural ways to incorporate these
skills into your daily routine.
W h y a re c o u n t i n g s k i l l s i m p o r t a n t ?
Verbal counting patterns are essential to systematic, accurate
counting. Similarly, learning automatic associations between
number words and numerals is a building block for future work.
When counting and numeral skills are automatic, children are able
to use them as reliable tools to support their growing
understanding of our number system. Fluency in counting and
numeral recognition frees up short-term memory, allowing children
to focus on important conceptual goals instead of struggling to
retrieve relatively low-level associations. This section uses multi-
sensory activities to provide the visual, verbal and kinesthetic
involvement children need to commit these skills to memory.
C O N N E C T I O N TO T H E K - 1 E A R LYN U M E R AC Y A S S E S S M E N T
This section is a valuable resource for children who had difficulty
with the following tasks on the Early Numeracy Assessment:
Item 5—Verbal Counting Forward
Item 6—Verbal Counting Back
Item 9—Build and Change
Item 13—Reading Numerals
Item 15 (optional)—Building Coin Sets
Item 17 (optional)—100 Chart
S U P P O R T I N G E A R L Y N U M E R A C Y60
The following assessment items also connect to these activities,
although more loosely:
Item 1—Number Awareness
Item 2—Recognizing Dot Patterns
Item 7—Estimate and Check
Item 14—Numeral Printing
U S I N G T H E C O U N T I N G A N D N U M E R A LR E C O G N I T I O N A C T I V I T I E S
The quick and easy-to-use activities in this section are organized by
specific skill areas. They are meant to supplement your existing
math program by allowing you to zero in on a skill. This is a useful
section to include when shaping an intervention program for small
groups. The key is to use the skills as often as possible to begin, then
reinforce occasionally. Most sections involve creating a chart or
visual to remind students what they have learned (and show you
what needs to be reinforced). These visual aids help to connect
verbal learning with visual-spatial information.
There are 14 Counting and Numeral Recognition activities in this
section, and each includes the following headings:
● What do you need?
● What are you looking for?
● What might you try?
Prepare or collect the following materials ahead of time:
● Large numeral cards on stiff card for group work. Laminate if
possible. Enlarge Master 8 or hand print.
● Individual sets of numeral cards printed on stiff card for easy
handling and durability. Use Master 8 or hand print. One set per
student.
● 100 Chart. Large and clear reference chart for the wall. Can be
constructed by enlarging Master 9, cutting and pasting. Laminate
if possible.
● Number Line. Good-sized reference chart for the wall, 0 to 50
minimum, with 10s highlighted. Can be constructed by enlarging
Master 9, cutting and pasting. Laminate if possible. Extend as the
term progresses.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 61
● Calendar. Good-sized reference chart for the wall, with easy to
read numerals.
● Flip-card holders and strip cards. Use a strip of stiff card 8cm x
40cm. Cover the strip with 8cm x 8cm cards that can flip up to
show one number at a time. Tape the top edge of each card
securely to the strip so the flip chart is durable. Make different
number sequence cards to use under the flip cards. (It works best
to hand print these to ensure the size is right.)
S U P P O R T I N G E A R L Y N U M E R A C Y62
Counting and Numeral Recognition Activities
Activity Stage/Level Math Focus Page
Verbal Counting Verbal Counting 63
Counting Objects Counting Objects 64
Reading Numerals Reading Numerals 65
Matching Numerals and Sets Matching Numerals and Sets 66
Ordering Ordering 67
One Greater Number One Greater 68
One Less Number One Less 69
Counting On Counting On 70
Counting to 100 Counting to 100 71
Find and Read Two-Digit Numbers Two-Digit Numbers 72
Teen Numbers Teen Numbers 73
Counting by 10s Counting by 10s 75
Counting by 5s Counting by 5s 76
Counting by 2s Counting by 2s 77
● ● ❍ ❍ ❍
● ● ❍ ❍ ❍
● ● ❍ ❍ ❍
● ● ❍ ❍ ❍
● ● ❍ ❍ ❍
● ● ❍ ❍ ❍
● ● ❍ ❍ ❍
● ● ❍ ❍ ❍
❍ ● ● ❍ ❍
❍ ● ● ❍ ❍
❍ ● ● ❍ ❍
❍ ● ● ❍ ❍
❍ ● ● ❍ ❍
❍ ● ● ❍ ❍
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 63
Verbal CountingVerbal Counting
Math Focus: Verbal Counting
W H AT D O YO U N E E D ?
No special materials are required for these ideas.
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● count consistently to 10 minimum?
● count by 1s to 30 minimum? (may need
teens or transition help)
W H AT M I G H T YO U T RY ?
● Connect rhythm, action, tone and pacing
with the count so that children have many
ways to internalize the pattern.
● Focus on bridges between decades to over-
learn those transitions. Use rhythm, tone,
volume and actions to do this.
● Have any children made the connection
between verbal counting and the number
line or 100 chart? Watch for that awareness
to emerge.
● Establish the forward count to 10 verbal
pattern through many and varied methods
throughout the day (e.g., Calendar, books,
steps, objects, fingers).
● Use a rhythm with the count, either 2s or 5s.
Use tone to build up to 10.
● Choose a motor pattern to associate with
counting by 1s. Make it simple, as you will
use it often. Use a build-up to another action
for reaching 10 and, later, multiples of 10.
(e.g., finger-climbing up to a clap over the
head for 10).
● ● ❍ ❍ ❍
● Count aloud while doing actions to 10
minimum (e.g., steps, jumps, claps, taps,
snaps). Build in a rhythm in 2s or 5s.
● Play Guess my Count: have one child clap up
to 10 times while the others, eyes closed,
count the claps.
● Count around the circle and at 10 (and
multiples thereof), everyone claps. Use the
motor, rhythm and tone patterns with the
count.
● Extend the verbal counting chain as you
walk, clap or do rhythmic movements.
S U P P O R T I N G E A R L Y N U M E R A C Y64
Counting ObjectsCounting Objects
Math Focus: Counting Objects
W H AT D O YO U N E E D ?
● Unifix cubes
● small objects for counting
● 10-holder egg cartons (cut off the last pair of
holders in an egg carton)
● 10-Frame Cards (Master 20)
● 10-Frame Mats (Master 5)
● large Numeral Cards 0-9 (enlarge Master 8
onto stiff card and laminate, if possible)
● individual sets of Numeral Cards 0-9
(Master 8)
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● count up to 10 objects accurately using a
move-and-count strategy (rather than
random pointing)?
What might you try?● Count sets to 5 using Unifix cubes on fingers.
(Drop cubes, count on ground, move
around, count again…still 5?)
● Use 10-holder egg cartons for students to
build and count. To begin, work left to right,
top to bottom until students have
established the patterns. You want a stable
and reliable visual image before looking at
other ways to build numbers in the frame.
● Introduce 10-frame cards for students to
match and build. As appropriate, match to
numeral cards.
● Use Master 5 to make 10-frame mats. Practise
building sets up to 10 and back down using
the left to right, top to bottom pattern.
● Continue counting sets to 10 to establish the
counting pattern and the connection to the
number words. Use “move and count” and
visual organization of groupings of 2s, 3s, 4s
or 5s rather than random piles.
● Gradually introduce the rest of the numerals,
one per day as appropriate, so that students
can name them on sight. Use the association
games as described in the previous sections.
Integrate these counting and naming skills into
as many real-life situations as possible.
● ● ❍ ❍ ❍
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 65
Reading NumeralsReading Numerals
Math Focus: Reading Numerals
W H AT D O YO U N E E D ?
● counters
● large Numeral Cards 0-9 (enlarge Master 8)
● poster board, newspapers, scissors and glue
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● recognize numerals to 5 by saying the
number and showing that number of fingers
or counters?
● show the appropriate numeral card when
given a number verbally?
W H AT M I G H T YO U T RY ?
● Work on recognizing 1 and 2: Introduce the
two numerals, playing a game of showing
with fingers.
● Once 1 and 2 are solid, gradually build
recognition to 5.
● Have the children trace their fingers over
numerals, in the air and on the floor in the
patterns of each numeral to help internalize
the shapes.
● Ask the children to find all the 3s (or 2s or 4s)
in a set of magnetic numerals.
● Have the children make numeral posters:
Search in newspapers for specific numerals
and glue all different fonts and sizes of that
number on their poster.
● In the computer lab, experiment with
different fonts. Print out a variety in at least
24 point. Have the children cut out and sort
the numerals and then glue them into
number books.
● Have the children place the numeral cards
around the room and play I Spy. Ask them to
point to the numeral when they hear the
number name.
● ● ❍ ❍ ❍
S U P P O R T I N G E A R L Y N U M E R A C Y66
Matching Numerals and SetsMatching Numerals and Sets
Math Focus: Matching Numerals and Sets● ● ❍ ❍ ❍
W H AT D O YO U N E E D ?
● Numeral Cards 0-9 (Master 8)
● dice
● blocks for building
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● build the set, when given the number name?
● label the set, when given the number name?
W H AT M I G H T YO U T RY ?
● Practise finding numerals on a chart or in a
card pile.
● Practise calling out number names while
rolling numeral dice.
● Practise finding numeral cards while rolling
dot dice.
● Play I Spy, where the children count objects
(e.g., doors) and show numeral cards to
match.
● Play Build and Label with numerals:
Say 5, have the child build 5 and show the
5 card.
Show the 3 card, have the child build 3 and
say 3.
Clap 2 times, have the child build 2 and
show the 2 card.
Any number of matching games fit this skills set.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 67
OrderingOrdering
Math Focus: Ordering
W H AT D O YO U N E E D ?
● like objects in a range of sizes and lengths
(e.g., ribbon, pencils, nesting cups)
● bead strips
● Unifix cubes
● Numeral Cards 0-9 (Master 8)
● flip-card holders and strip cards
(instructions can be found on page 61)
● wall-size number line
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● order materials from least to greatest?
W H AT M I G H T YO U T RY ?
● Order numerals to 10.
● Order many types of materials by length
(e.g., ribbon, pencils), by area (e.g., lids,
pieces of card), by volume (e.g., nesting
shapes) so that students connect the
concept of ordering with the ordering of
number specifically.
● Use bead strips cut in lengths from 1 to 10.
● Use ribbon lengths with differences of 2cm
or 3cm each, so that comparisons are clear.
● Build linking stairs to 10. Mix up, then reorder.
● Connect numeral cards to ordered materials
where the number differences are clear (e.g.,
Unifix cubes).
● Focus on comparing, ordering, one more
than, one less than.
● Have the children order numeral cards.
● Create a flip chart counting card (see
instructions on page 61). Have the children
try to predict what is hidden under a flap. Ask
one child to lift one cover while the others try
to name one more (right side) and one less
(left side).
● Show the children a starting number of 0 or
1. Ask, “Where’s 2? What’s next? What’s here?
Find 4,” and so on.
● Change the hidden number sequence as
appropriate by substituting the number strip
(e.g., 1-5, 0-4, 2-6, 5-9).
● Work with two counting strips beside each
other (two strips of five, 1 to 5 and 6 to 10) to
practise one more/one less to 10.
● If the children haven’t noticed it, introduce
the number line. Integrate extended
counting practice into the routine, using the
line as a reference point.
● ● ❍ ❍ ❍
S U P P O R T I N G E A R L Y N U M E R A C Y68
One GreaterOne Greater
Math Focus: Number One Greater● ● ❍ ❍ ❍
W H AT D O YO U N E E D ?
● Unifix cubes
● Numeral Cards 0-9 (Master 8)
● paper plate
● small counters
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● identify the number one greater, one more
than, or next to 10?
W H AT M I G H T YO U T RY ?
● Build linking stairs together, modeling one
more than each time. Mix up the stairs, and
have the students reorder them by length
and number. Count them together.
● Show the children how to use cards to label
each step. This way, the children will be able
to match and order the cards independently
in the future.
● Focus on ordering to 5, then to 10 (or as
appropriate). Add 0 after 1 to 10 are
established.
● Play Pass the Plate: Pass a paper plate around
the circle. Have each child add one counter
as everyone counts the number on the plate.
When the leader claps, the child with the
plate leads a count of the objects, moving
each piece to show it has been counted.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 69
One LessOne Less
Math Focus: Number One Less
W H AT D O YO U N E E D ?
● paper plate
● small counters
● card stock and crayons
● flip-card holder and strip cards (instructions
can be found on page 61)
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● identify the number that comes before, or is
one less?
What might you try?● Use the same procedure as in One Greater
(p. 69), working backwards. Ensure the
forward counting sequence is solid before
reversing.
● For Pass the Plate, when the leader claps,
have the children count, then start working
backwards. You may need to count to check
after each move.
● “5, 6, 7, clap. Jon, how many are on the plate?
7. Now we go backwards. If you take one off
the plate, how many will there be? Do it,
then let’s count and check.”
● Have the students each draw a bus (or ferry
or hot air balloon) on a card. Using counters
to represent the passengers on the bus (draw
the driver), go for a drive.
● “At the first stop, 3 people get on. At the next
stop, 1 person gets off. How many now? Now
3 more get on. How many now? (Jazz it up!)
● ● ❍ ❍ ❍
● Work backwards with the flip-card holders
and counting strips. Have the children
predict the number that is hidden, then
check by lifting the flap.
S U P P O R T I N G E A R L Y N U M E R A C Y70
Counting OnCounting On
Math Focus: Counting On
W H AT D O YO U N E E D ?
● bags
● dice
● blocks or other counters
● 10-frames (made from egg cartons, or 10-
Frame Mats—Master 5)
● wall-size number line
● pennies
● flip-card holder and strip cards (instructions
can be found on page 61)
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● count on from 5, up to 15?
● given a bag with up to 10 objects in it, count
on 2 or 3 more objects as you add them in?
The ability to keep a double count (adding 1, 2,
3 but saying 6, 7, 8) requires considerable skill
and is an important developmental milestone.
It shows that the child has moved beyond one-
to-one correspondence and can grasp the part/
whole relationship of number (i.e., that 5 is a
part of 8 and that counting on from 5 will name
the other part).
W H A T M I G H T Y O U T R Y ?
● Provide lots of opportunities to build a set,
cover it and add 1, 2 or 3. If the student is
unsure of how many are hidden, show them,
count to check, cover and continue. (“Boy, I
can’t fool you!”)
● Discuss the different ways to keep a tally of
the count (e.g., fingers, keeping a beat or
rhythm, pointing to each block).
● Roll a die, have the children build that number
with counters and put them in a bag. Establish
how many are in the bag, then record by
showing a numeral card or printing to keep
track of the bag contents. Roll again, build,
then count on to the bag contents as you add
in the roll number. “Five here now…6, 7, 8.”
Predict how many: “Who thinks 8?” Open the
bag to check. Work up from 2 rolls to 3, 4 or 5
in a row before checking. Children can play
this game in pairs and do their own recording.
● “Five in a bag—now how many?” (Count on
from 5.) Practise with many different starting
quantities, ensuring the children are clear on
what is actually in the bag to start. (Eventu-
ally you can pretend what is in the bag.)
● Count on from 5 using fingers 5…6, 7, 8.
Practise showing 6-to-10 fingers, starting
with the hand as 5.
● Use the 10-frames as mats or holders. Work
with the idea of starting with 5 or 10 and
adding on.
● Practise starting at different places on the
number line, flip charts or counting charts
and counting on.
● Use sets of pennies. Put them in the bank and
keep track by counting on. If children are
familiar with dimes and pennies, count on
from a dime or two dimes.
● ● ❍ ❍ ❍
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 71
Counting to 100Counting to 100
Math Focus: Counting to 100
W H AT D O YO U N E E D ?
● 100 Chart (enlarge Master 9)
● adding machine tape
● old calendar
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● count to 100 by 1s?
● count on from a starting number?
● name the number that comes before, after
and in between?
W H AT M I G H T YO U T RY ?
● Use activities in the Estimation section for
practice in counting to 100.
● Read number lines, count on calculators,
turn pages in a book and read the number-
ing, read the calendar, and so on. Any
context children see and are familiar with is
a good one for focusing on number to 100.
● Enlarge Master 9, colour the 10s column, cut
the decade strips, and give out the strips for
the children to help you make a number line.
Glue the strips onto adding machine tape to
make a number line to 100. Compare the new
number line to the wall chart.
● Demonstrate that a calendar is a number line
cut and stacked. Cut up a calendar page, and
glue the parts onto a number line.
❍ ● ● ❍ ❍
S U P P O R T I N G E A R L Y N U M E R A C Y72
Find and Read Two-Digit NumbersFind and Read Two-Digit Numbers
Math Focus: Two-Digit Numbers❍ ● ● ❍ ❍
W H AT D O YO U N E E D ?
● wall-size 100 Chart
● wall calendar
● individual sets of Numeral Cards 0-9 (Master 8)
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● count to 100?
● give the number that comes after, to 100?
● give the number that comes before, to 100?
● give the number that comes between two
other two-digit numbers?
● find given two-digit numbers on the 100
chart and number line?
● print or use cards to show given two-digit-
numbers?
● find two-digit numbers on the calendar, 100
chart or number line?
● recognize and name numerals to 100?
The ability to recognize and read two-digit
numbers can support children’s early
understanding of place value. Similarly,
knowing that 12 is “twelve” in the counting
sequence precedes recognizing 12 as 10 and 2.
W H AT M I G H T YO U T RY ?
● Introduce the 100 chart (the wall chart may
already have been noticed). Focus on the 10s
column, and count together. Ask the children
what patterns they can see on the chart. Ask
them to show the patterns they see. Do this
on a regular basis. Your most adept math
students will find patterns that the other
children will gradually be able to see.
● Practise counting daily on the wall 100 chart.
● On the calendar, focus on reading 20 to 31.
Then look at the 100 chart and practise
reading 20 to 100.
● Play I Spy: “Can you find 75? What row will it
be in on the 100 chart? Point to it.” Model
analytical thinking, and have the children
explain how they knew where the numbers
would be found.
● Use individual numeral cards to show two-
digit numbers. Point to 36, for example, on
the number line, and ask the students to
make that number with their cards. At first
this will be a simple matching task. Later, try
it from memory.
● Continue to work with extending the children’s
counting chains up to 100. Emphasize the
decade shifts with your expression. Build
rhythm into the counting. Connect this
counting to the Estimation work.
● Connect this counting to work the children
are doing in the Visual-Spatial section,
particularly with 10-frames.
● Practise naming the number before, after or
between, using the 100 chart and number
line as a reference at first, then working
toward doing it with eyes closed. Different
children will develop the mental imagery at
different times.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 73
Teen NumbersTeen Numbers
Math Focus: Teen Numbers
W H AT D O YO U N E E D ?
● number line
● 100 Chart
● baggies and small counters
● Unifix cubes
● dimes and pennies
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● count verbally from 1 into the 20s or 30s?
● give the next number when given a teen
number?
● give the number that comes before when
given a teen number?
● describe 14 as 10 and 4 when given a 10 and
1s model?
● find teen numbers in a random collection of
numerals?
● read teen numbers accurately and match
them to the 100 chart?
The teen numbers can be challenging for young
children because of their conflicting number
names (i.e., seventeen suggests 7teen and is
often written as 71). There are also auditory
challenges due to the similar sounding number
names of teens with multiples of 10 (i.e., thirty
sounds like thirteen and can cause confusion if
not addressed).
W H AT M I G H T YO U T RY ?
● Ensure the students have a grasp of number
above 20 for counting, reading and even writing
before going back and re-emphasizing teens.
● Ensure the students are familiar with the 100
chart before focusing on teens, so they can
place them within the counting framework.
● Clearly articulate and focus on the verbal
difference between teens and the decades
(i.e., 30, 40, 50). This is especially important
for ESL students.
● Use the number line and 100 chart to show
13 vs. 30, 15 vs. 50, and so on.
● Introduce a new way to read the teen numbers
by building up from 10, saying 10 and 1, 11 in
all; 10 and 2, 12 in all; 10 and 3, and so on.
Sometimes this verbal pattern can help to
establish both the correct printing pattern for
teens and an intuitive understanding of the
place value that underlies our system.
● Bag and label sets of 10 so that you can practise
counting together 10 and 1, 10 and 2, and so on.
● Provide Unifix cubes for building 5s in one
colour. Use these to build 10-sticks in two
colours. Use the 10-sticks with 1s to build
teen numbers.
● Introduce the dime as 10 cents, and use
dimes and pennies to practise teens. (This is
useful even for children who don’t count on.
Familiarity will help connect the conceptual
and procedural when it makes sense.)
❍ ● ● ❍ ❍
S U P P O R T I N G E A R L Y N U M E R A C Y74
Teen Numbers continued
● Use place value blocks to practise building
teen numbers without counting from 1
(counting on from a given 10). Again, this
ability (verbal counting on) can be
developed ahead of the conceptual
understanding and can help children to
make the important shift to cardinal
counting on.
Teen Numbers continued
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 75
Counting by 10sCounting by 10s
Math Focus: Counting by 10s
W H AT D O YO U N E E D ?
● Unifix cubes
● 10-frames
● baggies or bundles holding sets of 10
● laminated dime shapes (enlarge Master 15)
● dimes
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● count by 10s to 100?
● find sets that have been grouped in 10s?
● count up the value of given sets of 10, such
as five linking 10s trains?
● find that multiple of 10 on the 100 chart?
● given a multiple of 10 such as 40, use
materials to show 40?
W H AT M I G H T YO U T RY ?
● Practise the 10s chain like a song so it comes
easily. Gradually connect it to
representations for 10s.
● Use fingers and toes—the more real
connections the better.
● Have the children build 10s models (e.g.,
linking 10s trains with two groups of 5,
coloured 10-frames, bundles or baggies of
materials).
● Introduce dimes using large, laminated dime
shapes. Use real dimes, dropping them into
a dish as children count by 10s when they
hear the sound.
❍ ● ● ❍ ❍
● Practise counting by 10s on the 100 chart and
number line. Highlight multiples of 10 with a
colour and/or by size so the pattern jumps
out.
● Use 10-frames for students to build 10s and
add 10s. Read the values with them. (You can
use 10-frame mats or 10-holder egg cartons.)
S U P P O R T I N G E A R L Y N U M E R A C Y76
Counting by 5sCounting by 5s
Math Focus: Counting by 5s
W H AT D O YO U N E E D ?
● nickels and pennies
● number line
● 100 Chart (Master 9)
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● count by 5s to 50?
● find sets that have been grouped in 5s?
● count up the value of given sets of 5, such as
7 hands?
● find multiples of 5 on the 100 chart?
● given a multiple of 5 such as 25, use
materials to model the number?
W H AT M I G H T YO U T RY ?
● Trace hands and cut out for practice with 5s.
Make a wall chart of hands (glue them in a
line left to right, with thumbs on the right).
With the children, count and label the chart,
using a different colour and size for the
multiples of 5 (the thumb numbers). Use the
whisper/count process to begin. Integrate
practice at counting by 5s into the routine.
● Highlight the 5s chain on the number line
and the 100 chart.
● Practise counting by 5s on both the hand
chart and the 100 chart.
● Introduce a motor pattern for the 5s
sequence (e.g., moving elbows back and
forth or some other active cue to connect
only with 5s).
❍ ● ● ❍ ❍
● Introduce nickels for counting by 5s. Use
soft-loud counting (1, 2, 3, 4, 5) to count out
the nickels. The children will gradually
internalize the count.
● Once counting by 5s is established, add
pennies so the students have practice
counting on to 5.
● Introduce the motor pattern for stars,
counting to 5 as each star is drawn. Up (1)
then down (2) to make a point (like an A),
across and up to the left (3), straight across to
the right (4), down to meet the starting point
(5). Count points together, labeling each star
in the count with 5, 10, 15. Use the set of stars
for counting and ordering practice.
1 ➠
2 ➠
4 ➠
3
➠
5➠
Start
6 ➠
7 ➠
9 ➠
8
➠
10➠
Start
11 ➠
12 ➠
14 ➠
13
➠
15➠
Start
16 ➠
17 ➠
19 ➠
18
➠
20➠
Start
21 ➠
22 ➠
24 ➠
23
➠
25➠
Start
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 77
Counting by 2sCounting by 2s
Math Focus: Counting by 2s❍ ● ● ❍ ❍
W H AT D O YO U N E E D ?
● number line
● 100 Chart (Master 9)
● construction paper, clear MacTac and
duct tape
W H AT A R E YO U L O O K I N G F O R ?
Can the children:
● count by 2s to 10? 20? Beyond?
● find sets that have been grouped by 2s?
● count up the value of given sets of 2, such as
5 pairs of shoes?
● find multiples of 2 on the 100 chart? Can
they see the pattern?
● use materials to show a multiple of 10?
W H AT M I G H T YO U T RY ?
● Count ears, eyes, feet or fingers for practice.
Think of all the real-life examples for 2s, and
use these for counting practice.
● Introduce soft-loud counting if needed. For
the 2s pattern, whisper the odd numbers,
and say the even numbers aloud. (This
allows children to build on their 1s counting
and see the connection.) Start to establish
the “song,” visually connecting to jumps on
the number line.
● Have the children trace footprints or draw
bikes on paper to make a 2s counting chart
for the wall. With the children, label the
count of feet or wheels with small odd
numbers and large even numbers (the visual
match to soft-loud counting). Integrate the
count-by-2s chain into the practice routine.
● Highlight the 2s chain on your number line
(e.g., with coloured circles, jumps of 2).
● Look for patterns on the 100 chart involving
2s and multiples of 2.
● Draw two footprints, and photocopy them
onto construction paper in two colours (e.g.,
15 pairs of blue, 15 pairs of green). Have the
children cut these out. Use these to make a
footprint model at the door at which the
children usually line up. Space the footprints
to model where they would stand in line.
Cover the line-up with clear MacTac, and
tape down the edges with duct tape. This will
make a durable counting model for a host of
mathematical ideas, including counting by
2s, dividing by 2s, doubling, problem solving,
odd and even numbers—and may even
simplify lining up single file!
S U P P O R T I N G E A R L Y N U M E R A C Y78
Visual-Spatial Pattern Recognition
A B O U T T H E V I S UA L - S PAT I A L P AT T E R NR E C O G N I T I O N A C T I V I T I E S
This section is designed to provide sequenced development of
specific visual-spatial patterns that support early numeracy. Visual-
spatial patterns are quantities arranged in a way that helps the
brain recognize how many there are in the collection. Dice patterns
are examples of spatial arrangements that the brain can learn to
recognize without counting by 1s.
W h y a re v i s u a l - s p a t i a l s k i l l s i m p o r t a n t ?
Using systematic visual-spatial arrangements of quantity can
establish mental imagery of number that supports number sense.
In terms of mathematical power, recognizing quantities without
counting by 1s is the basis of grouping concepts. This skill is a
natural bridge between one-to-one and many-to-one
correspondence.
The suggestions in this section will help with:
● visual imagery and visual memory
● instant recognition of quantities without counting
● analyzing visual information
● combining, comparing and ordering visual information
● modeling using visual patterns
● spatial sense-making
C O N N E C T I O N TO T H E K - 1 E A R LYN U M E R A C Y A S S E S S M E N T
This section provides a scaffold for some and a learning
opportunity for others. As children work through the K-1
assessment, you will have an opportunity to see which children rely
heavily on spatial information. Often these children arrange
materials into patterns, and many perform strongly on the visual-
spatial tasks. These children can benefit from using their visual-
spatial strength as a scaffold for learning about number and will
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 79
benefit from the activities in this section. This section is also
valuable for children who struggled with the following tasks on the
Early Numeracy Assessment:
Item 2—Recognizing Dot Patterns
Item 10—Pattern Tasks
Item 12—Squares Puzzle
Item 16 (optional)—Cube Building
U S I N G T H E V I S UA L - S PAT I A L P AT T E R NR E C O G N I T I O N A C T I V I T I E S
The Visual-Spatial section of this resource includes 10 parts that are
cumulative, in that each part builds on the previous one. Within
each part is a set of brief activities from which you can choose one
or two each day. Depending on your group, with 5 minutes a day
devoted to these activities, a section may take between one and two
weeks to complete. The activities are meant to be quick and snappy,
with lots of celebration when students learn to recognize quantities
in different arrangements. Use the children’s responses to the
activities to gauge an appropriate pace.
Each of the activities in this section includes the following
headings:
● What do you need?
● What are you looking for?
● What might you try?
S U P P O R T I N G E A R L Y N U M E R A C Y80
Visual-Spatial Pattern Recognition Activities
Activity Stage/Level Math Focus Page
Building Visual Memory Building Visual Memory 81
Matching and Comparing Matching and Comparing Patterns 82
Patterns
More/Less and Ordering More/Less and Ordering 83
10-Frames Recognizing 0 to 5 in Relation to 10 84
Analyzing Number Patterns Analyzing Number Patterns 85
Doubles Symmetrical Number Patterns 86
Parts and Wholes Parts and Wholes 87
Patterns for 6 to 10 Patterns for 6 to 10 88
Seeing Groupings Seeing Groupings 89
Larger Quantities Larger Quantities 90
● ● ❍ ❍ ❍
● ● ❍ ❍ ❍
● ● ❍ ❍ ❍
● ● ❍ ❍ ❍
● ● ❍ ❍ ❍
❍ ● ● ❍ ❍
❍ ● ● ❍ ❍
❍ ● ● ❍ ❍
❍ ● ● ❍ ❍
❍ ● ● ❍ ❍
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 81
Building Visual MemoryBuilding Visual Memory
Math Focus: Building Visual Memory
W H AT D O YO U N E E D ?
● a tray with objects
● Dot Pattern Cards (enlarge Master 18)
● round counters
● Dice Mats, one per student (Master 16)
● dominoes
● Domino Mats, one per student (Master 17)
W H AT A R E YO U L O O K I N G F O R ?
Before moving on to the next section, ensure
that the children can:
● recognize dot patterns 1 to 5 without counting
● display one-hand finger patterns for 1 to 5
without counting
● connect dot, domino and finger patterns for
1 to 5 without counting (i.e., given a domino,
the child shows fingers; given a dot pattern,
the child finds the appropriate domino)
W H A T M I G H T Y O U T R Y ?
V i s u a l Me m o r y G a m e s
● Place objects on a tray, starting with 3 or 4
items. Cover and remove one. Can the
children recall what is missing? Where it
was? Adapt this game with size, number and
type of items. Use an organized arrangement
for the items.
● Use matching games with pairs of matching
cards, starting with 5 or 6 pairs laid out in a
pattern. Have the children turn over two
cards; if they match, they keep them. (There
are many ways to adapt this game.)
R e c o g n i z i n g D o t Pa t t e r n s
● Introduce dot patterns using cards. Show 1
and 2, have the children practise saying the
number as fast as possible, and gradually add
3. Once the children can immediately
recognize and name 1, 2 and 3, add 4 and 5 to
the mix over the next few days.
● Show the children dot pattern cards, and
have them model the arrangement using
chips and dice mats. Develop a snappy
routine for this activity.
R e c o g n i z i n g D o m i n o Pa t t e r n s
● Introduce real dominoes. Look for patterns
for 1, 2, 3, 4, 5. Use activities as above,
including domino mats.
C re a t i n g F i n g e r Pa t t e r n s
● Using cards for 1-to-5 dot patterns, work
toward automatic finger pattern responses
on one hand. Use the hand pattern of 5 as a
reference point. Point out that 4 is easy (no
thumb). Work with these until the patterns
are automatic, not counted out one by one.
(e.g., When you show the 5-dice card, the
child shows 5 fingers without counting
them out.)
● ● ❍ ❍ ❍
S U P P O R T I N G E A R L Y N U M E R A C Y82
Matching and Comparing PatternsMatching and Comparing Patterns
Math Focus: Matching and Comparing Patterns
W H AT D O YO U N E E D ?
● large Dot Pattern Cards and Domino Cards
(enlarge Masters 18 and 19)
● individual Dice and Domino Mats (Masters
16 and 17)
● round counters
W H AT A R E YO U L O O K I N G F O R ?
Before moving on to the next section, ensure
that the children can:
● create dice patterns for 1 to 5 from memory
by choosing the correct number of counters
and arranging them on their dice mat
● show finger patterns with eyes closed and
without counting for numbers 1 to 5
W H A T M I G H T Y O U T R Y ?
R e c o g n i z i n g S i m i l a r i t i e s a n d D i f f e r e n c e s
● Use the cards, counters and mats to build
recognition of what is different and what
changes in each dot pattern from 1 to 5.
● Show 1 and have the children model it, then
show 2 and ask how they would change their
cards to make the 2 pattern.
● Encourage spatial language and detail. (e.g.,
“I need to move this dot down a bit and put
another dot above it.”)
B u i l d i n g V i s u a l Me m o r y f o r Pa t t e r n s
● Show a dot pattern card for three seconds,
then hide it and see if the students can
model the number. Then show the card and
● ● ❍ ❍ ❍
discuss what is the same and different about
their models and the card.
● Build matching patterns as above, using
domino cards and mats.
H i d d e n F i n g e r Pa t t e r n s
● Show a dot pattern card for 1 to 5. Have the
children look, create the finger pattern
behind their backs, then show it above their
heads without looking. Have them check
each other. Make this fast and fun. The idea is
to build mental imagery of what the finger
pattern looks like.
M a t c h i n g Pa t t e r n s O n e t o O n e
● Say a number from 1 to 5. Have the children
pick up that many counters and set them out
on their domino or dice mat in the pattern
for the number.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 83
More/Less and OrderingMore/Less and Ordering
Math Focus: More/Less and Ordering
W H AT D O YO U N E E D ?
● large Dot Pattern Cards 1 to 5 (enlarge
Master 18)
● individual Dot Pattern Cards 1 to 5 (Master 18)
● dominoes
● pegboards and pegs
W H AT A R E YO U L O O K I N G F O R ?
Before moving on to the next section, ensure
that with number to 5, the children can:
● name the number that is one more
● find the dot pattern card for one more
● name the number that is one less
● find the dot pattern card for one less
● order dot pattern cards
● find the hidden dot pattern card in a 1 to 5
sequence
W H A T M I G H T Y O U T R Y ?
O n e - Mo r e Pa t t e r n s
● Provide the children with individual dice
pattern cards 1 to 5. Call out numbers, and
ask them to show the appropriate card.
● Ask them to find the card that is one more
than the number you call. Encourage the
children to do this without counting. Ask
them to note what is different between the
dot pattern card for the called number and
the dot pattern card that is one more, using
language of position and quantity.
● Use dominoes to find one more.
O n e - L e s s Pa t t e r n s
● Show the children a dot pattern card between
2 and 5, and ask them which card has one
less dot. Cover a dot to illustrate one less, or
take away one, or hide one.
● Once the children find the card, discuss the
difference between the two in terms of
spatial arrangement.
● Use pegboards to build one-more/one-less
patterns.
O rd e r i n g D o t C a r d s
● Have the children order their dot pattern
cards from 1 (left) to 5 (right) without
counting (based on visual one-more-than).
● Then ask them to turn the cards over to hide
the dots. Call 5, and see if they can find where
5 is and show it. Repeat with other numbers.
● If appropriate, add in the 6-dot card at this
point, and repeat some of the previous
activities with the 1-to-6 set.
“What is special about 6?”
“What do you see in the dot pattern
arrangement?”
● ● ❍ ❍ ❍
S U P P O R T I N G E A R L Y N U M E R A C Y84
10-Frames10-Frames
Math Focus: Recognizing 0 to 5 in Relation to 10● ● ❍ ❍ ❍
W H AT D O YO U N E E D ?
● 10-holder egg cartons, one per child (cut off
the last pair of holders in an egg carton)
● Dot Pattern Cards (Master 18)
● cubes
● 10-Frame Mats (Master 5)
● 10-Frame Cards (Master 20)
● cards, 10cm x 10cm minimum
● dots and glue or stickers for making dot
pattern cards
W H AT A R E YO U L O O K I N G F O R ?
Before moving on to the next section, ensure
that with number to 5, the children can:
● automatically recognize random and dice
patterns for 1 to 5
● model 1 to 5 using a 10-frame
● match dot patterns and 10-frame patterns
● name 10-frame patterns
W H A T M I G H T Y O U T R Y ?
3 - D 1 0 - Ho l d e r s
● Introduce 10-frames using egg cartons
with the last two holders cut off to make a
10-holder.
● Ask the children to make sets of 1 to 5, to
match a given dot pattern card.
● Introduce the idea of adding counters one at
a time to the top row, left to right.
● Whisper a different number from 1 to 5 for
each child to build with their 10-holder.
● Then ask the students which holds the least
and which the most. Ask them to order the
10-holders from least to greatest or most.
1 0 - Fr a m e s
● Introduce 10-frame mats and practise
building sets to match numbers 1 to 5.
Emphasize the left to right development
across the top row.
● Provide 10-frame cards for students to colour
to represent patterns for 1 to 5. Use the
created set to flash, and work toward
immediate recognition of the quantity.
● Add 6 into the mix.
R a n d o m Pa t t e r n s f o r 1 t o 5
● Have the students make sticker dot pattern
cards for 1 to 5, one set in the standard dice
patterns and one set in any arrangement
they like.
● Practise flashing and naming the patterns.
Once the cards are automatic, have the
children take them home to practise and
show their skill.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 85
Analyzing Number PatternsAnalyzing Number Patterns
Math Focus: Analyzing Number Patterns
W H AT D O YO U N E E D ?
● 10-holders
● counters
● playing cards
● instruments (e.g., drum, bell, triangle)
● individual Dot Pattern Cards (Master 18)
W H AT A R E YO U L O O K I N G F O R ?
Before moving on to the next section, ensure
that the children can:
● model and describe different arrangements
for 5
● recognize and describe likenesses and
differences in patterns to 5
● mentally count and tally up to 5 sounds
W H A T M I G H T Y O U T R Y ?
D e c o m p o s e / R e c o m p o s e Na m e s f o r Nu m b e r s
● Introduce the idea of many ways to make,
for example, 5.
● Have the children put 5 counters in their 10-
holder or on a 10-frame mat, then together
analyze patterns to find smaller groupings.
“Look at our ways to show 5. Lily has 4 and 1,
Tom has 2 and 2 and 1, and Sam has 2 and 3.”
● Further develop the decomposition idea
using two-handed finger patterns for
numbers 1 to 5.
“Show me 5. Now show me 5 using two
hands. Read your pattern for me.”
● ● ❍ ❍ ❍
● “Analyze” patterns for 1 to 5 on playing cards.
Ask the children how they are the same as or
different from dot pattern cards.
He a r i n g Nu m b e r Pa t t e r n s
● Count sound sequences (e.g., clapping,
drum, bell). Count and tally first with fingers,
then count mentally—this builds mental
imagery and one-to-one correspondence.
● Use rhythm, or groupings of 2, 3 or 4 beats as
the sequences grow.
● Using dot pattern cards, repeat the sound
patterns, but have the children show how
many using dot pattern cards.
● Clap patterns for the children to join in.
Continue and analyze (e.g., xxx xxx xxx).
S U P P O R T I N G E A R L Y N U M E R A C Y86
DoublesDoubles
Math Focus: Symmetrical Number Patterns❍ ● ● ❍ ❍
W H AT D O YO U N E E D ?
● hole punches
● blank newsprint or thin paper
● construction paper or card in colours
● cards, approximately 10cm x 20cm for
making doubles pattern cards
● Ladybug Mats (Master 4)
● Ladybug Cards (Master 21)
● dominoes
● MIRAs or a mirror
● individual Domino Cards (Master 19)
W H AT A R E YO U L O O K I N G F O R ?
Before moving on to the next section, ensure
that the children can:
● recognize symmetry doubles patterns for 2,
4, 6, 8.
● recognize domino doubles patterns for 2, 4,
6, 8.
W H A T M I G H T Y O U T R Y ?
Sy m m e t r y D o u b l e s
● Use hole punches with newsprint to make
and analyze symmetry dot patterns. Fold
and punch, open and describe.
● Work toward predicting where the matching
dots will be, using a chalk board example.
● Create 2, 4, 6, 8 and 10.
● Make some large, sturdy cards for group
practice. Glue onto contrasting paper so the
holes show.
● Using the ladybug mats, have the students
build a set to 5 on one side and then predict
where the matching set would go.
● Check some by folding and comparing, or
use a MIRA to check the symmetry.
● Children can make their own ladybug models
using Master 21. This can be done by
colouring or with hole punches (fold and
punch to get a symmetrical pattern).
D o m i n o D o u b l e s
● Using a set of dominoes, find doubles
dominoes and analyze them (not
symmetrical, but side by side).
● With the students’ help, create doubles
pattern cards in domino format for 1, 2, 3, 4
and 5. Use these for group practice in
recognizing sets of 2, 4, 6, 8 and 10.
● Make smaller practice cards to send home for
practice as the children begin to recognize
the groupings of 2, 4, 6, 8 and 10.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 87
Parts and WholesParts and Wholes
Math Focus: Parts and Wholes❍ ● ● ❍ ❍
W H AT D O YO U N E E D ?
● 10-Frame Mats (Master 5)
● counters, Unifix cubes
● interlocking construction blocks (such as
Lego or Duplo)
● paper and felts for making the wall display of
10s patterns
W H AT A R E YO U L O O K I N G F O R ?
Before moving on to the next section, ensure
that the children can recognize different
patterns for 6, 8 and 10, using:
● domino formats
● interlocking construction blocks
● 10-frame formats
● finger formats
W H A T M I G H T Y O U T R Y ?
1 0 - Fr a m e Pa t t e r n s
● Review patterns for 1 to 5, then gradually
work up to 10, using 10-frame mats and
counters.
● Always emphasize adding on to the 5, to
establish 5 as a benchmark.
“Is it more than 5? Where is 5? How many
more?”
● Practise doubles finger patterns for 6, 8 and
10, using matching finger sets on each hand
(3+3, 4+4, 5+5). Work toward automatic
showing of fingers without counting one
by one.
2 s Pa t t e r n s
● Use interlocking construction blocks to build
recognition of dot patterns in rows of two
(blocks come in 2, 4, 6, 8 dot patterns).
“Find me a 6.”
● Practise counting by 2s in conjunction.
● Explore how doubles patterns can be created
on the 10-frame using top-and-bottom
matching. Compare these patterns to the
construction blocks.
Nu m b e r Pa t t e r n s
● Highlight seeing parts and patterns within
quantities. Use Unifix cubes to develop colour
patterns. (e.g., “Make a train of 6 with two
colours. Mary, use 3 red and 3 blue, 6 in all.
Glen, use 2 white, 2 red and 2 white, 6 in all.”)
● Break the colours apart, and stack them into
an array 3+3, 2+2+2.
● Repeat with eight blocks.
Pa t t e r n s f o r 1 0
● Make a wall display of many ways to show 10:
trace two hands, colour a full 10-frame, draw
construction block dots, make a 10 domino.
● Build a pyramid, counting out four round
chips for the base (1,2,3,4,). Count on 5,6,7
for the second layer, then 8, 9 then 10.
S U P P O R T I N G E A R L Y N U M E R A C Y88
Patterns for 6 to 10Patterns for 6 to 10
Math Focus: Patterns for 6 to 10❍ ● ● ❍ ❍
W H AT D O YO U N E E D ?
● Dice Pattern Cars (enlarge Master 7)
● individual sets of Dice Pattern Cards (Master 7)
● 10-Frame Mats (Master 5)
● counters
● poster paper for 10s arrangements
● blank cards to make 10s patterns for practice
(use stiff card, approximately 10cm x 10cm)
W H AT A R E YO U L O O K I N G F O R ?
Before moving on to the next section, ensure
that the children can:
● match different patterns for numbers.
● recognize 6, 8, 9 and 10 in different
arrangements (7 may take longer).
● name a full 10-frame as 10.
W H A T M I G H T Y O U T R Y ?
Pa t t e r n s f o r 6 t o 1 0
● Develop finger patterns for 6 to 10 using 5+x,
count on to 5.
● Use 10-frames and counters to count on to 5,
making 6 (5+1), 7 (5+2), 8 (5+3), 9 (5+4) and
10. Encourage the children to practise
recognizing the numbers based on how
many less than 10.
● Analyze 6 to 10 cards to find component
parts (partitioning spatial patterns).
“I see 3+3+3…that makes 9.”
● Provide 1 to 5 cards for students to use to
combine and get 6 to 10 (e.g., two 3s for 6, 3
and 4 for 7). Check with pattern cards for 6 to
10 and dominoes patterns.
● Use counters on 10-frames to discover all the
arrangements for 6, then 8.
● Make a wall display.
● Practise describing each arrangement.
● Create nifty patterns for numbers to 10 (e.g.,
a stack of 3, 2, 1 as a model for 6).
● Make posters of nifty arrangements.
● Make cards of arrangements that the
children particularly like, and use them to
practise recognition.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 89
Seeing GroupingsSeeing Groupings
Math Focus: Seeing Groupings
W H AT D O YO U N E E D ?
● Geoboards (Master 27) and elastics
● Double 10-Frame Mats (Master 22)
● counters
● large square grid paper
● crayons and scissors
W H AT A R E YO U L O O K I N G F O R ?
Before moving on to the next section, ensure
that the children can:
● recognize parts within wholes with
quantities to 10 using visual patterns.
● recognize all 10-frame arrangements.
● recognize groupings for quantities to 10
using different arrangements.
● show finger groupings for numbers to 10.
(For numbers above 5, children should show
5 without counting plus x more fingers.)
W H A T M I G H T Y O U T R Y ?
S e e i n g Pa t t e r n s w i t h i n Nu m b e r s
● Develop conceptual subitizing (seeing
groups within groups) by combining small
groups. Work on a floor or table with
counters (6, 8, 9 and 10 work well for this).
“Make 3 rows of 3. What have you got?”
“Find a pattern for 8. Show me.”
● Ask the children to show 8 pegs on a geoboard
and analyze the different ways to do it. Look
for recognizable groupings within 8.
● Have the students colour large square grid
paper to show 6 (2x3), 8 (2x4), 9 (3x3) and 10
(2x5). Cut these out, and use them to practise
seeing the arrangements two different ways
(e.g., 6 is two 3s or three 2s).
● Emphasize counting on to a group you
recognize. (e.g., “I see 4, and 2 more is 5, 6.”)
Pay special attention to 7 (6 and 1 more, 5
and 2 more, 4+3).
● Practise finger patterns for numbers above 5
(“Show me 6”). Recognizing the hand as 5 or
two hands as 10 should be automatic. How
many more than 5 is 6, 7, 8, 9? Practise 9 as
one less than 10. Have the children show the
numbers above their heads.
A d d i n g o n t o 1 0
● Introduce counting on to a full 10-frame to
develop teen numbers. (Ensure that students
can say the number chain to at least 20 before
attempting this and that they have had lots of
exposure to numbers to at least 30.)
● Use the double 10-frame mat. Have the
children build 10 on one frame, then add 1, 2,
3 and so on to the other, naming 10 and ___
(e.g., 10 and 2, 12 in all).
❍ ● ● ❍ ❍
S U P P O R T I N G E A R L Y N U M E R A C Y90
Larger QuantitiesLarger Quantities
Math Focus: Larger Quantities❍ ● ● ❍ ❍
W H AT D O YO U N E E D ?
● square tiles or blocks
● cards for making group practice patterns for
teen numbers
● Double 10-Frame Mats (Master 22)
● Double 10-Frame Cards (Master 23) for take-
homes
● 100 Chart (Master 9)
W H AT A R E YO U L O O K I N G F O R ?
This section is the springboard for moving into
two-digit number patterns. 5s and 10s are the
building blocks of two-digit numbers.
● Can the children recognize 5s and 10s
without counting when presented in spatial
arrangements?
● Are the children established in their patterns
to 10?
● Can the children find 10s in a greater
pattern, such as a 100 chart?
W H A T M I G H T Y O U T R Y ?
S e e i n g Pa t t e r n s W i t h i n Q u a n t i t i e s
● Have the children draw grids of buildings
with floors and rooms (e.g., two floors, two
rooms on each floor). Next ask them to build
what they have drawn with tiles or blocks.
“Who has a different building?” (describe
rectangles in terms of number of rows)
● Analyze buildings (e.g., 3 floors tall, 2 rooms
wide, 2+2+2, 6 rooms in all).
● Practise verbal descriptions. Remember to
emphasize recognizing chunks (i.e., each
floor, not one-by-one counting).
● Emphasize the vocabulary of position (e.g.,
top floor, bottom floor, second from the top,
left, middle, right).
Te e n Nu m b e r s
● Create dot pattern cards for teen numbers
using a 10 grouping (choose the children’s
favourite arrangement) and dice patterns for
the 1s. Practise analyzing the patterns so that
children accept the 10, see the other part and
mentally combine the 10 and x to get the
teen number.
● Create a set of 10-frame cards for the teen
numbers, both a large set for group practice
and a small set for individual practice and to
take home.
S e e i n g 1 0 s i n 1 0 0
● Using the 100 charts, have the students look
for 10s within the 100—not rows of 10 this
time but 10-frames, 2x5 chunks. “Colour the
10-frames each a different colour. How many
10s did you find in the 100 chart?”
● Create a blank wall chart of the 100 chart and
record the numbers the children know: 1 to
10 and the counting pattern for 10s down the
right-hand side. Add only the patterns all the
children know, leaving the other numbers
blank.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 91
Math Playground
A B O U T T H E M AT H P L AYG R O U N D A C T I V I T I E S
Math Playground provides fun, hands-on spatial explorations in a
context that allows success for all and lets the spatial thinkers shine.
The Math Playground activities are opportunities for children to
model, draw and use mental imagery. The activities in this section
are designed to be revisited often. Once the materials have been
gathered, most of the activities require very little preparation or
instruction. Once a few students learn how to use the activities,
they can teach others.
These activities are designed to be:
● highly engaging and cooperative in nature
● play-like and interactive
● flexible and responsive to the needs of the group
● easily adapted and modified by the teacher
W h y a re s p a t i a l e x p l o r a t i o n s i m p o r t a n t ?
Spatial thinking is a key aspect of numeracy. It involves the ability to
use spatial information to construct meaning. Spatial activities
involving hands-on experiences provide the sensory input that
helps children develop mental imagery—a building block to
making sense of mathematics. The spatial explorations in this
section provide positive boosts for children’s self-confidence and
self-esteem. These activities are opportunities to enhance children’s
critical thinking and problem-solving abilities while having fun.
C O N N E C T I O N TO T H E K - 1 E A R LYN U M E R AC Y A S S E S S M E N T
Like the section on Visual-Spatial Pattern Recognition, this section
provides a scaffold for some and a learning opportunity for others.
Children who perform strongly on visual-spatial tasks can benefit
from using their visual-spatial strength as a scaffold for learning
about number. These children will benefit from the activities in this
section. This section is also valuable for children who struggled with
the following tasks on the Early Numeracy Assessment:
Item 2—Recognizing Dot Patterns
Item 10—Pattern Tasks
S U P P O R T I N G E A R L Y N U M E R A C Y92
Item 12—Squares Puzzle
Item 16 (optional)—Cube Building
U S I N G T H E M AT H P L AYG R O U N D A C T I V I T I E S
These spatial explorations are divided into five areas of
concentration:
● Shapes
● Pattern Blocks
● Tangrams
● Puzzles
● Number Lines
You will notice that the format for these activities differs from that
of the previous sections. Math Playground activities are easy to use,
and the directions are given in simple point form.
G u i d e l i n e s f o r Us i n g t h e Ma t h P l a y g r o u n d
As you use these activities, ask plenty of questions to help you
understand the children’s thinking:
● How did you do that?
● How did you know that?
● Tell me how you did that.
● If you’re not sure, how can we find out?
● Yes, that’s right. But how did you know it was right?
● Can you think of another way we could do this?
● Where have you done that before to help you solve a problem?
Look for indications that the children:
● have a good eye for detail and colour;
● think in pictures and images and learn through visuals;
● see solutions to problems by visualization; and,
● use the spatial arrangement of materials to help them make sense.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 93
List of Materials for Math Playground Activities
Shape Detective • no materials needed
Shape Tickle • no materials needed
Shape Bag • set of tangrams and a paper bag for each pair
Shape Construction • toothpicks and mini-marshmallows
Playdough Shapes • playdough
Rice Shapes • dyed rice and a large, shallow container
Building Constructions • interlocking construction blocks (e.g., Lego or Duplo)
Shape Hunt • assorted shapes and a box or hat
Rubber Shapes • Geoboard and elastics for each student (Master 27)
Shape Memory • pairs of cards with matching shapes
Shape Bingo • Bingo Cards (Master 28)
Exploration • pattern blocks (for every activity)
Cover the Blocks • Cover the Blocks (Masters 29, 30, 31)
Cover and Copy • Cover and Copy (Master 32)
Pattern Block Challenge • Pattern Block Challenge (Master 33)
Combinations • Combinations (Masters 34, 35, 36)
How Many? • How Many Triangles? (Masters 37 to 41)
Exploration Time • multiple sets of tangrams (for every activity)
Tangram Creations • tangrams
Tangram Matching • Tangram Matching (Master 42)
Tangram Cover-Up • Tangram Cover Up (Masters 43 to 49)
Tangram Tales • book Grandfather Tang’s Journey by Ann Tompert
Tangram Detective • tangrams
Jigsaw Names • two matching pieces of card per child (10cm x 20cm or so)
Number Puzzles • two cards, one with 1-10 Number Line as model (Master 10)
Colour Jumps • tape and felts to make unnumbered floor number line, beanbags
Number Jumps • floor number line marked 0 to 10
Race to the End • Number Lines (Master 10), dice, counters
S U P P O R T I N G E A R L Y N U M E R A C Y94
ShapeShape
S H A P E D E T E C T I V E
● Have the children take turns being a “shape
detective.”
● The detective gives the group clues about
the shape he or she is thinking of. (e.g., “It
has four sides and has the word angle in it.”)
S H A P E T I C K L E
● The students take turns drawing a shape on
their partner’s back.
● The partner guesses what shape is drawn.
S H A P E B AG
● Have the children work with a partner.
● One student chooses a shape from a pile of
concealed tangrams.
● He or she secretly puts it into a paper bag.
● The other student reaches inside the bag
and uses his or her knowledge of shapes to
determine what shape is inside the bag.
S H A P E C O N S T RU C T I O N
● Have the children use toothpicks and
marshmallows to build a variety of shapes.
● You may want to provide cards as models for
children who need additional support.
P L AY D O U G H S H A PE S
● Introduce playdough to the group.
● Have the students make shapes with their
playdough.
● Other Ideas with Playdough
- Once the students are comfortable
creating playdough shapes, have them
work with a partner.
- Ask the students to take turns closing
their eyes and using their sense of touch
to determine what shape their partner
has made.
- Encourage the students to explain to their
partner how they guessed the shape. (e.g.,
“It is a closed shape. It is round. Is it a
circle?”)
R I C E S H A P E S
● Have the children dye white rice with food
colouring.
● Place the rice in a large bowl.
● Encourage the children to use their fingers to
practise tracing shapes in the rice.
B U I L D I N G C O N S T RU C T I O N S
● Give the students interlocking construction
blocks (e.g., Lego).
● Ask them to build a construction using as
many shapes as they can.
● Share the students’ constructions, and
discuss what shapes have been incorporated
into the construction.
S H A P E H U N T
● Have the students select a shape out of a hat
or box.
● With the group, name the shape and discuss
its properties.
● Invite the students to hunt for that shape in
the classroom environment.
● When they find an example of their shape,
have them draw or sketch their object on a
piece of paper and report back to the group.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 95
● For example, if the student chose a rectangle,
they could sketch the window pane.
R U B B E R S H A PE S
● Have the students use a geoboard and
rubber bands to create different shapes.
● This could be a quick activity where the
teacher concentrates on creating one shape,
or the group could work for a longer time,
making a variety of shapes.
R U B B E R S H A PE S F O L L OW- U P
● Have the students re-create a shape on their
geoboard from the previous day.
● Give each student a geoboard (Master 27—
enlarge the grids as necessary).
● Ask the students to experiment with
different ways of drawing the same shape on
their page (e.g., three different squares).
S H A P E M E M O RY
● Have the students play in pairs, taking turns
flipping over cards with a variety of shapes
on them.
● If a pair matches, the student wins the cards
and takes another turn.
● The student who is able to remember and
locate the most matching shapes wins the
game.
S H A P E B I N G O
● Give each child a unique bingo card (can be
made from Master 28).
● Explain how the column and row identifiers
work.
● Show the children a card with a picture on it.
● Ask the students to see if their card fits.
● The first student to fill their bingo card wins!
O t h e r I d e a s f o r S h a p e B i n g o
● Use a 5cm x 5cm or 5cm x 8cm card.
● Use numerals rather than shapes.
● Have the students play with a partner rather
than the whole group.
S U P P O R T I N G E A R L Y N U M E R A C Y96
Pattern BlocksPattern Blocks
E X P L O R AT I O N
● Have the students build a variety of pattern
block pictures.
● This activity can be open-ended, or you can
offer directing statements. (e.g., “Let’s try to
build a garden.” “Let’s make spaceships.”)
C OV E R T H E B L O C K S
● Give each child a Cover the Blocks sheet
(Masters 29, 30, 31).
● Have the children cover the patterns with
blocks that match.
● Once they have done this, they can colour
the pattern to match the blocks.
C OV E R A N D C O P Y
● Give each child a Cover and Copy sheet
(Master 32).
● Have the children cover each pattern with
blocks.
● Have them copy the pattern again beside the
covered picture.
● Ask the children to trace the blocks or draw
them using the model.
P AT T E R N B L O C K C H A L L E N G E
● Give each child a Pattern Block Challenge
sheet (Master 33).
● Ask: “Who can fill this shape up with blocks
without going over the edges?”
● Encourage the children to show the different
strategies they use.
● Discuss which strategies were more effective
and why.
● Extend this activity by asking: “What is the
fewest number of blocks that cover the
shape? The greatest number?” Encourage the
children to estimate and check. Make a chart
to show the various ways.
C O M B I N AT I O N S
● Give the students a Combinations sheet
(Masters 34, 35, 36).
● Ask them to see how many different ways
they can make the shape using a variety of
pattern blocks. Have the students colour
their ways and/or record them in the charts
at the bottom of the page.
H OW M A N Y T R I A N G L E S ?
● Give the students a copy of How Many
Triangles? (Masters 37, 38, 39, 40, 41) and ask:
“How many triangles fit in this shape?”
● Explore the children’s thinking processes by
asking them to explain how they arrived at
their answer.
● Extend this activity by asking: “Can any other
colour of block cover the patterns?” (Blue will
cover the most and leads to a discussion of
half units.) “How many of that colour will it
take? What do you notice about how many it
takes?” (It takes half as many as the green
triangles.) “Why?”
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 97
TangramsTangrams
E X P L O R AT I O N T I M E
● Some children will not be familiar with
tangram shapes. Provide one set per child if
possible, but for exploration, mix sets together.
● By beginning with a period of free
exploration time, the children are able to
experiment and gain confidence with this
new material.
● Later, show the children how many pieces
there are in one set, and store each set in a
zip-lock bag. The children can trace one full
set of 7 pieces onto a card to use for checking
a complete set. This can help them be
responsible for the sets.
T A N G R A M C R E AT I O N S
● Encourage the students to use a variety of
tangrams to make pictures and designs from
their imagination.
T A N G R A M M ATC H I N G
● Have the students match the tangram pieces
to a variety of shapes (e.g., Master 42).
● Use multiple sets of tangrams.
● Have the students create new matching
puzzles for others to try.
T A N G R A M C OV E R - U P
● A set of Tangram Cover-Up sheets (Masters
43 to 49) is provided to help the children
practise covering the shapes with an
increasing level of difficulty.
T A N G R A M T A L E S
● Read Grandfather Tang’s Journey by Ann
Tompert to the group.
● Ask the students to tell a story using their
tangrams.
● Encourage them to transform existing
creations into new ones to enhance and
develop their story.
T A N G R A M D E T E C T I V E
● Pose a question for the “detective” to solve.
(e.g., “How many triangles are in a
parallelogram?” “How many triangles are in
an octagon?”)
● Help the students use the tangrams to solve
these problems.
S U P P O R T I N G E A R L Y N U M E R A C Y98
PuzzlesPuzzles
J I G S AW N A M E S
● Have the students print their names on two
pieces of card (roughly 10cm x 20cm). For
children who do not yet print, print on one
card, and have them copy on the other.
● One card becomes a model to which the
child refers to, while the other is cut between
the letters to create a puzzle. For young
children, gradually work up to cuts between
every letter.
● Ask the child to compare each letter to the
model and determine how each letter is the
same or different from the rest.
O T H E R I D E A S F O R J I G S AW N A M E S
● Have the students draw pictures and cut
them into puzzles.
● Ask the students to switch jigsaw names with
a partner.
N U M B E R P U Z Z L E S
● Have the students make a puzzle based on
the number line (1-10).
● Use one piece as a model to which the child
can refer. On it, write the numbers 1-10.
● On the other piece, have the students write
the numbers 1-10 and cut between them to
create a puzzle (or use Master 10).
● Challenge the children to put the numbers
in the correct order.
● Ask the children to compare each number to
the model and determine how each number
is the same or different from the rest.
O t h e r I d e a s f o r N u m b e r P u z z l e s
● Challenge the students by making number
puzzles to 20 or 50.
● Ask the students to assemble the puzzle in
descending order.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 99
Number LinesNumber Lines
C O L O U R J U M P S
● Make an unnumbered floor line—a line with
a clear starting point (0) and equally spaced
marks for units of roughly one footstep in
length.
● Place different coloured beanbags or coloured
tiles at different points along the line.
● Ask the students to count how many jumps
to the green tile or how many jumps from
the green to the yellow tile. “How many jumps
back to the red tile, from the yellow tile?”
N U M B E R J U M P S
● Change the floor line to a numbered floor line.
● Using the number line (0-10), students line
up at 0 and take turns following the teacher’s
directions: “Jump to 5 on one leg and to 10
on the other.”
● The entire group counts with the student.
● Discuss the difference between the left and
right leg jumps.
● Pose a variety of problems. (e.g., Find a
different way to reach 10 by jumping with
your left and right legs.)
O t h e r I d e a s f o r N u m b e r J u m p s
● Ask the students to share their thinking with
a friend.
● Have the students record their thoughts
visually on paper and/or model them to the
small group.
R A C E TO T H E E N D
● Have the children place a counter at 0 on
their number line and then take turns rolling
a die (0-10, 0-20, 0-50, depending on ability).
● Have the students count out the number they
roll, using their marker to keep track.
● The first one to reach the end of the number
line wins.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 101
Name: _____________________________________________________
Master 1: Sorting BoardsMaster 1: Sorting Boards
S U P P O R T I N G E A R L Y N U M E R A C Y102
Name: _____________________________________________________
Master 2: Two-column Bar GraphMaster 2: Two-column Bar Graph
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 103
Name: _____________________________________________________
Master 3: Comparison StripsMaster 3: Comparison Strips
S U P P O R T I N G E A R L Y N U M E R A C Y104
Name: _____________________________________________________
Master 4: Ladybug MatMaster 4: Ladybug Mat
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 105
Name: _____________________________________________________
Master 5: Ten-frame MatMaster 5: Ten-frame Mat
S U P P O R T I N G E A R L Y N U M E R A C Y106
Name: _____________________________________________________
Master 6: Dice Game Record SheetMaster 6: Dice Game Record Sheet
11111 22222 33333 44444 55555 66666
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 107
Master 7: Dot Pattern CardsMaster 7: Dot Pattern Cards
Name: _____________________________________________________
S U P P O R T I N G E A R L Y N U M E R A C Y108
Name: _____________________________________________________
Master 8: Numeral Cards 0–9Master 8: Numeral Cards 0–9
55 55566 666
77 77788 888
99 999
00 00011 111
22 22233 333
44 444
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 109
Name: _____________________________________________________
Master 9: 100 ChartMaster 9: 100 Chart
11111 22222 33333 44444 55555 66666 77777 88888 99999 1010101010
1111111111 1212121212 1313131313 1414141414 1515151515 1616161616 1717171717 1818181818 1919191919 2020202020
2121212121 2222222222 2323232323 2424242424 2525252525 2626262626 2727272727 2828282828 2929292929 3030303030
3131313131 3232323232 3333333333 3434343434 3535353535 3636363636 3737373737 3838383838 3939393939 4040404040
4141414141 4242424242 4343434343 4444444444 4545454545 4646464646 4747474747 4848484848 4949494949 5050505050
5151515151 5252525252 5353535353 5454545454 5555555555 5656565656 5757575757 5858585858 5959595959 6060606060
6161616161 6262626262 6363636363 6464646464 6565656565 6666666666 6767676767 6868686868 6969696969 7070707070
7171717171 7272727272 7373737373 7474747474 7575757575 7676767676 7777777777 7878787878 7979797979 8080808080
8181818181 8282828282 8383838383 8484848484 8585858585 8686868686 8787878787 8888888888 8989898989 9090909090
9191919191 9292929292 9393939393 9494949494 9595959595 9696969696 9797979797 9898989898 9999999999 100100100100100
S U P P O R T I N G E A R L Y N U M E R A C Y110
Name: _____________________________________________________
Master 10: Number LinesMaster 10: Number Lines
0000 01111 1
2222 23333 3
4444 45555 5
6666 67777 7
8888 89999 9
101010
10 10•
••
••
••
••
••
0000 01111 1
2222 23333 3
4444 45555 5
6666 67777 7
8888 89999 9
101010
10 10•
••
••
••
••
••
0000 01111 1
2222 23333 3
4444 45555 5
6666 67777 7
8888 89999 9
101010
10 10•
••
••
••
••
••
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 111
Name: _____________________________________________________
Master 11: Record Sheet 1Master 11: Record Sheet 1
Activity Estimate Actual
S U P P O R T I N G E A R L Y N U M E R A C Y112
Name: _____________________________________________________
Master 12: Record Sheet 2Master 12: Record Sheet 2
Activity Estimate Actual
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 113
Name: _____________________________________________________
Master 13: 5-Way Sorting MatMaster 13: 5-Way Sorting Mat
S U P P O R T I N G E A R L Y N U M E R A C Y114
Name: _____________________________________________________
Master 14: 100 Chart GridMaster 14: 100 Chart Grid
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 115
Name: _____________________________________________________
Master 15: Coin Cut-outsMaster 15: Coin Cut-outs
S U P P O R T I N G E A R L Y N U M E R A C Y116
Name: _____________________________________________________
Master 16: Dice MatMaster 16: Dice Mat
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 117
Name: _____________________________________________________
Master 17: Domino MatMaster 17: Domino Mat
S U P P O R T I N G E A R L Y N U M E R A C Y118
Master 18: Dot Pattern CardsMaster 18: Dot Pattern Cards
Name: _____________________________________________________
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 119
Name: _____________________________________________________
Master 19a: Domino CardsMaster 19a: Domino Cards
S U P P O R T I N G E A R L Y N U M E R A C Y120
Name: _____________________________________________________
Master 19b: Domino CardsMaster 19b: Domino Cards
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 121
Name: _____________________________________________________
Master 20: Ten-frame CardsMaster 20: Ten-frame Cards
S U P P O R T I N G E A R L Y N U M E R A C Y122
Name: _____________________________________________________
Master 21: Ladybug CardsMaster 21: Ladybug Cards
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 123
Name: _____________________________________________________
Master 22: Ten-frame MatsMaster 22: Ten-frame Mats
S U P P O R T I N G E A R L Y N U M E R A C Y124
Name: _____________________________________________________
Master 23: Double Ten-frame CardsMaster 23: Double Ten-frame Cards
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 125
Name: _____________________________________________________
Master 24: Pattern CardsMaster 24: Pattern Cards
S U P P O R T I N G E A R L Y N U M E R A C Y126
Name: _____________________________________________________
Master 25: Pattern Game BoardMaster 25: Pattern Game Board
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 127
Name: _____________________________________________________
Master 26: Small 100 ChartsMaster 26: Small 100 Charts
11111 22222 33333 44444 55555 66666 77777 88888 99999 1010101010
1111111111 1212121212 1313131313 1414141414 1515151515 1616161616 1717171717 1818181818 1919191919 2020202020
2121212121 2222222222 2323232323 2424242424 2525252525 2626262626 2727272727 2828282828 2929292929 3030303030
3131313131 3232323232 3333333333 3434343434 3535353535 3636363636 3737373737 3838383838 3939393939 4040404040
4141414141 4242424242 4343434343 4444444444 4545454545 4646464646 4747474747 4848484848 4949494949 5050505050
5151515151 5252525252 5353535353 5454545454 5555555555 5656565656 5757575757 5858585858 5959595959 6060606060
6161616161 6262626262 6363636363 6464646464 6565656565 6666666666 6767676767 6868686868 6969696969 7070707070
7171717171 7272727272 7373737373 7474747474 7575757575 7676767676 7777777777 7878787878 7979797979 8080808080
8181818181 8282828282 8383838383 8484848484 8585858585 8686868686 8787878787 8888888888 8989898989 9090909090
9191919191 9292929292 9393939393 9494949494 9595959595 9696969696 9797979797 9898989898 9999999999 100100100100100
11111 22222 33333 44444 55555 66666 77777 88888 99999 1010101010
1111111111 1212121212 1313131313 1414141414 1515151515 1616161616 1717171717 1818181818 1919191919 2020202020
2121212121 2222222222 2323232323 2424242424 2525252525 2626262626 2727272727 2828282828 2929292929 3030303030
3131313131 3232323232 3333333333 3434343434 3535353535 3636363636 3737373737 3838383838 3939393939 4040404040
4141414141 4242424242 4343434343 4444444444 4545454545 4646464646 4747474747 4848484848 4949494949 5050505050
5151515151 5252525252 5353535353 5454545454 5555555555 5656565656 5757575757 5858585858 5959595959 6060606060
6161616161 6262626262 6363636363 6464646464 6565656565 6666666666 6767676767 6868686868 6969696969 7070707070
7171717171 7272727272 7373737373 7474747474 7575757575 7676767676 7777777777 7878787878 7979797979 8080808080
8181818181 8282828282 8383838383 8484848484 8585858585 8686868686 8787878787 8888888888 8989898989 9090909090
9191919191 9292929292 9393939393 9494949494 9595959595 9696969696 9797979797 9898989898 9999999999 100100100100100
11111 22222 33333 44444 55555 66666 77777 88888 99999 1010101010
1111111111 1212121212 1313131313 1414141414 1515151515 1616161616 1717171717 1818181818 1919191919 2020202020
2121212121 2222222222 2323232323 2424242424 2525252525 2626262626 2727272727 2828282828 2929292929 3030303030
3131313131 3232323232 3333333333 3434343434 3535353535 3636363636 3737373737 3838383838 3939393939 4040404040
4141414141 4242424242 4343434343 4444444444 4545454545 4646464646 4747474747 4848484848 4949494949 5050505050
5151515151 5252525252 5353535353 5454545454 5555555555 5656565656 5757575757 5858585858 5959595959 6060606060
6161616161 6262626262 6363636363 6464646464 6565656565 6666666666 6767676767 6868686868 6969696969 7070707070
7171717171 7272727272 7373737373 7474747474 7575757575 7676767676 7777777777 7878787878 7979797979 8080808080
8181818181 8282828282 8383838383 8484848484 8585858585 8686868686 8787878787 8888888888 8989898989 9090909090
9191919191 9292929292 9393939393 9494949494 9595959595 9696969696 9797979797 9898989898 9999999999 100100100100100
11111 22222 33333 44444 55555 66666 77777 88888 99999 1010101010
1111111111 1212121212 1313131313 1414141414 1515151515 1616161616 1717171717 1818181818 1919191919 2020202020
2121212121 2222222222 2323232323 2424242424 2525252525 2626262626 2727272727 2828282828 2929292929 3030303030
3131313131 3232323232 3333333333 3434343434 3535353535 3636363636 3737373737 3838383838 3939393939 4040404040
4141414141 4242424242 4343434343 4444444444 4545454545 4646464646 4747474747 4848484848 4949494949 5050505050
5151515151 5252525252 5353535353 5454545454 5555555555 5656565656 5757575757 5858585858 5959595959 6060606060
6161616161 6262626262 6363636363 6464646464 6565656565 6666666666 6767676767 6868686868 6969696969 7070707070
7171717171 7272727272 7373737373 7474747474 7575757575 7676767676 7777777777 7878787878 7979797979 8080808080
8181818181 8282828282 8383838383 8484848484 8585858585 8686868686 8787878787 8888888888 8989898989 9090909090
9191919191 9292929292 9393939393 9494949494 9595959595 9696969696 9797979797 9898989898 9999999999 100100100100100
S U P P O R T I N G E A R L Y N U M E R A C Y128
Name: _____________________________________________________
Master 27: GeoboardsMaster 27: Geoboards
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 129
Name: _____________________________________________________
Master 28: Bingo CardsMaster 28: Bingo Cards
B I N G O
S U P P O R T I N G E A R L Y N U M E R A C Y130
Name: _____________________________________________________
Master 29: Cover the Blocks 1Master 29: Cover the Blocks 1
1.
3.
5.
4.
2.
6.
7.
8.
Cover the patterns with blocks.
Colour the patterns to match the blocks.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 131
Name: _____________________________________________________
Master 30: Cover the Blocks 2Master 30: Cover the Blocks 2
1. 2.
3.
4.5.
Cover the patterns that match.
Colour the patterns to match the blocks.
S U P P O R T I N G E A R L Y N U M E R A C Y132
Name: _____________________________________________________
Master 31: Cover the Blocks 3Master 31: Cover the Blocks 3
1. 2.
3.
4.
Cover the patterns that match.
Colour the patterns to match the blocks.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 133
Name: _____________________________________________________
Master 32: Cover and CopyMaster 32: Cover and Copy
1.
2.
3.
4.
Cover the patterns with blocks.Copy with the blocks. Trace andrecord.
S U P P O R T I N G E A R L Y N U M E R A C Y134
Name: _____________________________________________________
Master 33: Pattern Block ChallengeMaster 33: Pattern Block Challenge
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 135
Name: _____________________________________________________
Master 34: Combinations 1Master 34: Combinations 1
How can you fill this shape in 2 or 3 different ways?
S U P P O R T I N G E A R L Y N U M E R A C Y136
Name: _____________________________________________________
Master 35: Combinations 2Master 35: Combinations 2
How can you fill this shape in 2 or 3 different ways?
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 137
Name: _____________________________________________________
Master 36: Combinations 3Master 36: Combinations 3
How can you fill this shape in 2 or 3 different ways?
S U P P O R T I N G E A R L Y N U M E R A C Y138
Name: _____________________________________________________
Master 37: How Many Triangles? 1Master 37: How Many Triangles? 1
How many triangles does it take to build this design?
S
How did you know?
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 139
Name: _____________________________________________________
Master 38: How Many Triangles? 2Master 38: How Many Triangles? 2
How many triangles does it take to build this design?
How did you know?
S
S U P P O R T I N G E A R L Y N U M E R A C Y140
Name: _____________________________________________________
Master 39: How Many Triangles? 3Master 39: How Many Triangles? 3
How many triangles does it take to build this design?
How did you know?
S
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 141
Name: _____________________________________________________
Master 40: How Many Triangles? 4Master 40: How Many Triangles? 4
How many triangles does it take to build this design?
How did you know?
S
S U P P O R T I N G E A R L Y N U M E R A C Y142
Name: _____________________________________________________
Master 41: How Many Triangles? 5Master 41: How Many Triangles? 5
How many triangles does it take to build this design?
How did you know?
S
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 143
Name: _____________________________________________________
Master 42: Tangram MatchingMaster 42: Tangram Matching
Match the piece to these shapes.
S U P P O R T I N G E A R L Y N U M E R A C Y144
Name: _____________________________________________________
Master 43: Tangram Cover-up 1Master 43: Tangram Cover-up 1
Cover each shape.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 145
Name: _____________________________________________________
Master 44: Tangram Cover-up 2Master 44: Tangram Cover-up 2
Cover each shape.
2.
1.
S U P P O R T I N G E A R L Y N U M E R A C Y146
Name: _____________________________________________________
Master 45: Tangram Cover-up 3Master 45: Tangram Cover-up 3
Cover each shape.
2.
1.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 147
Name: _____________________________________________________
Master 46: Tangram Cover-up 4Master 46: Tangram Cover-up 4
Cover each shape.
2.
1.
S U P P O R T I N G E A R L Y N U M E R A C Y148
Name: _____________________________________________________
Master 47: Tangram Cover-up 5Master 47: Tangram Cover-up 5
Cover each shape.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 149
Name: _____________________________________________________
Master 48: Tangram Cover-up 6Master 48: Tangram Cover-up 6
Cover each shape.
S U P P O R T I N G E A R L Y N U M E R A C Y150
Name: _____________________________________________________
Master 49: Tangram Cover-up 7Master 49: Tangram Cover-up 7
Cover each shape.
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 151
Master 50: Surprise Box Record SheetMaster 50: Surprise Box Record Sheet
Name: _______________________________ Date: _______________
Date: _______________
Teacher/Class: ________________________ Date: _______________
Skill: To 5 To 10 Beyond Comments
Count sets accurately
Count back from
Recognize numerals
Compare and order sets
Match numerals and sets
Compare sets
Compare numerals
Order sets and numerals
Increase/decrease
Invariance for sets
Verbal counting on
Counting on with materials
Describe parts and wholes
Decompose/recompose/rename
Find a missing part (5+?=8)
Date Completed Comments
Part One
Part Two
Part Three
Part Four
Part Five
Part Six
Part Seven
S U P P O R T I N G E A R L Y N U M E R A C Y152
Master 51: Large Traingles for TriangleChallenge
Master 51: Large Traingles for TriangleChallenge
Name: _____________________________________________________
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 153
Master 52: Squared PaperMaster 52: Squared Paper
Name: _____________________________________________________
S U P P O R T I N G E A R L Y N U M E R A C Y154
Master 53: Triangle PaperMaster 53: Triangle Paper
Name: _____________________________________________________
B C E A R L Y N U M E R A C Y P R O J E C T ( K – 1 ) 155
Master 54: Assessment Class CompilationMaster 54: Assessment Class Compilation
1.N
um
ber
Aw
aren
ess
2.D
ot P
atte
rns
3.M
atch
ing
Nu
mb
er S
ets
4.O
rder
ing
0-9
5.C
ou
nti
ng
Forw
ard
6.C
ou
nti
ng
Bac
kwar
ds
7.E
stim
ate
and
Ch
eck
8.C
ou
nti
ng
On
9.B
uild
an
d C
han
ge
10.
Patt
ern
Tas
ks
11.
Pro
ble
m S
olv
ing
12.
Squ
ares
Pu
zzle
13.
Rea
din
g N
um
eral
s
14.
Pri
nti
ng
Nu
mer
als
15.
Co
in S
ets
16.
Cu
be
Bu
ildin
g
17.
100
Ch
art