Mathematics Grade3 Curriculum Guide

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Mathematics

Grade Three

Interim Edition

Curriculum Guide

September 2010


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GRADE 3 MATHEMATICS CURRICULUM GUIDE - INTERIM i

TABLE OF CONTENTS

Table of Contents

Acknowledgements....................................iii

Foreword......................................v

Background ...........................................1

Introduction Purpose of the Document........................................2

Beliefs About Students and Mathematics Learning.....................................2

Affective Domain...........................................3

Early Childhood..........................................3

Goal for Students...........................................4

Conceptual Framework for K9 Mathematics...................................4Mathematical Processes................................................5

Nature of Mathematics............................................9

Strands....................................................12

Outcomes and Achievement Indicators.......................................13

Summary.................................................13

Instructional FocusPlanning for Instruction............................................ 14

Resources................................................14

Teaching Sequence..........................................15

Instruction Time per Unit..................................................15

General and Specifc Outcomes.............................................................16

General and Specifc Outcomes by Strand Grades 2 4.......17Patterning....................................................................................31

Numbers to 1000..........................................................83

Data Analysis.....................................................125

Addition and Subtraction........................................................149Geometry..............................................................................203

Multiplication and Division................................................... 237

Fractions............................................................................... 273

Measurement .................................................291

Appendix A: Outcomes with Achievement Indicators (Strand).......325

References................................................................339


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GRADE 3 MATHEMATICS CURRICULUM GUIDE - INTERIM iii

The Department of Education would like to thank the Western and Northern Canadian Protocol (WNCP)

for Collaboration in Education, The Common Curriculum Framework for K-9 Mathematics- May 2006 and

The Common Curriculum Framework for Grades 10-12 - January 2008, which has been reproduced and/oradapted by permission. All rights reserved.

We would also like to thank the provincial Grade 3 Mathematics curriculum committee, the Alberta

Department of Education, the New Brunswick Department of Education, and the following people for their

contribution:

Trudy Porter, Program Development Specialist Mathematics, Division

of Program Development, Department of Education

Kimberly Pope, Teacher Greenwood Academy, Campbellton

Nicole Kelly, Teacher Smallwood Academy, Gambo

Shannon Best, Teacher Gander Academy, Gander

Lisa Piercey, Teacher Mary Queen of Peace, St. Johns

Valerie Wells, Teacher Bishop Abraham Elementary, St. Johns

Yolanda Anderson, Teacher St. Edwards, Kelligrews

Sherry Mullett, Teacher Lewisporte Academy, Lewisporte

Every effort has been made to acknowledge all sources that contributed to the development of this document.

Any omissions or errors will be amended in future printings.

Acknowledgements

ACKNOWLEDGEMENTS


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GRADE 3 MATHEMATICS CURRICULUM GUIDE - INTERIM v

Foreword

The WNCP Common Curriculum Frameworks for Mathematics

K 9 (WNCP, 2006), formed the basis for the development of this

curriculum guide. While minor adjustments have been made, the

outcomes and achievement indicators established through the WNCP

Common Curriculum Framework are used and elaborated on for

teachers in this document. Newfoundland and Labrador has used

the WNCP curriculum framework to direct the development of this

curriculum guide.

This curriculum guide is intended to provide teachers with the

overview of the outcomes framework for mathematics education. It also

includes suggestions to assist teachers in designing learning experiences

and assessment tasks.

FOREWORD


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GRADE 3 MATHEMATICS CURRICULUM GUIDE - INTERIM 1

INTRODUCTION

The province of Newfoundland and Labrador commissioned an

independent review of mathematics curriculum in the summer of 2007.

This review resulted in a number of significant recommendations.

In March of 2008, it was announced that this province accepted all

recommendations. The first four and perhaps most significiant of the

recommendations were as follows: That the WNCP Common Curriculum Frameworks for

Mathematics K 9 and Mathematics 10 12 (WNCP, 2006 and

2008) be adopted as the basis for the K 12 mathematics curriculum

in this province.

That implementation commence with Grades K, 1, 4, 7 in

September 2008, followed by in Grades 2, 5, 8 in 2009 and Grades

3, 6, 9 in 2010.

That textbooks and other resources specifically designed to match the

WNCP frameworks be adopted as an integral part of the proposed

program change. That implementation be accompanied by an introductory

professional development program designed to introduce the

curriculum to all mathematics teachers at the appropriate grade levels

prior to the first year of implementation.

As recommended, the implementation schedule for K - 6 mathematics is

as follows:

Implementation Year Grade Level

2008 K, 1 and 4

2009 2, 5

2010 3, 6

BACKGROUND


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GRADE 3 MATHEMATICS CURRICULUM GUIDE - INTERIM2

INTRODUCTION

Purpose of the

Document

INTRODUCTION

The Mathematics Curriculum Guides for Newfoundland and Labrador

have been derived from The Common Curriculum Framework for K9

Mathematics: Western and Northern Canadian Protocol, May 2006

(the Common Curriculum Framework). These guides incorporate the

conceptual framework for Kindergarten to Grade 9 Mathematics and

the general outcomes, specific outcomes and achievement indicators

established in the common curriculum framework. They also include

suggestions for teaching and learning, suggested assessment strategies,

and an identification of the associated resource match between the

curriculum and authorized, as well as recommended, resource materials.

The curriculum guide

communicates high

expectationsfor students.

Beliefs AboutStudents and

Mathematics

Learning

Students are curious, active learners with individual interests, abilitiesand needs. They come to classrooms with varying knowledge, life

experiences and backgrounds. A key component in successfully

developing numeracy is making connections to these backgrounds and

experiences.

Students learn by attaching meaning to what they do, and they need

to construct their own meaning of mathematics. This meaning is best

developed when learners encounter mathematical experiences that

proceed from the simple to the complex and from the concrete to the

abstract. Through the use of manipulatives and a variety of pedagogical

approaches, teachers can address the diverse learning styles, cultural

backgrounds and developmental stages of students, and enhance

within them the formation of sound, transferable mathematical

understandings. At all levels, students benefit from working with a

variety of materials, tools and contexts when constructing meaning

about new mathematical ideas. Meaningful student discussions provide

essential links among concrete, pictorial and symbolic representations

of mathematical concepts.

The learning environment should value and respect the diversity

of students experiences and ways of thinking, so that students are

comfortable taking intellectual risks, asking questions and posing

conjectures. Students need to explore problem-solving situations inorder to develop personal strategies and become mathematically literate.

They must realize that it is acceptable to solve problems in a variety of

ways and that a variety of solutions may be acceptable.

Mathematical

understanding is fostered

when students build on

their own experiences and

prior knowledge.


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INTRODUCTION

A positive attitude is an important aspect of the affective domain and

has a profound impact on learning. Environments that create a sense of

belonging, encourage risk taking and provide opportunities for success

help develop and maintain positive attitudes and self-confidence within

students. Students with positive attitudes toward learning mathematicsare likely to be motivated and prepared to learn, participate willingly

in classroom activities, persist in challenging situations and engage in

reflective practices.

Teachers, students and parents need to recognize the relationship

between the affective and cognitive domains, and attempt to nurture

those aspects of the affective domain that contribute to positive

attitudes. To experience success, students must be taught to set

achievable goals and assess themselves as they work toward these goals.

Striving toward success and becoming autonomous and responsible

learners are ongoing, reflective processes that involve revisiting thesetting and assessing of personal goals.

Affective Domain

Early Childhood Young children are naturally curious and develop a variety ofmathematical ideas before they enter Kindergarten. Children make

sense of their environment through observations and interactions at

home, in daycares, in preschools and in the community. Mathematics

learning is embedded in everyday activities, such as playing, reading,

beading, baking, storytelling and helping around the home.Activities can contribute to the development of number and spatial

sense in children. Curiosity about mathematics is fostered when

children are engaged in, and talking about, such activities as comparing

quantities, searching for patterns, sorting objects, ordering objects,

creating designs and building with blocks.

Positive early experiences in mathematics are as critical to child

development as are early literacy experiences.

To experience success,students must be taught

to set achievable goals and

assess themselves as theywork toward these goals.

Curiosity about mathematicsis fostered when children

are actively engaged in their

environment.


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INTRODUCTION

The main goals of mathematics education are to prepare students to:

use mathematics confidently to solve problems

communicate and reason mathematically

appreciate and value mathematics

make connections between mathematics and its applications

commit themselves to lifelong learning

become mathematically literate adults, using mathematics to

contribute to society.

Students who have met these goals will:

gain understanding and appreciation of the contributions of

mathematics as a science, philosophy and art

exhibit a positive attitude toward mathematics

engage and persevere in mathematical tasks and projects

contribute to mathematical discussions

take risks in performing mathematical tasks

exhibit curiosity.

Goals For

Students

Mathematics education

must prepare students

to use mathematics

confidently to solve

problems.

CONCEPTUALFRAMEWORKFOR K-9MATHEMATICS

The chart below provides an overview of how mathematical processes

and the nature of mathematics influence learning outcomes.


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PROCESS STANDARDS

There are critical components that students must encounter in a

mathematics program in order to achieve the goals of mathematics

education and embrace lifelong learning in mathematics.

Students are expected to:

communicate in order to learn and express their understanding

connect mathematical ideas to other concepts in mathematics, to

everyday experiences and to other disciplines

demonstrate fluency with mental mathematics and estimation

develop and apply new mathematical knowledge through problem

solving

develop mathematical reasoning

select and use technologies as tools for learning and for solving

problems

develop visualization skills to assist in processing information,

making connections and solving problems.

This curriculum guide incorporates these seven interrelated

mathematical processes that are intended to permeate teaching and

learning.

MathematicalProcesses

Communication [C] Connections [CN]

Mental Mathematics

and Estimation [ME]

Problem Solving [PS]

Reasoning [R]

Technology [T]

Visualization [V]

Communication [C] Students need opportunities to read about, represent, view, write about,listen to and discuss mathematical ideas. These opportunities allow

students to create links between their own language and ideas, and theformal language and symbols of mathematics.

Communication is important in clarifying, reinforcing and modifying

ideas, attitudes and beliefs about mathematics. Students should be

encouraged to use a variety of forms of communication while learning

mathematics. Students also need to communicate their learning using

mathematical terminology.

Communication helps students make connections among concrete,

pictorial, symbolic, oral, written and mental representations of

mathematical ideas.

Students must be able to

communicate mathematical

ideas in a variety of ways

and contexts.


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Contextualization and making connections to the experiences

of learners are powerful processes in developing mathematical

understanding. When mathematical ideas are connected to each other

or to real-world phenomena, students begin to view mathematics as

useful, relevant and integrated.

Learning mathematics within contexts and making connections relevantto learners can validate past experiences and increase student willingness

to participate and be actively engaged.

The brain is constantly looking for and making connections. Because

the learner is constantly searching for connections on many levels,

educators need to orchestrate the experiencesfrom which learners extract

understanding. Brain research establishes and confirms that multiple

complex and concrete experiences are essential for meaningful learning

and teaching (Caine and Caine, 1991, p.5).

Connections [CN]

PROCESS STANDARDS

Through connections,

students begin to viewmathematics as useful and

relevant.

Mental Mathematics and

Estimation [ME]

Mental mathematics is a combination of cognitive strategies that

enhance flexible thinking and number sense. It is calculating mentally

without the use of external memory aids.

Mental mathematics enables students to determine answers without

paper and pencil. It improves computational fluency by developing

efficiency, accuracy and flexibility.

Even more important than performing computational procedures or

using calculators is the greater facility that students needmore thanever beforewith estimation and mental math (National Council of

Teachers of Mathematics, May 2005).

Students proficient with mental mathematics become liberated from

calculator dependence, build confidence in doing mathematics, become

more flexible thinkers and are more able to use multiple approaches to

problem solving (Rubenstein, 2001, p. 442).

Mental mathematics provides the cornerstone for all estimation

processes, offering a variety of alternative algorithms and nonstandard

techniques for finding answers (Hope, 1988, p. v).

Estimation is used for determining approximate values or quantities orfor determining the reasonableness of calculated values. It often uses

benchmarks or referents. Students need to know when to estimate, how

to estimate and what strategy to use.

Estimation assists individuals in making mathematical judgements and

in developing useful, efficient strategies for dealing with situations in

daily life.

Mental mathematics and

estimation are fundamental

components of number sense.


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Learning through problem solving should be the focus of mathematics

at all grade levels. When students encounter new situations and

respond to questions of the type How would you? or How could you?,

the problem-solving approach is being modelled. Students develop their

own problem-solving strategies by listening to, discussing and trying

different strategies.A problem-solving activity must ask students to determine a way to get

from what is known to what is sought. If students have already been

given ways to solve the problem, it is not a problem, but practice. A

true problem requires students to use prior learnings in new ways and

contexts. Problem solving requires and builds depth of conceptual

understanding and student engagement.

Problem solving is a powerful teaching tool that fosters multiple,

creative and innovative solutions. Creating an environment where

students openly look for, and engage in, finding a variety of strategies

for solving problems empowers students to explore alternatives and

develops confident, cognitive mathematical risk takers.

Problem Solving [PS]

Reasoning [R]

PROCESS STANDARDS

Learning through problemsolving should be the focus

of mathematics at all grade

levels.

Mathematical reasoning helps students think logically and make sense

of mathematics. Students need to develop confidence in their abilities to

reason and justify their mathematical thinking. High-order questions

challenge students to think and develop a sense of wonder about

mathematics.

Mathematical experiences in and out of the classroom provideopportunities for students to develop their ability to reason. Students

can explore and record results, analyze observations, make and test

generalizations from patterns, and reach new conclusions by building

upon what is already known or assumed to be true.

Reasoning skills allow students to use a logical process to analyze a

problem, reach a conclusion and justify or defend that conclusion.

Mathematical reasoning

helps students thinklogically and make sense of

mathematics.


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Technology contributes to the learning of a wide range of mathematical

outcomes and enables students to explore and create patterns, examine

relationships, test conjectures and solve problems.

Calculators and computers can be used to:

explore and demonstrate mathematical relationships and patterns

organize and display data

extrapolate and interpolate

assist with calculation procedures as part of solving problems

decrease the time spent on computations when other mathematical

learning is the focus

reinforce the learning of basic facts

develop personal procedures for mathematical operations

create geometric patterns

simulate situations

develop number sense.

Technology contributes to a learning environment in which the

growing curiosity of students can lead to rich mathematical discoveries

at all grade levels.

Technology [T]

Visualization [V]

PROCESS STANDARDS

Technology contributes

to the learning of a wide

range of mathematical

outcomes and enables

students to explore

and create patterns,

examine relationships,

test conjectures and solve

problems.

Visualization involves thinking in pictures and images, and the ability

to perceive, transform and recreate different aspects of the visual-spatial

world (Armstrong, 1993, p. 10). The use of visualization in the study

of mathematics provides students with opportunities to understand

mathematical concepts and make connections among them.

Visual images and visual reasoning are important components of

number, spatial and measurement sense. Number visualization occurs

when students create mental representations of numbers.

Being able to create, interpret and describe a visual representation is

part of spatial sense and spatial reasoning. Spatial visualization and

reasoning enable students to describe the relationships among and

between 3-D objects and 2-D shapes.

Measurement visualization goes beyond the acquisition of specific

measurement skills. Measurement sense includes the ability to

determine when to measure, when to estimate and which estimation

strategies to use (Shaw and Cliatt, 1989).

Visualization is fostered

through the use of concrete

materials, technology

and a variety of visual

representations.


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Mathematics is one way of trying to understand, interpret and describe

our world. There are a number of components that define the nature

of mathematics and these are woven throughout this curriculum

guide. The components are change, constancy, number sense, patterns,

relationships, spatial sense and uncertainty.

It is important for students to understand that mathematics is dynamic

and not static. As a result, recognizing change is a key component in

understanding and developing mathematics.

Within mathematics, students encounter conditions of change and are

required to search for explanations of that change. To make predictions,students need to describe and quantify their observations, look for

patterns, and describe those quantities that remain fixed and those that

change. For example, the sequence 4, 6, 8, 10, 12, can be described

as:

the number of a specific colour of beads in each row of a beaded

design

skip counting by 2s, starting from 4

an arithmetic sequence, with first term 4 and a common difference

of 2

a linear function with a discrete domain

(Steen, 1990, p. 184).

Different aspects of constancy are described by the terms stability,

conservation, equilibrium, steady state and symmetry (AAAS

Benchmarks, 1993, p. 270). Many important properties in mathematics

and science relate to properties that do not change when outside

conditions change. Examples of constancy include the following:

The ratio of the circumference of a teepee to its diameter is the

same regardless of the length of the teepee poles.

The sum of the interior angles of any triangle is 180.

The theoretical probability of flipping a coin and getting heads is

0.5.

Some problems in mathematics require students to focus on properties

that remain constant. The recognition of constancy enables students to

solve problems involving constant rates of change, lines with constant

slope, direct variation situations or the angle sums of polygons.

Nature ofMathematics

Change

Constancy

NATURE OF MATHEMATICS

Change

Constancy

Number Sense Patterns

Relationships

Spatial Sense

Uncertainty

Change is an integral part

of mathematics and the

learning of mathematics.

Constancy is described by the

terms stability, conservation,

equilibrium, steady state andsymmetry.


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Number sense, which can be thought of as intuition about numbers,

is the most important foundation of numeracy (British Columbia

Ministry of Education, 2000, p. 146).

A true sense of number goes well beyond the skills of simply counting,

memorizing facts and the situational rote use of algorithms. Mastery

of number facts is expected to be attained by students as they developtheir number sense. This mastery allows for facility with more

complex computations but should not be attained at the expense of an

understanding of number.

Number sense develops when students connect numbers to their own

real-life experiences and when students use benchmarks and referents.

This results in students who are computationally fluent and flexible

with numbers and who have intuition about numbers. The evolving

number sense typically comes as a by product of learning rather than

through direct instruction. However, number sense can be developed

by providing rich mathematical tasks that allow students to make

connections to their own experiences and their previous learning.

Number Sense

Patterns


An intuition about numberis the most important

foundation of a numerate

child.

Mathematics is about recognizing, describing and working with

numerical and non-numerical patterns. Patterns exist in all strands of

mathematics.

Working with patterns enables students to make connections within

and beyond mathematics. These skills contribute to students

interaction with, and understanding of, their environment.

Patterns may be represented in concrete, visual or symbolic form.

Students should develop fluency in moving from one representation to

another.

Students must learn to recognize, extend, create and use mathematical

patterns. Patterns allow students to make predictions and justify their

reasoning when solving routine and nonroutine problems.

Learning to work with patterns in the early grades helps students

develop algebraic thinking, which is foundational for working with

more abstract mathematics.

Mathematics is about

recognizing, describing andworking with numerical

and non-numerical

patterns.


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Mathematics is one way to describe interconnectedness in a holistic

worldview. Mathematics is used to describe and explain relationships.

As part of the study of mathematics, students look for relationships

among numbers, sets, shapes, objects and concepts. The search for

possible relationships involves collecting and analyzing data and

describing relationships visually, symbolically, orally or in written form.

Spatial sense involves visualization, mental imagery and spatial

reasoning. These skills are central to the understanding of mathematics.

Spatial sense is developed through a variety of experiences and

interactions within the environment. The development of spatial sense

enables students to solve problems involving 3-D objects and 2-D

shapes and to interpret and reflect on the physical environment and its

3-D or 2-D representations.

Some problems involve attaching numerals and appropriate units

(measurement) to dimensions of shapes and objects. Spatial sense

allows students to make predictions about the results of changing these

dimensions; e.g., doubling the length of the side of a square increases

the area by a factor of four. Ultimately, spatial sense enables students

to communicate about shapes and objects and to create their own

representations.


Relationships

Spatial Sense

Uncertainty In mathematics, interpretations of data and the predictions made fromdata may lack certainty.

Events and experiments generate statistical data that can be used to

make predictions. It is important to recognize that these predictions

(interpolations and extrapolations) are based upon patterns that have a

degree of uncertainty.

The quality of the interpretation is directly related to the quality of

the data. An awareness of uncertainty allows students to assess the

reliability of data and data interpretation.

Chance addresses the predictability of the occurrence of an outcome.As students develop their understanding of probability, the language

of mathematics becomes more specific and describes the degree of

uncertainty more accurately.

Mathematics is used to

describe and explain

relationships.

Spatial sense offers a way tointerpret and reflect on the

physical environment.

Uncertainty is an inherent

part of making predictions.


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The learning outcomes in the mathematics program are organized

into four strands across the grades K9. Some strands are subdivided

into substrands. There is one general outcome per substrand across the

grades K9.

The strands and substrands, including the general outcome for each,

follow.

Strands

Number

Patterns and Relations

Shape and Space

Statistics and Probability

STRANDS

Number

Patterns and Relations

Shape and Space

Statistics and

Probability

Number

Develop number sense.

Patterns

Use patterns to describe the world and to solve problems.

Variables and Equations

Represent algebraic expressions in multiple ways.

Measurement

Use direct and indirect measurement to solve problems.

3-D Objects and 2-D Shapes

Describe the characteristics of 3-D objects and 2-D shapes, and

analyze the relationships among them.

Transformations

Describe and analyze position and motion of objects and shapes.

Data Analysis

Collect, display and analyze data to solve problems.

Chance and Uncertainty

Use experimental or theoretical probabilities to represent and solve

problems involving uncertainty.


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The mathematics program is stated in terms of general outcomes,

specific outcomes and achievement indicators.

General outcomesare overarching statements about what students areexpected to learn in each strand/substrand. The general outcome for

each strand/substrand is the same throughout the grades.

Specific outcomes are statements that identify the specific skills,

understanding and knowledge that students are required to attain by

the end of a given grade.

In the specific outcomes, the word includingindicates that any ensuing

items must be addressed to fully meet the learning outcome. The phrase

such asindicates that the ensuing items are provided for illustrative

purposes or clarification, and are not requirements that must beaddressed to fully meet the learning outcome.

Achievement indicatorsare samples of how students may demonstrate

their achievement of the goals of a specific outcome. The range of

samples provided is meant to reflect the scope of the specific outcome.

Achievement indicators are context-free.

The conceptual framework for K9 mathematics describes the nature

of mathematics, mathematical processes and the mathematical concepts

to be addressed in Kindergarten to Grade 9 mathematics. The

components are not meant to stand alone. Activities that take place

in the mathematics classroom should stem from a problem-solving

approach, be based on mathematical processes and lead students

to an understanding of the nature of mathematics through specific

knowledge, skills and attitudes among and between strands.

Outcomes andAchievementIndicators

General Outcomes

Specific Outcomes

Achievement Indicators

Summary

OUTCOMES


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Resources

INSTRUCTIONAL FOCUS

Consider the following when planning for instruction:

Integration of the mathematical processes within each strand is

expected.

By decreasing emphasis on rote calculation, drill and practice, and the

size of numbers used in paper and pencil calculations, more time is

available for concept development.

Problem solving, reasoning and connections are vital to increasing

mathematical fluency and must be integrated throughout the

program.

There is to be a balance among mental mathematics and estimation,

paper and pencil exercises, and the use of technology, including

calculators and computers. Concepts should be introduced

using manipulatives and be developed concretely, pictorially andsymbolically.

Students bring a diversity of learning styles and cultural backgrounds

to the classroom. They will be at varying developmental stages.

The resource selected by Newfoundland and Labrador for students and

teachers is Math Makes Sense 3(Pearson). Schools and teachers have

this as their primary resource offered by the Department of Education.

Column four of the curriculum guide references Math Makes Sense 3 for

this reason.

Teachers may use any resource or combination of resources to meet the

required specific outcomes listed in column one of the curriculum guide.

INSTRUCTIONALFOCUS

Planning for Instruction


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Instruction Time Per Unit The suggested number of weeks of instruction per unit is listed in theguide at the beginning of each unit. The number of suggested weeks

includes time for completing assessment activities, reviewing andevaluating.

INSTRUCTIONAL FOCUS

Teaching Sequence The curriculum guide for Grade 3 is organized by units from Unit 1 toUnit 8. The purpose of this timeline is to assist in planning. The use of

this timeline is not mandatory; however, it is mandtory that all outcomes

are taught during the school year so a long term plan is advised. There

are a number of combinations of sequences that would be appropriate for

teaching this course. The arrow showing estimated focus does not mean

the outcomes are never addressed again. The teaching of the outcomes is

ongoing and may be revisited as necessary.


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GENERAL AND SPECIFIC OUTCOMES

GENERAL AND SPECIFIC OUTCOMES BY STRAND

(pages 1730)

This section presents the general and specific outcomes for each strand,

for Grade 2, 3 and 4.

Refer toAppendix Afor the general and specific outcomes with

corresponding achievement indicators organized by strand for Grade 3.

GENERAL AND SPECIFIC OUTCOMES WITH ACHIEVEMENT

INDICATORS(beginning at page 31)

This section presents general and specific outcomes with corresponding

achievement indicators and is organized by unit. The list of indicators

contained in this section is not intended to be exhaustive but rather to

provide teachers with examples of evidence of understanding to be used

to determine whether or not students have achieved a given specific

outcome. Teachers should use these indicators but other indicators

may be added as evidence that the desired learning has been achieved.

Achievement indicators should also help teachers form a clear picture of

the intent and scope of each specific outcome.

GENERAL

AND SPECIFICOUTCOMES


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GENERAL AND SPECIFIC OUTCOMES BY

STRAND

(Grades 2, 3 and 4)


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[C] Communication [PS] Problem Solving[CN] Connections [R] Reasoning[ME] Mental Mathematics [T] Technology and Estimation [V] Visualization

Grade 2 Grade 3 Grade 4

General OutcomeDevelop number sense.



Specific Outcomes Specific Outcomes Specific Outcomes

1. Say the number sequence from0 to 100 by: 2s, 5s and 10s, forward andbackward, using starting pointsthat are multiples of 2, 5 and 10respectively 10s, using starting points from1 to 9 2s, starting from 1.[C, CN, ME, R]

2. Demonstrate if a number (up to100) is even or odd.[C, CN, PS, R]

3. Describe order or relativeposition, using ordinal numbers(up to tenth).[C, CN, R]

4. Represent and describenumbers to 100, concretely,pictorially and symbolically.

[C, CN, V]

1. Say the number sequence 0 to1000 forward and backward by:

5s, 10s or 100s, using anystarting point 3s, using starting points thatare multiples of 3 4s, using starting points thatare multiples of 4 25s, using starting points thatare multiples of 25.

[C, CN, ME]

2. Represent and describenumbers to 1000, concretely,pictorially and symbolically.[C, CN, V]

3. Compare and order numbers to1000.[C, CN, R, V]

4. Estimate quantities less than1000, using referents.

[ME, PS, R, V]

1. Represent and describe wholenumbers to 10 000, pictoriallyand symbolically.[C, CN, V]

2. Compare and order numbers to10 000.[C, CN, V]

3. Demonstrate an understandingof addition of numbers with

answers to 10 000 and theircorresponding subtractions(limited to 3- and 4-digitnumerals) by:

using personal strategies foradding and subtracting estimating sums anddifferences solving problems involvingaddition and subtraction.

[C, CN, ME, PS, R]

Number


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5. Compare and order numbersup to 100.[C, CN, ME, R, V]

6. Estimate quantities to 100,using referents.[C, ME, PS, R]

7. Illustrate, concretely andpictorially, the meaning of placevalue for numerals to 100.

[C, CN, R, V]

8. Demonstrate and explainthe effect of adding zero to,or subtracting zero from, anynumber.[C, R]

5. Illustrate, concretely andpictorially, the meaning of placevalue for numerals to 1000.[C, CN, R, V]

6. Describe and apply mentalmathematics strategies for addingtwo 2-digit numerals, such as:

adding from left to right taking one addend to thenearest multiple of ten and then

compensating using doubles.[C, CN, ME, PS, R, V]

7. Describe and apply mentalmathematics strategies forsubtracting two 2-digit numerals,such as:

taking the subtrahend to thenearest multiple of ten andthen compensating thinking of addition

using doubles.[C, CN, ME, PS, R, V]

4. Explain and apply theproperties of 0 and 1 formultiplication and the property of1 for division.[C, CN, R]

5. Describe and apply mentalmathematics strategies, such as:

skip counting from a knownfact using doubling or halving

using doubling or halvingand adding or subtracting onemore group using patterns in the 9s factsusing repeated doubling

to determine basic multiplicationfacts to 9 9 and related divisionfacts.[C, CN, ME, R]

Number


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9. Demonstrate an understandingof addition (limited to 1- and2-digit numerals) with answersto 100 and the correspondingsubtraction by:

using personal strategies foradding and subtracting withand without the support ofmanipulatives creating and solving problemsthat involve addition and

subtraction using the commutativeproperty of addition (the orderin which numbers are addeddoes not affect the sum) using the associative propertyof addition (grouping a set ofnumbers in different ways doesnot affect the sum) explaining that the order inwhich numbers are subtractedmay affect the difference.

[C, CN, ME, PS, R, V]

8. Apply estimation strategiesto predict sums and differencesof two 2-digit numerals in aproblem-solving context.[C, ME, PS, R]

9. Demonstrate an understandingof addition and subtraction ofnumbers with answers to 1000(limited to 1-, 2- and 3-digitnumerals), concretely, pictorially

and symbolically, by: using personal strategies foradding and subtracting withand without the support ofmanipulatives creating and solving problemsin context that involve additionand subtraction of numbers.


6. Demonstrate an understandingof multiplication (2- or 3-digit by1-digit) to solve problems by:

using personal strategies formultiplication with and withoutconcrete materials using arrays to representmultiplication connecting concreterepresentations to symbolicrepresentations

estimating products applying the distributiveproperty.


7. Demonstrate an understandingof division (1-digit divisor andup to 2-digit dividend) to solveproblems by:

using personal strategies fordividing with and withoutconcrete materials

estimating quotients relating division tomultiplication.


Number


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10. Apply mental mathematicsstrategies, such as:

counting on and countingback making 10 using doubles using addition to subtract

for basic addition facts and relatedsubtraction factsto 18.[C, CN, ME, PS, R, V]

10. Apply mental mathematicsstrategies and number properties,such as:

1. using doubles2. making 103. using addition to subtract4. using the commutativeproperty5. using the property of zero

for basic addition facts and relatedsubtraction facts to 18.


8. Demonstrate an understandingof fractions less than or equal toone by using concrete, pictorialand symbolic representations to:

name and record fractions forthe parts of a whole or a set compare and order fractions model and explain that fordifferent wholes, two identicalfractions may not represent thesame quantity

provide examples of wherefractions are used.[C, CN, PS, R, V]

9. Represent and describedecimals (tenths and hundredths),concretely, pictorially andsymbolically.[C, CN, R, V]

Number


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11. Demonstrate anunderstanding of multiplication to5 5 by:

representing and explainingmultiplication using equalgrouping and arrays creating and solving problemsin context that involvemultiplication modelling multiplicationusing concrete and visual

representations, and recordingthe process symbolically relating multiplication torepeated addition relating multiplication todivision.

[C, CN, PS, R]

10. Relate decimals to fractionsand fractions to decimals (tohundredths).[C, CN, R, V]

11. Demonstrate anunderstanding of addition andsubtraction of decimals (limited tohundredths) by:

using compatible numbers estimating sums and

differences using mental mathematicsstrategies

to solve problems.[C, ME, PS, R, V]

Number


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12. Demonstrate anunderstanding of division(limited to division related tomultiplication facts up to 5 5)by:

representing and explainingdivision using equal sharingand equal grouping creating and solving problemsin context that involve equalsharing and equal grouping modelling equal sharing andequal grouping using concreteand visual representations,and recording the processsymbolically relating division to repeatedsubtraction relating division tomultiplication.

[C, CN, PS, R]13. Demonstrate anunderstanding of fractions by:

explaining that a fractionrepresents a part of a whole describing situations in whichfractions are used comparing fractions ofthe same whole with likedenominators.

[C, CN, ME, R, V]

Number


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General OutcomeUse patterns to describe the

world and to solve problems.





Specific Outcomes Specific Outcomes Specific Outcomes1. Demonstrate an understandingof repeating patterns (three to fiveelements) by:

describing extending comparing creating

patterns using manipulatives,diagrams, sounds and actions.[C, CN, PS, R, V]

2. Demonstrate an understandingof increasing patterns by:

describing reproducing extending creating

patterns using manipulatives,diagrams, sounds and actions(numbers to 100).[C, CN, PS, R, V]

1. Demonstrate an understandingof increasing patterns by:



2. Demonstrate an understandingof decreasing patterns by:



1. Identify and describe patternsfound in tables and charts,including a multiplication chart.[C, CN, PS, V]

2. Translate among differentrepresentations of a pattern, suchas a table, a chart or concretematerials.[C, CN, V]

3. Represent, describe and extendpatterns and relationships,using charts and tables, to solveproblems.[C, CN, PS, R, V]

4. Identify and explainmathematical relationships, usingcharts and diagrams, to solveproblems.[CN, PS, R, V

Patterns and Relations(Patterns)


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General OutcomeRepresent algebraic expressions inmultiple ways.

Specific Outcomes Specific Outcomes Specific Outcomes3. Demonstrate and explainthe meaning of equality andinequality by using manipulativesand diagrams(0 100)[C, CN, R, V]

4. Record equalities andinequalities symbolically, usingthe equal symbol or the not equal

symbol.[C, CN, R, V]

3. Solve one-step addition andsubtraction equations involvingsymbols representing an unknownnumber.[C, CN, PS, R, V]

5. Express a given problem as anequation in which a symbol isused to represent an unknownnumber.[CN, PS, R]

6. Solve one-step equationsinvolving a symbol to represent anunknown number.[C, CN, PS, R, V]

Patterns and Relations(Variables and Equations)


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General OutcomeUse direct or indirectmeasurement to solve problems.



Specific Outcomes Specific Outcomes Specific Outcomes1. Relate the number of days to aweek and the number of monthsto a year in a problem-solvingcontext.[C, CN, PS, R]

2. Relate the size of a unit ofmeasure to the number of units(limited to nonstandard units)used to measure length and mass .

[C, CN, ME, R, V]

3. Compare and order objects bylength, height, distance aroundand mass, using nonstandardunits, and make statements ofcomparison.[C, CN, ME, R, V]

4. Measure length to the nearestnonstandard unit by: using multiple copies of a unit

using a single copy of a unit(iteration process).[C, ME, R, V]

1. Relate the passage of timeto common activities, usingnonstandard and standard units(minutes, hours, days, weeks,months, years).[CN, ME, R]

2. Relate the number of seconds toa minute, the number of minutesto an hour and the number of

days to a month, in a problemsolving context.[C, CN, PS, R, V]

3. Demonstrate an understandingof measuring length (cm, m) by:

selecting and justifyingreferents for the units cm andm modelling and describing therelationship between the unitscm and m

estimating length, usingreferents measuring and recordinglength, width and height.


1. Read and record time, usingdigital and analog clocks,including 24-hour clocks.[C, CN, V]

2. Read and record calendar datesin a variety of formats.[C, V]

3. Demonstrate an understanding

of area of regular and irregular 2-D shapes by: recognizing that area ismeasured in square units selecting and justifyingreferents for the units cm2or m2

estimating area, using referentsfor cm2or m2

determining and recordingarea (cm2or m2) constructing differentrectangles for a given area (cm2

or m2) in order to demonstratethat many different rectanglesmay have the same area.


Shape and Space(Measurement)


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Specific Outcomes Specific Outcomes Specific Outcomes5. Demonstrate that changingthe orientation of an object doesnot alter the measurements of itsattributes.[C, R, V]

4. Demonstrate an understandingof measuring mass (g, kg) by:

selecting and justifyingreferents for the units g and kg modelling and describing therelationship between the units gand kg estimating mass, usingreferents measuring and recording mass


5. Demonstrate an understandingof perimeter of regular andirregular shapes by:

estimating perimeter, usingreferents for cm or m measuring and recordingperimeter (cm, m) constructing differentshapes for a given perimeter(cm, m) to demonstrate that

many shapes are possible for aperimeter.

[C, ME, PS, R, V]

Shape and Space(Measurement)


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General OutcomeDescribe the characteristics of3-D objects and 2-D shapes, and

analyze the relationships amongthem.






6. Sort 2-D shapes and 3-Dobjects, using two attributes, andexplain the sorting rule.[C, CN, R, V]

7. Describe, compare andconstruct 3-D objects, including:

cubes

spheres cones cylinders pyramids.

[C, CN, R, V]

8. Describe, compare andconstruct 2-D shapes, including:

triangles squares rectangles circles.

[C, CN, R, V]

9. Identify 2-D shapes as parts of3-D objects in the environment.[C, CN, R, V]

6. Describe 3-D objects accordingto the shape of the faces and thenumber of edges and vertices.[C, CN, PS, R, V]

7. Sort regular and irregularpolygons, including:

triangles

quadrilaterals pentagons hexagons octagons

according to the number of sides.[C, CN, R, V]

4. Describe and construct rightrectangular and right triangularprisms.[C, CN, R, V]

Shape and Space(3-D Objects and 2-D Shapes)


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General OutcomeDescribe and analyze positionand motion of objects and shapes.



Specific Outcomes Specific Outcomes Specific Outcomes5. Demonstrate an understandingof line symmetry by:

identifying symmetrical 2 Dshapes creating symmetrical2-D shapes drawing one or more lines ofsymmetry in a 2-D shape.

[C, CN, V]

6. Demonstrate an understandingof congruency, concretely andpictorially.[CN, R, V]

Shape and Space(Transformations)


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General OutcomeCollect, display and analyze datato solve problems.




1. Gather and record dataabout self and others to answerquestions.[C, CN, PS, V]

2. Construct and interpretconcrete graphs and pictographsto solve problems.[C, CN, PS, R, V]

1. Collect first-hand data andorganize it using:

tally marks line plots charts lists

to answer questions.[C, CN, PS, V]

2. Construct, label and interpretbar graphs to solve problems.[C, PS, R, V]

1. Demonstrate an understandingof many-to-one correspondence.[C, R, T, V]

2. Construct and interpretpictographs and bar graphsinvolving many-to-onecorrespondence to draw

conclusions.[C, PS, R, V]

Statistics and Probability(Data Analysis)


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31

Patterning

Suggested Time: 3 Weeks

1

2

This is the first explicit focus on Patterning in Grade 3 but, as with other

outcomes, it is ongoing throughout the year.


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PATTERNING

Unit Overview

Focus and Context

Math Connects

In Grade 3, students continue working with increasing patterns. They

build on what they have learned in Grade 2 by communicating theirunderstanding of increasing patterns and by representing increasing

patterns in a variety of ways: concretely, pictorially and symbolically.

Students verbalize and communicate rules to help them understand the

predictability of a pattern. A large focus in Grade 3 is the introduction

and development of decreasing patterns. Students use their knowledge

of increasing patterns to make connections to the concept of decreasing

patterns, since similar understandings are developed. These patterning

concepts are the basis for further algebraic thinking and will be

extended in later grades.

It is important that students see the connection between increasingand decreasing patterns. Many opportunities should be provided forthem to connect both types of patterns. Since increasing and decreasingpatterns introduce students to a higher level of algebraic thinking,students will also make connections to the patterns embedded in otherstrands of mathematics.

Historically, much of the mathematics used today was developedto model real-world situations, with the goal of making predictionsabout those situations. As patterns are identified, they can be expressednumerically, graphically, or symbolically and used to predict howthe pattern will continue. It is important that students identify thatpatterns exist all around us. Viewing and discussing patterns in a realworld context creates authentic experiences for patterning concepts tobe applied and developed. Identifying patterns in the yearly/monthlycalendar, house numbers and money can be used to solve real lifeproblems.


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GRADE 3 MATHEMATICS CURRICULUM GUIDE - INTERIM

PATTERNING

33

STRAND OUTCOME PROCESSSTANDARDS

Patterns andRelations(Patterns)

3PR1 Demonstratean understanding ofincreasing patterns by:

describing

extending

comparing

creating

patterns usingmanipulatives,diagrams, sounds andactions (numbers to1000).

[C, CN, PS, R, V]

Patterns andRelations(Patterns)

3PR2 Demonstratean understanding ofdecreasing patterns by:

describing

extending

comparing

creating

patterns usingmanipulatives,diagrams, sounds and

actions (numbers to1000).

[C, CN, PS, R, V]

Process Standards

Key

Curriculum

Outcomes

[C] Communication [PS] Problem Solving

[CN] Connections [R] Reasoning

[ME] Mental Mathematics [T] Technology

and Estimation [V] Visualization


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34 GRADE 3 MATHEMATICS CURRICULUM GUIDE - INTERIM

Outcomes

PATTERNING

ElaborationsStrategies for Learning and Teaching

Students will be expected to

Strand: Patterns and Relations (Patterns)

3PR1 Demonstrate anunderstanding of increasingpatterns by:

describing

extending

comparing

creating

patterns using manipulatives,diagrams, sounds and actionsand numbers to 1000.

[C, CN, PS, R, V]

In Grade 2, students described, extended, compared and createdrepeating patterns and increasing patterns. Grade 3 students will review

and learn more about increasing shape/number patterns, as well as

explore decreasing patterns. They will begin with building patterns and

talking about them in a logical step-by-step process. Increasing patterns

are sometimes referred to as growing patterns a pattern where the size

of the elements increase in a predictable way. An element is any single

item or step of a pattern. E.g.

28, 31, 34, 37... the pattern begins at 28 and increases by 3. Each

number in the pattern is an element.

... in this example, each figure (group of

triangles) is an element

It is common for students to confuse a repeating pattern with an

increasing or decreasing pattern. Increasing and decreasing patterns do

not have a core. Students will be familiar with the mathematical term

core from working with repeating patterns in Grade 2. Ask students to

look for a core first. The core is the shortest part of the pattern that

repeats. If they cannot find a core, then the pattern is not a repeating

pattern and it must be an increasing or decreasing pattern.

Students need sufficient time to explore increasing patterns throughvarious manipulatives, such as link-its, tiles, flat toothpicks, counters,

pattern blocks, base ten blocks, bread tags, stickers, buttons, etc., to

realize they increase or decrease in a predictable way. Later, students

will connect patterns to numbers, and work with patterns found in the

hundreds chart or record patterns in a T-chart.Achievement Indicator:

3PR1.1 Describe a given

increasing pattern by stating a

pattern rule that includes the

starting point and a description

of how the pattern continues; e.g.,for 42, 44, 46 the pattern

rule is start at 42 and add 2 each

time.

Give students the first three or four

elements of an increasing pattern.

Ask them to determine the pattern

rule and explain how the pattern

continues. A pattern rule tells howto make the pattern and can be

used to extend an increasing or

decreasing pattern. Both have a

starting point and a change that

happens each time.

(continued)


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35GRADE 3 MATHEMATICS CURRICULUM GUIDE - INTERIM

Suggested Assessment Strategies Resources/Notes

PATTERNING

General Outcome: Use Patterns to Describe the World and to Solve Problems

PortfolioAsk students to complete a concept map. Use it to inform instructionby determining what students already know about growing patterns.Note any misconceptions to clarify throughout the unit.

Ask students to place the concept map in a portfolio. After further

instruction, ask students to complete another allowing them the

opportunity to compare it to the first. This allows students to assess

their own development. This strategy can also be used to determinetheir growth and understanding of other concepts. (3PR1)

Performance/Student-Teacher Dialogue

Calculator Activity In Grade 3, students can benefit fromexperiences working with calculators and examining patterns. Askstudents press 0 on a calculator. Ask them to select a number from 1to 9. E.g., 3. Press + followed by 3, then press =. The calculator willadd 3 to the previous sum. Record the number displayed. Press =again. Record the new number. Continue pressing = and recording

the new number displayed. After several entries, ask the students topredict the next few numbers. Ask: What are some other numbersthat are and are not part of the Add 3 pattern? Is there a rule wecan use to predict the numbers? If so, give the rule. Ask students toexplore several different numbers from 1 to 9 and see what happensif they start with 0 and then continue to add the chosen number.(Navigating through Algebra in Grades 3-5, 2001, p. 15) (3PR1.1)

Math Makes Sense 3Launch

TG pp. 2 3

Lesson 1: Exploring Increasing

Patterns

3PR1

TG pp. 4 6

Additional Activities:

Missing Figures

TG p. ix and 41

Game:Whats the Pattern Rule?

TG pp.18

This game may be used repeatedly

during this unit as extra practice to

reinforce 3PR1


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Outcomes

PATTERNING




3PR1 Continued As students describe increasing shape patterns, help them recognize thateach element has a numeric value. E.g.

Other numeric patterns include:

2, 4, 8, 16, The pattern rule is: Start at 2. Double each time.

3, 4, 6, 9, 13, The pattern

rule is: Start at 3. Add 1 and

increase the number added

by 1 more each time.

103, 108, 113, 118, 123, The pattern rule is: Start at 103. Add 5

each time.

Note: A pattern rule must have a starting point. E.g., if a student

describes the pattern 3, 7, 11, 15, as an add 4 pattern without

indicating that it starts at 3, the pattern rule is incomplete.

Leaping Lizards - Take students to an open area such as a gym orplayground to jump like Leaping Lizards while skip-counting an

increasing pattern. They jump 8 times in a row, stop to feel their hearts

beating, then jump 8 more times.

Name the Rule - Tell students the following story: On Earth Day, Mr.

Hann and his students planted a vegetable garden in the school yard.

He put 2 plants in the first section, 4 in the second section and 6 in the

third section. Ask students to:

create the pattern with blocksdescribe the rulepredict what comes nextextend the pattern. E.g., How many plants will they put in thetenth section?

Achievement Indicator:

3PR1.1 Continued


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PATTERNING


Performance10-frame Patterns build an increasing pattern by placing counterson the 10-frame and ask students to identify how the pattern is

growing. E.g., Pattern 5, 10, 15, 20

These 10-frames show that the numbers increase by 5 because

another full row of 5 is filled each time.

(3PR1.1)Headband Guess my Pattern - Students play with a partner. Oneplayer will wear a headband with a number pattern strip pickedfrom a bag. The player wearing the headband cannot see the numberpattern but must ask his/her partner questions to figure out thepattern. They must ask questions to find out the starting number,the pattern rule, and a missing term or three additional terms. (Or

the start number can be given.) Examples of questions students

might ask their partner:

Does the pattern start with an even or odd number?

Is it a multiple of 10?

Does it have 1 digit, 2 digits, 3 digits?Is it greater than 10?

Is the pattern increasing? Or decreasing?

Is the rule (add or subtract) by 2, 5, 6, etc.

Does the pattern increase by 5s?

Does it increase by more (less) than 5?

(3PR1.1)

Paper and Pencil

Give students a number pattern and ask them to write the patternrule. Check that students have included a starting point and how the

pattern continues. (3PR1.1)

Math Makes Sense 3Lesson 1 (Contd): Exploring

Increasing Patterns

3PR1

TG pp. 4 6

Additional Reading:

Navigating through Algebra in

Grades 3-5( 2001)

Small, Marion (2008)Making

Math Meaningful for Canadian

Students K-8. Chapter 20.


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Outcomes

PATTERNING




3PR1 Continued

Students are given the beginning of a pattern (at least three elements)

then asked to extend the pattern by three more elements. They should

always look backward to the beginning of the pattern to see that their

idea works for the rest of their pattern.

50, 100, 150, 200,

6, 13, 20, 27,

5, 8, 12, 17,

2, 2, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6,

Ask students to work on word problems in pairs:

1. Ms. Mercers class planted a special seed. On Monday the plantis 2 cm high. On Tuesday the plant has doubled its height and is 4

cm high. Each day the plant doubles its height from the day before.

How high will the plant be on Friday? Students can make a table

showing each day of the week and how tall the plant is on each day

(they can also use manipulatives to make the pattern.)

2. Lilys new puppy, Pokey, is growing fast. When Lily first got

Pokey he weighed only 1 kg. After 1 month Pokey weighed 7

kg. After 2 months, Pokey weighed 12 kg. After 3 months Pokey

weighed 16 kg. Lily saw a pattern. Find a pattern to tell how much

Pokey weighed after 5 months.

Ask students to complete a table like the one below:

Pattern: Start at 2 kg. Add 4 kg and then 1 kg less each time.


3PR1.2 Identify the pattern rule

of a given increasing pattern, and

extend the pattern for the next

three elements.

1st element 2nd element3rd element


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PATTERNING


JournalProvide students with a choice of3 increasing patterns. Students areasked to choose one pattern to extendfor the next three elements andexplain the rule.

(3PR1.2)

Paper and Pencil

Extending Patterns Ask students to complete a chart similar to theone below:

Ask them to extend each pattern three times and record each numberpattern. (3PR1.2)

Portfolio

Provide 1 cm grid paper for the students. Present a pattern such asthe one below. Students will use coloured pencils to continue thepattern. Next, ask the students to create their own growing patterns.

(3PR1.2)

Ask students: How many tiles are needed to make the next 3 figures?

( 3PR1.2)


Increasing Patterns

3PR1

TG pp. 4 6


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Outcomes

PATTERNING




3PR1 Continued

Students are provided with a variety of increasing patterns which

contain errors. Students determine what the pattern is and then explain

the error. E.g., 3, 7, 11, 15, 19, 23, 26, 31, 35, 39. The pattern rule

is: Start at 3. Add 4 each time.

Therefore, 26 is an error since it

is only adding on 3 not 4 and 31

is a second error since it is adding

5 and not 4.

Hint: To help students visualize this pattern they can shade numbers ona hundreds chart and look for the mistake:

Students can see that 26 does not fit the number pattern. It is an error.

In the following example, the shape pattern rule is: Start with 1 counter.

Add 1 to each row and column each time.

Therefore the fourth element is a error. There should be 4 counters inthe column not 3.

3PR1.3 Identify and explain

errors in a given increasing

pattern.



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PATTERNING


PerformanceProvide the start of an increasing pattern. Ask studenta to continuethe pattern for the next 3 elements and to describe the pattern

rule. (3PR1.2)

Paper and Pencil

Give students number patterns such as those below and ask them tofind and circle the error.

475, 575, 685, 775

233, 243, 253, 262

25, 28, 32, 34

7, 12, 15, 19 (3PR1.3)

Journal

Present students with the following growing pattern. Ask them to

find the error and explain how they know.

(3PR1.3)


Increasing Patterns

3PR1

TG pp. 4 6


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Outcomes

PATTERNING




3PR1 Continued

Since patterns increase in a predictable way, to determine a missing step

students will look at the pattern that comes before and after. They must

identify the pattern rule.

15, 26, 37, 48, ___, 70, 81 Start at 15. Add 11 each time.

5, 6, 8, 11, ___, 20, 26, 33, 41 Start at 5. Add 1, and then increase the

number added by 1 more each time.

13, 26, ___, 52, 65, 78, 91 Start at 13. Add 13 each time.

Ask students to practice finding missing elements by making patterns,

covering a step and asking a partner Whats missing?

Literature Connection - Read the following Skip Count Cheerleaders

chants from Riddle-iculous MATHby Joan Holub. Ask students to fill in

the missing element as they chant:

2, 4, 6, 8,

Who do we appreciate?

8, 10, 12, _?_

Our soccer coach, Ms. Morteen.

5, 10, 15, 20,

Who do we all like, and plenty?

20, 25, 30, _?_

Our lunch lady, Mrs. Dive.

20, 30, 40, 50,

Who do we all think is nifty?

50, 60, 70, _?_

Our principal, Mr. Grady.


3PR1.4 Identify and apply a

pattern rule to determine missing

elements for a given pattern.


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PATTERNING


PerformancePattern BANG! Have a variety of cards in a paper bag, such as theexamples below:

Include 1 BANG card for every 4 or 5 question cards.

Give each small group a bag. Students take turns drawing a card out

and answering the question. If the student answers correctly, she/he

gets to keep the card, (group members can help each other with the

answer). They then pass the bag to the next player. If a student pulls

out a BANG card, she/he must put all of her/his cards back into the

bag (leaving the BANG card out). They continue playing until there

are no cards left in the bag and whoever has the most cards wins.

(3PR1.1, 3PR1.2, 3PR1.3, 3PR1.4)

Ask each student to make a growing pattern using manipulatives.Next she/he covers one element of the pattern to reveal it to aclassmate. The classmate will then recreate the pattern putting inthe missing element. The initial pattern is uncovered and the twopatterns compared.

(3PR1.8, 3PR1.4)

Paper and Pencil

In pairs, ask students to make up their own chants and riddles which

include including a missing element, to put into a class Riddle-iculousMATHbook.

(3PR1.4)


Increasing Patterns

3PR1

TG pp. 4 6

Childrens Literature(not

provided):

Holub, Joan. Riddle-iculous Math

ISBN: 9780807549964


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Outcomes

PATTERNING




3PR1 Continued

Students identify the pattern rule and then describe how they discovered

that rule. E.g., 3, 6, ___, 12, 15

The rule is: Start at 3. Add 3 each time.

Possible strategies to determine missing elements include use of:

Number lines

Hundreds chart

Pictures

Manipulatives

Skip counting

It is important to accept other possible strategies that students use and

to discuss them.


3PR1.5 Describe the strategy used

to determine missing elements in

a given increasing pattern.


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PATTERNING


Paper and Pencil/PortfolioWanted Poster students will make wanted posters, asking readers tofind the missing element of an increasing pattern. See sample below:

Students create a number

or shape pattern, leaving

one element out. They

will include a hint flap,

which tells the pattern

rule for those who need

to use it. Also, they will

create a pull tab, which

will give the missingelement so that the

detectives can check to

see if they are correct.

Note: To make pull

tab, tape half of an

envelope to the back of

the poster for sliding

the tab card in and out

(be sure the tab is longer than the envelope).

(3PR1.5, 3PR1.4)Student-Teacher Dialogue

Where is the Birthday Party today? (Can be included in MorningRoutine). Present students with a pattern of numbers on a displayof houses. Add six extra houses with no number. Ask students to tellwhat the pattern is. Tell students that the party will be at a certainhouse (pick an extended number from the pattern). Ask students topick out the location of the house and describe the strategy (pattern

rule) they used. Examples of streets could be:

Street # 170, 180, 190, House 4, House 5, House 6 Rule: Start at170. Go up by 10 each time. The party is at house number 200.

Street # 31, 36, 41, House 4, House 5, House 6 . Rule: Start at31. Increase by 5 each time. We are looking for the house whichwould have the street number 61.Street # 101, 104, 107, House 4, House 5, House 6. Rule: Startat 101. Increase by 3 each time. The party is at house number116. (3PR1.1, 3PR1.5, 3PR1.9)


Increasing Patterns

3PR1

TG pp. 4 6


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Outcomes

PATTERNING




3PR1 ContinuedAchievement Indicator:

3PR1.6 Create a concrete,

pictorial or symbolic

representation of an increasing

pattern for a given pattern rule.

Give students various pattern rules to create their own model, picture or

number representation.

To represent concretely they can choose from a variety of manipulatives

(such as pattern blocks, coins or buttons) or they may choose to draw a

picture or use numbers. E.g.,

Start at 2 and double each time.

2, 4, 8, 16,

Examples of other increasing number patterns include:

1, 2, 2, 3, 3, 3, each digit repeats according to its value

2, 4, 6, 8, 10, even numbers skip counting by 2

1, 2, 4, 8, 16, double the previous number

2, 5, 11, 23, double the previous number and add 1

1, 2, 4, 7, 11, 16, successively add 1, then 2, then 3, and so on

2, 2, 4, 6, 10, 16, add the preceding two numbers


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PATTERNING


PerformanceStaircase Give students the first 3 frames of a staircase pattern (seebelow). Ask them to use square tiles pattern blocks, base-ten units,or multi-link cubes to build the next three frames of the staircasepattern. Students then predict what each frame will look like beforethey build it.

A growing pattern can be recorded in a table. This allows students

to see the relationship between a concrete/pictorial pattern and the

corresponding number pattern. Ask students make a table and recordthe number of frames, the number of squares added each time and

the number of squares in each frame.

(3PR1.6, 3PR1.7)

Math Makes Sense 3Lesson 2: Exploring Increasing

Patterns

3PR1

TG pp. 7 9

Childrens Literature (not

provided):

Hutchins, Pat. The Doorbell Rang

ISBN: 0688092349

Anno, Mitsumasa.Annos Magic

Seeds

ISBN: 9780698116184

Crews, Donald. Ten Black Dots

ISBN: 978-0688135744

Hong, Lily Toy. Two of Everything

ISBN: 978-0807581575


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Outcomes

PATTERNING




3PR1 ContinuedAchievement Indicator:

3PR1.7 Create a concrete,

pictorial or symbolic increasing

pattern; and describe the

relationship, using a pattern rule.

Students may use base ten blocks to concretely create an increasing

pattern with larger numbers. For example,

Pattern Rule: Start at 222. Add 10 each time.


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PATTERNING


Performance/Paper and PencilStudents will build a concrete pattern of their choice using objectssuch as pattern blocks, square tiles, base ten blocks, buttons, coins,etc. Next, ask students to create a flip book with each page slightlybigger than the next (stapling the smallest page on the top andlargest page on the bottom). Students draw the increasing patternon the top of each page and label the bottom of each page withthe correct numeric value. When the book is closed the numberpattern will be visible and as they open each page the picture will be

revealed.The last page of the book reveals the pattern rule. Extendthe above activity by having students exchange their flip book with

a partner. Each student will then use manipulatives to concretelycreate the number pattern represented on the outside flaps. Then askstudents to describe to their partner the pattern rule before checkingthe last page. Observe students concrete representations and ability

to describe the pattern rule to each other.

(3PR1.7, 3PR1.8)


Increasing Patterns

3PR1

TG pp. 7 9


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Outcomes

PATTERNING




3PR1 Continued

Students should have frequent experiences with solving real-world

problems that interest and challenge them. Ask students to solve the

following problems:

Carrie buys Yummy cat food for her cat, Cleo. One can of Yummycosts 15. How many cans can she buy for 90?

Complete a table

Robert decided to count

Documents

Mathematics Grade3 Curriculum Guide