Math Album-Sr Marjorie Garcia

Album for Montessori

Math Methods

Dr. Louise Bogart

Prof. Elizabeth Park

By:

Sr. Marjorie Garcia, OP

Table of Contents

Rationale Early Childhood Materials:

Numeration to 10

Introduction to Base 10 Place Value

Linear Counting

Whole Number Operations with Golden Bead

Rational Number Concept Development –

Fractions

Cohorts Lesson Plans

Student’s Lesson Plans

Rationale

Math is important for young children to learn because they are

in a stage when they are beginning to learn basic concepts in

life. Math in the Pre-K level is one of the effective tools in

making the child understand the basic concept of numbers by

using the red rods, sandpaper numbers to learn the abstract

number symbols, blue and red rods for computation, spindles for

counting, binomial and trinomial cubes to show children how it

embodies the trinomial or binomial formula, geometric solids, to

develop stereognostic sense, meaning to develop the ability to

perceive the form of an object by the sense of touch. Memory

games, cards and counters are used to remember and associate

quantity to symbol. Children come in contact with numbers early on in life, as our

daily existence revolves on mathematics, from counting pennies

to baking cookies. The practical purpose of helping children

learn early the concept is for them to develop mathematical

skills that they will use in interacting with others.

In a true Montessori classroom, mathematics curriculum is

reality based, where concrete materials are used to present

abstract mathematical concepts. The teacher creatively uses

appropriate and beautiful didactic materials to attract the

children’s attention and thus make them understand better the

concepts that include computation.

Basic mathematical concepts are first introduced to a young

child through the use of materials in the practical life area.

Montessori set up this activity basing from Piaget’s findings

that intelligence is an active process and that children acquire

more information by interacting with objects, ideas, and other

people, and also their concepts of the world around them

changes. For Montessori, she wanted to give children a rich

visual experience to make them work intensely in an ordered

sequence step, doing it in an exact way helps the children

progress in their development because Montessori believed that

order and precision were the keys to spontaneous work and that

children will develop the “mathematical mind”.

The concept of one-to-one correspondences, or pairing, is

taught in the Practical Life area with such activities as: using

keys and locks, matching cups to saucers, and buttoning or

snapping on the dressing frames. In the Sensorial area the same

concept is at work in the Knobbed Cylinders activity, as well as

in matching pairs of colors with the Color Tablets; while in

Language the children might match pictures to concrete objects.

These are some of the activities that introduce and allow the

exploration of Math related concepts in Montessori classroom.

The Montessori math lessons allow the child to build a

concrete association between memorized symbols and quantities.

The child holds and feels the quantity of ten as he counts it.

He then labels it with the symbol ten. Math includes

introduction to numbers, extensive work with the decimal system

including the addition, subtraction multiplication and division

of complex numbers, how to count to and write the numbers 1-100,

work with the teens and tens, and skip counting and beginning

memorization work for simple math facts.

According to Montessori, a child has a twofold sense of order.

One is external that pertains to his perception of his relations

with his environment. The second is internal and makes him aware

of the different parts of his own body and their relative

positions, and this can be called “inner orientation.” The

sensitive periods are connected with psychic facts. They are

insights and impulses that lay the foundation for consciousness,

spontaneous energy giving rise to fundamental principles that

form the basis of psychic growth (The Secret, p.55).

At this time it is easier for him/her to be introduced to

concepts of numeration, the decimal place value system and

linear counting. The role of the mother/teacher is to prepare

her/himself with the working knowledge of Mathematical skills

and to set-up the environment with the appropriate materials

necessary for the child to experience yet another dimension of

the world he/she lives in.

Teachers recognize children’s interest in making sense of

their world with mathematics; they build on their intuitive,

informal notions and encounters relating to math. They

“mathematize” children’s everyday encounters, they used various

learning context and provide focused mathematics time that is

interesting and meaningful to children, and they integrate math

with other curriculum areas throughout the day (DAP, p.171-172).

Summary:

Teaching math in early years is possible and can be

successful, given the right materials and method children will

easily understand the concepts because they have the ability to

concentrate, to put things in order and to integrate math in

everything around them. Sometimes the child will just burst in

his discoveries like, “I got ten seeds!” or “The wheels look

like zeros!” One time a girl said, “In my dream, I am counting.”

Math would be fun if it was presented in a concrete and fun way

and not something abstract as if they only exist in the cloud.

It is easy to remember if children can touch objects and its

equivalent symbols.

NUMERATION TO 10 Quantity - Number Rods

Age: 3 1/2 - 6 Materials: Mat Ten wooden rods measuring from one decimeter to one meter in length with alternate divisions of red and blue (each division is one decimeter) Presentation 1 (Lesson): 1. Invite the child(ren). 2. Prepare a long floor mat and bring rods to the mat beginning with the shortest rod. Place rods on the mat in mixed array. 3. Arrange rods in staircase fashion from shortest to longest placing rod #2 above rod #1. 4. Return rods to the shelf beginning with the longest rod. Continue so that all ten rods are in the stair. 5. Return mat. Presentation 2 (Lesson): 1. When child(ren) can correctly build the entire stair by themselves, do a three period lesson to teach the names of the quantities. Direct Aim (Objective): To teach the names for the quantities one through ten. Indirect Aims (Scaffolding): Preparation for higher math Preparation for science Preparation for language Preparation for art Develop visual memory, and physical internalization of the base ten Develop order, concentration, coordination, and independence Points of Interest (Motivation): Color pattern Making stair Handling the rods Three period lesson

Control of Error (Self-Assessment): Visual - the stair, color divisions The smallest rod Vocabulary: one, two, three, four, five, six, seven, eight, nine, ten, red, blue, rods, long, longer, longest, short, shorter, shortest Extensions : Place numerals with rods in stair. Place numerals on rods which are in random array.

Adaptation: Mini blue and red rods in box maybe used for table activity.

Hawaii Preschool Content Standards:

Domain IV: Cognitive Development (Mathematics)

Standard 2: Recognize and create patterns and become aware of relationships.

Hawaii Content and Performance Standards:

Topic Numbers and Number Systems

Benchmark MA.K.1.2

Represent whole numbers up to 30 in flexible ways (e.g., relating, composing, and decomposing numbers)

Sample Performance Assessment (SPA)

The student: Demonstrates a variety of ways that a number can be represented.

Rubric

Advanced Proficient Partially Proficient Novice

Represent whole numbers up to 30 in a variety of ways, using different forms of representation

Represent whole numbers up to 30 in a variety of ways, with no significant errors

Represent whole numbers up to 30 in one way, with no significant errors

Represent whole numbers up to 30 in one way, with significant errors

NUMERATION TO 10 Symbol - Sandpaper Numerals

Age: 3 1/2 - 6 Materials: Table/desk Sandpaper numerals 0 to 9 Presentation (Lesson) : 1. Invite the child(ren). 2. Place numerals on table. 3. Choose two numerals that look different. Provide name and show how to trace using the index and middle finger of the appropriate hand. State name of numeral at the end of tracing motion. 4. Using a three period lesson, teach the names of the two numerals. 5. Continue the process described in step 3 until all numerals can be named and traced correctly. 6. Return numerals to the shelf. Direct Aim (Objective): To teach the names for the numerals zero through nine and how to write them. Indirect Aims (Scaffolding): Preparation for higher math Preparation for science Preparation for language Preparation for art Develop visual memory, and physical internalization of the base ten Develop order, concentration, coordination, and independence Points of Interest (Motivation): Sandpaper Rough and smooth surfaces Numerals shapes and names Color on backing

Three period lesson Control of Error (Self-Assessment): Visual - shape of numeral Kinesthetic - hand moving off the sandpaper Vocabulary: zero, one, two, three, four, five, six, seven, eight, nine, sandpaper, rough, smooth, color of background Extensions: Associate the sandpaper numerals to the numeral cards that will be used to label the number rods. Adaptations: Allow the child to do the activity as long as he finds interest. Hawaii Preschool Content Standards:


Standard 1: Learn about number, numerical representation, and simple numerical operations.



Benchmark MA.K.1.2




Rubric






NUMERATION TO 10 Association of Quantities and Symbols

Age: 4 - 6 Materials:

Mat Ten number rods (1-10) Ten symbols (1-10)

Presentation 1 (Lesson)

1. Invite the child(ren) and have them bring the rods and

numerals to the floor mat.

Place rods and symbols in mixed array.

2. Teacher holds up a numeral. A child identifies it and finds

the rod that matches. If a group activity, children take turns

placing numerals with corresponding rods.

3. Return rods and numerals to shelf.

4. Return mat.


1. Invite the child(ren) to bring the rods and numeral cards to

the floor mat placing rods in mixed array.

2. Have the child(ren) arrange rods in sequence and then place

numerals with corresponding rod.

3. Return rods and numerals to the shelf.

4. Return mat.


1. With rods on mat, set the ten rod above and apart from

others.

2. Teacher says, “Let’s see how many ways we can make 10 using

only two rods.”

Teacher places 9 rod below the ten and asks a child which rod is

needed to make ten. The child who answers gets the rod and

places it next to the nine rod. Continue until all combinations

are done.

3. The same procedure can be used for combinations that make 9,

8, etc.

Note: After the introduction to addition with Golden Beads/Base Ten Blocks, child(ren) can be shown how to illustrate an equation for addition using signs for plus and equal with numeral cards. Direct Aim (Objective):

Lessons 1 & 2: To associate quantity and symbol.

Lesson 3: To find combinations that make 10

Indirect Aims (Scaffolding):

Preparation for higher math, science, language, art

Develop visual memory

Develop order, concentration, coordination, and independence

Points of Interest (Motivation):

Hunt to match Working with friends

Colors Rods

Control of Error (Self-Assessment):

Teacher or other children Control chart

Vocabulary:

number, numeral, quantity, symbol, names 1-10, combinations

Adaptation: Lower numbers for beginners






Benchmark MA.K.1.2




Rubric

Advanced Proficient Partially Proficient

Novice





NUMERATION TO 10

Spindle Boxes

Age: 4 - 6

Materials:

Mat

Two wooden boxes each with five divisions 0 - 4 and 5 - 9

Box of 45 wooden spindles

Presentation (Lesson):

1. Invite the child(ren).

2. On table or floor mat, place spindle boxes and box of

spindles in front of you.

3. Teacher explains that the purpose of this activity is to

place the correct number of spindles in each division.

4. Point to the numeral one and say, “one.” Using your dominant

hand to count and the

other to hold the spindles, count one spindle and place it into

the hand.

5. Using two hands, slide the spindle(s) into the corresponding

division.

6. Follow the procedure in steps four and five until divisions 1

- 9 are filled.

7. Return to the division marked “0” and indicate that there are

no spindles left for this division because zero is the number

property for the empty set.

8. Return spindles to box and boxes to shelf.

9. Return Mat.

Direct Aim (Objective):

To introduce the concept of making quantities (sets) from

discrete units/objects.

To introduce the concept of zero as the empty set.


Preparation for higher math Preparation for science

Preparation for language Preparation for art




Spindles zero

number sequence divisions for sets


Just enough spindles (45)

Vocabulary:

zero, empty set, sets, divisions/compartments, spindles

Variation:

Use objects to follow class theme in place of spindles.

Adaptation: If spindles are not available, sticks may be used.






Benchmark MA.K.1.2




Rubric






NUMERATION TO 10 Cards and Counters

Age: 4 to 6

Materials:

Mat Numeral cards labeled 1 – 10 55 counters



2. Place container in upper left corner of mat.

3. Place numeral cards in mixed array on mat. Indicate that the

numerals will be placed in order along top of mat and that they

must be spaced to accommodate objects to be counted.

4. Place the corresponding number of counters below each numeral

card and demonstrate how to arrange them in pairs or sets of

two.

5. Count the counters as you place them below the numerals as

you proceed 1 - 10.

6. Return materials to container and return container to shelf.

7. Return mat.


To provide practice in association of symbol and quantity.

To introduce the concept of odd and even.


Preparation for higher math Preparation for science

Preparation for language Preparation for art




Counters

Pattern made with counters


Just enough counters (55) Pattern

Vocabulary:

pattern, counters, odd and even

Extensions:

Use objects to follow class theme in place of disks.

Ask children to point out pattern and to explain concept of odd

and even.

Adaptations: Arranging counters with a pair/without a pair can

help the child identify odd or even.






Benchmark MA.K.1.2




Rubric






NUMERATION TO 10 Mystery Game

Age: 4 - 6

Materials:

Mat Folded numeral cards labeled 1 – 10 55 counters




3. Choose any numeral, unfold the card, and then count out the

correct number of counters.

4. Continue with the procedure described in step 3 until all

cards are unfolded and each one has the correct number of

counters with it.

5. Check work.

6. Return materials to shelf.

7. Return mat.


To test for mastery of numeration to 10.


Preparation for higher math

Preparation for science

Preparation for language

Preparation for art




1. Counters

2. Folded numerals

3. The mystery


Just enough counters (55)

Vocabulary:

mystery, folded, names of numerals and quantities zero to ten

Variation: Use object to follow class theme.

Adaptation: Repeat the activity as the children finds interest.






Benchmark MA.K.1.2




Rubric






NUMERATION TO 10 Introduction to the Short Bead Stair

Age: 4 - 6

Materials:

Mat

Bead bars of lengths for quantities 1 - 10 (each quantity a

different color)




3. Place bead bars in mixed array on the mat.

4. Select the red “1” and place it at the left side of the mat.

5. Select the green “2” and place it below the red bar.

6. Continue on through the ten bar.

7. Using the three period lesson, teach the names of all the

bars.

8. Replace the beads and return container to shelf.

9. Return mat.


To introduce the colored bead stair


Preparation for further study of math




Colors

Stair formation


Stair formation

Vocabulary:

colors, names of quantities

Extensions: Match each bead bar to its corresponding symbol.

Adaptations: Allow the child to get familiar with the bead

colors and its appropriate quantity.






Benchmark MA.K.1.2




Rubric






NUMERATION TO 10 Search for Ten

Age: 4 - 6

Materials:

Mat

Bead bars of lengths for quantities 1 - 9 (each quantity a

different color)

Five tens

Set of black and white place savers




3. Place bead bars in a stair on the mat.

4. Place the black and white beads in a stair on the mat.

5. Place the tens on the mat.

6. Arrange the colored bead bars in a snake configuration across

the bottom of the mat mixing them up.

7. Start counting the colored beads until you get to ten. If there are any uncounted beads on the bead bar that is part of the ten, use a black and white place saver in place of the uncounted beads. Then place a ten in the snake and remove the colored beads. 8. Continue the procedure described in step 7 until the colored beads have all been counted.

9. Replace beads on shelf. 10. Return mat. Direct Aim (Objective): To practice numeration to ten. Indirect Aims (Scaffolding): Preparation for further study of math Develop visual memory Develop order, concentration, coordination, and independence Points of Interest (Motivation): Colors Stair Formation Changing colored beads to gold. Control of Error (Self-Assessment): Correct number for exchange Teacher or other children Vocabulary: colors, counting 1 - 10, place savers, change, exchange Extensions: Use more bars and have exchange not come out even. Adaptations: Allow the child to do the activity until she masters it. Hawaii Preschool Content Standards:





Benchmark MA.K.1.2




Rubric






BASE TEN PLACE VALUE INTRODUCTION TO GOLDEN BEAD MATERIAL

Introduction to Quantity Age: 4 to 7 Materials: 1 one 1 ten 1 hundred 1 thousand Mat Presentation (Lesson): 1. Invite child(ren). 2. Carry introduction tray for quantity to mat prepared on table or floor and place it on the left side of the mat. (If a child has not experienced the “golden beads” allow him the chance to just hold and feel the beads before you begin). 3. As child(ren) already know quantities 1 - 10, use third period of 3 period lesson and show the “one” and ask “What is this?” Wait for response. Show the “ten” and ask “What is this?” Wait for response. 4. Using three period lesson, teach vocabulary for 100 and 1000. 5. Return golden beads to tray. 6. Return tray to shelf. 7. Return mat. Direct Aim (Objective): To introduce the child(ren) to the language for base ten place value quantities Indirect Aims (Scaffolding): Preparation for higher math, Preparation for science Preparation for language, Preparation for art Internalize place value kinesthetically Independence Develop visual memory Concentration Points of Interest (Motivation): Golden beads Size and shape of beads Control of Error (Self Assessment): Teacher

Vocabulary: One, ten, hundred, thousand, place value, base ten, golden beads Extension: Montessori Wooden Bead Materials: Before using the wooden material in an exercise, the teacher should bring out a hundred beads square and a hundred wooden square for the child to compare. The same is done with the bead cube and wooden cube. Teacher can explain the reason for using wood is that beads are very expensive so we cannot afford a lot of them. Adaptation: Allow the child to play and get familiar with the materials. Hawaii Preschool Content Standards: Domain IV: Cognitive Development (Mathematics) Standard 1: Learn about number, numerical representation, and simple numerical operations. Hawaii Content and Performance Standards:


Benchmark MA.2.1.1

Represent whole numbers up to 1000 in flexible ways (e.g., relating, composing, and decomposing numbers), including the use of tens and hundreds as units


The student: Represents a three-digit number (e.g., 416) with different configurations of hundreds, tens, and ones units.

Rubric


Novice

Accurately represent whole numbers up to 1000 in a variety of ways and using

Represent whole numbers up to 1000 in a variety of ways, including the use of tens


Have difficulty representing whole numbers up to 1000 in a variety of ways, including

different forms of representation, including the use of tens and hundreds as units

and hundreds as units, with no significant errors

and hundreds as units, with a few significant errors

the use of tens and hundreds as units


Introduction to Symbol Age: 4 to 7 Materials: Large numeral cards for 1 (green), 10 (blue), 100 (red), 1000 (green) Mat Presentation (Lesson): 1. Invite the child(ren). 2. Carry introduction tray for symbols to mat prepared on table or on the floor. 3. As child(ren) already know quantities 1 - 10, use third period of 3 period lesson and show the “one” and ask “What is this?” Wait for response. Show the “ten” and ask “What is this?” Wait for response. 4. Using three period lesson, teach vocabulary for 100 and 1000. 5. Return symbols to tray. 6. Return tray to shelf. 7. Return mat. Direct Aim (Objective): To introduce numerals for base ten place value Indirect Aims (Scaffolding): Preparation for higher math Preparation for science Preparation for language Internalize place value kinesthetically Preparation for art Develop visual memory Independence Concentration Points of Interest (Motivation): Three period lessons Colors on numerals and numerals themselves Control of Error (Self Assessment): Teacher Vocabulary: Symbol, names for 1, 10, 100, 1000, base ten, place value

Extension: Stack cards showing all zeroes, then slide to right and expose all ones composing the numeral. Read numeral. Adaptation: Allow the child to be familiar with the symbols. Hawaii Preschool Content Standards:





Benchmark MA.2.1.1




Rubric


Novice

Accurately represent whole numbers up to 1000 in a variety of ways and using different forms of representation, including the use of tens and

Represent whole numbers up to 1000 in a variety of ways, including the use of tens and hundreds as units, with no significant errors

Represent whole numbers up to 1000 in a variety of ways, including the use of tens and hundreds as units, with a few significant errors

Have difficulty representing whole numbers up to 1000 in a variety of ways, including the use of tens and hundreds as units

hundreds as units


Association of Quantity and Symbols Age: 4 to 7 Materials: Large numeral cards for 1, 10, 100, 1000 Mat One each of golden bead quantities 1, 10, 100, 1000 Presentation (Lesson): 1. Invite the child(ren). 2. Take materials to mat. 3. Place both the quantity and the symbols on the mat, in mixed array. 4. Teacher shows the one bead and asks, “What is this?” When the child responds, “One”, teacher asks her to find the symbol that matches the quantity, that is, the symbol that shows how to write “one.” The “one” is matched with the symbol “1 .” 5. Teacher repeats this procedure for 10, 100, 1000. 6. Return materials to respective trays. 7. Return trays to shelf. 8. Return mat. Direct Aim (Objective): Associate base ten place value symbols with quantities. Indirect Aims (Scaffolding):Preparation for higher math Preparation for science Preparation for language Internalize place value kinesthetically Independence Concentration Preparation for art Develop visual memory Points of Interest (Motivation): beads, numerals, matching, Control of Error (Self Assessment): Teacher Vocabulary: numeral, symbol, quantity, base ten place value

Adaptations: If the child cannot get whole numbers up to one thousand, allow more time to do the activity. Hawaii Preschool Content Standards:





Benchmark MA.2.1.1




Rubric


Novice

Accurately represent whole numbers up to 1000 in a variety of ways and using different forms of representation, including the

Represent whole numbers up to 1000 in a variety of ways, including the use of tens and hundreds as units, with no significant

Represent whole numbers up to 1000 in a variety of ways, including the use of tens and hundreds as units, with a few significant


use of tens and hundreds as units

errors errors


Crisis of Nine Age: 4 to 7 Materials: Mat 9 Ones 9 Tens 9 Hundreds 1 Thousand Presentation (Lesson): 1. Invite child(ren) to join activity. 2. Lay out a mat. 3. Place tray with materials on the left side of the mat. 4. Beginning at the right side of the mat, count the 9 ones as you place them in a line vertically. Place the ones so they touch each other. 5. When you get to nine, say, “And one more would be...?” Wait for student to say “10.” 6. Teacher says, “Yes. And 10 has its own place.” As you say, “own place,” put one 10 to the left of the ones so that children can see it is exactly one more than the 9 ones. Pause. Remove the ones. 7. Teacher counts,” One ten, two tens, three tens, etc. and after counting 9 tens teacher says, “And one more ten would be...?” Wait for student to answer “10 tens.” 8. Teacher then responds, “And 10 tens is the same as...?’ (Show 100 as you ask that question.) Wait for a response. 9. “Yes, 100 and 100 has its own place.” Put 100 to the left of the tens so that children can see that it is exactly one more than 9 tens. Pause. Remove the tens. 10. Continue with the lesson in the same manner counting 9 hundreds to 1000. 11. Return beads to the tray. 12. Return the beads and mat to shelf. Direct Aim (Objective): To introduce the concept that in the base ten, the largest digit that can be written in any place is 9. Therefore, after counting 9 you must change place. Indirect Aim (Scaffolding): Preparation for higher math, science, art, language

Develop visual memory, and physical internalization of place value and base ten. Develop order, concentration, and independence. Points of Interest (Motivation): Materials exchanging and moving to next place counting Control of Error (Self Assessment): Teacher Vocabulary: Names of quantities 1 - 9, ones, tens, hundreds, thousands, place value, base ten Extensions: Exchanging game Do the crisis for other bases using the material in the bead cabinet.

Adaptations: Do the lesson slowly or repeat the lesson if the child is having confusion.






Benchmark MA.2.1.1




Rubric

Advanced Proficient Partially Novice

Proficient

Accurately represent whole numbers up to 1000 in a variety of ways and using different forms of representation, including the use of tens and hundreds as units





Quantity Layout Age: 4 1/2 to 8 Materials: Mat , 9 ones, 9 tens , 9 hundreds, 9 thousands Presentation (Lesson): 1. Invite child(ren) to sit next to you at mat on floor. 2. Spread out mat and place quantity layout tray to left. 3. Teacher counts out 9 ones starting in top right corner of mat and works top to bottom leaving about 5 inches between each bead (hands width or use a ten). When she gets to 9 teacher asks, “And one more would be...?” Wait for response. 4. “Yes, and ten has its own place.” 5. Teacher places ten to left of one bead at top of mat leaving space between rows. She counts out 9 tens working top to bottom as with ones, saying “one ten, two tens, etc. When she gets to nine tens, she asks “And one more would be...?” Wait for response. 6. “Yes, ten tens which are the same as...?” (Show the 100 as you ask.) Wait for response. After students respond, teacher says, “Yes, and 100 has its own place.” 7. Teacher places 100 to left of first ten leaving space between rows and continues the procedures in steps 5 - 7 through 9000. 8. When layout is complete, have child count it all by himself. Later child can lay it out by himself, counting. 9. Return materials to tray. 10. Return tray to shelf. 11. Return mat. Direct Aim (Objective): To practice place value with quantity

Indirect Aims (Scaffolding):Develop visual memory of place value. Internalize place value kinesthetically Preparation for higher math, science, language, art Point of Interest Motivation): Beads Pattern Layout Using hand or ten to measure space Control of Error (Self Assessment): Teacher Material on tray Vocabulary: Layout, pattern, ones, tens, hundreds, thousands, place value, base ten Extension: Fetching Games Adaptation: Repeat the lesson if the child cannot get for the first time. Hawaii Preschool Content Standards:





Benchmark MA.2.1.1




Rubric


Novice

Accurately represent whole numbers up to

Represent whole numbers up to 1000 in a

Represent whole numbers up to 1000 in a

Have difficulty representing whole numbers

1000 in a variety of ways and using different forms of representation, including the use of tens and hundreds as units

variety of ways, including the use of tens and hundreds as units, with no significant errors

variety of ways, including the use of tens and hundreds as units, with a few significant errors

up to 1000 in a variety of ways, including the use of tens and hundreds as units


Fetching Quantities Age: 4 1/2 to 8 Materials: Tray Mat 9 ones 9 tens 9 hundreds 9 thousands Presentation (Lesson): 1. Child(ren) lay out quantities. 2. Teacher says “We’re going to make some large numbers. Let’s make 1 thousand, 8 hundreds, 4 tens, 2 ones. Can you get me the quantity 1842?” 3. Child gets quantity on tray and takes to teacher. 4. Teacher asks child, “What did you bring?” Child reads quantity. 5. Teacher verifies. 6. Child returns quantity to layout and returns to teacher with empty tray. 7. Teacher gives child another quantity to fetch. 8. Procedure continues as long as child is interested. 9. Child(ren) return materials to tray. 10. Child(ren) return trays to shelf. 11. Return mat. Direct Aim (Objective): Practice with base ten place value Indirect Aims (Scaffolding): Preparation for higher math, science, language, art Develop auditory memory Points of Interest (Motivation): bead layout shapes of quantities pattern Control of Error (Self Assessment):Teacher, Material Vocabulary: Names of base ten place values Variations: If child cannot remember four places, try three, then 2, if necessary Adaptation: If the child cannot get the symbols at once repeat the activity if needed.






Benchmark MA.2.1.1




Rubric


Novice






Symbols Layout Age: 4 ½ to 8 Materials: Mat Large Numeral Cards 1 - 9000 Presentation (Lesson): 1. Invite child(ren) to sit next to you at mat on floor. 2. Spread out mat and place quantity layout tray to left. 3. Teacher counts 1- 9, starting at top right corner of mat and works top to bottom, while placing cards for 1 - 9 in a row vertically. When she gets to “9” teacher asks, “And one more would be...?” Wait for response. 4. “Yes, and ten has its own place.” 5. Teacher places 10 to left of 1 at top of mat leaving space between rows. She counts out 9 tens working top to bottom as with 1 - 9, saying “one ten, two tens” etc. When she gets to nine tens, she asks “And one more would be...?” Wait for response. 6. “Yes, ten tens which is the same as...?” (Show the 100 as you ask.) Wait for a response. After students respond, teacher says, “Yes, and 100 has its own place.” 7. Teacher places 100 to left of first ten leaving space between rows and continues the procedures in steps 5-7 through 9000. 8. When layout is complete, have child count it all by him. Later child can lay it out by himself, counting. 9. Return materials to tray. 10. Return tray to shelf and return mat. Direct Aim (Objective): To practice place value with symbols Indirect Aims (Scaffolding): Develop visual memory of place value Internalize place value kinesthetically Preparation for higher math, science, language, art Point of Interest (Motivation): Symbols and colors Pattern Layout Seeing large numerals

Control of Error (Self Assessment): Teacher Material on tray Vocabulary: Layout, pattern, ones, tens, hundreds, thousands, place value, base ten Extension: Fetching Games Adaptations: Allow the child to play with the materials and get familiar with the number symbols. Hawaii Preschool Content Standards:





Benchmark MA.2.1.1




Rubric


Novice

Accurately represent whole numbers up to 1000 in a variety of ways and using different forms of

Represent whole numbers up to 1000 in a variety of ways, including the use of tens and hundreds as units, with no

Represent whole numbers up to 1000 in a variety of ways, including the use of tens and hundreds as units, with a

Have difficulty representing whole numbers up to 1000 in a variety of ways, including the use of tens and hundreds as

representation, including the use of tens and hundreds as units

significant errors

few significant errors

units


Fetching Symbols Age: 4 1/2 to 8 Materials: Tray Mat Large numeral cards 1 - 9000 Presentation (Lesson): 1. Child(ren) lay out symbols. 2. Teacher says “We’re going to make some large numerals. Let’s make 1 thousand, 8 hundreds, 4 tens, 2 ones. Can you get me the numeral 1842?” 3. Child gets symbols on tray and takes to teacher. 4. Teacher asks child, “What did you bring?” Child reads numeral. 5. Teacher verifies. 6. Child returns symbols to layout and returns to teacher with empty tray. 7. Teacher gives child another numeral to fetch. 8. Procedure continues as long as child is interested. 9. Child(ren) return materials to tray. 10. Child(ren) return trays to shelf. 11. Return mat. Direct Aim (Objective): Practice with base ten place value using symbols Indirect Aims (Scaffolding): Preparation for higher math, science, language, art Develop auditory memory Points of Interest (Motivation): symbols layout colors pattern Control of Error (Self Assessment): Teacher Material Vocabulary: Names of base ten place values Variations: If child cannot remember four places, try three, then 2, if necessary.

Adaptation: Allow the child to try the activity, repeat the lesson if necessary.






Benchmark MA.2.1.1




Rubric


Novice






Birdseye View (45 Layout) Age: 4 1/2 to 8 Materials: Large Mat Set of Large Numeral Cards 45 ones, 45 tens, 45 hundreds, 45 thousands Presentation (Lesson): 1. Invite children to sit next to you on the floor. 2. Spread out mat and place materials on the left side of the mat. 3. Teacher asks students to layout the large numeral cards being careful to show children how to space the places value to allow space for the quantities. 4. Teacher demonstrates placing a one bead beside the numeral one, two ones beside the numeral two, and three ones beside the numeral three. Children are then asked to continue the process to the numeral nine. 5. Teacher begins placing the tens beside the numerals for one ten and two ten and then asks children to continue to nine tens. 6. Teacher begins placing hundreds beside the numerals for one hundred and two Hundred, being careful to place the quantities side by side moving from right to left. Children are asked to continue the process to nine hundred. 7. Follow step 6 for thousands place. 8. When the layout is complete, children marvel at their creation and help to collect the numerals and quantity. 9. Return materials to shelf. 10. Fold or roll mat and return it. Direct Aim (Objective): To build place value with symbols and matching quantities Indirect Aims (Scaffolding): Develop visual memory of place value symbols with matching quantities

The step pattern that is created by this layout Preparation for higher math, science, language and art Points of Interest (Motivation): Beads and symbols pattern layout building on large mat Control of Error (Self Assessment): Teacher or other children 45 of each quantity symbols Vocabulary: layout, pattern, one, tens, hundreds, thousands, base ten, place value Adaptation: Assist the child if she needs help in doing the activity. Hawaii Preschool Content Standards:

Domain IV: Cognitive Development (Mathematics) Standard 1: Learn about number, numerical representation, and simple numerical operations. Hawaii Content and Performance Standards:


Benchmark MA.2.1.1




Rubric


Novice

Accurately represent whole numbers up to 1000 in a variety of ways and using



Have difficulty representing whole numbers up to 1000 in a variety of ways, including

different forms of representation, including the use of tens and hundreds as units

and hundreds as units, with no significant errors

and hundreds as units, with a few significant errors

the use of tens and hundreds as units

LINEAR COUNTING TEENS: 11 - 19 Quantity

Age: 4 to 7 Material: Short bead stair 1 - 9 9 ten bars Counter Mat Presentation (Lesson): 1. Invite the child(ren). 2. Build short bead stair in upper left corner of mat with ten bars below 3. Take one ten and place the red 1 bead next to it, “One ten one has another name, 11” 4. To the right of 11, place another 1 ten with the green 2 next to it. “One ten two has another name, 12.” 5. Continue this procedure through nineteen. 6. Using 3 Period Lesson teach names of bead combinations 11 - 19. 7. When child(ren) know all combinations, have him put them in sequence. 8. Return beads to box. 9. Return box to shelf. 10. Return mat. Direct Aim (Objective): To learn quantities 11 – 19, their sequence, and their names Indirect Aim (Scaffolding): Preparation for higher math Points of Interest (Motivation): Bead stair, Combinations of bead bars. Control of Error (Self Assessment): Teacher, Materials Vocabulary: eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen

Extension: Using other sets of bead stairs, make other combinations of 11 – 19 besides 10 + one to nine Example: 9+2=11 8+3=11 7+4=11

Adaptation: Guide the child if she needs help in doing the activity, or repeat the lesson if needed.






Benchmark MA.K.1.2




Rubric


Novice





LINEAR COUNTING TEENS: Symbols

Age: 4 to 7 Materials: Teen Boards - Two wooden boards with vertical rows of nine 10’s. A slot is provided to cover the zero with a numeral to compose the numerals from 11 to 19 Mat Presentation (Lesson): 1. Invite the child(ren). 2. Place the boards in front of the child(ren) with symbols stacked to right of board. 3. Pointing to top “10” teacher names “one ten one” sliding in symbols for “1,” “is eleven.” “This is the way we write 11.” 4. Teacher presents symbols for 12 through 19 in the same manner. 5. Using a three period lesson, teacher teaches names for the numerals. 6. Return boards to box. 7. Return box to shelf. 8. Return mat. Direct Aim (Objective): To learn symbols, sequence and names for numerals 11 – 19 Indirect Aims (Scaffolding): Preparation for high math Points of Interest (Motivation): New numerals Sliding in numbers Control of Error (Self Assessment): Teacher Materials Vocabulary: Names for symbols 11 – 19

Variation: Mix up numerals and have children place quantity

Adaptation: Repeat the lesson if the child is not familiar with the symbol.






Benchmark MA.K.1.2




Rubric


Novice





TEENS: Quantity and Symbols

Age: 4 to 7 Materials : Mat Teen boards Short bead stair 9 ten bars Presentation (Lesson): 1. Invite the chiId(ren) 2. Place boards on the mat in front of the child (ren). 3. Place beads for ten and one beside the board and say “one ten one is eleven.” 4. Slip symbol into board over the first zero and say “this is how we write eleven.” 5. Follow same procedure for remaining quantities and symbols. 6. Return boxes to shelf. 7. Return mat. Direct Aim (Objective): Associate quantity and symbols 11 – 19 Indirect Aim (Scaffolding): Preparation for high math Points of Interest (Motivation): Short bead stair Slots Sequence Control of Error (Self Assessment): Teacher Materials Vocabulary: Names for quantities and symbols for 11 – 19 Extension: Use other combinations of bead stair 1 - 9 to make teen quantities. Mix numerals and have child(ren) put the matching

bead combinations alongside each numeral. Mix quantities next to board and have child(ren) put matching numerals on the board. Adaptation: Allow the child to play with the materials or repeat the lesson if needed. Hawaii Preschool Content Standards:





Benchmark MA.K.1.2




Rubric


Novice





LINEAR COUNTING TENS: Quantity

Age: 4 1/2 to 7 Materials: 45 tens Mat Presentation (Lesson): 1. Invite the child(ren). 2. Place the materials in front of the child(ren). 3. Place one ten at the left side of the mat and ask child(ren) to name it. Place two tens nearby and to the right of ten. “Two tens has another name, twenty.” 4. Continue with this procedure through ninety. 5. Using a Three period lesson, teach the names of twenty to ninety. 6. When child(ren) know all quantities, have them put the beads in sequence. 7. Return materials to box. 8. Return box to shelf. 9. Return mat. Direct Aim (Objective): Learn names for quantities 20 – 90 and their sequence Indirect Aim (Scaffolding): Preparation for higher math Points of Interest (Motivation): Beads, New vocabulary Control of Error (Self Assessment): Teacher, Number of Beads Vocabulary: Ten, twenty, thirty, forty, fifty, sixty, seventy, eighty, nine Adaptation: If the child is having difficulty, repeat the lesson next time. Hawaii Preschool Content Standards: Domain IV: Cognitive Development (Mathematics)




Benchmark MA.1.1.1 Count whole numbers up to 100 in a variety of ways (e.g., skip counts by 2's, 5's, 10's)


The student: Counts out a certain number of objects in more than one way (e.g., puts 55 beads into groups of 5 and skip counts by 5).

Rubric


Novice

Count whole numbers up to 100 in a variety of ways and selectively use strategies depending on the situation

Count whole numbers up to 100 in a variety of ways, with no significant errors

Count whole numbers up to 100 in a variety of ways, with a few significant errors

Have difficulty counting whole numbers up to 100 in a variety of ways

LINEAR COUNTING TENS: Symbols

Age: 4 1/2 to 7 Materials: Ten boards Mat Presentation (Lesson): 1. Invite the child(ren). 2. Place materials at left side of mat. 3. Remove boards and place in front of the child(ren). 4. Ask child(ren) to name the ten. Then, “Two tens has another name, twenty, and this is how we write twenty.” 5. Continue with procedure thirty through ninety. 6. Using a 3 period lesson, teach the names for the symbols 20, 30, 40, 50, 60, 70, 80, 90. 7. Return materials box. 8. Return box to shelf. 9. Return mat. Direct Aim (Objective): Learn names of symbols 20-90 and their sequence Indirect Aim (Scaffolding): Preparation for higher math Points of Interest (Motivation): Wooden boxes Boards Numerals and their names Control of Error (Self Assessment): Teacher, Materials Vocabulary: Names 10 – 90 Adaptation: Give assistance to the child if needed during her play.

Hawaii Preschool Content Standards: Domain IV: Cognitive Development (Mathematics) Standard 1: Learn about number, numerical representation, and simple numerical operations.






Rubric


Novice





LINEAR COUNTING TENS: Quantity and Symbol

Age: 4 1/2 to 7 Materials: ten boards Mat 9 tens and 9 ones Presentation (Lesson): 1. Lay ten boards out in front of child(ren). 2. Teacher places a ten alongside of the numeral 10, saying “Ten,” and placing one bead with the ten, says “One ten one” is eleven.” 3. Pointing to “10” and sliding “1” into slot, teacher says “This is the way we write 11.” 4. Teacher removes a symbol (symbols are always kept face down in beginning) and continues with 12 - 19, adding one bead and changing the symbol to match. 5. “9 and one more is…?” Wait for response. Exchange for ten “now we have two tens which is the same as…?” Wait for response. Move the two tens down to the numeral 20 and say “this is how we write twenty.” 6. Continue procedure 21 through 99. 7. Let child(ren) do it as soon as he realizes what to do. 8. Return materials to boxes. 9. Return boxes to shelf. 10. Return mat. NOTE: Children should go at least to number 30 during their first lesson. Always bring the beads down so the child can see the progression. Direct Aims (Objective): To associate quantity, name and symbols for 11 - 99 Build numbering system one bead at a time Indirect Aim (Scaffolding): Preparation for higher math Point of Interest (Motivation): Beads increasing and sliding down with each 10 Control of Error (Self Assessment):

Teacher Materials Vocabulary: Names for numerals and quantities 11 – 99 Extension: Provide materials so that children can make a number roll.

Adaptation: Extend the activity or repeat it next time if the child didn’t get the first time.









Rubric


Novice





LINEAR COUNTING Hundred Board

Age: 5 - 8 Materials: Board with 10 rows of 10 Tiles 1 - 100 Mat Presentation (Lesson): 1. Invite the child(ren). 2. Sort tiles by tens. 3. Place first group of tiles (1 - 10) in mixed array. 4. Starting in upper left hand corner and working left to right child places tiles in correct numerical sequence. 5. Child(ren) work(s) chart row by row with appropriate group of tiles until board is filled 1 - 100. OR Some children may choose to work from mixed array to fill the board with tiles 1 - 100 as a matter of learning style. Allow them to do so. Note: The tiles should not be presorted according to tens. Doing so does not meet the objective of this lesson nor does it allow for development of concentration. Points of Interest (Motivation): Matrix Tiles Filling in all the blanks Sorting Direct Aim (Objective): Test for ten boards (test knowledge of 1 - 100) Indirect Aims (Scaffolding): Practice in counting 1 - 100 Preparation for higher math Control of Error (Self Assessment): Visual - pattern of numbers Exact amount of tiles

Control chart Vocabulary: Hundred, board & tiles, tens, sort, numerals 1-100 Extensions: Skip count by 2’s, 5’s, and 10’s

Adaptation: if the child cannot get it the first time, allow her to use the number chart as a guide.









Rubric


Novice





LINEAR COUNTING Hundred Chain

Age: 5 – 7 Materials: 100 chain 100 square Arrows 10 - 100 Mat Presentation (Lesson): 1. Teacher shows the child(ren) how to carry chain to mat and lay it out. 2. Teacher shows 100 square saying “This is 100.” 3. Teacher folds 100 chain into square and compares to square - “This is 100 also.” 4. Pull chain out to make line. 5. Place arrows in mixed array on mat. 6. Start counting chain from the left “1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10” Select arrow that says “10” and place it on 10 bead. 7. Continue counting individual beads until 100 and mark each ten with an arrow. When you get to 100, place 100 square at end of chain. 8. Read arrows. Child(ren) may record numerals on tags in journals. 9. Replace chain and arrows on shelf. 10. Return mat. Direct Aims (Objective): To give practice in linear counting To introduce skip counting (by 10’s) Indirect Aim (Scaffolding): Preparation for higher math Points of Interest (Motivation): Folding and unfolding square

Arrows Counting by 10 Vocabulary: Numerals 1 - 100, square, chain, skip counting, arrows Variation: After this linear counting is very familiar, the child gets skip counting aspect and does it that way. Extension: Give the child more time to play as long as she gets interested. Adaptation: Assist the child if she cannot count up to a hundred yet. Hawaii Preschool Content Standards:








Rubric






LINEAR COUNTING 1000 Chain

Age: 5+ Materials: 1000 chain 1000 cube 100 chain 9 - 100 squares Arrows 10 - 1000 Large mat Presentation (Lesson): 1. Teacher shows child(ren) how to carry chain to mat and lay it out. 2. Teacher shows 1000 cube saying “This is 1000.” 3. Teacher folds 1000 chain into ten 100 squares then stacks ten 100 squares to compare to cube - “This is 1000 also.” 4. Start counting chain from the left by 10’s placing arrows, measuring with 100 chains and placing 100 squares at proper places. 5. Stack 100 squares to make 1000 cube at end. 6. Replace chains and arrows. 7. Return mat. Direct Aim (Objective): To give practice in linear and skip counting Indirect Aim (Scaffolding): Preparation for higher math Points of Interest (Motivation): Length of chain Folding and unfolding Arrows Control of Error (Self Assessment): Teacher Beads Vocabulary:

Names of numerals 1 - 1000, chain, square, cube, arrow, skip counting

Adaptation: Allow the child to try and give guidance when she needs help.






Benchmark MA.2.1.2 Compare whole numbers up to 1000 using words (e.g., greater than, less than, equal to)


The student: Compares numbers to determine which number is greater in a pair.

Rubric


Novice

Accurately order whole numbers up to 1000, and provide a rationale for the comparison

Compare and order whole numbers up to 1000, with no significant errors

Compare and order whole numbers up to 1000, with a few significant errors

Have difficulty comparing and ordering whole numbers up to 1000

WHOLE NUMBER OPERATIONS GOLDEN BEADS

Addition - Static - No Exchanging Age: 41/2 to 7 Materials: Trays Mat Yarn or ribbon Addition sign Base ten blocks or Golden Beads One large and two small sets of numeral cards Presentation (Lesson): 1. Invite children to the lesson. 2. Ask children to lay out the three sets of numeral cards. 3. Teacher asks two students individually to get a tray and to bring a numeral from one of the two sets of small numeral cards. Teacher is careful to provide two numerals that do not require exchanging. 4. As each student returns, (s)he reads the numeral, the teacher verifies and asks the student to get the quantity that matches the numeral and put it in his/her tray. 5. When students return with quantity, the students read their quantity, the teacher verifies that it is correct. 6. Teacher takes numeral from one of the trays and places it on the left side of the mat. To the right and parallel to the numeral, the teacher places the quantity. 7. The teacher then asks the other student to place his/her numerals below the first student’s numeral and to place the quantity below the quantity already on the mat. 8. The teacher recaps “name brought amount and name brought amount and asks, “I wonder how much we’d have if we put them all together?” 9. Teacher places yarn, to simulate a line, just below the two numerals and quantities. 10. The teacher then asks one of the students to please bring the ones below the line and count them. The student does so and tells the group how many there are. 11. The teacher then asks a student to get the numeral, from the large set of numerals that matches the quantity just counted. 12. This procedure continues for tens, hundreds and thousands until all places are counted and the numeral card that matches has been retrieved.

13. The teacher then asks one of the students to compose the numeral and another to read it. 14. The teacher recaps the entire process: “name brought amount and name brought amount. When we put them together we counted total. This operation is called addition and addition has a special sign.” Place sign. 15. Students return materials to learning center. Direct Aim (Objective): To provide a concrete experience with the concept of addition without exchanging. Indirect Aim (Scaffolding):Preparation for higher math Cooperative learning Points of Interest (Motivation): Materials Yarn or ribbon Addition sign Working with friends Operating with “big numbers” Control of Error (Self Assessment): Teacher or another student Control chart Vocabulary: add, addition, plus, addend, total, sum Adaptation: If the child get confused, repeat the lesson. Hawaii Preschool Content Standards:




Topic Operations

Benchmark MA.K.2.1 Demonstrate addition as "putting together" or "combining sets"


The student: Counts the objects in each of two groups, combines the two sets of objects, and recounts the new group.

Rubric


Demonstrate addition as "putting together" or



Have difficulty demonstrating addition as "putting

"combining sets" and determine the total, with accuracy

"combining sets" and determine the total, with no significant errors

"combining sets" and determine the total, with a few significant errors

together" or "combining sets" and are unable to determine the total

Whole Number Operations Golden Beads

Addition-Dynamic-With exchanging Age: 4 ½ to 7 Materials: Trays Mat Yarn or ribbon Addition sign Base ten blocks or Golden Beads One large and two small sets of numeral cards Presentation (Lesson): 1. Invite children to the lesson. 2. Ask children to lay out the three sets of numeral cards. 3. Teacher asks two students individually get a tray and to bring a numeral from one of the two sets of small numeral cards. Teacher is careful to provide two numerals that do not require exchanging in the thousands place. 4. As each student returns, (s)he reads the numeral, the teacher verifies and asks the student to get the quantity that matches the numeral and put it in his/her tray. 5. When students return with quantity, the students read their quantity, the teacher verifies that it is correct. 6. Teacher takes numeral from one of the trays and places it on the left side of the mat. To the right and parallel to the numeral, the teacher places the quantity. 7. The teacher then asks the other student to place his/her numerals below the first student’s numeral and to place the quantity below the quantity already on the mat. 8. The teacher recaps “name brought amount and name brought amount and asks, “I wonder how much we’d have if we put them all together?” 9. Teacher places yarn, to simulate a line, just below the two numerals and quantities. 10. The teacher then asks one of the students to please bring the ones below the line and count them. The student does so and tells the group how many there are and then makes the appropriate exchange. 11. The teacher then asks a student to get the numeral, from the large set of numerals that matches the quantity just counted. 12. This procedure continues for tens, hundreds and thousands until all places are counted and the numeral card that matches has been retrieved. 13. The teacher then asks one of the students to compose the numeral and another to read it.

14. The teacher recaps the entire process: “name brought amount and name brought amount. When we put them together we counted total. This operation is called addition and addition has a special sign.” Place sign. 15. Students return materials to learning center. Direct Aim (Objective): To provide a concrete experience with the concept of addition with exchanging. Indirect Aim (Scaffolding): Preparation for higher math Cooperative learning Points of Interest (Motivation): Materials Yarn or ribbon Addition sign Working with friends Operating with “big numbers” Control of Error (Self Assessment): Teacher or another student Control chart Vocabulary: add, addition, plus, addend, total, sum, exchange, change, regroup, rename, trade Adaptation: More practice to master the activity. Hawaii Preschool Content Standards: Domain IV: Cognitive Development (Mathematics) Standard 1:Learn about number, numerical representation, and simple numerical operations. Hawaii Content and Performance Standards:

Topic Operations

Benchmark MA.K.2.1 Demonstrate addition as "putting together" or "combining sets"

Sample Performance Assessment (SPA) The student: Counts the objects in each of two groups, combines the two sets of objects, and recounts the new group.

Rubric


Demonstrate addition as "putting together" or "combining sets" and determine the total, with accuracy

Demonstrate addition as "putting together" or "combining sets" and determine the total, with no significant errors

Demonstrate addition as "putting together" or "combining sets" and determine the total, with a few significant errors

Have difficulty demonstrating addition as "putting together" or "combining sets" and are unable to determine the total

Whole Number Operations Golden Beads

Age: 4 ½ to 7 Materials: Trays Mat Yarn or ribbon Multiplication sign Base ten material or Golden bead material One large and three small sets of numeral cards Presentation (Lesson): 1. Invite children. 2. Have children lay out all sets of numeral cards. 3. Teacher asks three children individually to bring a four digit numeral from one of the three sets of small numeral cards. Teacher is careful to give a numeral that will not require exchanging. 4. As each student returns, (s)he reads the numeral, teacher verifies then asks the student to get the quantity that matches the numeral. Upon return, student reads quantity and teacher verifies. 5. Each student places numeral and quantity on the mat using the same format that was used for addition. 6. Teacher recaps problem: “name brought amount, name brought amount, name brought amount. The three of you took amount 1 time, 2 times, three times. I wonder how many we have all together?” Place ribbon across bottom of materials. 7. Individual students are invited to bring quantities below the line and count. The numeral that matches is retrieved from the large set of numeral cards. 8. When all places are counted and labeled, one student is asked to compose the numeral and another is asked to read it. 9. Teacher recaps the entire process: “name brought amount, name brought amount, name brought amount. So you took amount 1 time, 2 times, three times. When we put them all together we counted product. This operation is called multiplication and multiplication has a special sign.”

10. Children return materials and mat to the shelf. Direct Aim (Objective): To introduce the concept of multiplication without exchanging through a concrete experience. Indirect Aim (Scaffolding): Preparation for higher math Cooperative Learning Points of Interest (Motivation): Materials Multiplication sign Yarn or ribbon Working with friends Operating with “big numbers” Control of Error (Self Assessment): Teacher or another student Control cards or charts Vocabulary: multiply, multiplication, product, take, multiplier, multiplicand, times, factor Extension: Teacher explains: “There is a special way to record multiplication. Because we took the same amount 3 times, we only need to write the amount once.” Remove second 2 numerals and replace them with a 3 and the multiplication sign saying, “You took amount 1 time, 2 times, 3 times.” Place the 3 as you say “three” and the X as you say “times”.

Adaptation: Assist the children if they are doing it the first time.





Topic Operations

Benchmark MA.2.2.2 Demonstrate multiplication as repeated addition of equal groups


The student: Represents multiplication by arranging equal groups of objects and

determining the total number of objects (e.g., shows 3 x 5 as three groups of 5 blocks and skip counts by 5 to arrive at the answer of 15).

Rubric


Demonstrate multiplication as repeated addition of equal groups and accurately determine the total number of objects

Demonstrate multiplication as repeated addition of equal groups and determine the total number of objects, with no significant errors

Demonstrate multiplication as repeated addition of equal groups and determine the total number of objects, with significant errors

Unable to demonstrate multiplication as repeated addition of equal groups


Multiplication - Dynamic - With Exchanging Age: 5 to 7 Materials: Trays Mat Yarn or ribbon Multiplication sign Base ten material or Golden bead material, One large and three small sets of numeral cards Presentation (Lesson): 1. Invite children. 2. Have children lay out all sets of numeral cards. 3. Teacher asks three children individually to bring a four digit numeral from one of the three sets of small numeral cards. Teacher is careful to give a numeral that will not require exchanging in the thousands place. 4. As each student returns, (s)he reads the numeral, teacher verifies then asks the student to get the quantity that matches the numeral. Upon return, student reads quantity and teacher verifies. 5. Each student places numeral and quantity on the mat using the same format that was used for addition. 6. Teacher recaps problem: “name brought amount, name brought amount, name brought amount. The three of you took amount 1 time, 2 times, three times. I wonder how many we have all together?” Place ribbon across bottom of materials. 7. Individual students are invited to bring quantities below time line and count, exchanging as appropriate. The numeral that matches is retrieved from the large set of numeral cards. 8. When all places are counted and labeled, one student is asked to compose the numeral and another is asked to read it. 9. Teacher recaps the entire process: “name brought amount, name brought amount, name brought amount. So you took amount 1 time, 2 times, three times. When we put them all together we counted product. This operation is called multiplication and multiplication has a special sign.” 10. Children return materials and mat to the shelf.

Direct Aim (Objective): To introduce the concept of multiplication with exchanging through a concrete experience. Indirect Aim (Scaffolding): Preparation for higher math Cooperative Learning Points of Interest (Motivation): Materials Yarn or ribbon Multiplication sign Working with friends Operating with “big numbers” Control of Error (Self Assessment): Teacher or another student Control cards or charts Vocabulary: Multiply, multiplication, product, take, multiplier, multiplicand, times, factor,change, exchange, regroup, rename, trade. Extension: Teacher explains: “There is a special way to record multiplication. Because we took the same amount 3 times, we only need to write the amount once.” Remove second 2 numerals and replace them with a 3 and the multiplication sign saying, “You took amount 1 time, 2 times, 3 times.” Place the 3 as you say “three” and the X as you say “times”.

Adaptation: Repeat the activity for children who cannot get it the first time.





Topic Operations

Benchmark MA.2.2.2 Demonstrate multiplication as repeated addition of equal groups


The student: Represents multiplication by arranging equal groups of objects and determining the total number of objects (e.g., shows 3 x 5 as three groups of 5 blocks and

skip counts by 5 to arrive at the answer of 15).

Rubric


Demonstrate multiplication as repeated addition of equal groups and accurately determine the total number of objects

Demonstrate multiplication as repeated addition of equal groups and determine the total number of objects, with no significant errors

Demonstrate multiplication as repeated addition of equal groups and determine the total number of objects, with significant errors

Unable to demonstrate multiplication as repeated addition of equal groups


Subtraction - Static - Without Exchanging Age: 5 to 8 Materials: Mat Trays Subtraction sign Yarn or ribbon Base Ten Materials 1 large and 2 small sets of numeral cards Presentation (Lesson): 1. Invite children. 2. Have children lay out all sets of numeral cards. 3. Teacher asks two children individually to bring a four digit numeral, the first from the large set of numeral cards and the second from one of the small sets of numerals. Teacher is careful to give a numeral that will not require exchanging. 4. Each student returns, (s)he reads the numeral, teacher verifies. Only the student with the large numeral cards is asked to get the quantity that matches the numeral. Student reads quantity and teacher verifies. 5. The student with the large numeral cards places his/her numeral and quantity on the mat using the same format as was used in addition. 6. The student with the small numeral cards takes the quantity that matches his/her numeral from the quantity that has been placed on the mat by the first student and places the quantity on his/her tray. 7. Teacher recaps problem: “name brought amount. name took his/her quantity from name and put it on his/ her tray. I wonder how much name has left?” Place ribbon across bottom of materials. 8. Individual students are invited to bring quantities below the line and count. The numeral that matches is retrieved from the unused small set of numeral cards. 9. When all places are counted and labeled- one student is asked to compose the numeral and another is asked to read it.

10. Teacher recaps the entire process: name brought amount. name took his/her quantity from name and put it on a tray. When we counted what name had left, we got difference. This operation is called subtraction and subtraction has a special sign. 11. Children return materials and mat to the shelf. Direct Aim (Objective): To introduce the concept of subtraction without exchanging through a concrete experience. Indirect Aims (Scaffolding): Preparation for higher math Cooperative Learning Points of Interest (Motivation): Materials Yarn or ribbon Subtraction sign Working with friends Operating with “big numbers” Control of Error (Self Assessment): Teacher or another student Control cards or charts Vocabulary: subtraction, subtract, take away, minus, minuend, subtrahend, difference Adaptation: Give time for children to play and master the activity. Hawaii Preschool Content Standards:

Domain IV: Cognitive Development (Mathematics) Standard 1: Learn about number, numerical representation, and simple numerical operations. Hawaii Content and Performance Standards:

Topic Operations

Benchmark MA.K.2.2 Demonstrate subtraction as "taking away," "separating sets," or "counting back"


The student: Removes some objects from a set, then recounts the remaining objects or counts backwards as each object is removed.

Rubric


Novice

Demonstrate subtraction as "taking away,"



Have difficulty demonstrating subtraction as

"separating sets," or "counting back" and determine the difference, with accuracy

"separating sets," or "counting back" and determine the difference, with no significant errors

"separating sets," or "counting back" and determine the difference, with a few significant errors

"taking away," "separating sets," or "counting back" and are unable to determine the difference


Subtraction - Dynamic - With Exchanging Age: 5 to 8 Materials: Trays Mat Subtraction sign Yarn or ribbon Base Ten Materials 1 large and 2 small sets of numeral cards Presentation (Lesson): 1. Invite children. 2. Have children lay out all sets of numeral cards. 3. Teacher asks two children individually to bring a four digit numeral, the first from the large set of numeral cards. and the second from one of the small sets of numerals. 4. Each student returns, (s)he reads the numeral, teacher verifies. Only the student with the large numeral cards is asked to get the quantity that matches the numeral. Student reads quantity and teacher verifies. 5. The student with the large numeral cards places his/her numeral and quantity on the mat using the same format as was used in addition. 6. The student with the small numeral cards takes the quantity that matches his/her numeral from the quantity that has been placed on the mat by the first student and places the quantity on his/her tray. 7. Teacher recaps problem: “name brought amount. name took his/her quantity from name and put it on his/ her tray. I wonder how much name has left?” Place ribbon across bottom of materials. 8. Individual students are invited to bring quantities below the line and count, exchanging as necessary. The numeral that matches is retrieved from the unused small set of numeral cards. 9. When all places are counted and labeled, one student is asked to compose the numeral and another is asked to read it 10. Teacher recaps the entire process: name brought amount. name took his/her quantity from name and put it on a tray. When we

counted what name had left, we got difference. This operation is called subtraction and subtraction has a special sign. 11. Children return materials and mat to the shelf. Direct Aim (Objective): To introduce the concept of subtraction without exchanging through a concrete experience. Indirect Aims (Scaffolding): Preparation for higher math Cooperative Learning Points of Interest (Motivation): Materials Yarn or ribbon Subtraction sign Working with friends Operating with “big numbers” Control of Error (Self Assessment): Teacher or another student Control cards or charts Vocabulary: subtraction, subtract, take away, minus, minuend, subtrahend, difference, exchange, change, rename, regroup, trade Adaptation: Children who are slow to get the steps maybe given assistance. Hawaii Preschool Content Standards: Domain IV: Cognitive Development (Mathematics)



Topic Operations

Benchmark MA.K.2.2 Demonstrate subtraction as "taking away," "separating sets," or "counting back"


The student: Removes some objects from a set, then recounts the remaining objects or counts backwards as each object is removed.

Rubric


Novice




Have difficulty demonstrating subtraction as

"separating sets," or "counting back" and determine the difference, with accuracy

"separating sets," or "counting back" and determine the difference, with no significant errors

"separating sets," or "counting back" and determine the difference, with a few significant errors

"taking away," "separating sets," or "counting back" and are unable to determine the difference


Division - Static - Without Exchanging Age: 5 to 8 Materials: Trays Mat Yarn or ribbon Division sign Base Ten Materials 1 large and 3 small sets of numeral cards Presentation (Lesson): 1. Invite children. 2. Have children lay out all sets of numeral cards. 3. Teacher asks one student to bring a four digit numeral from the large set of numeral cards. Teacher is careful to give a numeral that will not require exchanging. 4. The student returns, (s)he reads the numeral, teacher verifies. Student with the large numeral cards is asked to get the quantity that matches the numeral. Student reads quantity and teacher verifies. 5. The student with the large numeral cards places his/her numeral and quantity on the mat using the same format as was used in addition. 6. Each student involved in the lesson gets a tray (no more than 9) and sits around the mat containing the quantity. 7. The teacher tells the students that they are going to share equally the quantity on the mat. The teacher shares the quantity equally among trays starting with thousands. Teacher stops after each round and has children check to make sure they all have the same amount (an equal share). Continue until all quantities that can be are shared equally. 8. Teacher recaps problem: “name brought amount. We then took that quantity and shared it equally among the three of you. I wonder how much each of you has.” 9. Individual students are invited to count the quantity on their trays. Each student retrieves the numeral that matches from one of the small set of numeral cards. 10. Each student is asked to compose the numeral on his/her tray and read it.

11. Teacher recaps process: name brought amount. We shared it equally among the three of you. When each of you counted what was on your tray, each of you had quotient. So, when we take quantity and divide it into three equal shares, each share has quotient.” Place quantity ÷ 3 = quotient while recapping. “This operation is called division and division has a special sign.” 12. Children return materials and mat to the shelf. Direct Aim (Objective): To introduce the concept of division without exchanging through a concrete experience. Indirect Aim (Scaffolding): Preparation for higher math Cooperative learning Points of Interest (Motivation): Materials Yarn or ribbon Division sign Working with friends Operating with “big numbers” Control of Error (Assessment): Teacher or another student Control cards or charts Vocabulary: division, divide, divisor, dividend, quotient, equals Adaptation: Give another lesson if children cannot get it the first time. Hawaii Preschool Content Standards: Domain IV: Cognitive Development (Mathematics) Standard 1: Learn about number, numerical representation, and simple numerical operations. Hawaii Content and Performance Standards:

Topic Operations

Benchmark MA.2.2.3 Demonstrate division as "separating equal groups"


The student: Uses block to represent the dividend and separates the blocks into equal number of groups according to the divisor (e.g., For the expression 24 ÷ 6, separates 24 blocks into six equal groups).

Rubric


Demonstrate division as "separating equal groups" and accurately determine the number of equal groups

Demonstrate division as "separating equal groups" and determine the number of equal groups, with no significant errors

Demonstrate division as "separating equal groups" and determine the number of equal groups, with significant errors

Unable to demonstrate division as "separating equal groups"


Division - Dynamic - With Exchanging Age: 5 - 8 Materials: Trays Mat Yarn or ribbon Division sign Base Ten Materials 1 large and 3 small sets of numeral cards Presentation (Lesson): 1. Invite children. 2. Have children lay art all sets of numeral cards. 3. Teacher asks one student to bring a four digit numeral from the large set of numeral cards. 4. The student returns, (s)he reads the numeral, teacher verifies. The student with the large numeral cards is asked to get the quantity that matches the numeral. Student reads quantity and teacher verifies. 5. The student with the large numeral cards places his/her numeral and quantity on the mat using the same format as was used in addition. 6. Each student involved in the lesson gets a tray (no more than 9) and sits around the mat containing the quantity. 7. The teacher tells the students that they are going to share equally the quantity on the mat. The teacher shares the quantity equally among trays starting with thousands. Teacher stops after each round and has children check to make sure they all have the same amount (an equal share). Continue until all quantities that can be are shared equally. 8. Teacher recaps problem: “name brought amount. We then took that quantity and shared it equally among the three of you. I wonder how much each of you has.” 9. Individual students are invited to count the quantity on their trays. Each student retrieves the numeral that matches from one of the small set of numeral cards.

10. Each student is asked to compose the numeral on his/her tray and read it. 11. Teacher recaps process: name brought amount. We shared it equally among the three of you. When each of you counted what was on your tray, each of you had quotient. So, when we take quantity and divide it into three equal shares, each share has quotient.” Place quantity ÷ 3 = quotient while recapping. “This operation is called division and division has a special sign.” 12. Children return materials and mat to the shelf. Direct Aim (Objective): To introduce the concept of division with exchanging through a concrete experience. Indirect Aim (Scaffolding): Preparation for higher math Cooperative learning Control of Error (Self Assessment): Teacher or another student Control cards or charts Points of Interest (Motivation): Materials Yarn or ribbon Division sign Working with friends Operating with “big numbers” Vocabulary: division, divide, divisor, dividend, quotient, equal, exchange, change, regroup, rename, trade Note: The quotient is defined as one share or “what one skittle gets.” Adaptation: Assist the child to do the exchanging if they cannot do it the first time. Hawaii Preschool Content Standards:




Topic Operations

Benchmark MA.2.2.3 Demonstrate division as "separating equal groups"

Sample Performance Assessment The student: Uses block to

(SPA) represent the dividend and separates the blocks into equal number of groups according to the divisor (e.g., For the expression 24 ÷ 6, separates 24 blocks into six equal groups).

Rubric


Demonstrate division as "separating equal groups" and accurately determine the number of equal groups

Demonstrate division as "separating equal groups" and determine the number of equal groups, with no significant errors

Demonstrate division as "separating equal groups" and determine the number of equal groups, with significant errors

Unable to demonstrate division as "separating equal groups"

FRACTIONS Concept Development - Regional Model

Age: 4 to 8

Materials: Set of ten circle insets, from one whole to circles divided into equal parts from 2 through 10; circles are red and frames are green. Apple, knife, cutting board, plastic gloves, and one golden bead A sphere of playdough or clay Slips of paper and marker to write on them Mat Presentation 1 (Lesson 1): 1. Invite the child(ren). 2. Ask if they have ever shared food with someone. Ask them to talk about how they shared. 3. Show the child(ren) the apple. We can share this apple equally by cutting it. Cut the apple in half. “Now the apple is no longer whole because we have divided it into two equal parts. How many children could have a share?” (Wait for response.) “Each child would get one-half of the apples.” 4. Cut each half in half. “Now how many children can have a share?” (Wait for response.) “Each child receives one-fourth of the apple.” 5. If you have more children, divide the fourths into eighths so there are enough parts for each child to have a piece. If there are more children, have enough apples to repeat the process. 6. Pass out the pieces of apple. Presentation 2 (Lesson 2): 1. Invite the child(ren). 2. Prepare a long floor mat and bring two trays of circle insets to the mat. 3. Show child(ren) the golden one bead and explain that in order to find numbers smaller than one we would have to divide this “one” into equal pieces. An easy way to do that is to flatten it into a circle.

4. Take the sphere of playdough or clay and flatten it into a circle. Now I can divide this circle into equal parts. Relate this circle to the whole circle inset. 5. Trace the whole circle and cut it into two pieces that are not equal explaining that although there are two pieces because they are not equal, they are not halves. Explain that when we divide the whole (one) into equal parts we call each part a fraction. 6. Relate fractions to everyday life, for example, time, recipes, food buying. 7. Return materials to the shelf. 8. Return mat. Presentation 3 (Lesson 3): 1. Invite the child(ren). 2. Prepare a long floor mat and bring the two trays of fractional insets to the mat. 3. Show the whole circle and ask the children how many circles you have. 4. Write “1” on a slip of paper. 5. Reminding child(ren) that the whole can be divided into equal parts, move on to the circle divided into two equal parts. Pick up the two parts and put them back to back to show they are equal. 6. “How many parts is this circle divided into?” (Write the line for division as you say the word “divided” and wait for response.)

7. Write the “2” below the line indicating that “2” is the family name, i.e., it is the part of their name that they all have in common. 8. Remove one-half from the inset and place it on the mat. Ask, “How many members of the family of “2” did I place on the mat?” Write “1” above the line and place the label on the fractional part on the mat. 9. Ask, “How many members of the family of “2” remain in the inset?” Write “1” above the line and place the label on the fractional part still in the inset. 10. Continue this procedure until all fractional parts are labeled. 11. Show child(ren) the prepared slips that will be with the material for them to work with. 12. Return materials to the shelf. 13. Return mat. Presentation 4 (Lesson 4): 1. Invite the child(ren). 2. Prepare a long floor mat and bring the two trays of fractional insets to the mat. 3. Take the fractional insets for halves out of the inset and ask the child(ren)< “How many parts is this circle divided into?” (Write the line for division as you say the word “divided” and wait for a response.) 4. Write “2” below the line and ask, “How many family members am I pointing to?” Write the “1” above the line. 5. Provide the language for numerator and denominator indicating the number below the line is the name of the family and tells us how many parts the circle is divided into. This number is called the denominator. The number above the line tells us how many of the family members we have to work with and that is called the numerator. 6. Do a three period lesson to teach vocabulary. 7. Return materials to the shelf. 8. Return mat. Direct Aim (Objective): To help children develop the concept of fractional parts and the numbering system that goes with them. Indirect Aims (Scaffolding): Preparation for higher math Preparation for science Preparation for art Preparation for language Develop visual memory and internalization of sizes of fractional parts

Points of Interest (Motivation): Colors Circles, Insets and Frames Different sizes of fractional parts, New numbering system New vocabulary Control of Error (Self-Assessment): Inset frames and insets Teacher Vocabulary: Circles, insets, frames, fractions, fractional parts, numerator, denominator, family, family members, whole, half, halves, thirds, fourths, fifths, sixths, sevenths, eighths, ninths, tenths Extensions: Use other geometric shapes Have children trace fractional parts into their math journals, color and label them Have children trace fractional parts onto construction paper, cut them out, glue them on large poster board, and label them for display.

Have students trace fractional parts onto construction paper, cut them out, glue them onto pages to make a booklet and label them Add derivations of words: Fraction is from the Latin “frangere” which means to break or to divide Numerator has the same root as number Denominator has the same root as denomination which is used for money and for delineation of groups like religions Add history: Romans wrote division as 8 fractus 4 and later modified it to 8 F 4. A further modification was 8/4 and today we write 8 ÷ 4 Because of this notation for division, we write fractions the way we do Note: Lesson on concept development should also be done with linear & set models.

Adaptation: Assist the children if they will do the activity for the first time. Hawaii Preschool Content Standards: Domain IV: Cognitive Development (Mathematics) Standard 1: Learn about number, numerical representation, and simple numerical operations. Hawaii Content and Performance Standards: Topic Numbers and Number Systems

Benchmark MA.1.1.2 Identify representations of simple fractions (e.g., one-half, one-third, one fourth)


The student: Names the fraction that matches a picture that represents the fraction.

Rubric


Consistently identify representations of simple fractions and provide representations

Usually identify representations of simple fractions

Sometimes identify representations of simple fractions

Rarely identify representations of simple fractions

of common fractions

Cohorts Lesson Plan

MEASUREMENT ACTIVITY

AGES

• 4 to 6 years MATERIALS

• String • Paper • Scissors • Small Red Rod • Tape • Chart

PRESENTATION

1. Invite child 2. Child stands back against the wall and teacher marks the

paper to the top of their head 3. Child holds one end of string on floor and teacher cuts the

string at the mark on the wall 4. Child uses small Red Rod to measure length of string 5. Chart the length 6. Repeat lesson with as many students who show interest 7. Have children explain what they see on the chart

DIRECT AIMS

• Introduction to measurement

• Introduction to charts INDIRECT AIMS

• Making comparisons POINTS OF INTEREST

• Height on wall • Length of string • Using Red Rods in new

ways • Chart

CONTROL OF ERROR

• Teacher overview

VOCABULARY

• Height • Length • Chart

VARIATIONS

• Use different lengths of Red Rods

ADAPTATION

• For elementary age children, trace whole body on large paper and find height, width, perimeter, and are

HAWAII PRESCHOOL CONTENT STANDARDS Domain IV: Cognitive Development Mathematics

• Standard 4: Develop and use measurement concepts HAWAII CONTENT AND PERFORMANCE STANDARDS Standard 4: Measurement: FLUENCY WITH MEASUREMENT: Understand attributes, units, and systems of units in measurement; and develop and use techniques, tools, and formulas for measuring Topic Measurement Attributes and Units

Benchmark MA.K.4.1 Compare and order objects according to length, weight, capacity, area, and volume


The student: Compares objects, physically or virtually, to each other (e.g., places two objects side-by-side to determine which is longer; picks up two objects to determine which is heavier; fills a liquid from one container to another to determine which one has more capacity).

Rubric


Use and describe an appropriate method to compare and order objects according to length, weight, capacity, area, and volume, with accuracy

Compare and order objects according to length, weight, capacity, area, and volume, with no significant errors

Compare and order objects according to length, weight, capacity, area, and volume, with a few significant errors

Use an inappropriate method to compare and order objects according to length, weight, capacity, area, and volume

How many do you have?

Ages: 4-6 years Materials: Mat Folded numeral cards labeled 1-10 55 counters Container Presentation: 1. Invite the child 2. Lay out the mat 3. Place the container between the child and yourself 4. Teacher takes a folded numeral card, looks at it and hides it without showing anyone 5. Teacher gets the appropriate number of counters her folded numeral card says 6. Teacher asks the child if they would like to choose a number 7. Child picks a folded number card, looks at the

number and gets the number of counters needed.

8. Teacher counts the number of counters she has, modeling one to one correspondence, touching each apple as she counts.

9. Teacher states how many counters she had and shows the folded number card she has

10. The child completes steps 8 and 9 11. If child is still interested teacher and child

grab another number and repeat the same steps Direct Aim: Test for mastery of numeration to 10 One to one correspondence Indirect Aim: Preparation for higher math Develop visual memory Order Concentration Coordination Independence Points of Interest: The mystery Folded numeral cards Counters

Control of Error: Just enough counters (55) Vocabulary: mystery, folded, names of numerals Variations: Different types of counters Adaptation: Take two or more cards and add the numbers together if the child is beyond 10. Standards: HCPS III -Standard 1: Numbers and Operations: NUMBER SENSE: Understand numbers,

ways of representing numbers, relationships among numbers, and number

systems.

-Topic: Numbers and Number Systems

-Benchmark MA.K.1.2

-Rubric:


Represent whole

numbers up to 30 in

a variety of ways,

using different forms

of representation

Represent whole

numbers up to 30 in

a variety of ways,

with no significant

errors

Represent whole

numbers up to 30 in

one way, with no

significant errors

Represent whole

numbers up to 30 in

one way, with

significant errors

HPCS -Domain IV: COGNITIVE DEVELOPMENT MATHEMATICS

-Standard 1: Learn about number, numerical representation, and simple

numerical operations.

Lesson Plan

Numeration to Ten

Cards and Counters

Age: 3 to 4 years

Materials: Mat Cards with number and printed objects 55 counters Presentation: (Lesson)

1. Invite the child(ren). 2. Place container in upper left corner of mat. 3. Place the card in any order on the mat and match them with the number in

the story. 4. Read the numeric name and trace the symbol with two fingers and match it

with the counters. 5. Count each counters as you place them beside the card, from 1 to 10. 6. Say to the child that a counter without a pair is called an odd and if it has a

pair, it is called an even. 7. In every number emphasized if it is an odd or even, let the child repeat what

you said. 8. Return materials to container and return container to shelf. 9. Return the mat. 10. Tell the child to feel free to do the activity anytime she wants.


To provide practice in association of symbol and quantity.

To introduce the concept of odd and even.


Preparation for higher Math Develop visual memory

Preparation for language Preparation for science


Colorful counters Colorful story page


Exact amount of counters Number of pictures

Vocabulary:

Pounce, crawl, petals, slither, blossoms, nibble, odd and even

Extension:

Let the child(ren) group the objects and check the ones without a partner.

Adaptation:

Let the child explore and read the story as he wishes.

Put the counters and the cards beside the story book.

Standards: HPCS

Domain III- Communication, Language development and Literacy

Standard 3- Acquire increasingly rich vocabulary and sentence structure.

Domain IV- Cognitive development

Standard 1- Learn about number, numerical representation and simple numerical operations.


Benchmark MA.K.1.2 Represent whole numbers up to 30 in flexible ways (e.g., relating, composing, and decomposing numbers)



Rubric


Represent whole numbers up to 30 in a variety of ways, using different forms of




representation

Student’s Lesson Plan

LINEAR COUNTING (Hundred Board)

Age: 5 - 8 Materials: Laminated board with 10 rows of 10 Laminated numbers 1-100 Laminated board with numbers 1-100 Mat Presentation (Lesson): 1. Invite the child(ren). 2. Sort numbers by tens. 3. Arrange the number 1-10 in mixed array. 4. Starting in upper left hand corner and working left to right put the number in sequence 5. Arrange the number 11-20 in mixed array and so on. 6. Allow the child if she wants to help 7. Invite the child to continue the activity and finish it, give assistance if needed. 8. Return the materials on the shelf. Points of Interest (Motivation): Laminated board with numbers Filling in all the blanks, sorting Direct Aim (Objective): Test for ten boards (test knowledge of 1 - 100) Indirect Aims (Scaffolding): Practice in counting 1 - 100 Preparation for higher math Control of Error (Self Assessment): Visual - pattern of numbers Exact amount of laminated squares with numbers Laminated Control chart Vocabulary: Hundred, laminated numbers, tens, sort, numerals 1-100

Extensions: Skip count by 2’s, 5’s, and 10’s

Adaptation: if the child cannot do the activity, give assistance and more practice if needed. Hawaii Preschool Content Standards: Domain IV: Cognitive Development (Mathematics) Standard 1: Learn about number, numerical representation, and simple numerical operations. Hawaii Content and Performance Standards:





Rubric


Novice





Operations- Decimal Fractions-Money

Addition-Static-No Exchanging

Ages: 5 to 9 years Materials: Mat or table A ribbon Addition sign Box with problems Play money (bills and coins) Presentation:

1.Invite the children and bring materials to the mat or table.

2. Teacher explains that the fraction problem do not require exchanging, they have to choose only one.

3.Teacher takes coins that match the first addend and places them on the mat or table.

4.Students are asked to place the coins that match the second addend below the quantity placed on the mat by the teacher.

5.Teacher makes a review of the process while using language that describes what is being done, places the addition sign to the left of the second addend, and places a ribbon across the bottom of the coins.

6.Students write a problem in their journals. 7.Students are invited to bring coins below the line,

starting with the pennies, and to count the quantity. Students agree on the quantity and then record it in their journals.

8.Continue for dimes and dollars. 9.Teacher will make a review from the beginning and ask

one of the students to read the answer written in their journals. 10.Children return materials to the shelf.

Direct aim (Objective): to introduce the concept of addition of decimal fraction using money. Indirect Aim (scaffolding): Preparation for higher Math Independence Cooperation Points of Interest (Motivation): Coins, ribbon or yarn, addition sign, problem cards

Control of error (Self-assessment): Teacher or another student Control cards or charts Language: Decimal fraction, penny, dime, dollar, cents, tenths hundredths, whole, addition, plus, addend, and sum. Extension: Do the same lesson with problems that require exchanging. Adaptation: Give time and more practice to children who still get mixed up with coins and bills. Hawaii Preschool Content Standards: Domain IV: Cognitive Development (Mathematics) Standard 1: Learn about number, numerical representation, and simple numerical operations. Hawaii Content and Performance Standards: Topic Numbers and Number Systems

Benchmark MA.2.1.3

Represent fractions with denominators no larger than ten using pictures, numbers, words, or models


The student: Draws a picture or makes a model to show what a given fraction, such as 3/4, looks like.

Rubric


Novice

Represent fractions with denominators no larger than ten using pictures, numbers, words, or models, with accuracy

Represent fractions with denominators no larger than ten using pictures, numbers, words, or models, with no significant

Represent fractions with denominators no larger than ten using pictures, numbers, words, or models, with a few

Represent fractions with denominators no larger than ten using pictures, numbers, words, or models, with many

errors significant errors

significant errors

Fractions

Concept Development

Ages: 4 to 8 years Materials: A box of apple fractions (2 through 10) Fresh apple, knife, cutting board, and plastic gloves One golden bead A sphere of playdough or clay Paper and marker, mat Presentation 1 (Lesson 1):

- Invite the children - Ask if they have ever shared food with someone. Ask them to

talk about how they shared. - Show the fresh apple. Teacher will tell the children that

they can share the apple equally by cutting it. The teacher will say, “Now the apple is no longer whole because we have divided it into two equal parts. How many children could have a share?” (Wait for response). “Each child would get one-half of the apples.”

- Cut each half in half. “Now how many children can have a share?” (Wait for response) “Each child receives one-fourth of the apple.”

- Try to divide the pieces of apples into equal parts so there are enough parts for each child.

- Pass out the pieces of apples. -

Presentation 2 (Lesson 2): - Invite the children - Prepare a long floor mat and bring two trays of circles

insets to the mat. - Show children the golden one bead and explain that in order

to find numbers smaller than one we would have to divide this “one” into equal pieces. An easy way to do that is to flatten it into a circle.

- Take the sphere of playdough and flatten it into a circle. The teacher will say, “Now I can divide this circle into equal parts. Relate this circle to the whole apple picture.

- Trace the whole circle and cut it into two pieces that are not equal explaining that although there are two pieces because they are not equal, they are not halves. Teacher

will explain that when a whole divided into equal parts, each part is called a fraction.

- Relate fractions to everyday life, for example, time, recipes, food buying.

- Return materials to the shelf - Return the mat.

Presentation 3 (Lesson 3):

- Invite children. - Prepare a long floor mat and bring the box of apple

fractions - Show the whole apple picture and ask the children how many

apples in the picture. - Write “1” on a slip of paper. - Remind children that the whole can be divided into equal

parts, move on to picture apple divided into equal parts. Pick up the two parts and put them back to back to show how they are equal.

- “How many parts is this apple divided into?” (Write the line for division as you say the word “divided” and wait for response.)

- Write the “2” below the line indicating that “2” is the family name (ex.) “It is the part of their name that they all have in common.

- Remove one-half of the apple pictures and place it on the mat. Ask. “How many members of the family of “2” did I place on the mat?” Write “1” above the line and place the label on the fractional part on the mat.

- Teacher will ask, “How many members of the family of “2” remain on the mat?” Write “1” above the line and place the label on the fractional part still on the mat.

- Continue this procedure until all fractional parts are labeled.

- Show children the prepared slips that will be with the material for them to work with.

- Return materials to the shelf. - Return mat.

Presentation 4 (Lesson 4):

- Invite the children. - Prepare a long floor mat and bring the apple fractions to

the mat. - Take the apple fractions (halves) and ask the children,

“How many parts is this apple divided into?” (Write the line for division as you say the word “divided” and wait for a response.)

- Write “2” below the line and ask, “How many family members am I pointing to?” Write the “1” above the line.

- Provide the language for numerator and denominator indicating the number below the line is the name of the family and tells us how many parts of the apple is divided into. This number is called the denominator. The number above the line tells us how many of the family members we have to work with and that is called the numerator.

- Do a three period lesson to teach vocabulary. - Return materials to the shelf. - Return mat.

Direct Aim (Objective): To help children develop the concept of fractional parts and the numbering system that goes with them. Indirect Aim (Scaffolding): Preparation for higher math Preparation for science Preparation for art preparation for language Develop visual memory and internalization of sizes of fractional parts Points of interest (Motivation): Colors, new vocabulary, different sizes of fractional parts. Control of error (Self-Assessment): apple fractions, teacher Vocabulary: Fractions, fractional parts numerator, denominator, family, family members, whole, half, halves, thirds, fourths, fifths, sixths, sevenths, eights, ninths, tenths Extensions: Use other geometric shapes -Have children trace fractional parts into their math journals, color and label them. -Have children trace fractional parts onto construction paper, cut them out, glue them on large poster board, and label them for display. -Have children trace fractional parts onto construction paper, cut them out, glue them onto pages to make a booklet and label them. -Add derivations of words: Fraction is from the Latin “frangere” which means to break or to divide -Numerator has the same root as number -Denominator has the same root as denomination which is used for money and for delineation of groups like religions -Add history:

Romans wrote division as 8 fractus 4 and later modified it to 8 F4 -A further modification was 8/4 and today we write fractions the way we do. Adaptation: For children who cannot get the long process at once, the lesson maybe be repeated next time, and fewer children involved. Hawaii Preschool Content Standards: Domain IV: Cognitive Development (Mathematics) Standard 2: Recognize and create patterns and become aware of relationships. Hawaii Content and Performance Standards: Topic Numbers and Number Systems

Benchmark MA.1.1.2 Identify representations of simple fractions (e.g., one-half, one-third, one fourth)


The student: Names the fraction that matches a picture that represents the fraction.

Rubric


Novice

Consistently identify representations of simple fractions and provide representations of common fractions

Usually identify representations of simple fractions

Sometimes identify representations of simple fractions

Rarely identify representations of simple fractions

References

In C. Copple,& S. Bredekamp (Eds.),(2009). Developmentally

Appropriate Practice in Early Childhood Programs Serving

Children from Birth through Age 8: United States of America.

National Association for the Education of Young Children:

Lillard, A., (2007) Montessori: The Science Behind The Genius.

198 Madison Avenue, New York, New York 10016: Oxford University

Press, Inc.

Montessori, M., (1966) The Secret of Childhood. Random

House, Inc., New York/ Canada by Random House of Canada Limited,

Toronto: Fides Publishers, Inc.

Piaget J.,(2003) Piaget’s Cognitive Developmental Theory. In R.

Fabes and C. Martin (Eds.) Exploring Child Development (pp.35-

36) United States of America. Pearson Education, Inc.

www.joymontessori.net

Documents

Math Album-Sr Marjorie Garcia