visual learning tools - harding

Learning Module Activity Guide

Number Sense 2

Multiplication & DivisionCommon Factors

Fractions

Visual Learning Tools

3-6 MATH

Learning Module Activity Guide

Number Sense 2

Multiplication & DivisionCommon Factors

Fractions


3-6 MATH

Learning Activities developed by

Keys to Learning, LLC

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c o n t e n t s

Table of Contents

the Foundation of VariQuest Learning Modules . . . . . . . . . . . . . . . . . . . 4

overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Activity 1: Multiplication = Addition’s cousin . . . . . . . . . . . . . . . . . . . . . . 6

Activity 2: Multiplication Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Activity 3: Division = subtraction’s cousin . . . . . . . . . . . . . . . . . . . . . . . 10

Activity 4: Division Puzzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Activity 5: Factors BInGo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Activity 6: Passing Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Activity 7: Adding Fractions with Like Denominators . . . . . . . . . . . . . . 18

Activity 8: Mixed numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Activity 9: subtracting Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Activity 10: Fractions and Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Additional Activity Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Rubric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

content List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Work order template . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4

The FOUNdATION OF VArIQUeST LeArNINg MOdULeS

VariQuest supports educators by providing countless opportunities to introduce a variety

of visuals and hands-on manipulatives into their classrooms. The use of visuals in the

classroom helps students understand and retain information, specifically abstract concepts.

Visuals can also help bridge the gap for students who struggle with vocabulary and/or language

barriers. hands-on manipulatives create learning experiences in which students interact with

knowledge kinesthetically. research shows that exposing students to a variety of learning

experiences, including visual and kinesthetic, will increase student retention and help students

learn to construct meaningful knowledge from information. The VariQuest Visual Learning Tools

enhance classroom teachers’ ability to provide learning experiences that meet the learning styles

of all students.

The aim of the following Learning Activities is to coordinate the VariQuest Visual Learning Tools

with lessons and activities that incorporate visual and hands-on learning strategies to reinforce

basic skills and provide fun and motivational activities that will supplement your school’s

curriculum. For best practices and additional information on how to customize VariQuest posters,

banners, flashcards, awards, cutouts and manipulatives, review the VariQuest Implementation

guide prior to use.

For the following learning activities, use construction paper for all cutouts unless otherwise

specified. Pre-laminating construction paper using a cold laminator adds durability to cut out

letters, shapes, numbers and collections.

5

NUMBer SeNSe 2 OVerVIeW

Students in the intermediate grades are ready for more challenging math: multiplication and

division, including how those operations relate to each other and to what they already know about

addition and subtraction; factors and common factors; fractions and operations with fractions;

and decimals. It is important for students to understand the concepts behind the equations,

and so each activity is introduced with plenty of hands-on practice. The learning activities in this

VariQuest Learning Module are designed to meet educational standards in innovative and creative

ways. Before turning to the learning activities, familiarize yourself with general information that will

guarantee ease of use and flexibility.

ASSeSSMeNTFollowing the learning activities, you will find a rubric that can be used to guide you in making

observational assessments of students’ abilities related to the objectives outlined in the learning

activities. It is recommended that you make a copy for each student to guide your ongoing

informal assessments, making anecdotal notes on the back when appropriate.

VArIQUeST CONTeNTYou will find a complete list of all of the content included in this module between the rubric

and Work Order template. The content Id #s (ex. VIS001) for content referenced in the learning

activities are listed in the materials section for each activity and are color-coded to help distinguish

between templates for the Poster Maker (red) and Awards Maker (purple) and cutouts and

collections for the Cutout Maker (gold).

WOrK OrderSYou will also find a work order template on the last page of the Activity guide. This template

can be photocopied and used for placing orders for customized VariQuest posters, banners,

stickers, awards, cutouts and collections. It is designed to be submitted to the primary user of the

VariQuest Visual Learning Tools by those who may not have direct access to them.

A c t I V I t y o n e

6

ACTIVITY ONe

Multiplication = Addition’s Cousinobjectives Students will understand the concept of multiplication.

Students will understand multiplication as repeated addition.

Students will multiply whole numbers quickly and from memory.

Materials

Preparation Print and display Multiplication Table poster.

edit bottom text box of Math Stars poster to read “For excellence in

Multiplication.” Print and display.

Cut out Window Boards 2, custom-sized to 8”, one

for each student. Attach the window board cut out

to a piece of 8 1/2” x 11” cardstock using tape or

glue around the border of the board only so that the

windows can be opened and closed.

Cut out one (1) Multiplication symbol on magnet

material.

Cut out one (1) equal to, and six (6) Addition symbols from your font

collection on magnet material.

Cut out five (5) sets of numerals 0 through 9 on magnet material.

POSTer MAKer:

Multiplication Table: VIS067

Math Stars: RCG055

CUTOUT MAKer:

Multiplication Symbol: MTH287

Font Symbol Addition: +

Font Symbol equal to: =

Window Boards 2: MTH115 (Basic)

Font Numerals: 0 – 9

OTher:

8 ½” x 11” cardstock

Pencils

Math manipulatives (optional)

Multiplication Table VIS067

Math Stars RCG055

Multiplication Symbol

MTH287

Font Symbol Addition

+

Font Symbol equal to

=

Window Boards 2 MTH115

Font Numerals 0 – 9

Whole class

remind students that multiplication is a shortcut for addition when you

need to add the same number several times. Using the magnetic numbers

and symbols, show the equation 4+4+4+4=16. Ask a volunteer to use the

magnetic numbers and symbols to show the problem as multiplication.

repeat, having student volunteers show other examples of multiplication

as repeated addition using magnet numbers and symbols. have students

check their work using the Multiplication Table.

As students show each equation correctly, add their names to the Math

Stars Poster.

Individual distribute Window Boards to students and have them pick 9 multiplica-

tion facts that they feel they need extra practice with. have students label

the top of their window board, then write one fact (ex. 6x7) on the front of

each window and the product (ex. 42) on the page beneath the window.

have them use these to practice their multiplication facts. Make additional

Window Boards available to students that would like to make them for

more than nine multiplication facts.

7

MuLtIPLIcAtIon = ADDItIon’s cousIn

MoDIFIcAtIon

Select multiplication facts for the

number 1 (ex. 1x1, 1x2, 1x3, 1x4, 1x5,

1x6, 1x7, 1x8, 1x9) and write them

on the front of each window. have

students write the product inside, then

use the window board to study these

facts. repeat for numbers 2-9.

extensIon

Use the Multiplication Maze poster:

VIS146 to create a game. edit the

poster by adding numbers in the

boxes to make the correct paths for

multiples of 3, 4, 5, and 6 (or larger

numbers, depending on students’

prior knowledge). Fill out the rest

of the maze with other numbers.

have students draw lines to follow

the paths of multiples using different

colored markers.

8

A c t I V I t y t W o

ACTIVITY TWO

Multiplication Patterns objectives Students will recall multiplication facts from memory.

Students will understand effects of reversing the order of numbers

multiplied.

Students will recognize the commutative property of multiplication.

Materials

POSTer MAKer:

Multiplication Chart: ORG045


game Board Multiplication: VIS201

OTher:

Pencils

Math manipulatives

Preparation Make 8 ½” x 11” copies of Multiplication Chart, one for each student.

Print and display Multiplication Table poster.

Print and display game Board Multiplication poster.

Whole class

A good way to help students remember their multiplication facts is to show

them the commutative property of multiplication; when two numbers are

multiplied together the product is the same, no matter the order of the

numbers. As students learn this property, it helps them memorize the facts.

Begin with the Multiplication Table poster. Point out that they can arrive at

the same product (answer) by starting with either number in the problem.

Ask for a volunteer to come to the poster and find the product of 4 x 5,

8

Multiplication Chart ORG045


game Board Multiplication

VIS201

9

MuLtIPLIcAtIon PAtteRns

using the 4 from the top row and the 5 from the left-hand column (20).

Then ask the same volunteer to find the product of 5 x 4 (20). Ask another

volunteer to come to the poster and find the product of 6 x 3 (18). Then

ask the same volunteer to find the product of 3 x 6 (18). (If your students

are more advanced, use bigger numbers; if they are less advanced, use

smaller numbers.) repeat until students see the pattern.

go to the game Board and show students how, when the numbers are

organized differently, (the column starts with the largest numbers at the

top instead of the bottom), that the principle still holds: when you multiply

two numbers together, the order does not matter and the product will be

the same.

PartnersPair up students and give them each copies of the Multiplication Chart.

Ask one member of each pair to write down these problems in the proper

columns on the Multiplication Chart and use either the game Board or the

Multiplication Table to solve them.

2 x 7, 3 x 7, 4 x 7, 5 x 7, 6 x 7, 7 x 7, 8 x 7, 9 x 7, 10 x 7

give the same directions to the other member of each pair, but challenge

them with these problems.

7 x 10, 7 x 9, 7 x 8, 7 x 7, 7 x 6, 7 x 5, 7 x 4, 7 x 3, 7 x 2

have students compare answers. If students arrived at different answers

ask them to explain how they found their answer. Make sure all students

understand how to use the game Board and the Multiplication Table to

arrive at the correct answers.

repeat as necessary with other multiplication facts until students

demonstrate a clear understanding of the commutative property. Then,

have students work together to write their own definition of the commutative

property of multiplication on the back of their Multiplication Chart.

MoDIFIcAtIon

Students use only the Multiplication

Table to solve the problems.

extensIon

give students a blank Multiplication

Table and have them fill it in for the

numbers 11-20. remind them to use

repeated addition, and to look for

patterns as they multiply the numbers

from the top row with the numbers in

the first column. Tell them that they

do not have to fill out the entire table;

once they have filled out half, look for

the products for the other half.

9

10

A c t I V I t y t h R e e

ACTIVITY Three

Division = Subtraction’s Cousin objectives Students will understand the concept of division.

Students will understand division as repeated subtraction.

Materials:

POSTer MAKer:

Math Stars Poster: RCG055

CUTOUT MAKer:

division Symbol: MTH288

Font Symbol Subtraction: -



OTher:

Math manipulatives

Pencils

Index cards

Preparation Cut out one (1) division symbol on magnet material.

Cut out one (1) equal to, and six (6) Subtraction symbols from your font


Cut out six (6) sets of numerals 0-9 on magnet material.

edit bottom text box of Math Stars poster to read “For excellence in

division.” Print and display.

Math Stars Poster RCG055

division Symbol MTH288

Font Symbol Subtraction

-


=


11

DIVIsIon = suBtRAct I o n ’ s c o u s I n

Whole class demonstrate to students how division is repeated subtraction, using

manipulatives or common classroom objects, like pencils. Begin with six

pencils. Say, “If I want to divide 6 into three equal parts, I would subtract two

pencils at a time, and I would then have three equal groups of two. Another

way to say that is to say 6 divided by 3 equals 2.”

Using the magnetic numbers and the subtraction symbol, show 6 – 2 – 2 –

2 = 0. Then show the equation 6 ÷ 3 = 2.

Ask for a student volunteer to show how to divide 8 into four equal parts,

using pencils (or other manipulatives). help the student subtract four groups

of two pencils from the 8. Ask the volunteer to show the problem with the

solution as subtraction and then again as division.

Ask for more volunteers to show the division problems: 10÷5, 12÷3,

14÷2 as repeated subtraction. have them use the magnetic numbers and

symbols, then explain what they did.

Write each volunteer’s name on the Math Stars Poster.

PartnersWrite these instructions on the chalkboard:

Make 21 into 7 groups




In pairs, challenge students to write on index cards (without using

manipulatives) the repeated subtraction on one side and the division

equation on the other side. Students should compare index cards to

check for accuracy.

MoDIFIcAtIon

have students continue using

manipulatives to practice division.

Challenge them to make equal groups

out of 12, 14, 16, 18, and 20. have

them write their solutions as repeated

subtraction and as division equations

on index cards.

extensIon

Challenge students to use the

problems from the partners activity and

find other ways to divide 21, 18, 20,

and 30 into groups, in addition to the

ones you’ve listed on the chalkboard.

For example, 21 can be 7 groups

of 3 or 3 groups of 7; 18 can be 3

groups of 6 or 9 groups of 2, etc. Then

challenge them to write their own

problems and exchange them with

their fellow students.

12

A c t I V I t y F o u R

ACTIVITY FOUr

Division Puzzles objectives Students will understand division is the opposite of multiplication.

Students will recall division facts from memory.

Students will understand the effects of reversing the order of things

divided.

MaterialsPOSTer MAKer:


CUTOUT MAKer:

2 Piece Puzzle: PUZ068 (Basic)

OTher:

Pencils

envelopes (one for each small group of students)


Cut out 2 Piece Puzzle custom-sized to 8” on cardstock. Make enough

so that each student has four sets of puzzle pieces.

Whole classUsing the Multiplication Table poster, model for students how to think

about division problems by beginning with the numbers on the inside of the

table. Say, “I’m going to show you how to use this table to help you with

basic division facts.” Point to the number 15. Say, “how can I find out how

to divide the number 15 using this table? Let’s see, if I move my finger up

from 15 I get to 5. If I move my finger to the side from 15, I get to 3. What

does that tell me?”


2 Piece Puzzle PUZ068

13

DIVIs Ion PuzzLes

Write the numbers 3, 5, and 15 on the chalkboard. Write the two

equations, 15÷3 = 5 and 15÷5 = 3. Say, “It tells me that the same

numbers I use to multiply to get 15, I can use to divide 15. 15 divided by

3 equals 5 and 15 divided by 5 equals 3.” Point out on the Multiplication

Table poster that 5 times 3 equals 15 and 3 times 5 equals 15. Tell

students, “The numbers that I multiply together to get 15 are the same

numbers I can use to divide 15 into equal groups.”

Ask for volunteers to find the numbers 20, 28, and 40 on the Multiplication

Table poster (or larger or smaller numbers, depending on your students).

Challenge them to show at least two different ways to divide those numbers

and what numbers they would use to multiply to get those numbers. Invite

students to write their equations on the chalkboard and to explain their

thinking. encourage students to use all combinations of numbers they can

think of or find on the table.

cooperative Groupsdivide students into small groups and put four sets of puzzle pieces for

each student on each of the groups’ tables. Challenge students to select

a number from the inside of the Multiplication Table, then write one way to

show a division problem on one of the puzzle pieces, (e.g. 24÷4 = 6) and

another way to show that same division problem on the other puzzle piece

(e.g. 24÷6 = 4).

Check their work to make sure they have done it correctly before they put

their puzzle pieces inside the envelope. Then invite all the students to place

their individual puzzle pieces in the envelope.

Swap envelopes so that each small group has an envelope full of puzzle

pieces they did not create. Challenge students in each group to pick a

puzzle piece and then talk to the other students in their group until they

find their matching puzzle piece. have students connect matching pieces,

working together to find all of the matching division problems.

MoDIFIcAtIon

give students 8 ½” x 11” copies

of division Chart: Org046 and

Multiplication Table: VIS067. Challenge

students to use the Multiplication Table

to record division equations on the

division Chart.

extensIon

give students an 8 ½” x 11” copy

of Prime Numbers: VIS071 and

Multiplication Table: VIS067. Challenge

students to find the numbers in the first

row of the Prime Numbers chart on the

Multiplication Table. Can the numbers

be found anywhere other than the top

row or the first column?

Ask students to try and figure out how

to get these numbers by multiplying.

hopefully it will generate discussion,

and students will understand that the

only way to get to prime numbers by

multiplying is to multiply the number

itself x 1.

14

A c t I V I t y F I V e

ACTIVITY FIVe

Factors BINGOobjectives Students will understand and apply the basic number theory concept

of factors.

Materials


Cut out Square Bingo Card on cardstock, custom-sized to largest

possible on page, one for each student.

Print and display Common Factors poster. Make 8 ½” x 11”copies, two

for each student.

PARt 1Whole class

On the chalkboard write the word factors. define the word for students:

factors are numbers that are multiplied together to make up other

numbers. For example, the number 12 has six factors using multiplication:

1, 2, 3, 4, 6, and 12. Show students why these numbers are factors:

1 x 12 = 12; 2 x 6 = 12; 3 x 4 = 12. The number 12 also has the same six

factors using division: 12÷1 = 12; 12÷2 = 6; 12÷3 = 4; 12÷4 = 3;

12÷6 = 2.

Ask for volunteers to come to the chalkboard and show the factors of six and

explain their thinking (6, 1, 2, 3). have a few volunteers practice this until you

POSTer MAKer:

Common Factors: ORG066


CUTOUT MAKer:

Square Bingo Card: MTH119 (Basic)

OTher:

Pencils

Markers in different colors

Common Factors ORG066


Square Bingo Card MTH119

15

feel comfortable that students understand what factors are. remind students

to use the Multiplication Table poster if they need it.

Partnersgive each student a Bingo card and have them fill in

the numbers 1-25 on the spaces of the Bingo card,

starting with the number 1 in the top, left square.

explain that they will be playing the Factor game

with their partner.

how the game is played:

The first player chooses a number on the card and circles it in red. The

second player circles in blue all the factors of that number. Then the

second player chooses a number and circles it in blue and the first player

circles all the factors of that number in red. Students keep playing until

there are no numbers remaining with uncircled factors. each person then

adds up the numbers they’ve circled and the winner is the person with the

most numbers circled.

have students play one round, then ask if any students could think of

strategies after playing once. have students play again using the other

Bingo card.

PARt 2Whole classreview common factors: numbers that will divide evenly into two different

numbers.

distribute two Common Factor sheets to each student and have them fill

one in as you work through an example using 18 and 36. As you work

through the example, call on students to

help you fill in the factors for each number

separately, then use those factors to

complete the Venn diagram to show the

common factors for 18 and 36.

Partnershave students work in partners to find the common factors of 25 and 50.

FActoRs BInGo

MoDIFIcAtIon

Use smaller numbers with these

students, and only numbers that can

be found on the Multiplication Table.

extensIon

Print 8 1/2” x 11” copies of Numbers

1 to 100 Chart: VIS070 (Basic). give

copies to students to play the Factor

game with numbers 1-100.

16

A c t I V I t y s I x

ACTIVITY SIX

Passing Fractions objectives Students will understand the concept of fractions.

Students will understand the equivalence among fractions.

Materials

Preparation Print and display Fraction Strips poster.

Make 8 1/2” x 11” copies, one for each

student. Laminate and cut into strips.

Set aside strips for 1/9, 1/10 and 1/12.

Place the strips for 1, 1/2, 1/3, 1/4, 1/5,

1/6 and 1/8 in an envelope. Tip: Make

copies on four or six different colors of paper (depending on the number

of small groups) to help students keep track of the strips during the game.

Cut the following Circle Fraction pieces out of cardstock. Tip: Use a

different color paper for each fraction to help students differentiate

between the pieces. Cut one set for each student and place into

envelopes.

eight (8) whole pieces: custom-sized to 8”

two (2) 1/2 pieces: custom-sized to 4”

three (3) 1/3 pieces: custom-sized to 6”

four (4) 1/4 pieces: custom-sized to 4”

five (5) 1/5 pieces: custom-sized to 4”

six (6) 1/6 pieces: custom-sized to 4”

eight (8) 1/8 pieces: custom-sized to 4”

POSTer MAKer:

Fraction Strips: VIS200

CUTOUT MAKer:

Circle Fraction Whole: MTH144

1/2 Circle Fraction Piece: MTH147






OTher:

Paper

Pencils

envelopes

Fraction Strips VIS200

Circle Fraction Whole

MTH144

1/2 Circle Fraction Piece

MTH147


MTH149


MTH151


MTH153


MTH155


MTH157

17

PA s s I n G F R A c t I o n s

MoDIFIcAtIon

Cut out Triangle Fraction Pieces ½:

MTh116, 1/3: MTh117, ¼: MTh118,

1/6: MTh129, and 1/8: MTh130

in different colors. give them to

students and help them determine

the appropriate denominator based

on the number of pieces, label each

piece and put them together to form

one whole.

extensIon

Use all the Fraction Strips for

these students (ninths, tenths, and

twelfths). Challenge them to create a

new game with new rules using all the

fraction strips.

Whole class

review students’ knowledge of fractions by giving them each a set of

fraction shapes and time to explore the cutouts. have students write the

fraction (numerator and denominator) on each piece.

Invite them to put the pieces together in different ways, (e.g. how many

ways can they make a whole? how many ways can they make a fourth?

how many ways can they make a half?). encourage them to use as many

pieces as they can.

give students a sheet of paper and challenge them to draw each fraction

and write the name of each part – one whole, one half, one third, one

fourth, etc. in size order. Ask, “Which fractions are largest? Which are

smallest?” Then challenge them to write the fractions with the numerator

and denominator: 1/2, 1/3, 1/4, 1/5, 1/6, 1/8 on each piece. Ask, “Why

are the smallest-looking fractions the ones with the largest denominator?”

cooperative Groupsdivide students into groups with an even number of students (four or six)

and give every student a set of fraction strips. explain that the goal of

the game is to get rid of as many of the fraction strips as possible. (Note:

results are not dependent on what students receive, the only thing that

counts is what they give away.) Advise students to use what they know

about equivalent fractions and have Fraction Strips poster visible for

reference.

Tell students that they are responsible for checking the fraction pieces that

they receive. Then, read aloud the following instructions:

1. Pass one half to the person on their right. The half can be any

combination of fractions that equals one half (1/2, 2/4, 3/6, 4/8).

2. Pass two thirds to the person on their left. Again, any combination of

fractions that equals two thirds (2/3, 4/6) is acceptable.

3. Pass four fifths (4/5) to the person sitting across from them.

4. Pass three fourths to the person on their right (3/4 or 6/8).

5. Pass two eighths to the person on their left (1/4 or 2/8).

6. Finally, pass one fifth (1/5) to the person across the table.

At this point, have students count the remaining number of strips and the

person with the fewest left is the winner.

18

A c t I V I t y s e V e n

ACTIVITY SeVeN

Adding Fractions with Like Denominatorsobjectives Students will understand the concept of adding fractions.

Students will be able to add fractions with like denominators.

Materials

Preparation Cut the following Circle Fraction Pieces out of magnet. Tip: Use a

different color magnet for each fraction to help students differentiate

between the pieces.

one (1) whole piece: custom-sized to 8”

four (4) 1/2 pieces: custom-sized to 4”

six (6) 1/3 pieces: custom-sized to 6”

eight (8) 1/4 pieces: custom-sized to 4”

ten (10) 1/5 pieces: custom-sized to 4”

twelve (12) 1/6 pieces: custom-sized to 4”

sixteen (16) 1/8 pieces: custom-sized to 4”

Cut out two (2) equal to and two (2) Addition symbols from your font


POSTer MAKer:


CUTOUT MAKer:












OTher:

Paper

Pencils

envelopes



+


=




MTH144


MTH147


MTH149


MTH151


MTH153


MTH155


MTH157

19

A D D I n G F R A c t I o n s

MoDIFIcAtIon

Students continue to use the

manipulatives to add fractions with like

denominators.

extensIon

Challenge students to use the

Fraction Strips to add fractions with

different denominators. To do this

they must find ways to convert the

different denominators to common

denominators. remind them about the

activity on common factors.

Cut out two (2) division Symbols on magnet material. Set aside the circle

pieces from the division Symbol and use the line as a fraction bar.

Cut out Font Numerals 0-9 out of magnet material, four (4) of each

numeral.

NOTe: If you completed Activity Six, use the fraction strips and

circle fraction pieces created during that activity. If not, complete the

Preparation steps from Activity Six for this activity as well.

Whole classreview when fractions are used and the terms numerator and denominator.

Say, “We will be concentrating today on adding fractions with the same

denominator.”

Say, “I am very hungry so I eat 1/3 of a pizza, followed by another 1/3

of a pizza. how much of the whole pizza have I eaten?” Show the pizza

addition problem using magnetic circle fraction pieces and symbols. Below

the circle fraction pieces, show how to write the equation using numerals

and symbols.

Ask, “So when we add these fractions, what do we do to the denominator?”

(We keep it.) “What do we do to the numerators?” (We add them.)

give each student a set of Circle Fraction Pieces cut out of cardstock and

have them practice showing the following equations with the cutout pieces:

I have one fourth of a banana and a friend gives me two fourths of a

banana. how many fourths of a banana do I have? (3/4)

My mother eats a half of my apple and I eat the other half. how many

halves have we eaten? (2/2 = 1 whole)

have volunteers come to the board to show the addition problems in two

ways: using magnetic fraction pieces and numerals and symbols. repeat

with fractions that have 3, 5, 6 and 8 as the denominator.

Partnersgive each student an envelope with

the Fraction Strips inside and five

index cards. Challenge partners

to write addition problems using

fractions with like denominators on

the front of the card and the answer

on the back. have them use their

Fraction Strips to help them write and

answer the problems.

Once both students have written

problems with answers on five

cards, have them exchange cards

and answer the problems on their

partner’s cards without looking at the

answer. When both partners have

answered all five problems, they can

flip them over to check the answer.

20

A c t I V I t y e I G h t

ACTIVITY eIghT

Mixed Numbers objectives Students will understand the concept of mixed numbers.

Students will understand the relationships among whole numbers,

fractions, and mixed numbers.

Materials

Preparation Cut the following Square Fraction Pieces out of magnet material,

custom-sized to 8”.

three (3) Whole pieces

six (6) 1/2 pieces

nine (9) 1/3 pieces

twelve (12) 1/4 pieces

twenty-four (24) 1/6 pieces

Cut out a set of Square Fractions: Whole,1/2, 1/3, 1/4, 1/6, custom-

sized to 6”. Make enough for each student to have one set, place in

envelope. Tip: Use a different color paper for each fraction to help

students differentiate between the pieces.

NOTe: If you completed Activity Seven, use the symbol and numeral

CUTOUT MAKer:

1/2 Square Fraction Piece: MTH165




Square Fraction Whole: MTH162

1/2 Square Fraction: MTH164








OTher:

Stapler (one for each pair)

Pencils

Tape or glue

envelopes

Markers

1/2 Square Fraction Piece

MTH165


MTH167


MTH169


MTH173

Square Fraction Whole

MTH162

1/2 Square Fraction MTH164






+


=

21

M I x e D n u M B e R s

MoDIFIcAtIon

give students pre-labeled Square

Fractions for one whole, 1/2, 1/3, 1/4,

and 1/6. have students use these

pieces to show the mixed numbers.

extensIon

have students add together the

fraction pieces that they have left

over after making the mixed numbers

from the whole class activity. They will

need to convert them all to a common

denominator (24) to add them

together. have them write the number

as a mixed number and an improper

fraction (4 1/2 and 9/2).

magnet cutout pieces created during that activity. If not, complete the

Preparation steps from Activity Seven to create magnetic symbols

and numerals.

Whole classPose this problem to students: You and your friends have just bought two

bananas. You have cut each banana in half. Then another friend joins you

and brings another half banana. how many halves do you have?

Show this problem on a magnetic board using Square Fraction Pieces and

symbols. remind them that when adding fractions with like denominators,

the denominator remains the same and they add the numerators.

Ask for a volunteer to come up to the board and, using the magnet

numbers, show the correct number of halves. explain to students that

5/2 is called an improper fraction. Improper

fractions are fractions that have a larger

numerator than denominator.

Improper fractions can be changed to mixed numbers. Mixed numbers are

whole integers plus a fraction. Ask for a volunteer to come to the board and

use numerals and symbols to show 5/2 as a mixed number (2 1/2). repeat

using other problems and Square Fraction Pieces for 1/3, 1/4 and 1/6.

Partnersdivide students into pairs and give each student

a set of square fraction cutouts. Ask them to

discuss among themselves how to label the

pieces, then, label them.

Once all of the pieces are labeled, have partners pool their fraction pieces

and make the following mixed numbers by stapling the pieces to the whole:

1 1/2, 1 2/3, 1 3/4, 1 1/6, 1 1/4, 1 5/6, 2 1/3.

Note: For the fraction 2 1/3 students will have to

figure out how to make the second whole using

leftover fraction pieces.

have students write the name of the fraction as a mixed number and an

improper fraction on the back of the whole piece.


22

A c t I V I t y n I n e

ACTIVITY NINe

Subtracting Fractions objectives Students will understand the concept of subtraction of fractions.

Students will be able to subtract simple fractions.

Materials

Preparation Cut out Square Fractions: 1/2, 1/3, 1/4 and 1/5 on cardstock, custom-

sized to 6”, enough for each student to have one set. Place in an

envelope. Tip: Use a different color paper for each fraction to help

students differentiate between the pieces.

NOTe: If you completed Activity Six or Seven, use the fraction strips

created during that activity. If not, follow the preparation steps in

Activity Six to create a Fraction Strips poster and set of fraction strips

for each student.

Whole classUsing the Fraction Strips poster, present a fraction subtraction problem to

students. Point to the row with 3/3. remind students that 3/3 is the same

amount as 1 whole. Say, “how many thirds do I have left when I subtract

2/3 from 3/3?” (1/3). Show students the correct answer by covering up

two of the three thirds.

Invite volunteers to come to the poster and pose additional subtraction

problems to the class. Ask all volunteers to show the correct answer on

the poster and to explain their thinking. Write the equation with the correct

answer on the board.

POSTer MAKer:


CUTOUT MAKer:





OTher:

envelopes, one for each student






23

suBtRActInG FRActIons

MoDIFIcAtIon

When students play the Individual

game, make sure they have an

8 ½” x 11” sheet of the fraction strips

in front of them to help them figure out

the answers.

extensIon

Students continue playing the

Individual Subtraction game, using

Square Fraction cutouts for 1/8:

MTh174, 1/10: MTh176, and 1/12:

MTh178 mixing up the denominators

(e.g. 4/8 – 1/4 = 2/8 or 1/4).

Partnersdivide students into pairs and give each student a set of Square Fraction

cutouts. Instruct students to place their Square Fraction pieces on the

matching Square Fraction whole squares (e.g. the two 1/2 Square Fraction

pieces sit on the 1/2 Square Fraction). Tell students they are going to play

a game.


Call out a subtraction problem (e.g. 5/5 – 2/5). Students must remove the

correct number of Square Fraction pieces from the Fraction Square and

figure out how many are left to arrive at the correct

answer. The student who is the first to say the correct

number of Square Fraction pieces left wins one point.

If a student calls out a wrong answer he loses a point.

Partners keep track of each other’s scores. The student

in each pair with the most points wins the game.

You continue calling out subtraction problems such as:

Individualgive each student an envelope with a full set of fraction strips.


You call out the subtraction problems and the student who has the answer

first raises their hand and says the answer. If that student is correct he or

she gets a point. If that student gets it wrong, he or she loses a point. If the

student is able to give the answer in the lowest common denominator, that

student gets two points. The student with the most points at the end of the

game wins. Keep track of students’ names and points on the chalkboard.

The following are some sample subtraction problems:

2/2 – 1/2

5/5 – 3/5

4/4 – 1/4

3/3 – 2/3

1 – 2/6 = 4/6 (or 2/3)

2/3 - 1/3 = 1/3

1 – 1/3 = 2/3

4/8 – 2/8 = 2/8 or 1/4

5/5 – 4/5 = 1/5

3/5 – 3/5 = 0

3/6 – 2/6 = 1/6

3/4 – 1/4 = 2/4 or 1/2

1 – 1/2 = 1/2

24

A c t I V I t y t e n

ACTIVITY TeN

Fractions and Decimalsobjectives Students will understand the concept of decimals.

Students will understand the equivalence and magnitude of fractions

and decimals.

Materials

Preparation Print and display Place Value poster.

Print 8 ½” x 11” copies of Fraction Strips, one for each pair of students.

Cut out ten 1/10 Circle Fraction Pieces, custom-sized to 4”, on magnet

material.

Cut out one Circle Fraction Whole, custom-sized to 8”, on magnet

material.

POSTer MAKer:

Fractions Strips: VIS200

Place Value: ORG049

AWArdS MAKer:

Fraction Whole Sticker: STK329

Fraction 1/2 Sticker: STK330









decimal .1 Sticker: STK368











decimal 1.0 Sticker: STK379

CUTOUT MAKer:



OTher:

Paper

Pencil

Fractions Strips

VIS200

Place Value ORG049

Fraction Whole Sticker

STK329

Fraction 1/2 Sticker STK330








Fraction 1/12 Sticker

STK342

decimal .1 Sticker

STK368

decimal .2 Sticker

STK369

decimal .25 Sticker STK370




25

FRActIons AnD DecIMALs

MoDIFIcAtIon

Show students the value of decimals

using a dollar bill, dimes, quarters, and

pennies.

extensIon

give students an 8 ½” x 11” copy of

Number Place Value: VIS069 (Basic),

plus paper and pencil and challenge

them to write, in words, the value of

each of the numbers to the right of the

decimal point (eight tenths, eighty-

nine hundredths, eight-hundred ninety

thousandths, and eight-thousand nine-

hundred one ten thousandths).

Print three copies of each of the

following Fraction and decimal stickers:

whole, 1/2, 1/4, 1/10, 1/3, 1/5, 1/6,

1/8, 1/9, 1/12, and .1, .25, .3, .4, .5, .6,

.7, .75, .8, .9, 1.0; attach cardstock to

create a deck of cards. Make enough for

one deck for every pair of students.

Whole classAsk students, “What is a fraction?” discuss how fractions are parts of a

whole; they are less than a whole.

explain to students that there is another way to talk about numbers that

are less then a whole. They are called decimals. On the magnet board,

place the Circle Fraction Whole. Show students the ten 1/10 Circle

Fraction Pieces in your hands. One by one add the 1/10 Circle Fraction

Pieces on top of the Circle Fraction Whole, counting up by tenths as you

add each piece, “one tenth, two tenths, etc.”

Point out the Place Value poster. With your hand, cover up the numbers

to the right of the decimal point and read the number. Then point to and

name the decimal point. explain that numbers to the right of the decimal

point are less than a whole. The first column to the right shows the

number of tenths, just like the 10 pieces of the circle we just counted.

The second column is for hundredths, then thousandths, then ten

thousandths. The further to the right you go, the smaller the numbers are.

Partnershow the game is played:

Play this card game the way you play the game War. each pair has a

full set of flashcards and a Fraction Strips Sheet. One student shuffles

the deck and deals out an equal number of cards, face down, to each

student. Players remove the top card from their deck and place it face up

on the table. Whoever has the biggest number wins those two cards. The

winner of that round must explain why their card was the bigger one.

If both players put down cards of the same value, “War” is declared. Both

players place three cards face down, turn the fourth one face up, and

compare values. Whoever has the larger number keeps all the cards

after explaining why their number is bigger.


decimal .7 Sticker

STK375

decimal .75 Sticker

STK376



decimal 1.0 Sticker STK379


MTH159


MTH144

26

ADDIt IonAL ActIV It Ies

ADDITIONAL ACTIVITIES

WOrd PrOBLeMSWith all of these operations, students need to learn how to use them when situations are

presented as word problems. Use the Word Problems poster: Org050 (Basic) to give students

strategies for breaking down the word problems into math problems they can solve.

eQUATION MANIPULATIVeSPlay games with the fraction pieces that help students understand problems like: Is 2/6 greater

than or less than 2/8? Use the Less Than Symbol: MTh290, greater Than Symbol: MTh291 or

equal to Symbol from your font collection to complete the equations.

FrACTION FLAShCArdSCreate flashcards using the fraction stickers: Fraction 1/2 Sticker: STK330, Fraction 1/3 Sticker:

STK332, Fraction 1/4 Sticker: STK334, Fraction 1/5 Sticker: STK336, Fraction 1/6 Sticker:

STK338, Fraction 1/8 Sticker: STK340, Fraction 1/9 Sticker: STK380, Fraction 1/10 Sticker:

STK341, Fraction 1/12 Sticker: STK342. have students write equivalent fractions or decimals on

the back of each flashcard.

IMPrOPer FrACTION ANd MIXed NUMBer PUzzLeSPair up students and give them each sets of 2 Piece Puzzle: PUz068 (Basic). Ask them to work

together to write the mixed number on one of the puzzle pieces and the matching improper

fraction on the other puzzle piece. Make sure they are doing it correctly. have them put their

puzzle pieces in an envelope. Collect the envelopes and give them out randomly to the other pairs

so that no pairs end up with their own envelopes. Challenge students to match up the puzzle

pieces correctly. Check their work.

26

27

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R u B R I c

28

NUMBer SeNSe 2 CONTeNT LIST

c o n t e n t L I s t

Poster Maker ID name ActivitiesOrg045 Multiplication Chart 2

Org046 division Chart 4

Org049 Place Value 10

Org066 Common Factors 5

rCg055 Math Stars 1, 3

VIS067 Multiplication Table 1, 2, 4, 5

VIS071 Prime Numbers 4

VIS146 Multiplication Maze 1

VIS200 Fraction Strips 6, 7, 9, 10

VIS201 game Board Multiplication 2

VIS202 Order of Operations

Awards Maker ID name Activities

AWd030 Math Award 123

AWd140 Math Award symbols

AWd210 Math Numbers Award

STK329 Fraction whole Sticker 10

STK330 Fraction 1/2 Sticker 10, Additional








STK343 Order of Operations Sticker

STK368 decimal .1 Sticker 10











STK379 decimal 1.0 Sticker 10


29


NUMBer SeNSe 2 CONTeNT LIST (cont.)

cutout Maker ID name ActivitiesMTh116 1/2 Triangle Fraction 6

MTh117 1/3 Triangle Fraction 6




MTh144 Circle Fraction Whole 6, 7, 10

MTh147 1/2 Circle Fraction Piece 6, 7






MTh159 1/10 Circle Fraction Piece 10

MTh161 1/12 Circle Fraction Piece

MTh162 Square Fraction Whole 8

MTh164 1/2 Square Fraction 8, 9

MTh165 1/2 Square Fraction Piece 8





MTh170 1/5 Square Fraction 9

MTh171 1/5 Square Fraction Piece









MTh180 Whole Fraction Fringe

MTh181 1/2 Fraction Fringe






30

cutout Maker ID (cont.) name Activities





MTh287 Multiplication Symbol 1

MTh288 division Symbol 3, 7, 8

MTh290 Less Than Symbol Additional

MTh291 greater Than Symbol Additional

MTh292 greater Than or equal To Symbol

MTh293 Less Than or equal To Symbol

MTh398 Parentheses Symbol


NUMBer SeNSe 2 CONTeNT LIST (cont.)

31

VArIQUeST WOrK Order TeMPLATeThis template can be photocopied and used for placing orders for customized posters, banners, stickers, awards, cutouts and collections.

date Order Placed: __________________________________ Order #: _________________________________________

date Order Needed By: ______________________________ date Completed: _________________________________

Staff Name: ___________________________________________________________________________________________

room #: _________________________ Phone #: ___________________________________________________________

e-mail: ________________________________________________________________________________________________

special Instructions:

_____________________________________________________________________________________________________

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VARIQuest WoRk oRDeR


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