Chapter 7

Lessong9 Making Equivalent Fractions NCTM Standards 10

STUDENT OBJECTIVES Lesson Planner To make equivalent fractions with and without models or pictures

To compare and order fractions

1 Daily Activities (IG p. 555)

Skills Practice and Review- Open- -Ended Problem Solving/Headline Story

Is the Fraction Closes to 0, J, or 12

22 Teach and Practice (TG pp 556-559) RIALS A

@ Finding Equivalent Fractions transparency of AM66 (optional)

(TG pp. 556- -557) TR: Activity Master, AM66- -AM68

stopwatch or clock with a second hand @ Making Equivalent Fractions (TG p. 558)

LAB PP. 139-140 @ Playing a Game: Fraction Least to

SH P. 121 Greatest (TG p. 559)

Dififerentiated Instruction (IG p. 560)

Practice Book P58 Leveled Problem Solving (TG p. 560)

Extension Book E58 Intervention Activity (TG p, 560)

Spiral Review Book SR58 Extension Activity (TG p. 560)

Lesson Notes About the Mathematics About the Lesson

Students can look for patterns in equivalent fractions In the previous lesson, students saw how equivalent

by examining the numbers that appearin the fractions can be produced by dividing the parts of a

fractions. In the and, for 3

whole into equal numbers of equal parts. They saw 12,

example, students might notice that the denominator that the fractional part of a rectangle that is shaded

of each fraction is 4 times the numerator. Or they remains the same when the number of shaded parts

might notice that each number in the second fraction and the total number of parts are scaled by the same

is 3 times the number that appears in the same multiple. Students now use this understanding to

position in the first fraction. Both patterns are useful describe patterns they notice in the numbers that

in describing what makes the fractions equivalent. form equivalent fractions. They also make equivalent

fractions without relying on physical models or

pictures. At the end of the lesson, they play a game

where they order fractions by size

139-140 Use with Lesson Activity Book pp 554 Chapter 7 Lesson 9

1 paily Activities

Developing

Open-Ended Problem Solving Mathematical

Language Read the Headline Story to the students. Encourage them to create

problems that can be solved using information from the story Vocabulary: greater than, less

than, greatest, least

Headline Story A fraction is commonly said to be

greater than another fraction, rather

than bigger than the other, because The shirt store is having a

we are comparing the values of the

sale, and everything is half fractions, not how large we write the

digits. Regardless of the values of two price. Jonah spent of his

fractions, the fractions themselves

money to buy 2 shirts willbe physically about the same size

Similarly, one fraction is less than rather

than smaller than the other, one of

three fractions is the greatest rather

If Jonah had $40, then he spent $10. Jonah saved Possible responses than the biggest of the three, and one

$10 by buying the shirts on sale. If Jonah spent $20, then he had $80 of three fractions is the least rather

If Jonah spent $12.50, then he had $50. than the smallest of the three. This

distinction will be drawn more carefully

in your students' future math courses

NT and, at this level, no harm will be done

if they use bigger, smaller, and so on

Skills Practice and Review MA

or 1? Is the Fraction Closest to 0 2

As in the previous lesson, write a fraction on the board and ask Familiarize students with the terms

students whether the fraction is closest to 0, to , or to 1. If you feel greatest and least. 2

students are ready for it, you might write fractions that are between

Beginning Write several fractions on 1 and 2, and ask students to decide whether the fraction is closest

paper. Have students circle the greatest to 1, t01), or to 2.

fraction and underline the least fraction

Intermediate Write several fractions

st to 2 st to 1 on the board. Point to the greatest

fraction and ask if it is the greatest or

leastfraction. Point to the least fraction

and ask if it is the greatest or least

fraction

Advanced Have students write three

fractions. Then have them label the

greatest and least of the fractions

555 Chapter 7 Lesson 9

2I Teach and Practice

s A Fractions D

15 .0

MIN

Materials

Purpose To use diagrams to make equivalent fractions For the teacher:

transparency of AM66

Introduce Give a copy of Activity Master 66 Making Equivalent Fractions (optional)

Making Equivalent Fractions to each student. Ask As you complete this page, look forpattems

For each student: in the fractions.

students to work with partners to complete the page AM66

NCTM Standards 1, 2, 6, 7, 8, 9, 10

Task Direct students to draw lines on the Draw a vertical line on the rectangle so that

there are 6equal pieces.

What fhaction

rectangles as indicated in the directions O Draw 2 more vertical lines so that all of the

pieces are equal.

What traction

Encourage students to look for patterns in

the groups of fractions that they write

0 of the rectangle is O Draw a vertical line on the rectangle so that

there are 8 equal pieces

shaded O Draw 2 more vertical lines so that all of the

pieces are equal.

What fraction of the rectangle

Activity Master G6 of the rectangle is

6

shaded

S

of the rectangle is shaded 12

3

of the rectangle is shaded

6 of the rectangle is shaded S

G

12

of the rectangle is shaded 16

Share When students have completed the page, invite them to share their

answers and to show the lines they drew on their rectangles

Ask students to describe any patterns they notice in the fractions. Students

should realize that the fractions representing the shaded portions of

Rectangles 1- -3 are all equivalent, as are those representing the shaded

portions of Rectangles 4-6. Furthermore, they may notice that the top and

bottom numbers of the equivalent fractions double with each successive

fraction. That is because the number of pieces that compose each rectangle

doubles when the first line is drawn, then doubles again when the next two

lines are drawn

556 Chapter 7 Lesson 9 Use with Lesson Activity Book pp. 139-140

Talk Math Differentiated

O Whatis amotherfraction that is equivalent to Instruction

and ? Explain how R

you found the fraction, Possible answver 16 Above Level Ask students

possible explanation: I used

the doubling pater, doubling the top anic to find a fraction equivalent

j and that has a O What is another fraction

I drew

5 vertical lines on Rectangle 4:

Use with Lesson Activity Book pp 139-140 Chapter 7 Lesson 9 557

(B) Making Equivalent

individuals

or pairs 20

9 MIN

Purpose To find and confirm equivalent fractions NCTM Standards 1, 2, 6, 7, 8, 9, 10

Lesson Activity Book p. 139 Lesson Activity Book p. 140

Name Date Use = or to show whether the fractions

are equal or not.

Mlaking Equivalent Fractions

X

NCTN 7t 00 Complete the fractions to make the sentences true.

Draw pictures to help you complete Problems 3

and 4, if it will help.

$

9

5

OIn the fourth grade, of the students were absent

on Monday and i were absent on Tuesday, Were

the numbers of absent students on the two days

the same or different? Explain how you found the

answer.

the same; Possible explanation: The fractions and ? are 10

equivalent, because the numbers in are double the 10

numbers in In both cases, the bottom number is

5 times the top number 20 15

Go 24

50 O Challenge Find a rule. Then complete the fractions. 10 _25

60

115 4o

12 60 G x O Write 3 fractions that

Challenge Find a rule. Then complete the fractions. 9 i Possible answers 10 150 25

56 32 Other answers are possible

prime CXXXIX one hundredthirty-nine 139 140 one hundred forty CXL

ABOUT THE PAGE NUMBER 139 is prime, and the number ABOUT THE PAGE NUMBER 140 = = 28 x 5: 140 days is

that is two less (137) is prime too-as dose as two primes 20 weeks (about four and a half months); 35 is a quarter

can be (unless they are 2 and 3). Prime numbers this close of 140 (140 quarters are worth $35)

together are called twin primes: 137 and 139 are twin

primes.

Teaching Notes for LAB page 140 Teaching Notes for LAB page 139

On this page, students use their knowledge of Have students complete the page individually or with partners

equivalent -fraction patterns to test whether given pairs of

On this page, students find missing numbers in order to make fractions are equivalent. In Problem 6, for example, they can

equivalent fractions. In Problems 1- -2, pictures are provided to 2

conclude that either because each denominator is 4 times 8 4

help students complete the equivalences. In Problems 3-4, they the numerator, or because each number on the left is twice the

can make their own drawings if they wish. In Problem 5, they number on its right.

can use their knowledge of equivalent- -fraction patterns to find

Challenge Problem In Problem 9, the rule is that each the missing numbers

denominator is 6 times the numerator. The last fraction shows

the algebraic representation of this rule: if the top number isn

then the bottom number is 6 times n.

Use with Lesson Activity Book pp 139-140 558 Chapter 7 Lesson 9

Playing a Game: Fraction Least to Greatest pairs

VD

15

MIN

Purpose To practice comparing fractions Materials

For each pair: AM67-

Goal The object of this game, Fraction Least to AM68, stopwatch or

0000 clock with a second Greatest is to place fraction cards in order. The winner

hand Fraction Least to Greatest

is the player who is better able to order the cards

NCTM Standards 1, 2,6, 7, 8, 9, 10 67 (ractian

Prepare Materials Each pair of players will Mow To Flay The Game

need AM67: Fraction Cards 1 and AM68: Fraction t place the

The other

Cards 2, as well as a stopwatch or clock with a second Differentiated When yne fieer the Placer tures owr one

hand at a tone and of uardh wth

Instruction i e at the end of

The Timer order of the

Basic Level The Fraction Least r The Placer may

How to Play therd

to Greatest game involves for each uard

0

h

comparison under time O One player is chosen to be the Placer. The Placer

pressure, and some students mixes the Fraction Cards thoroughly, arranges

may find this stressful. You them in a neat pack, and holds them face down

might have them play a solitaire Student Handbook p. 121 The other player is the Timer. The Timer's job will be

version of the game, where to time the Placer for 60 seconds

the goal is to place 10 (or

When the Timer says "Start," the Placer turns some other number that you Fraction Cards 1

choose) cards in order without over one card at a time and places it where it 2

4

time pressure. Once students belongs in a growing line of cards. The goal is Fra

3 2 5 4

have a line of 10 cards, they to place as many cards as possible in order from

II can use manipulatives or

least to greatest scratch paper to check the

5

3

E The Timer announces when 60 seconds are up If there are errors ordering 4 6

8

then checks the ordering of the cards. If the II

they can remove as many

Timer finds an error, the Placer is allowed to cards as necessary in order to

have a correctly ordered line remove cards from the line in an effort to create 2 2 3

8 2 Then, they can draw more a correctly ordered line of cards. When the

3 5

cards from the deck and try Timer agrees there are no errors left, the Placer

to place them in line without receives a point for each card in the line

Activity Master 67 using manipulatives or scratch

The players switch roles. The first player to earn paper. A student who creates Activity Master 68

a line of 10 or more correctly 50 points wins

ordered cards before the deck

runs out wins the game. This

version of the game can also be

played cooperatively, by having

students take turns placing the

cards in line

Reflect and Summarize the Lesson

Write What is another fraction that is equivalent

? Explain how you found the answer 2 Math to 5

Use pictures, numbers, or words. Possible

possible explanation: I multiplied 4

answer 10

2

by 2. Another 4

2

the top and bottom numbers in 5 10

5

possible explanation is shown at the right

559 Chapter 7 Lesson 9 Use with Lesson Activity Book pp. 139-140