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