s e s s i o n 1 . 4 b comparing fractions on number...

Vocabularygreater thanless thanequivalent

s e s s i o n 1 . 4 B

Ten-Minute MathToday’s Number Write the number 456 on the board. Ask students to write it in expanded form, and to share how they would round it to the nearest ten and hundred. Then, students create expressions that equal 456. They must use subtraction and multiples of 100 in each expression. For example, 600 − 200 + 60 − 4. Collect a few expressions to write on the board and ask students to explain how they know they equal 456.

Today’s Plan MaterialsDiscussion

Comparing Halves, Fourths, and Eighths 15 Min class

•Numberlinesonchartpaper(fromSession1.4A)

acTiViTy

Representing and Comparing Fractions 30 Min inDiViDuals

•Student Activity Book,p.8Dorc44, Representing and comparing Thirds and sixths Makecopies.(asneeded)

•Student Activity Book, p.8Eorc45, Representing and comparing Fourths and eighths Makecopies.(asneeded)

•c46, number lines Makecopies.(asneeded)

Discussion

Comparing Fractions15 Min class

•Students’completedcopiesofStudent Activity Book,pp.8D–8EorC44–C45(fromActivity2)

session Follow-uP

Daily Practice •Student Activity Book,p.8Forc47, comparing Fractions on a number line Makecopies.(asneeded)

Comparing Fractions on Number LinesMath Focus Points

Representing fractions on a number line

Comparing fractions

Identifying equivalent fractions

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1 Discussion 2 Activity 3 Discussion 4 Session Follow-Up

D i S c U S S i o n

Comparing Halves, Fourths, and Eighths

clASS15 Min

Math Focus Points for Discussion Comparingfractions

Identifyingequivalentfractions

Draw a number line on the board and mark 0 and 1.

Suppose there were two ants traveling along this line. One ant, let’s call him Ant A, traveled 1 _ 2 the distance from 0 to 1. The other ant, let’s call him Ant B, traveled 1 _ 4 the distance. Which ant traveled farther?

Encourage students to use the chart paper from the last session to help figure out which ant traveled farther.

Ask students to help you mark the number line to figure out and show which ant traveled farther. If they do not mark all the fourths, ask how they know the distance they marked is 1 _ 4 .

0 B A 1

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[Elena] said that Ant A traveled farther than Ant B. How do you know that 1 _ 2 is greater than 1 _ 4 ?

Students might say:

“One fourth is half of one half, so one half is greater.”

“Ant A went farther on the number line than Ant B.”

So 1 _ 2 is greater than 1 _ 4 . How could we use notation to show that?

Session 1.4B comparing Fractions on number lines cc63

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Differentiation1 EnglishLanguageLearners The

greater than and less than language and symbols may be unfamiliar to some English Language Learners. Use whole numbers to introduce and model the use of both the terms and the symbols.

Remind students that the greater than, less than, and equal signs are symbols for showing the results of a comparison. 1 Ask a student to use these symbols to compare the two fractions.

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This statement says that 1 _ 2 is greater than 1 _ 4 . Can someone use the less than symbol to compare these fractions? ( 1 _ 4 < 1 _ 2 )

We are going to compare some more fractions. To help us, let’s label all the halves and fourths on this line. If there are two names for the same distance, we will write one under the other.

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Suppose two more ants were traveling on the line. Ant C traveled 3 _ 8 of the distance from 0 to 1, and Ant D traveled 3 _ 4 of the distance from 0 to 1. Which ant traveled farther?

Encourage students to refer to the chart paper from the last session. Ask them to help you mark the number line to figure out and show which ant traveled farther.

0 B DC A 1

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[Edwin] said that Ant D traveled farther than Ant C. How do you know that 3_4 is greater than3_8?

Students might say:

“Three eighths is smaller than one half. Three fourths is bigger than one half.”

“They each went 3, but fourths are larger than eighths, so the ant that went three fourths went farther.”

How could we use symbols to show how 3_4 compares to3_8?

Askstudentstohelpyouwritethesentencesbelowontheboard.

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34 < 3

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Now let’s label all the eighths on this number line.

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During the last session we figured out that1_2, 2_4, and4_8are all equal. They are equivalent. Look at this number line. What are some other fractions that are equivalent?

Studentsmaypointoutthefollowingequivalentfractions:0_2,0_4,and0_8;1_4and2_8;3_4and6_8;and2_2,4_4,and8_8.

Session 1.4B Comparing Fractions on Number Lines CC65

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8DSession 1.4B Unit 7

Representing and Comparing Thirds and Sixths

0 1

1. Label the thirds on the number line. Divide the number line into sixths and label the sixths.

2.Ant A walked 1 _ 3 the distance from 0 to 1. Ant B walked 2 _ 3 the distance from 0 to 1. Show how far each ant walked on the number line. Use >, <, or = to compare the fractions.

1 __ 3 2 __ 3

3.Ant C walked 1 _ 3 the distance from 0 to 1. Ant D walked 1 _ 6 the distance from 0 to 1. Show how far each ant walked on the number line. Use >, <, or = to compare the fractions.

1 __ 3 1 __ 6

4.Ant E walked 1 _ 3 the distance from 0 to 1. Ant F walked 3 _ 6 the distance from 0 to 1. Show how far each ant walked on the number line. Use >, <, or = to compare the fractions.

1 __ 3 3 __ 6

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8E Unit 7 Session 1.4B

Representing and Comparing Fourths and Eighths

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1. Label the fourths on the number line. Divide the number line into eighths and label the eighths.


1 _ 4 2 _ 4


3 _ 8 1 _ 4


3 _ 4 6 _ 8

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A c t i v i t y

Representing and Comparing Fractions

inDiviDUAlS30 Min

Introduce Student Activity Book pages 8D and 8E or C44 and C45.

You are going to represent and name some more fractions and compare the size of some fractions, just like we’ve been doing together.

Point out that the number line on Student Activity Book page 8D or C44 is broken into thirds.

First, label the thirds. Then draw lines to show sixths, and label the sixths. Then use that number line to solve the problems. The second page involves fourths and eighths.

OngOing ASSeSSMent: Obser ving Student s at Work

Studentsnamethirdsandfourths,andrepresentandnamesixthsandeighthsonnumberlines.Theycomparepairsoffractions.

• Howdostudentsdivideandlabelthenumberlines?Dotheprovidedfractionshelpthem?

• Howdostudentsexplainhowtheyknowwhichfractionisgreater?Dotheyusethefraction’slocationonthenumberline?Reasonabouttherelativesizesofthepieces?Aretheyaccurateintheiruseofnotation?

DiFFerentiAtiOn: Suppor ting the range of lear ner s

Workwithstudentstoensurethattheylabeleachnumberlinecorrectlybeforecomparingthefractions.Somestudentsmaybenefitfromusinganewnumberline(C46)tocompareeachpairoffractions.Studentswhodon’tyetunderstandwhatthenumeralsinafractionrepresentmaybenefitfromusingbrowniestorepresentandcomparefractions.

Challengestudentstocomparemoredifficultfractions(e.g., 5 _ 8   and 3 _ 4   or 2 _ 3   and 3 _ 4  ).

▲ Student Activity Book, Unit 7, p. 8D;resource Masters, c44

▲ Student Activity Book, Unit 7, p. 8e;resource Masters, c45

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Unit 7 Session 1.4B


Number Lines

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8FSession 1.4B Unit 7

Comparing Fractions on a Number Line1.Fill in the missing fractions on the

number line.

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Write >, <, or = in each box to compare the fractions.

2.2 _ 8  1 _ 2 

3.3 _ 4  7 _ 8 

4.3 _ 4  5 _ 8 

5. 1 _ 4  1 _ 8 

6.6 _ 8  3 _ 4 

7. 2 _ 2  7 _ 8 

note Students label fractions on a number line and compare fractions.

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D i S c U S S i o n

Comparing FractionsclASS15 Min

Math Focus Points for Discussion Comparingthesizeoffractions

Identifyingequivalentfractions

Below the line marked in halves, fourths, and eighths from Activity 1, draw a new line and mark 0 and 1. Mark thirds on the number line and ask students to help you label them. Then ask students to help you mark sixths on the number line and label them.

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The distance from 0 to here [point to the 1 _ 3 mark] is labeled both 1 _ 3 and 2 _ 6 . Does 1 _ 3 equal 2 _ 6 ? 2

Ask students to look at their solutions for Problem 4 on Student Activity Book page 8D or C44.

Who traveled farther, the ant who stopped at 1 _ 3 or the ant who stopped at 3 _ 6 ? How do you know?

Finally, ask students to look at the number lines on Student Activity Book pages 8D and 8E or C44 and C45.

If one ant traveled 2 _ 3 of the distance from 0 to 1 and one ant traveled 2 _ 4 the distance from 0 to 1, which ant traveled farther?

S e S S i o n F o l l o w - U P

Daily Practice DailyPractice: For reinforcement of this unit’s content,

have students complete Student Activity Book page 8F or C47.

▲ Student Activity Book, Unit 7, p. 8F;Resource Masters, c47

▲ Resource Masters, c46

Teaching note 2 StrategiesforComparingFractions

Students are likely to think about the relationship between related fractions. For example, to make sixths, you divide thirds in half. If 1 _ 2  of 1 _ 3  is 1 _ 6  , then 2 _ 6  is the same as 1 _ 3  . Others think about the distance on the number line—you have to take two jumps of 1 _ 6  to get to 1 _ 3  . For other fraction comparisons, students compare the fractions to 1 _ 2  (e.g., “ 1 _ 3  is less than 1 _ 2  , and 3 _ 6  is 1 _ 2  .”) or think about the relative size of the pieces (e.g., “Fourths are smaller than thirds because they’re cut into more pieces.”).

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Unit 7 Session 1.4B

Representing and Comparing Thirds and Sixths

0 1

1. Label the thirds on the number line. Divide the number line into sixths and label the sixths.


1 __ 3 2 __ 3


1 __ 3 1 __ 6


1 __ 3 3 __ 6

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Unit 7 Session 1.4B

Representing and Comparing Fourths and Eighths

0 112

1. Label the fourths on the number line. Divide the number line into eighths and label the eighths.


1 _ 4 2 _ 4


3 _ 8 1 _ 4


3 _ 4 6 _ 8

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Unit 7 Session 1.4B


Number Lines

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DateNameFinding Fair Shares Daily Practice

Comparing Fractions on a Number Line1.Fill in the missing fractions on the

number line.

0 1

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Write >, <, or = in each box to compare the fractions.

2.2 _ 8  1 _ 2 

3.3 _ 4  7 _ 8 

4.3 _ 4  5 _ 8 

5. 1 _ 4  1 _ 8 

6.6 _ 8  3 _ 4 

7. 2 _ 2  7 _ 8 

Unit 7 Session 1.4B

notE Students label fractions on a number line and compare fractions.

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s e s s i o n 1 . 4 b comparing fractions on number...

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