Teaching the Lesson - Ellis Family

Teaching the Lesson materials

Key ActivitiesStudents use Fraction Cards to determine whether a fraction is greater or less thananother fraction and then order sets of Fraction Cards from smallest to largest. They also compare fractions to �

12� and write different sets of fractions in order.

Key Concepts and Skills• Compare fractions. [Number and Numeration Goal 6]• Order fractions. [Number and Numeration Goal 6]• Explain strategies used to compare and order fractions. [Number and Numeration Goal 6]• Use patterns to compare and order fractions. [Patterns, Functions, and Algebra Goal 1]

Ongoing Assessment: Informing Instruction See page 617.

Ongoing Assessment: Recognizing Student Achievement Use journal page 206.[Number and Numeration Goal 6]

Ongoing Learning & Practice materialsStudents play Over and Up Squares to practice plotting ordered number pairs on a coordinate grid.

Students practice and maintain skills through Math Boxes and Study Link activities.

Differentiation Options materials

Students explore relativesizes of fractions.

Students use digits tocreate specified fractions.

Students play Fraction Top-It.

� Student Reference Book, p. 247� Teaching Masters (Math Masters, pp. 229

and 230)� Game Master (Math Masters, p. 506)� Fraction Cards (Math Journal 2,

Activity Sheets 5 and 6)� scissors; tape

EXTRA PRACTICEENRICHMENTREADINESS

3

� Math Journal 2, p. 207 � Student Reference Book, p. 257� Study Link Master (Math Masters, p. 228)� Game Master (Math Masters, p. 494)� colored pencils� 2 six-sided dice per partnership

2

� Math Journal 2, pp. 205 and 206� Study Link 7�8 � Fraction Cards (Math Journal 2,

Activity Sheets 5 and 6)� slate� calculator (optional)

1

Lesson 7� 9 615

Objective To provide practice ordering sets of fractions.

Technology Assessment Management System

Journal page 206, Problem 6See the iTLG.

616 Unit 7 Fractions and Their Uses; Chance and Probability

205

Comparing FractionsLESSON

7�9

Date Time

53

Math Message: Eating Fractions

Quinn, Nancy, Diego, Paula, and Kiana were given 4 chocolate bars to share. All 4 bars were the same size.

1. Quinn and Nancy shared a chocolate bar. Quinn ate �14� of the bar, and Nancy ate �

24�.

Who ate more?

How much of the bar was left?

2. Diego, Paula, and Kiana each ate part of the other chocolate bars. Diego ate �23� of

a bar, Paula ate �25� of a bar, and Kiana ate �

56� of a bar.

Who ate more, Diego or Paula?

How do you know?

Comparing Fractions with �12

�

Turn your Fraction Cards fraction-side up. Sort them into three piles:

� fractions less than �12�

� fractions equal to �12�

� fractions greater than �12�

You can turn the cards over to check your work. When you are finished, write the fractions in each pile in the correct box below.

Diego

Nancy

Less than �12

� Equal to �12

� Greater than �12

�

�13�, �

14�, �

05�, �

15�, �

25�,

�26�, �

28�, �

39�, �1

00�,

�120�, �1

40�, �1

32�, �1

42�

�12�, �

24�, �

36�, �

48�,

�150�, �1

62�

�23�, �

34�, �

35�, �

45�, �

55�,

�46�, �

68�, �

69�, �1

60�,

�180�, �

1100�, �1

82�, �1

92�

�14�

Sample answer: Diego ate �23�, which is

more than �12�. Paula ate �

25�, which is less than �

12�.

Math Journal 2, p. 205

Student Page

� Math Message Follow-Up(Math Journal 2, p. 205)

Students should have had no trouble concluding that Nancy atemore chocolate than Quinn (Problem 1), but they may have hadmore difficulty comparing the amounts eaten by Diego and Paula(Problem 2). Ask them to share their solution strategies. Studentsmight have used any of these strategies:

� If Diego’s chocolate bar were divided into 3 equal pieces andPaula’s into 5 equal pieces, Diego’s pieces would have beenlarger than Paula’s pieces. There would be more chocolate intwo of Diego’s pieces than in two of Paula’s pieces, so Diego atemore chocolate than Paula did.

� Diego ate more than half a bar (�23� is more than half). Paula ate

less than half a bar (�25� is less than half). So Diego ate more.

� Only �13� of Diego’s bar is left, but �

35� of Paula’s bar is left. Since

less of Diego’s bar is left, he ate more.

Next, ask students who ate more, Diego or Kiana. Have themexplain their answers. Students might have used any of thefollowing strategies:

� If Diego’s chocolate bar were divided into 6 equal pieces, hewould have eaten 4 of the pieces because �

46� is equivalent to �

23�.

Diego ate �46� of a bar and Kiana ate �

56� of a bar, so Kiana ate

more chocolate.

� Kiana has only �16� of her bar left, but Diego has �

13� left. Because

�16� is less than �

13�, Kiana has less left over, so she must have

eaten more.

Finally, have students determine who ate more chocolate, Diego or Nancy, and give their reasoning. Discuss how they know Diegoate more.

WHOLE-CLASSDISCUSSION

1 Teaching the Lesson

Getting Started

Math MessageWork with a partner to solve Problems 1 and 2 on journal page 205.

Study Link 7�8 Follow-UpPartners compare answers. Ask students to explainhow they solved Problems 9 and 10.

Mental Math and Reflexes Write fraction addition and subtraction problems on theboard. Students estimate whether the sum or differenceis closest to 0, 1, or 2. Suggestions:

�12� � �

34� 1

�23� � �

13� 0

�66� � �

99� 2

�37� � �

57� 1

1�16� � �

78� 0

�38� � �

16� 0

�1112� � �

58� 2

1�19090� � �

15� 2

1�190� � �

1156� 1

24Nancy

14Quinn

23Diego

25Paula

56Kiana

46

Lesson 7�9 617

NOTE Fractions with 1 in the numerator arecalled unit fractions.

� Ordering Fractions(Math Journal 2, Activity Sheets 5 and 6)

Tell the class that in this lesson they will use their Fraction Cards (Activity Sheets 5 and 6) as a tool to help them compareand order fractions.

Like NumeratorsHave students take out all the Fraction Cards with 1 in thenumerator (�

12�, �

13�, �

14�, and �

15�) and turn them fraction-side up. Ask

them to line up the cards from smallest (at the left) to largest (at the right). They can check by turning the cards over. Ask:● What pattern do you notice? As the denominator gets larger,

the fraction gets smaller.● What is the reason for this pattern? As the denominator gets

larger, the pieces get smaller because the whole is being dividedinto more pieces.

Ongoing Assessment: Informing InstructionWatch for students who reason that, for example, 5 is more than 4, so fifths mustbe larger than fourths. Remind students that the denominator represents thenumber of pieces the whole is divided into.

Like DenominatorsHave students take out all the Fraction Cards with 10 in thedenominator (�1

00�, �1

20�, �1

40�, �1

50�, �1

60�, �1

80�, and �

11

00�). Ask them to turn the

cards fraction-side up and arrange them in a row from smallestfraction to largest fraction.● What pattern do you see? The larger the numerator is, the

bigger the fraction is.● What is the reason for this pattern? All the pieces are the

same size, so more pieces make a bigger fraction.

Different Numerators and DenominatorsHave students take out the cards for �

14�, �

24�, �

23�, �

25�, and �

68�, and turn

them fraction-side up. Have students line up these cards fromsmallest fraction to largest fraction.

� Tell students to place the �24� card in front of them.

� Name one of the other cards (�14�, �

23�, �

25�, or �

68�), and ask students

whether the fraction is more or less than �24� and how they know.

� Ask students to place that card in the correct position—to theright or left of the �

24� card to indicate if it is smaller or larger

than �24�.

� Name the rest of the cards one by one. Students place the cardsin order while you ask for justification for each card’s placement.

WHOLE-CLASS

ACTIVITY


�

206

Ordering FractionsLESSON

7�9

Date Time

53

Write the fractions in order from smallest to largest.

1. �140�, �1

70�, �1

80�, �1

20�, �1

10�

smallest largest

2. �14�, �

12�, �

19�, �

15�, �1

100�

smallest largest

3. �24�, �

22�, �

29�, �

25�, �1

200�

smallest largest

4. �245�, �2

15�, �

78�, �1

62�, �1

75�

smallest largest

5. Choose 5 fractions or mixed numbers. Write them in order from smallest to largest.

smallest largest

6. Which fraction is larger: �25� or �

27�? Explain how you know.

seventh.

�25�

�78��1

62��1

75��2

45��2

15�

�22��

24��

25��

29��1

200�

�12��

14��

15��

19��1

100�

�180��1

70��1

40��1

20��1

10�

than �27�, so each fifth is bigger than each

Sample answer: �25� has a smaller denominator

Answers vary.


Student Page

Adjusting the Activity

Have students work with partners to order the following Fraction Cards: �

12�, �1

20�, �

26�, �

23�, and �

34�. They should begin with the

cards fraction-side up. They can check the order by turning the cards over. Discuss strategies.

� Comparing Fractions with �12�

(Math Journal 2, p. 205)

Have students follow the directions at the bottom of journal page 205 to sort the Fraction Cards into three categories: lessthan �

12�, equal to �

12�, and greater than �

12�.

Encourage partnerships to check their work by comparing theirsort to that of another group before recording their answers onjournal page 205.

Have students explain how a calculator can help determine whether afraction is less than �

12�, equal to �

12�, or greater than �

12�. Possible strategies:

� Subtract the fraction from �12�. If the difference is positive, it is less than �

12�.

If the difference is 0, it is equal to �12�. If the difference is negative, it is greater

than �12�.

� Add the fraction to �12�. If the sum is less than 1, the fraction is less than �

12�.

If the sum is 1, then the fraction equals �12�. If the sum is greater than 1,

the fraction is greater than �12�.

� Find the decimal equivalent by dividing the numerator by the denominator,and compare each decimal to 0.5.

A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L

� Ordering Fractions(Math Journal 2, p. 206)

Students write fractions in order from smallest to largest. Theychoose their own set of fractions or mixed numbers and write them in order.

Ongoing Assessment:Recognizing Student Achievement

Use journal page 206, Problem 6 to assess students’ ability to compare fractions and explain their strategies. Students are making adequate progress if their explanations include information such as the following:� �

25� is larger than �

27�.

� The numerators are the same, so each fraction has the same number of pieces.� The size of the pieces (denominator) needs to be compared. The smaller the

denominator is, the bigger the pieces are.Some students may include pictures to support their answer or use a calculatorto rename the fractions as decimals.

[Number and Numeration Goal 6]

Journal

page 206

Problem 6�

PARTNER

ACTIVITY

PARTNER

ACTIVITY

Adjustingthe Activity

Draw a number line from 0 to 1 on the board.Have students estimate the relative size of thefractions and order the fractions by writing them on the number line.

AUDITORY � KINESTHETIC � TACTILE � VISUAL

ELL

0 112

26

23

34

210

� Playing Over and Up Squares(Student Reference Book, p. 257; Math Masters, p. 494)

Students play Over and Up Squares to practice plotting ordered number pairs on a coordinate grid. See Lesson 6-9 for additional information.

� Math Boxes 7�9(Math Journal 2, p. 207)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 7-11. The skill in Problem 6previews Unit 8 content.

Writing/Reasoning Have students write a response to the following: Explain why �

22� inch might have been given as a

possible answer in Problem 3. Sample answer: Some students might incorrectly think that to subtract fractions yousubtract the numerators and denominators. If this is done, then an incorrect answer is �

34� in. – �

12� in. � �

22� in.

� Study Link 7�9(Math Masters, p. 228)

Home Connection Students compare and order fractions.

INDEPENDENT

ACTIVITY

INDEPENDENT

ACTIVITY

494

Copyright ©

Wright G

roup/McG

raw-H

ill

Name Date Time

132

4Over & Up Squares Gameboard/Record Sheet

Player 2: __________________________________

Over UpRound x-coordinate , y-coordinate Score

1 ,2 ,3 ,4 ,5 ,6 ,7 ,8 ,9 ,10 ,

Total Score

Player 1: __________________________________

Over UpRound x-coordinate , y-coordinate Score

1 ,2 ,3 ,4 ,5 ,6 ,7 ,8 ,9 ,10 ,

Total Score

Score

Ordered pair 10 pointsLine segment 10 pointsSquare 50 points

y

x 0

1

2

3

4

5

6

0 1 2 3 4 5 6

257

PARTNER

ACTIVITY

2 Ongoing Learning & Practice

207

Math Boxes LESSON

7�9

Date Time

1. Sari spends �13� of the day at school. Lunch,

recess, music, gym, and art make up �14� of

her total time at school. How many hoursare spent at these activities?

hours

Show how you solved this problem.

2

18 19

162–166 129

2. Multiply. Use a paper-and-pencil algorithm.

� 92 � 565,152

59

Sample answer: �13� of 24 hr �

8 hr; �14� of 8 hr � 2 hr

�14000�

55–57 61 62

4. Write an equivalent fraction, decimal, orwhole number.

Decimal Fraction

a. 0.40

b.�130�

c.�1100

00

�

d. 0.6

1.00.3

�160�

6. Complete.

a. 17 in. � ft in.

b. 43 in. � ft in.

c. 6 ft � yd

d. 11 ft � yd ft

e. 73 yd � ft21923

27351

5. Complete the table and write the rule.

Rule: � 5.73in out

6.19 11.92

12.03 17.763.26 8.99

0.01 5.74

4.41 10.14

3. Adena drew a line segment �34� inch long.

Then she erased �12� inch. How long is the

line segment now? Fill in the circle next tothe best answer.

A �46� in.

B �22� in.

C �14� in.

D 1�14� in.


Student Page

STUDY LINK

7�9 Compare and Order Fractions

53 54

Name Date Time

Write , , or � to make each number sentence true.

1. �56� �

16� 2. �1

30� �

34� 3. �

23� �

1105�

4. �1400� �1

46� 5. �

49� �

79� 6. �

56� �

58�

7. Explain how you solved Problem 1. Sample answer: Each fraction has6 equal parts; 5 parts are more than 1 part.

8. Explain how you solved Problem 2. Sample answer: Fourths are biggerthan tenths, so 3 fourths are more than 3 tenths.

9. Circle each fraction that is less than �12�.

�78� �

14� �1

40� �1

72� �

59� �

37� �

2540� �1

6070�

Write the fractions in order from smallest to largest.

10. �132�, �1

72�, �1

12�, �

1112�, �1

82� smallest largest

11. �15�, �

13�, �2

10�, �

12�, �5


12. �45�, �1

400�, �

44�, �

48�, �1


�

�

�112�

�510�

�1400� �1

42� �

48� �

45� �

44�

�210� �

13� �

12��

15�

�132� �1

72� �1

82� �

1112�

Practice

13. �16� of 30 � 14. �

34� of � 75 15. �

45� of 45 � 361005

Math Masters, p. 228

Study Link Master

Lesson 7�9 619


� Sorting Fractions(Math Masters, p. 229)

To explore comparing fractions, have students sort fractionsrepresented as area and number-line models into groups accordingto their relative size. When they finish the sort, have studentsdescribe how they chose their groups.

� Using Digits to Create Fractions(Math Masters, p. 230)

To extend students’ ability to compare fractions, have them usedigits to create specified fractions. For each problem, havestudents share their reasoning.

� Playing Fraction Top-It(Student Reference Book, p. 247; Math Masters, p. 506)

To practice comparing and ordering fractions, have students playFraction Top-It. See Lesson 7-10 for additional information.

5–15 Min

SMALL-GROUP

ACTIVITYEXTRA PRACTICE

5–15 Min

PARTNER

ACTIVITYENRICHMENT

0 1

?

0 1

?

0 1

?

Very small Almost a whole

12About

5–15 Min

PARTNER

ACTIVITYREADINESS

3 Differentiation Options

Games

Fraction Cards 1

Fraction Cards 2

Fraction Top-It

Materials 1 set of Fraction Cards 1 and 2 (Math Journal 2, Activity Sheets 5 and 6)

Players 2 to 4Skill Comparing fractions Object of the game To collect the most cards. Directions

Advance Preparation Before beginning the game, write the fraction for the shaded part on the back of each card.

1. Deal the same number of cards, fraction-side up, to each player:

♦ If there are 2 players, 16 cards each. ♦ If there are 3 players, 10 cards each. ♦ If there are 4 players, 8 cards each.

2. Players spread their cards out, fraction-side up,so that all of the cards may be seen.

3. Starting with the dealer and going in a clockwisedirection, each player plays one card. Place the cardsfraction-side up on the table.

4. The player with the largest fraction wins the roundand takes the cards. Players may check who hasthe largest fraction by turning over the cards andcomparing the amounts shaded.

5. If there is a tie for the largest fraction, each playerplays another card. The player with the largestfraction takes all the cards from both plays.

6. The player who takes the cards starts the next round.

7. The game is over when all cards have been played.The player who takes the most cards wins.

Student Reference Book, p. 247

Student Page

LESSON

7�9

Name Date Time

Two-Digit Fractions

Any fraction can be made from the digits 0–9. A fraction can have two digits like �

34� or �

87� or many digits like �

394873�. A fraction may not have a denominator of 0.

Use any two digits to make each of the following fractions.

1. The smallest possible fraction greater than 0

2. The largest possible fraction

3. The largest fraction less than 1

4. The smallest fraction greater than �12�

5. Make up your own problem. Answers vary.

�19�

�91�

�89�

�59�

53

Math Masters, page 230

Teaching the Lesson - Ellis Family

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