Objective
1
To provide practice ordering sets of fractions.
materials
Teaching the Lesson
Key Activities
Students use Fraction Cards to determine whether a fraction is greater or less than
another fraction and then order sets of Fraction Cards from smallest to largest. They
1
also compare fractions to 2 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]
ⵧ Math Journal 2, pp. 205 and 206
ⵧ Study Link 7 8
䉬
ⵧ Fraction Cards (Math Journal 2,
Activity Sheets 5 and 6)
ⵧ slate
ⵧ calculator (optional)
Ongoing Assessment: Informing Instruction See page 617.
Ongoing Assessment: Recognizing Student Achievement Use journal page 206.
[Number and Numeration Goal 6]
2
materials
Ongoing Learning & Practice
Students play Over and Up Squares to practice plotting ordered number pairs on a
coordinate grid.
ⵧ Math Journal 2, p. 207
ⵧ Student Reference Book, p. 257
Students practice and maintain skills through Math Boxes and Study Link activities.
ⵧ Study Link Master (Math Masters, p. 228)
ⵧ Game Master (Math Masters, p. 494)
ⵧ colored pencils
ⵧ 2 six-sided dice per partnership
3
materials
Differentiation Options
READINESS
Students explore relative
sizes of fractions.
ENRICHMENT
Students use digits to
create specified fractions.
EXTRA PRACTICE
Students play Fraction
Top-It.
ⵧ Student Reference Book, p. 247
ⵧ Teaching Masters (Math Masters, pp. 229
and 230)
ⵧ Game Master (Math Masters, p. 506)
ⵧ Fraction Cards (Math Journal 2,
Activity Sheets 5 and 6)
ⵧ scissors; tape
Technology
Assessment Management System
Journal page 206, Problem 6
See the iTLG.
Lesson 7 9
䉬
615
Getting Started
Mental Math and Reflexes
Math Message
Write fraction addition and subtraction problems on the
board. Students estimate whether the sum or difference
is closest to 0, 1, or 2. Suggestions:
Work with a partner to solve Problems 1 and 2
on journal page 205.
1
3
1
2
4
2
1
0
3
3
6
9
2
6
9
11
5
2
12
8
1
99
1 100 5 2
15
9
110 16 1
3
5
1
7
7
1
7
1 6 8 0
3
1
0
8
6
2
4
1
Quinn
4
Nancy
Diego
2
5
Kiana
5
6
䉬
Partners compare answers. Ask students to explain
how they solved Problems 9 and 10.
1 Teaching the Lesson
䉴 Math Message Follow-Up
2
3
4
6
Paula
Study Link 7 8 Follow-Up
WHOLE-CLASS
DISCUSSION
(Math Journal 2, p. 205)
Students should have had no trouble concluding that Nancy ate
more chocolate than Quinn (Problem 1), but they may have had
more difficulty comparing the amounts eaten by Diego and Paula
(Problem 2). Ask them to share their solution strategies. Students
might have used any of these strategies:
䉯 If Diego’s chocolate bar were divided into 3 equal pieces and
Paula’s into 5 equal pieces, Diego’s pieces would have been
larger than Paula’s pieces. There would be more chocolate in
two of Diego’s pieces than in two of Paula’s pieces, so Diego ate
more chocolate than Paula did.
2
䉯 Diego ate more than half a bar (3 is more than half). Paula ate
2
less than half a bar (5 is less than half). So Diego ate more.
Student Page
Date
Time
LESSON
79
䉬
1
3
䉯 Only 3 of Diego’s bar is left, but 5 of Paula’s bar is left. Since
less of Diego’s bar is left, he ate more.
Comparing Fractions
Math Message: Eating Fractions
53
Quinn, Nancy, Diego, Paula, and Kiana were given 4 chocolate bars to share.
All 4 bars were the same size.
Next, ask students who ate more, Diego or Kiana. Have them
explain their answers. Students might have used any of the
following strategies:
1
2
1. Quinn and Nancy shared a chocolate bar. Quinn ate of the bar, and Nancy ate .
4
4
Who ate more?
Nancy
How much of the bar was left?
1
4
2
2. Diego, Paula, and Kiana each ate part of the other chocolate bars. Diego ate of
3
2
5
a bar, Paula ate 5 of a bar, and Kiana ate 6 of a bar.
䉯 If Diego’s chocolate bar were divided into 6 equal pieces, he
4
2
would have eaten 4 of the pieces because 6 is equivalent to 3.
4
5
Diego ate 6 of a bar and Kiana ate 6 of a bar, so Kiana ate
more chocolate.
Diego
2
How do you know? Sample answer: Diego ate 3 , which is
1
2
1
more than 2. Paula ate 5, which is less than 2.
Who ate more, Diego or Paula?
1
Comparing Fractions with 2
Turn your Fraction Cards fraction-side up. Sort them into three piles:
1
䉬 fractions less than 2
1
1
䉬 fractions greater than 2
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.
1
Less than 2
1 1 0 1 2
, , , , ,
3 4 5 5 5
2 2 3 0
, , , ,
6 8 9 10
2
4
3
4
, , , 10 10 12 12
1
Equal to 2
1 2 3 4
, , , ,
2 4 6 8
5
6
, 10 12
1
Greater than 2
Finally, have students determine who ate more chocolate, Diego
or Nancy, and give their reasoning. Discuss how they know Diego
ate more.
2 3 3 4 5
, , , , ,
3 4 5 5 5
4 6 6 6
, , , ,
6 8 9 10
8 10 8
9
, , , 10 10 12 12
205
Math Journal 2, p. 205
616
1
䉯 Kiana has only 6 of her bar left, but Diego has 3 left. Because
1
1
is less than , Kiana has less left over, so she must have
6
3
eaten more.
1
䉬 fractions equal to 2
Unit 7 Fractions and Their Uses; Chance and Probability
䉴 Ordering Fractions
WHOLE-CLASS
ACTIVITY
(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 compare
and order fractions.
Like Numerators
Have students take out all the Fraction Cards with 1 in the
1 1 1
1
numerator (2, 3, 4, and 5) 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 divided
into more pieces.
NOTE Fractions with 1 in the numerator are
called unit fractions.
Ongoing Assessment: Informing Instruction
Watch for students who reason that, for example, 5 is more than 4, so fifths must
be larger than fourths. Remind students that the denominator represents the
number of pieces the whole is divided into.
Like Denominators
Have students take out all the Fraction Cards with 10 in the
10
0
2
4
5
6
8
denominator (10, 10, 10, 10, 10, 10, and 10). Ask them to turn the
cards fraction-side up and arrange them in a row from smallest
fraction 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 Denominators
1 2 2 2
6
Have students take out the cards for 4, 4, 3, 5, and 8, and turn
them fraction-side up. Have students line up these cards from
smallest fraction to largest fraction.
2
䉯 Tell students to place the 4 card in front of them.
1 2 2
6
䉯 Name one of the other cards (4, 3, 5, or 8), and ask students
2
whether the fraction is more or less than 4 and how they know.
䉯 Ask students to place that card in the correct position—to the
2
right or left of the 4 card to indicate if it is smaller or larger
2
than 4.
䉯 Name the rest of the cards one by one. Students place the cards
in order while you ask for justification for each card’s placement.
Lesson 7 9
䉬
617
ELL
Adjusting
the Activity
Draw a number line from 0 to 1 on the board.
Have students estimate the relative size of the
fractions and order the fractions by writing
them on the number line.
0
2
10
䉬
AUDITORY
2
6
1
2
2 3
3 4
䉬
KINESTHETIC
TACTILE
䉴 Comparing Fractions with 12
PARTNER
ACTIVITY
(Math Journal 2, p. 205)
1
䉬
Have students work with partners to order the following
1 2 2 2
3
Fraction Cards: 2, 10, 6, 3, and 4. They should begin with the
cards fraction-side up. They can check the order by turning
the cards over. Discuss strategies.
VISUAL
Have students follow the directions at the bottom of journal
page 205 to sort the Fraction Cards into three categories: less
1
1
1
than 2, equal to 2, and greater than 2.
Encourage partnerships to check their work by comparing their
sort to that of another group before recording their answers on
journal page 205.
Adjusting the Activity
Have students explain how a calculator can help determine whether a
1
1
1
fraction is less than 2, equal to 2, or greater than 2. Possible strategies:
1
1
䉯 Subtract the fraction from 2. If the difference is positive, it is less than 2.
1
If the difference is 0, it is equal to 2. If the difference is negative, it is greater
1
than 2.
1
1
䉯 Add the fraction to 2. If the sum is less than 1, the fraction is less than 2.
1
If the sum is 1, then the fraction equals 2. If the sum is greater than 1,
1
the fraction is greater than 2.
䉯 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
䉬
T A C T I L E
䉬
V I S U A L
PARTNER
ACTIVITY
(Math Journal 2, p. 206)
Time
LESSON
Ordering Fractions
79
䉬
Write the fractions in order from smallest to largest.
53
4
1. ,
10
7
,
10
8
,
10
2
,
10
1
10
1
10
7
10
4
10
2
10
8
10
smallest
1
2. ,
4
1
,
2
1
,
9
1
,
5
1
100
1
9
1
2
1
4
1
5
smallest
2
3. ,
4
2
,
2
2
,
9
2
,
5
2
100
2
9
2
100
1
,
25
1
25
Ongoing Assessment:
Recognizing Student Achievement
largest
2
4
2
5
2
2
smallest
4
4. ,
25
Students write fractions in order from smallest to largest. They
choose their own set of fractions or mixed numbers and write
them in order.
largest
1
100
largest
7
,
8
6
,
12
7
15
4
25
6
12
7
15
7
8
smallest
largest
5. Choose 5 fractions or mixed numbers. Write them in order from smallest to largest.
Answers vary.
smallest
largest
夹
6. Which fraction is larger:
2
5
or
2
?
7
2
5
Explain how you know.
2
Sample answer: 5 has a smaller denominator
2
than 7, so each fifth is bigger than each
Journal
page 206
Problem 6
夹
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:
2
2
䉯 5 is larger than 7.
䉯 The numerators are the same, so each fraction has the same number of pieces.
䉯 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 calculator
to rename the fractions as decimals.
seventh.
206
Math Journal 2, p. 206
618
K I N E S T H E T I C
䉴 Ordering Fractions
Student Page
Date
䉬
Unit 7 Fractions and Their Uses; Chance and Probability
[Number and Numeration Goal 6]
Student Page
Date
2 Ongoing Learning & Practice
Time
LESSON
Math Boxes
79
䉬
1
1. Sari spends of the day at school. Lunch,
3
1
recess, music, gym, and art make up of
4
2. Multiply. Use a paper-and-pencil algorithm.
5,152
her total time at school. How many hours
are spent at these activities?
䉴 Playing Over and Up Squares
PARTNER
ACTIVITY
(Student Reference Book, p. 257; Math Masters, p. 494)
2
92 ⴱ 56
hours
Show how you solved this problem.
1
Sample answer: 3 of 24
1
8 hr; 4 of 8 hr 2 hr
hr 59
Students play Over and Up Squares to practice plotting
ordered number pairs on a coordinate grid. See Lesson 6-9
for additional information.
Name
Date
Time
1 2
4 3
Over & Up Squares Gameboard/Record Sheet
Round
,
Score
,
,
,
,
,
,
,
,
,
,
1
2
3
4
5
6
7
8
9
10
A
4
6
in.
B
2
2
in.
Decimal
40
100
1
4
14 in.
c.
in.
1
6.19
11.92
a. 17 in. b. 43 in. c. 6 ft 10 points
Line segment
10 points
12.03
17.76
Square
50 points
3.26
0.01
8.99
4.41
10.14
6
10
61 62
6. Complete.
5.73
out
100
100
d. 0.6
55–57
in
3
10
0.3
1.0
b.
D
y
Fraction
a. 0.40
C
Score
Ordered pair
whole number.
line segment now? Fill in the circle next to
the best answer.
Rule:
257
Up
y-coordinate
4. Write an equivalent fraction, decimal, or
5. Complete the table and write the rule.
Player 1: __________________________________
Over
x-coordinate
18 19
3
3. Adena drew a line segment inch long.
4
1
Then she erased 2 inch. How long is the
d. 11 ft e. 73 yd 5.74
1 ft 5
3 ft 7
2 yd
3 yd 2
219 ft
in.
in.
ft
162–166
129
6
207
Total Score
5
Math Journal 2, p. 207
4
3
2
1
Player 2: __________________________________
Over
x-coordinate
,
Up
y-coordinate
,
,
,
,
,
,
,
,
,
,
1
2
3
4
5
6
7
8
9
10
Score
x
0
1
2
3
4
5
6
Copyright © Wright Group/McGraw-Hill
Round
0
Total Score
494
䉴 Math Boxes 7 9
䉬
INDEPENDENT
ACTIVITY
Study Link Master
(Math Journal 2, p. 207)
Name
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 7-11. The skill in Problem 6
previews Unit 8 content.
Date
STUDY LINK
79
Write , , or to make each number sentence true.
5
1. 6
10
4. 40
Writing/Reasoning Have students write a response to the
2
following: Explain why 2 inch might have been given as a
possible answer in Problem 3. Sample answer: Some
students might incorrectly think that to subtract fractions you
subtract the numerators and denominators. If this is done, then
3
1
2
an incorrect answer is 4 in. – 2 in. 2 in.
䉴 Study Link 7 9
䉬
7.
(Math Masters, p. 228)
Home Connection Students compare and order fractions.
1
6
3
2. 10
4
5. 9
4
16
3
4
7
9
Explain how you solved Problem 1.
53 54
2
3. 3
10
15
5
6. 6
5
8
Sample answer: Each fraction has
6 equal parts; 5 parts are more than 1 part.
8.
Explain how you solved Problem 2. Sample
answer: Fourths are bigger
than tenths, so 3 fourths are more than 3 tenths.
9.
1
2
Circle each fraction that is less than .
7
8
1
4
4
10
5
9
7
12
3
7
24
50
67
100
Write the fractions in order from smallest to largest.
3
10. ,
12
INDEPENDENT
ACTIVITY
Time
Compare and Order Fractions
䉬
7
,
12
1
11. ,
5
1
,
3
4
12. ,
5
4
,
100
11
,
12
1
,
12
1
,
20
4
,
4
1
,
2
4
,
8
8
12
1
50
4
12
1
12
3
12
7
12
1
50
largest
1
20
1
5
1
3
smallest
4
100
11
12
8
12
smallest
1
2
largest
4
12
4
8
smallest
4
4
4
5
largest
Practice
1
13. 6
of 30 5
3
14. 4
of
100
75
4
15. 5
of 45 36
Math Masters, p. 228
Lesson 7 9
䉬
619
Name
Date
LESSON
Time
Two-Digit Fractions
79
䉬
Any fraction can be made from the digits 0–9. A fraction can have two digits
3
8
347
like or or many digits like . A fraction may not have a denominator of 0.
4
7
53
983
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 5.
Make up your own problem.
9
1
PARTNER
ACTIVITY
READINESS
8
9
1
2
3 Differentiation Options
1
9
䉴 Sorting Fractions
5
9
Answers vary.
5–15 Min
(Math Masters, p. 229)
To explore comparing fractions, have students sort fractions
represented as area and number-line models into groups according
to their relative size. When they finish the sort, have students
describe how they chose their groups.
Math Masters, page 230
About
1
2
?
0
Very small
1
Almost a whole
?
0
?
1
0
ENRICHMENT
Student Page
Games
䉴 Using Digits to Create Fractions
1
PARTNER
ACTIVITY
5–15 Min
(Math Masters, p. 230)
Fraction Top-It
Materials 䊐 1 set of Fraction Cards 1 and 2
(Math Journal 2, Activity Sheets 5 and 6)
Players
2 to 4
Skill
Comparing fractions
Fraction Cards 1
Object of the game To collect the most cards.
Directions
To extend students’ ability to compare fractions, have them use
digits to create specified fractions. For each problem, have
students share their reasoning.
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:
EXTRA PRACTICE
♦ If there are 2 players, 16 cards each.
♦ If there are 3 players, 10 cards each.
♦ If there are 4 players, 8 cards each.
䉴 Playing Fraction Top-It
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 clockwise
direction, each player plays one card. Place the cards
fraction-side up on the table.
4. The player with the largest fraction wins the round
and takes the cards. Players may check who has
the largest fraction by turning over the cards and
comparing the amounts shaded.
5. If there is a tie for the largest fraction, each player
plays another card. The player with the largest
fraction takes all the cards from both plays.
Fraction Cards 2
5–15 Min
(Student Reference Book, p. 247; Math Masters, p. 506)
To practice comparing and ordering fractions, have students play
Fraction Top-It. See Lesson 7-10 for additional information.
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
620
SMALL-GROUP
ACTIVITY
Unit 7 Fractions and Their Uses; Chance and Probability