Student Success Adapted Program
Lesson-by-lesson support for struggling students!
Lesson Sampler
Chapter 7: Fractions and Decimals:
Lessons 1–5
7.1
3.3
Fractions of a Whole
Student Book pp. 208–211
Teacher’s Resource pp. 12–15
GOAL
Name and represent fractions of a whole.
Preparation and Planning
About the Math
Masters
When you refer to fractions as parts of a whole, you are talking
about “parts of a region,” not “parts of a set.”
Key
Assessment
Question
0 !#"& &)+"*"& ((/
0 )&"& ((/
0 )+"'&!(*(
Keep the following considerations in mind:
A 7&(9.43&15&7982:89'*9-*8&2*8.?*
A +7&(9.43(&3349'*.)*39.+.*):31*889-*949&13:2'*74+
fractional parts in the whole is known.
A #<4+7&(9.4389-&9&7*9-*8&2*)43497*57*8*399-*8&2*
1
6:&39.9>.+9-*<-41*8&7*).++*7*398.?*8*, of a large
2
1
square is larger than of a small square).
2
A +7&(9.43(&3)*8(7.'*9-*8-&)*)479-*:38-&)*)5&7984+&
picture.
,*+"'&
Differentiating Instruction
Students need to learn how to write the words as well as the
2
8>2'418+47+7&(9.438*,9<49-.7)8&3)).
3
&;*89:)*398:8*9-*+7&(9.438-&5*82&89*7475&99*73'14(0894841;*9-*574'1*28.39-.81*884380
“How many equal parts are there altogether?” !*(47)9-*)*342.3&947
“How many equal parts are shaded or coloured?” !*(47)9-*3:2*7&947
“How do you read the fraction that we have written? What fraction does the picture show?”
Make sure students understand that the shaded parts of the fraction picture do not need to be next to one
another.
4789:)*398<-43**)8(&++41).3,):7.3,.3)*5*3)*3957&(9.(*574;.)*Checking and Practising BLM 7.1.
4789:)*398<-43**)-*157*57*8*39.3,8.251*+7&(9.438574;.)*Learning BLM 7.1, which provides pre-drawn
fractions for students to colour.
Answers to Learning BLM 7.1
*70
%2.7
*25.B
Reflecting: The numerators are all 1; The denominators are all different.
Copyright © 2008 by Nelson Education Ltd.
Overview 7.1: Fractions of a Whole
233
C&P Name:
7.1 Fractions of a Whole
Date:
Page 1
Student Book pages 208–211
GOAL
Name and represent fractions of a whole.
You will need
• pencil
crayons
Checking
1. a) How many equal parts are in the rectangle? ________
Colour 3 parts of the rectangle.
What fraction of the rectangle is coloured?
b) How many parts of the rectangle are white? ________
What fraction of the rectangle is white?
Practising
2. Hannah coloured some fraction pictures.
a) How many equal parts does the picture have? ________
How many parts are coloured? _________
How many parts are not coloured? _________
Write 2 fractions the picture shows.
b) Write a fraction that each picture shows.
230
Checking & Practising BLM 7.1: Fractions of a Whole
Copyright © 2008 by Nelson Education Ltd.
C&P Name:
7.1 Fractions of a Whole
Date:
Page 2
3. How many equal parts are in the rectangle? ________
a) Colour the rectangle to show a fraction.
Write the fraction your picture shows.
b) How many parts of the rectangle are white? ________
Write another fraction your picture shows.
5
7. Circle the picture that shows ��.
6
Hint: The picture must have 6 equal parts.
How do you know?
Copyright © 2008 by Nelson Education Ltd.
Checking & Practising BLM 7.1: Fractions of a Whole
231
L
Name:
Date:
7.1 Fractions of a Whole
Page 1
Student Book pages 208–211
You will need
GOAL
Name and represent fractions of a whole.
• pencil
crayons
Problem
Joshua’s rock-climbing team is making T-shirts.
Each T-shirt shows a different fraction.
1
Joshua’s T-shirt shows ��.
6
Joshua
Colour the T-shirts to show each fraction.
232
Lang
Tien
Hailey
1
4
1
3
1
2
Learning BLM 7.1: Fractions of a Whole
Copyright © 2008 by Nelson Education Ltd.
L
Name:
Date:
7.1 Fractions of a Whole
Page 2
Reflecting
How are the fraction pictures on the T-shirts the same?
Hint: Look at the numerators.
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
How are the fraction pictures on the T-shirts different?
Hint: Look at the denominators.
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
numerator
denominator
The number above the bar in a fraction. It
tells the number of equal parts the fraction
represents.
The number below the bar in a fraction. It
tells the number of equal parts in one
whole.
For example, this
fraction tells
about 1 of the
equal parts.
1
4
Copyright © 2008 by Nelson Education Ltd.
For example, this
whole is divided
into 4 equal parts.
1
4
Learning BLM 7.1: Fractions of a Whole
233
3.3
7.2
Fractions of a Group
Student Book pp. 212–214
Teacher’s Resource pp. 16–20
GOAL
Name, represent, compare, and order fractions of a group.
Preparation and Planning
About the Math
Masters
• Checking and Practising
BLM 7.2 pp. 235–236
• Learning BLM 7.2 pp. 237–238
Key
Assessment
Question
Question 4
This lesson introduces students to fractions of a group or set.
Sometimes students are confused by the fact that parts of a group
do not have to be identical. For example, a set of 5 musical
instruments (e.g., 2 violins, 1 viola, 1 clarinet, and 1 flute) could
3
be represented by various fractions: �� are string instruments,
5
2
and �� are wind instruments.
5
Differentiating Instruction
Discuss how fractions of a region (whole) and fractions of a set are alike and how they are different. Model
fractions of a set by assembling groups of students and using fractions to describe their attributes.
Assemble a group of students: 5 girls and 3 boys. Ask:
“How many students are in this group?” (8)
5
“What fraction tells the number of group members that are girls?” (5 out of 8 or ��)
8
3
“What fraction tells the number of group members that are boys?” (3 out of 8 or ��)
8
Continue asking about other attributes in the same group, such as hair colour or types of shoes, or have students
work in teams to model fractions of a group.
For students who need scaffolding during independent practice, provide Checking and Practising BLM 7.2.
For students who need extra learning support, provide Learning BLM 7.2, which presents scaffolded practice
naming simple fractions of a set. Note: The lesson goal has been changed in this BLM.
Answers to Learning BLM 7.2
Step 1: 4
1
Step 2: 1; ��
4
1
Step 3: 1; ��
4
2
Step 4: 2; ��
4
1
2
Reflecting: ��; Because it represents more items in a set or more parts in a whole than �
; Parts of a group can be
4
4
different sizes, but parts of a whole must be equal.
234
Overview 7.2: Fractions of a Group
Copyright © 2008 by Nelson Education Ltd.
C&P Name:
7.2 Fractions of a Group
Date:
Page 1
Student Book pages 212–214
GOAL
You will need
Name, represent, compare, and order fractions of
a group.
• pencil
crayons
Checking
1. a) Look at this group of animals.
How many animals are in the group? _________
Write a fraction to describe the number of
animals with flippers.
Show this fraction as a picture.
Write a fraction to describe the number of animals
with a mouth.
Show this fraction as a picture.
Write a fraction to describe the number of animals
with tusks.
Show this fraction as a picture.
b) Write the fractions in order from least to greatest.
Copyright © 2008 by Nelson Education Ltd.
Checking & Practising BLM 7.2: Fractions of a Group
235
C&P Name:
7.2 Fractions of a Group
Date:
Page 2
Practicing
4. Here are 6 crayons.
2
a) Colour �� of the crayons blue.
6
How many crayons are blue? _________
3
Colour �� of the crayons green.
6
How many crayons are green? _________
1
Colour �� of the crayons red.
6
How many crayons are red? _________
b) Write the fractions in order from least to greatest.
236
Checking & Practising BLM 7.2: Fractions of a Group
Copyright © 2008 by Nelson Education Ltd.
L
Name:
7.2 Fractions of a Group
Date:
Page 1
Student Book pages 212–214
GOAL
Name, represent, and compare fractions of a group.
Problem
Cole’s family saw these animals on a trip.
How can you use fractions to describe the animals in this group?
Step 1: How many animals are in the group? _________
Use this number as the denominator for your fractions.
Step 2: How many animals have feathers? _________
Write a fraction to describe the animals with feathers.
4
Step 3: How many animals live in the water? _________
Write a fraction to describe the animals that live in the water.
4
Step 4: How many animals have 4 legs? _________
Write a fraction to describe the animals that have 4 legs.
4
Copyright © 2008 by Nelson Education Ltd.
Learning BLM 7.2: Fractions of a Group
237
L
Name:
Date:
7.2 Fractions of a Group
Reflecting
Circle the greater fraction:
1
��
4
Page 2
2
��
4
Explain how you know.
How are parts of a group different from parts of a whole?
238
Learning BLM 7.2: Fractions of a Group
Copyright © 2008 by Nelson Education Ltd.
3.3
7.3
Sorting Fractions
Student Book p. 215
Teacher’s Resource pp. 21–23
GOAL
Describe how fractions are alike and different.
Preparation and Planning
About the Math
Masters
• Checking and Practising
BLM 7.3 p. 240
• Learning BLM 7.3 p. 241
Key
Assessment
Question
Entire exploration
In this lesson, students apply the fraction principles they learned
in Lessons 7.1 and 7.2. Students should be able to name and
record fractions for the parts of a whole or a group using
concrete materials and pictures. They should also know what the
numerator and denominator represent.
This lesson asks students to compare fractions with common
denominators and those that are equal to one whole,
3
4
such as �� and ��.
3
4
Differentiating Instruction
Have students work with fraction pieces or the fraction shapes master to solve the problems in this lesson. Focus
your questioning on the roles the numbers play in each fraction (the denominator tells the number of parts in the
whole; the numerator tells the number of parts in the fraction). Model situations in which the same number plays
a different role in two different fractions:
In this fraction, 4 is the denominator. It tells how many parts there are in the whole.
3
4
In this fraction, 4 is the numerator. It tells how many parts have been shaded.
4
5
For students who need scaffolding during independent practice, provide Checking and Practising BLM 7.3.
For students who need support discussing different representations of simple fractions, provide Learning BLM
7.3, which provides pre-drawn simple fractions for students to colour and compare.
Answers to Learning BLM 7.3
1 3 1
Step 1: ��, ��; ��
4 4 3
Step 2: Suggested answers:
1
1
3
��; It does not have the same denominator as �� and ��.
3
4
4
Copyright © 2008 by Nelson Education Ltd.
Overview 7.3: Sorting Fractions
239
C&P Name:
Date:
7.3 Sorting Fractions
Student Book page 215
You will need
GOAL
Describe how fractions are alike and different.
One of the fractions does not belong with the others.
3
Ken says, “I think �� does not belong.”
4
4
Julia says, “I think �� does not belong.”
4
3
Aneela says, “I think �� does not belong.”
3
• pencil
crayons
3
�
4
How can you show that Ken, Julia, and Aneela are
all correct?
3
�
3
4
�
4
Step 1: Colour the shapes to show each fraction.
3
3
4
4
3
4
3
Step 2: Explain why �� does not belong.
4
4
Step 3: Explain why �� does not belong.
4
3
Step 4: Explain why �� does not belong.
3
240
Checking & Practising BLM 7.3: Sorting Fractions
Copyright © 2008 by Nelson Education Ltd.
L
Name:
Date:
7.3 Sorting Fractions
Student Book page 215
You will need
GOAL
Describe how fractions are alike and different.
• pencil
crayons
Problem
Which of these fractions does not belong with the others?
1
4
3
4
Step 1: Circle the fractions with the same denominator:
1
3
1
�
4
3
��
4
1
��
3
Which fraction does not belong?
Step 2: Show the fractions using fraction shapes.
1
��
4
3
��
4
1
��
3
Which fraction does not belong?
How do you know?
Copyright © 2008 by Nelson Education Ltd.
Learning BLM 7.3: Sorting Fractions
241
3.3
7.4
Comparing and Ordering
Fractions
Student Book p. 216–218
Teacher’s Resource pp. 24–28
GOAL
Compare and order fractions with the same numerator and
different denominators.
Preparation and Planning
About the Math
Masters
• Checking and Practising
BLM 7.4 pp. 243–244
• Learning BLM 7.4 pp. 245–246
• Fraction Strips, TR Ch. 7 p. 90
• Fraction Circles, MB pp. 50–51
Key
Assessment
Question
Question 7
Students will compare fractions that have the same numerator.
They may find it difficult to compare fractions in symbolic form,
so use models such as fraction strips or fraction circles to help
students visualize the fractions. When comparing, students
1
should compare fractions with the same whole, since � of one
2
3
object could be greater than � of another.
4
Differentiating Instruction
Use fraction circles to model various fractions with the same numerator but different denominators. Begin by
modelling a whole pizza with a fraction circle.
1
Show a halves fraction circle. Say, “Each of these pieces represents � of the pizza. If two people shared the
2
pizza equally, this is the size of piece they would get.”
1
Show a thirds fraction circle. Say, “Each of these pieces represents �� of the pizza. If three people shared the
3
pizza equally, this is the size of piece they would get.”
1
Show a fourths fraction circle. Say, “Each of these pieces represents � of the pizza. If four people shared the
4
pizza equally, this is the size of piece they would get.”
Repeat the examples above using fraction strips.
For students who need scaffolding during independent practice, provide Checking and Practising BLM 7.4.
For students who need extra learning support, provide Learning BLM 7.4. Note: The lesson goal has been changed
in this BLM.
Answers to Learning BLM 7.4
Annie; Olivia; Tien; Annie
Tien
Olivia
Annie
Reflecting: Colouring the strips makes it easy to see how the fractions compare.
242
Overview 7.4: Comparing and Ordering Fractions
Copyright © 2008 by Nelson Education Ltd.
C&P Name:
Date:
7.4 Comparing and Ordering Fractions Page 1
Student Book pages 216–218
GOAL
Compare and order fractions with the same numerator
and different denominators.
Checking
1. Some students are running along a track.
Show how far each student has run by colouring the fraction strips.
1
a) Ken is �� of the way.
8
1
Cory is �� of the way.
5
How many parts of Ken’s strip are coloured? ___________
How many parts of Cory’s strip are coloured? __________
Who is farther along the track? _______________________
How do you know?
1
b) Aneela is �� of the way.
3
1
Julia is �� of the way.
5
Who is farther along the track? _____________________
How do you know?
Copyright © 2008 by Nelson Education Ltd.
Checking & Practising BLM 7.4: Comparing and Ordering Fractions
243
C&P Name:
Date:
7.4 Comparing and Ordering Fractions Page 2
Practising
7. These squares are the same size.
2
a) Colour �� of the first square.
5
Hint: Divide the square into 5 rectangles.
2
b) Colour �� of the second square.
6
Hint: Divide the square into 6 rectangles.
2
2
c) Which fraction is greater, �� or ��?
5
6
How do you know?
2
2
d) Is �� greater or less than ��? ______________________
8
5
How do you know?
244
Checking & Practising BLM 7.4: Comparing and Ordering Fractions
Copyright © 2008 by Nelson Education Ltd.
L
Name:
Date:
7.4 Comparing and Ordering Fractions Page 1
Student Book pages 216–218
GOAL
Compare and order fractions with the same denominator.
You will need
• pencil
crayons
Problem
Tien, Olivia, and Annie are racing on a track.
1
• Tien is �� of the way.
4
2
• Olivia is �� of the way.
4
3
• Annie is �� of the way.
4
Who is winning the race?
Shade the fraction strips to show how far each girl has run.
Tien
Olivia
Annie
Who has run the greatest distance? _________________________
1
Who has run �� the distance? ______________________________
2
Who has run the least distance? ____________________________
Who is winning the race? __________________________________
Copyright © 2008 by Nelson Education Ltd.
Learning BLM 7.4: Comparing and Ordering Fractions
245
L
Name:
Date:
7.4 Comparing and Ordering Fractions Page 2
Reflecting
How does colouring fraction strips help you compare fractions?
246
Learning BLM 7.4: Comparing and Ordering Fractions
Copyright © 2008 by Nelson Education Ltd.
3.3
7.5
Using Benchmarks to
Order Fractions
Student Book pp. 220–222
Teacher’s Resource pp. 31–34
GOAL
Order fractions on a number line.
Preparation and Planning
About the Math
Masters
• Checking and Practising
BLM 7.5 pp. 248–249
• Learning BLM 7.5 pp. 250–251
• Fraction Strips, TR Ch. 7 p. 90
• Number Lines, MB p. 38
Key
Assessment
Question
Question 2
In this lesson, students compare fractions by relating them to the
1
benchmark numbers 0, � , and 1. Have students use fraction
2
strips and number lines throughout the lesson to help them
visualize the relationships among the fractions and the
benchmarks. Having students work with a partner will encourage
communication and aid understanding.
Differentiating Instruction
Build a fraction wall with the whole class or with a small group of students.
1
Use adding machine tape or a clothesline to create a long number line. Label the line with the benchmarks 0, � ,
and 1. Make fraction cards showing the benchmarks symbolically, as fractions of a region, and as fractions of 2
a set, as shown below. Invite students to place number cards on the line. Have students justify their placement of
1
1
each number card. For example, ask, “Why do you think � is less than � ?”
4
2
As you work through the chapter, have students place fractions with different denominators on the line.
1
2
0
1
3
4
1
4
2
4
For students who need scaffolding during independent practice, provide Checking and Practising BLM 7.5.
For students who need extra learning support, provide Learning BLM 7.5. Note: The lesson goal has been
changed in this BLM.
Answers to Learning BLM 7.5
1
2
1
4
1
8
1
3
1
3
1
8
1
2
1
3
1
4
1
8
1
4
1
4
1
8
1
8
1
8
1
8
1
8
Cole and Joshua; Joshua
1 as a benchmark made it easier to see how the fractions compare to 1 and to each other.
Reflecting: Using �
�
2
2
Copyright © 2008 by Nelson Education Ltd.
Overview 7.5: Using Benchmarks to Order Fractions
247
C&P Name:
Date:
7.5 Using Benchmarks to Order Fractions Page 1
Student Book pages 220–222
GOAL
Order fractions on a number line.
You will need
• pencil
crayons
Checking
1. 4 golf balls rolled different distances toward the hole.
Show each fraction on its fraction strip.
1
Use �� as a benchmark.
2
1
��
2
Ball 1:
1
��
5
Ball 2:
7
��
8
6
Ball 3: ��
10
4
Ball 4: ��
10
a) Which balls rolled more than halfway to the hole? ___________________
Which ball rolled the least distance? _______________________________
Which ball rolled the greatest distance? ____________________________
b) Write the fractions in order from least to greatest.
248
Checking & Practising BLM 7.5: Using Benchmarks to Order Fractions
Copyright © 2008 by Nelson Education Ltd.
C&P Name:
Date:
7.5 Using Benchmarks to Order Fractions Page 2
Practising
2. Show each fraction on its fraction strip.
1
1
��
2
1
��
8
9
��
10
3
��
8
7
��
12
1
��
5
1
a) Circle the fractions that are closer to 1 than to � .
2
b) Estimate to mark each fraction on the number line.
0
1
1
2
c) Order the fractions from least to greatest.
Copyright © 2008 by Nelson Education Ltd.
Checking & Practising BLM 7.5: Using Benchmarks to Order Fractions
249
C&P Name:
Date:
7.5 Using Benchmarks to Order Fractions Page 1
Student Book pages 220–222
GOAL
Order fractions on a number line.
You will need
• pencil
crayons
Checking
1. 4 golf balls rolled different distances toward the hole.
Show each fraction on its fraction strip.
1
Use �� as a benchmark.
2
1
��
2
Ball 1:
1
��
5
Ball 2:
7
��
8
6
Ball 3: ��
10
4
Ball 4: ��
10
a) Which balls rolled more than halfway to the hole? ___________________
Which ball rolled the least distance? _______________________________
Which ball rolled the greatest distance? ____________________________
b) Write the fractions in order from least to greatest.
248
Checking & Practising BLM 7.5: Using Benchmarks to Order Fractions
Copyright © 2008 by Nelson Education Ltd.
C&P Name:
Date:
7.5 Using Benchmarks to Order Fractions Page 2
Practising
2. Show each fraction on its fraction strip.
1
1
��
2
1
��
8
9
��
10
3
��
8
7
��
12
1
��
5
1
a) Circle the fractions that are closer to 1 than to � .
2
b) Estimate to mark each fraction on the number line.
0
1
1
2
c) Order the fractions from least to greatest.
Copyright © 2008 by Nelson Education Ltd.
Checking & Practising BLM 7.5: Using Benchmarks to Order Fractions
249
L
Name:
Date:
7.5 Using Benchmarks to Order Fractions Page 1
Student Book pages 220–222
GOAL
You will need
Use benchmarks to compare and order fractions with
different denominators.
• pencil
crayons
benchmark
Problem
A familiar number or
measurement used
to compare other
numbers or
measurements
Cole and his friends played miniature golf.
This table shows how far each player hit the golf ball
on the first swing.
Cole
Joshua
Kate
3
� of the way to the hole �3� of the way to the hole
4
8
2
�� of the way to the hole
3
1
Which golf balls went more than �� the distance to
2
the hole?
1
Use � as a benchmark to help you decide.
2
Shade the fraction strips to show how far each ball went.
1
2
1
2
1
3
1
3
1
4
1
8
1
3
1
4
1
8
1
8
1
4
1
4
1
8
1
8
1
8
1
8
1
8
1
Which players hit their golf balls more than � the distance to the hole?
2
Whose golf ball went the greatest distance? ______________________
250
Learning BLM 7.5: Using Benchmarks to Order Fractions
Copyright © 2008 by Nelson Education Ltd.
L
Name:
Date:
7.5 Using Benchmarks to Order Fractions Page 2
Reflecting
1
How did using � as a benchmark help you compare the fractions?
2
Copyright © 2008 by Nelson Education Ltd.
Learning BLM 7.5: Using Benchmarks to Order Fractions
251