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and represent on a number line positive and negative
UNDERLYING SKILLS AND CONCEPTS:
integers, decimals, fractions and mixed numbers.
use a number line;
understand fraction families;
understand mixed numbers
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Mixed Numbers on a Number Line
A fraction represents a value between two whole numbers.
When the numerator is less than the denominator, the fraction is
between 0 and 1.
When the numerator is greater than the denominator, the fraction is greater than 1.
Hey! This fraction
Proper fractions are less than 1.
is greater than one.
Improper fractions are greater than 1.
It is an
improper fraction!
You can show fractions on number a line.
1
8
1
4
1
2
E x am p l E
3
4
7
8
1
1
0
1
10
2
10
3
10
4
10
5
10
6
10
Ms.
Fract
10 ! 1 " 11
10
10
10
The number line shows tenths between 0 and 1.
0
10
9
8
1
7
10
8
10
9
10
10
10
11
10
1 2 3 4 5 6 7 8 9 10
10
! , ! , ! , ! , ! , ! , ! , ! , ! , ! . Note: ! equals 1 or one whole.
The fractions are 10
10 10 10 10 10 10 10 10 10
10
1
2
! is the same as 0.1, ! is the same as 0.2, and so on.
Note also that 10
10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
9
10
10
10
11
10
E x am p l E
2
This number line shows mixed numbers between the numbers 1 and 2.
1
11
8
11
4
11
2
13
4
17
8
2
21
8
Remember that:
1
mixed numbers have two parts: a whole number and a fraction: 1 !4 is a mixed number.
mixed numbers are another way to show improper fractions:
page 162
1
5
1 !4 is equal to !4 .
Chapter 14 – Lesson 3
E – © CSL Associates, Inc. All rights reserved.
0
Name
P RAC T I C E
Complete a number line for each set of fractions or mixed numbers. Be sure to show the whole
numbers between which the fractions or mixed numbers belong.
1 2 3
1. 3, 3, 3
1 2 3 4 5 6
2. 6, 6, 6, 6, 6, 6
1 2 3 4
3. 2 5, 25, 25, 25
Look at each number line below. Answer each question.
P
4. What fraction is represented by
E – © CSL Associates, Inc. All rights reserved.
point P? Explain how you decided.
0
1
5
; there are 6 equal parts, and P is at the end of the fifth part.
6
5. What fraction is represented by
Q
point Q? Explain how you decided.
0
1
5
; there are 12 equal parts, and Q is at the end of the fifth part.
12
R
6. What mixed number is represented by
point R? Explain how you decided.
3
4
5
; there are 8 equal parts, R is at the end of the fifth part past the 3
38
Math
Reasoning
Fractions and Whole Numbers
7. Can you write a mixed number using only 3s?
MR 1.1, 2.3
Yes
Give an example and explain your thinking.
3
3
3
3
Possible answer: 3 , 3, 3 , ... Note that 3 is another way
3
3
33
333
to show the number 4.
Chapter 14 – Lesson 3
page 163
MCX94.HW.CL.G5.FM&Lesson.v211
8/2/04
18:03
Page 110
Name
…at home!
P RAC T I C E
Complete a number line for each set of fractions or mixed numbers. Be sure to show the whole
numbers between which the fractions or mixed numbers belong.
1 2 3 4 5
1. , , , , 5 5 5 5 5
1 2 3 4 5 6
2. , , , , , 8 8 8 8 8 8
1 2 3 4
3. 3 , 3 , 3 , 3 6 6 6 6
Look at each number line below. Answer each question.
P
4. What fraction is represented by
Q
5. What fraction is represented by
0
1
point Q? Explain how you decided.
9
;Count the segments between 0 and 1 to get the denominator.
12
Count the segments to Q to get the numerator.
Math
Reasoning
Fractions and Whole Numbers
6. Can you write a mixed number using only 3s?
MR 1.1, 2.3
Yes
Give an example and explain your thinking.
3
3
3
, 3, 3 , ...
Possible answer: 3 3
33
333
page 110
Home Resource and Homework
Chapter 14 Lesson 3
E – © CSL Associates, Inc. All rights reserved.
point P? Explain how you decided.
0
1
2
; Count the segments between 0 and 1 to get the denominator.
6
Count the segments to P for the numerator.
MCX94TEG5CH01_32.v7.4.2 2/24/01 19:46 Page 301
Name
P RAC T I C E
Complete a number line for each set of fractions or mixed numbers. Be sure to show the whole
numbers between which the fractions or mixed numbers belong.
1
1. ,
3
2 3
, 3 3
1
2. ,
6
2
,
6
0
1
3
5 6
, 6 6
0
1 2 3 4
3. 2 , 2 , 2 , 2 5 5 5 5
2
3
,
6
1
4
,
6
2
3
3
3
1
1
6
2
6
3
6
4
6
5
6
6
6
3
21
5
22
5
23
24
5
5
Look at each number line below. Answer each question.
P
4. What fraction is represented by
E – © CSL Associates, Inc. All rights reserved.
point P? Explain how you decided.
0
1
5
; there are 6 equal parts, and P is at the end of the fifth part.
6
5. What fraction is represented by
Q
point Q? Explain how you decided.
0
1
5
; there are 12 equal parts, and Q is at the end of the fifth part.
12
R
6. What mixed number is represented by
point R? Explain how you decided.
3
4
5
; there are 8 equal parts, R is at the end of the fifth part past the 3
38
Math
Reasoning
Fractions and Whole Numbers
7. Can you write a mixed number using only 3s?
MR 1.1, 2.3
Yes
Give an example and explain your thinking.
3
3
3
3
Possible answer: 3 , 3, 3 , ... Note that 3 is another way
3
3
33
333
to show the number 4.
Chapter 14 – Lesson 3
Student Book Page
page 163
Name
…at home!
P RAC T I C E
Complete a number line for each set of fractions or mixed numbers. Be sure to show the whole
numbers between which the fractions or mixed numbers belong.
1 2 3 4 5
1. 5, 5, 5, 5, 5
0
1 2 3 4 5 6
2. 8, 8, 8, 8, 8, 8
0
1 2 3 4
3. 3 6, 36, 36, 36
3
1
1
5
2
5
3
5
4
5
5
5
1
1
8
2
8
3
8
4
8
5
8
6
8
7
8
8
8
4
31
6
32
6
33
34
6
6
Look at each number line below. Answer each question.
P
4. What fraction is represented by
Q
5. What fraction is represented by
0
1
point Q? Explain how you decided.
9
;Count the segments between 0 and 1 to get the denominator.
12
Count the segments to Q to get the numerator.
Math
Reasoning
Fractions and Whole Numbers
6. Can you write a mixed number using only 3s?
MR 1.1, 2.3
Yes
Give an example and explain your thinking.
3
3
3
, 3, 3 , ...
Possible answer: 3 3
33
333
page 110
Home Resource and Homework
Chapter 14 Lesson 3
E – © CSL Associates, Inc. All rights reserved.
point P? Explain how you decided.
0
1
2
; Count the segments between 0 and 1 to get the denominator.
6
Count the segments to P for the numerator.