Topic 11 Fraction Equivalence and Ordering Exam Intervention Booklet
Topic 11 Fraction Equivalence and Ordering
Exam Intervention Booklet
Math Diagnosis and Intervention System Intervention Lesson
Name
G59
Factoring Numbers Materials color tiles or counters, 24 for each student The arrays below show all of the factors of 12.
1 12
26
34
43
62
1. What are all the factors of 12?
,
,
,
,
,
2. Create all the possible arrays you can with 17 color tiles. 3. What are the factors of 17?
12 1
,
Numbers which have only 2 possible arrays and exactly 2 factors are prime numbers. 4. Is 17 a prime number?
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5. Is 12 a prime number?
Numbers which have more than 2 possible arrays and more than 2 factors are composite numbers. 6. Is 17 a composite number? 7. Is 12 a composite number? 8. What are all the factors of 24? 9. Is 24 a prime number or a composite number?
Intervention Lesson G59
195
Math Diagnosis and Intervention System Intervention Lesson
Name
G59
Factoring Numbers (continued)
Find all the factors of each number. Tell whether each is prime or composite. 10. 7
11. 8
12. 21
13. 48
14. 51
15. 9
16. 13
17. 26
18. 40
19. 55
20. 70
21. 83
22. Mr. Lee has 18 desks in his room. He would like them
arranged in a rectangular array. Draw all the different possible arrays and write a multiplication sentence for each.
odd number. Is Lee’s reasoning correct? Give an example to prove your reasoning.
196 Intervention Lesson G59
© Pearson Education, Inc.
23. Reasoning Lee says 53 is a prime number because it is an
Math Diagnosis and Intervention System Intervention Lesson
Name
H5
Fractions on the Number Line Each fraction names a point on a number line. Name the missing fractions on the number line below by answering 1 to 3. 1 1 __
1 __
1 __
1 __
1 __
1 __
1 __
1 __
8
8
8
8
8
8
8
8
0
1 __
2 __
3 __
5 __
7 __
8
8
8
8
8
1
1. How many equal lengths is the distance between 0 and 1
divided into? Since, the distance between 0 and 1 is divided into 8 equal 1 lengths, each length is __ of the whole length. 8 2 __ 1 , __ __ , 3,
2. To name the first missing fraction, count by eighths.
8 8 8
4 Write __ in the first box above. 8 5 4 , __ __ ,
3. To name the next missing fraction, keep counting.
8 8
6 Write __ in the second box above. 8
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Name the missing numbers on the number line below by answering 4 to 6.
0
1 __
2 __
3 __
4 __
5
5
5
5
1
1 2 1__ 1__ 5 5
4 1__ 5
2
3 2 4 2__ 2__ 2__ 5 5 5
3
4. How many equal parts is the distance between 0 and 1
divided into? Since, the distance between 0 and 1 is divided into 5 equal lengths, 1 each length is __ of the whole length. 5 Intervention Lesson H5
93
Math Diagnosis and Intervention System Intervention Lesson
Name
H5
Fractions on the Number Line (continued) 5. To name the first missing fraction, count by fifths. 2 __ 4 1 __ 1 , __ __ , 3, __ , 1, 1__ , 12,
5 5 5 5 5 5 3 Write 1__ in the first box on the number line. 5
6. To name the second missing fraction, continue counting. 3 __ 1__ , 14 , 2, 5 5 1 Write 2__ in the second box on the number line. 5
Write the missing fraction or mixed number for each number line. 7.
0
1 __
2 __
5 __
7 __
9
9
9
9
1
8.
0
1 __
2 1__ 3
1
3
2
9. The number line shows how far Glen, Ned, and Lois ran in a one-mile
race. Write a fraction that shows how far Ned and Lois ran.
1 __
2 __
4
4
Ned stopped here.
Ned
94 Intervention Lesson H5
?
End
Lois stopped here.
Glen stopped here.
Lois
© Pearson Education, Inc.
Starting Point 0
Math Diagnosis and Intervention System Intervention Lesson
Name
H6
Using Models to Compare Fractions Materials fraction strips 4 2 Use ⬎, ⬍, or ⫽ to compare __ and __ by answering 1 to 3. 5 3 4 2 1. Show 1, __, and __ with 5 3
fraction strips. 2. Compare. Which is greater 4 2 __ in total length, __ or ? 5 3
1 1 __
1 __
1 __
1 __
5
5
5 1 __ 3
5
1 __ 3
4 2 3. Since __ is longer than __, 5 3 4 2 __ __ is greater than 3 . Write ⬎, ⬍, or ⫽. 5
4 __
2 __
5
3
1 1 and __ by answering 4 to 6. Compare ___ 4 10 1 1 4. Show 1, ___, and __ with fraction strips. 4 10
5. Compare. Which is greater 1 1 in total length, ___ or __ ? 4 10 1 1 6. Since ___ is shorter than __, 4 10 1 1 is less than __ ___ . Write ⬎, ⬍, or =. 4 10
1 1 ___ 10 1 __ 4 1 ___
1 __
10
4
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2 4 and ___ by answering 7 to 9. Compare __ 5 10 2 4 7. Show 1, __, and ___ with fraction strips. 5 10
8. Compare. Which is greater 2 4 in total length, __ or ___ ? 5 10
1 1 __
1 __
5
5
1 ___ 1 ___ 1 ___ 1 ___ 10 10 10 10
2 4 9. Since __ and ___ are the same length, 5 10 4 2 is equal to ___ __ . Write ⬎, ⬍, or ⫽. 10 5
2 __
4 ___
5
10
Intervention Lesson H6
95
Math Diagnosis and Intervention System Intervention Lesson
Name
H6
Using Models to Compare Fractions (continued)
Compare. Write , or =. 3 __
1 10. __ 4
2 __
3 11. __ 4
4
8
1 __ 4 1 __ 4
1 __
1 __
4
4
4 __
2 12. __ 3
1 __
1 __
4
4
4
1 __
1 __
8
8 5 ___
1 13. __ 5
6 1 __
1 __
3
3
10 1 __ 5
1 __
1 __
1 __
1 __
6
6
6
6
1 __
1 14. __ 2
1 __
5
1 ___ 1 ___ 1 ___ 1 ___ 1 ___ 10 10 10 10 10 3 __
7 15. __ 8
4
1 __
1 __
1 __
1 __
1 __
1 __
1 __
1 __
2
8
8
8
8
8
8
8
1 __ 5 1 __
2 16. __ 6
2 1 __
1 __
6
6 1 __ 2
1 __
1 __
1 __
4
4
4
1 __
3 17. __ 5
4 1 __
1 __
5 1 __ 4
5
19. Reasoning Two students are writing stories. 2 4 __ Eric’s story is __ of a page. Alba’s story is of 3 6
a page. Whose story is longer?
96 Intervention Lesson H6
5
© Pearson Education, Inc.
18. Reasoning Give 3 fractions with different 4 denominators that are less than __ . 6
1 __
Math Diagnosis and Intervention System Intervention Lesson
Name
H7
Using Models to Find Equivalent Fractions Materials fraction strips 3 Find a fraction equivalent to __ by answering 1 to 3. 4 3 1. Show a 1 and __ with fraction strips. 4 1 2. How many __ strips does 8 3 it take to equal __ ? 4
1 1 __
1 __
1 __
4
4
4
3 ⫽ _______ __ 4
8
1
3 1 3. So, __ is equal to six __ strips. 4 8
1 __
1 __
1 __
4
4
4
1 __
1 __
1 __
1 __
1 __
1 __
8
8
8
8
8
8
? 1 ____, Find the missing number in __ ⫽ 2 10 by answering 4 to 7. The denominators of the fractions tell which fraction strips to use. 1 4. Show 1 and __ with fraction strips. 2
5. What is the denominator of
the second fraction?
1 1 __ 2
6. Since the denominator of the second
1
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fraction is 10, find the number 1 1 strips equal to __ of ___ . 2 10
1 1 7. So, __ is equal to five ___ strips. 2 10
1 __ 2 1 ___ 1 ___ 1 ___ 1 ___ 1 ___ 10 10 10 10 10
1 __ ⫽ ____ 2
10
Intervention Lesson H7
97
Math Diagnosis and Intervention System Intervention Lesson
Name
H7
Using Models to Find Equivalent Fractions (continued)
Complete each number sentence. 8.
1
9.
1
1 __ 4 1 __
1 __
8
8
1 __
1 __
3
3
1 __
1 __
1 __
1 __
6
6
6
6
1 __ ⫽ _______ 4
2 __ ⫽ _______
8
10.
1
3
11.
1 __ 2 1 __
1 __
1 __
1 __
8
8
8
8
1 1 __
1 __
5
5
1 ___ 1 ___ 1 ___ 1 ___ 10 10 10 10
1 __ ⫽ _______ 2
12.
2 __ ⫽ _______ 5
8
1 1 __
1 __
3
3
1 ___ 1 ___ 1 ___ 1 ___ 1 ___ 1 ___ 1 ___ 1 ___ 12 12 12 12 12 12 12 12
12
10
13.
1 1 __
1 __
4
4
1 __
1 __
1 __
6
6
6 2 __ ⫽ _______ 4
2 14. Reasoning On Tuesday, __ of the class time was spent 3
on math projects. How many sixths of the class time was spent on math projects?
98 Intervention Lesson H7
6
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2 __ ⫽ _______ 3
6
Math Diagnosis and Intervention System Intervention Lesson
Name
H9
Comparing Fractions Materials fraction strips 3 7 Compare ___ and __ by answering 1 to 3. 10 8 1 Compare each fraction to __ . Write ⬎ or ⬍. 2 1 __
3 1. ___ 10
1 __
7 2. __ 8
2
2
1 __
1 __
2
2
1 ___ 1 ___ 1 ___ 10 10 10
3 3 1 7 1 3. Since ___ ⬍ __ and __ ⬎ __, then ___ 10 2 2 10 8
1 __
1 __
1 __
1 __
1 __
1 __
1 __
8
8
8
8
8
8
8
7 __ . 8
You can compare two fractions with the same denominator just by comparing the numerators. 5 1 Use equivalent fractions to compare __ and ___ by answering 4 to 6. 4 12 1 is the same as how many twelfths? 4. __ 4 3 3 5 1 5. Since __ = ___, you can now compare ___ and ___. 4 12 12 12
Which fraction has the greater numerator?
© Pearson Education, Inc.
6. Compare. Write ⬎ or ⬍.
3 ___
5 ___
12 1 So, __ 4
12 5 ___ . 12 1 1 7. Use fraction strips to compare __ and __. Write > or
Exam Intervention Booklet
Math Diagnosis and Intervention System Intervention Lesson
Name
G59
Factoring Numbers Materials color tiles or counters, 24 for each student The arrays below show all of the factors of 12.
1 12
26
34
43
62
1. What are all the factors of 12?
,
,
,
,
,
2. Create all the possible arrays you can with 17 color tiles. 3. What are the factors of 17?
12 1
,
Numbers which have only 2 possible arrays and exactly 2 factors are prime numbers. 4. Is 17 a prime number?
© Pearson Education, Inc.
5. Is 12 a prime number?
Numbers which have more than 2 possible arrays and more than 2 factors are composite numbers. 6. Is 17 a composite number? 7. Is 12 a composite number? 8. What are all the factors of 24? 9. Is 24 a prime number or a composite number?
Intervention Lesson G59
195
Math Diagnosis and Intervention System Intervention Lesson
Name
G59
Factoring Numbers (continued)
Find all the factors of each number. Tell whether each is prime or composite. 10. 7
11. 8
12. 21
13. 48
14. 51
15. 9
16. 13
17. 26
18. 40
19. 55
20. 70
21. 83
22. Mr. Lee has 18 desks in his room. He would like them
arranged in a rectangular array. Draw all the different possible arrays and write a multiplication sentence for each.
odd number. Is Lee’s reasoning correct? Give an example to prove your reasoning.
196 Intervention Lesson G59
© Pearson Education, Inc.
23. Reasoning Lee says 53 is a prime number because it is an
Math Diagnosis and Intervention System Intervention Lesson
Name
H5
Fractions on the Number Line Each fraction names a point on a number line. Name the missing fractions on the number line below by answering 1 to 3. 1 1 __
1 __
1 __
1 __
1 __
1 __
1 __
1 __
8
8
8
8
8
8
8
8
0
1 __
2 __
3 __
5 __
7 __
8
8
8
8
8
1
1. How many equal lengths is the distance between 0 and 1
divided into? Since, the distance between 0 and 1 is divided into 8 equal 1 lengths, each length is __ of the whole length. 8 2 __ 1 , __ __ , 3,
2. To name the first missing fraction, count by eighths.
8 8 8
4 Write __ in the first box above. 8 5 4 , __ __ ,
3. To name the next missing fraction, keep counting.
8 8
6 Write __ in the second box above. 8
© Pearson Education, Inc.
Name the missing numbers on the number line below by answering 4 to 6.
0
1 __
2 __
3 __
4 __
5
5
5
5
1
1 2 1__ 1__ 5 5
4 1__ 5
2
3 2 4 2__ 2__ 2__ 5 5 5
3
4. How many equal parts is the distance between 0 and 1
divided into? Since, the distance between 0 and 1 is divided into 5 equal lengths, 1 each length is __ of the whole length. 5 Intervention Lesson H5
93
Math Diagnosis and Intervention System Intervention Lesson
Name
H5
Fractions on the Number Line (continued) 5. To name the first missing fraction, count by fifths. 2 __ 4 1 __ 1 , __ __ , 3, __ , 1, 1__ , 12,
5 5 5 5 5 5 3 Write 1__ in the first box on the number line. 5
6. To name the second missing fraction, continue counting. 3 __ 1__ , 14 , 2, 5 5 1 Write 2__ in the second box on the number line. 5
Write the missing fraction or mixed number for each number line. 7.
0
1 __
2 __
5 __
7 __
9
9
9
9
1
8.
0
1 __
2 1__ 3
1
3
2
9. The number line shows how far Glen, Ned, and Lois ran in a one-mile
race. Write a fraction that shows how far Ned and Lois ran.
1 __
2 __
4
4
Ned stopped here.
Ned
94 Intervention Lesson H5
?
End
Lois stopped here.
Glen stopped here.
Lois
© Pearson Education, Inc.
Starting Point 0
Math Diagnosis and Intervention System Intervention Lesson
Name
H6
Using Models to Compare Fractions Materials fraction strips 4 2 Use ⬎, ⬍, or ⫽ to compare __ and __ by answering 1 to 3. 5 3 4 2 1. Show 1, __, and __ with 5 3
fraction strips. 2. Compare. Which is greater 4 2 __ in total length, __ or ? 5 3
1 1 __
1 __
1 __
1 __
5
5
5 1 __ 3
5
1 __ 3
4 2 3. Since __ is longer than __, 5 3 4 2 __ __ is greater than 3 . Write ⬎, ⬍, or ⫽. 5
4 __
2 __
5
3
1 1 and __ by answering 4 to 6. Compare ___ 4 10 1 1 4. Show 1, ___, and __ with fraction strips. 4 10
5. Compare. Which is greater 1 1 in total length, ___ or __ ? 4 10 1 1 6. Since ___ is shorter than __, 4 10 1 1 is less than __ ___ . Write ⬎, ⬍, or =. 4 10
1 1 ___ 10 1 __ 4 1 ___
1 __
10
4
© Pearson Education, Inc.
2 4 and ___ by answering 7 to 9. Compare __ 5 10 2 4 7. Show 1, __, and ___ with fraction strips. 5 10
8. Compare. Which is greater 2 4 in total length, __ or ___ ? 5 10
1 1 __
1 __
5
5
1 ___ 1 ___ 1 ___ 1 ___ 10 10 10 10
2 4 9. Since __ and ___ are the same length, 5 10 4 2 is equal to ___ __ . Write ⬎, ⬍, or ⫽. 10 5
2 __
4 ___
5
10
Intervention Lesson H6
95
Math Diagnosis and Intervention System Intervention Lesson
Name
H6
Using Models to Compare Fractions (continued)
Compare. Write , or =. 3 __
1 10. __ 4
2 __
3 11. __ 4
4
8
1 __ 4 1 __ 4
1 __
1 __
4
4
4 __
2 12. __ 3
1 __
1 __
4
4
4
1 __
1 __
8
8 5 ___
1 13. __ 5
6 1 __
1 __
3
3
10 1 __ 5
1 __
1 __
1 __
1 __
6
6
6
6
1 __
1 14. __ 2
1 __
5
1 ___ 1 ___ 1 ___ 1 ___ 1 ___ 10 10 10 10 10 3 __
7 15. __ 8
4
1 __
1 __
1 __
1 __
1 __
1 __
1 __
1 __
2
8
8
8
8
8
8
8
1 __ 5 1 __
2 16. __ 6
2 1 __
1 __
6
6 1 __ 2
1 __
1 __
1 __
4
4
4
1 __
3 17. __ 5
4 1 __
1 __
5 1 __ 4
5
19. Reasoning Two students are writing stories. 2 4 __ Eric’s story is __ of a page. Alba’s story is of 3 6
a page. Whose story is longer?
96 Intervention Lesson H6
5
© Pearson Education, Inc.
18. Reasoning Give 3 fractions with different 4 denominators that are less than __ . 6
1 __
Math Diagnosis and Intervention System Intervention Lesson
Name
H7
Using Models to Find Equivalent Fractions Materials fraction strips 3 Find a fraction equivalent to __ by answering 1 to 3. 4 3 1. Show a 1 and __ with fraction strips. 4 1 2. How many __ strips does 8 3 it take to equal __ ? 4
1 1 __
1 __
1 __
4
4
4
3 ⫽ _______ __ 4
8
1
3 1 3. So, __ is equal to six __ strips. 4 8
1 __
1 __
1 __
4
4
4
1 __
1 __
1 __
1 __
1 __
1 __
8
8
8
8
8
8
? 1 ____, Find the missing number in __ ⫽ 2 10 by answering 4 to 7. The denominators of the fractions tell which fraction strips to use. 1 4. Show 1 and __ with fraction strips. 2
5. What is the denominator of
the second fraction?
1 1 __ 2
6. Since the denominator of the second
1
© Pearson Education, Inc.
fraction is 10, find the number 1 1 strips equal to __ of ___ . 2 10
1 1 7. So, __ is equal to five ___ strips. 2 10
1 __ 2 1 ___ 1 ___ 1 ___ 1 ___ 1 ___ 10 10 10 10 10
1 __ ⫽ ____ 2
10
Intervention Lesson H7
97
Math Diagnosis and Intervention System Intervention Lesson
Name
H7
Using Models to Find Equivalent Fractions (continued)
Complete each number sentence. 8.
1
9.
1
1 __ 4 1 __
1 __
8
8
1 __
1 __
3
3
1 __
1 __
1 __
1 __
6
6
6
6
1 __ ⫽ _______ 4
2 __ ⫽ _______
8
10.
1
3
11.
1 __ 2 1 __
1 __
1 __
1 __
8
8
8
8
1 1 __
1 __
5
5
1 ___ 1 ___ 1 ___ 1 ___ 10 10 10 10
1 __ ⫽ _______ 2
12.
2 __ ⫽ _______ 5
8
1 1 __
1 __
3
3
1 ___ 1 ___ 1 ___ 1 ___ 1 ___ 1 ___ 1 ___ 1 ___ 12 12 12 12 12 12 12 12
12
10
13.
1 1 __
1 __
4
4
1 __
1 __
1 __
6
6
6 2 __ ⫽ _______ 4
2 14. Reasoning On Tuesday, __ of the class time was spent 3
on math projects. How many sixths of the class time was spent on math projects?
98 Intervention Lesson H7
6
© Pearson Education, Inc.
2 __ ⫽ _______ 3
6
Math Diagnosis and Intervention System Intervention Lesson
Name
H9
Comparing Fractions Materials fraction strips 3 7 Compare ___ and __ by answering 1 to 3. 10 8 1 Compare each fraction to __ . Write ⬎ or ⬍. 2 1 __
3 1. ___ 10
1 __
7 2. __ 8
2
2
1 __
1 __
2
2
1 ___ 1 ___ 1 ___ 10 10 10
3 3 1 7 1 3. Since ___ ⬍ __ and __ ⬎ __, then ___ 10 2 2 10 8
1 __
1 __
1 __
1 __
1 __
1 __
1 __
8
8
8
8
8
8
8
7 __ . 8
You can compare two fractions with the same denominator just by comparing the numerators. 5 1 Use equivalent fractions to compare __ and ___ by answering 4 to 6. 4 12 1 is the same as how many twelfths? 4. __ 4 3 3 5 1 5. Since __ = ___, you can now compare ___ and ___. 4 12 12 12
Which fraction has the greater numerator?
© Pearson Education, Inc.
6. Compare. Write ⬎ or ⬍.
3 ___
5 ___
12 1 So, __ 4
12 5 ___ . 12 1 1 7. Use fraction strips to compare __ and __. Write > or
