Topic 12 Adding and Subtracting Fractions and Mixed Numbers with ...
Topic 12 Adding and Subtracting Fractions and Mixed Numbers with Like Denominators
Exam Intervention Booklet
Math Diagnosis and Intervention System Intervention Lesson
Name
H36
Adding Fractions with Like Denominators Materials crayons or markers 2 1 Nur wove __ of a rug in February and __ of it in March. 5 5
Find what part of the rug she has finished in all by answering 1 to 4. 2 1. Color __ of the rectangle on the right. 5 1 __ 2. Color more of the rectangle on the right. 5 ____
3. How much of the rectangle
did you color in all? 3 2 1 2 1 This is the sum of __ and __ . So, __ __ __ . 5 5 5 5 5
4. What part of her rug has Nur finished in all? 2 2 Jamal wove __ of a rug in February and __ in March. 6 6
Find what part of the rug he has finished in all by answering 5 to 11. 2 5. Color __ of the rectangle on the right. 6 2 6. Color __ more of the rectangle on the right. 6
7. How much of the rectangle
____
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did you color in all? 2 2 8. What is __ __? 6 6 4 9. What is a fraction equivalent to __, 6
but with smaller numbers? Color the second rectangle to find out.
4 __ ____ 6
2 2 4 10. So, __ __ __ ____. 6 6 6
11. What part of his rug has Jamal finished in all? Intervention Lesson H36
155
Math Diagnosis and Intervention System Intervention Lesson
Name
H36
Adding Fractions with Like Denominators (continued) 1 4 12. Reasoning Explain how to add __ __. 9 9
Add. 13.
1 __
1 __
3
3
14.
15.
3
5
5
5
1 __
2 __
4
4
16.
4
5 2 __ 17. __ 8 8
1 __
1 __
1 __
1 __
1 __
6
6
6
6
6
3 2 __ __
2 1 __ __ 4
3 __
5
3 1 __ __
1 1 __ __ 3
1 __
6
6
2 3 ___ 18. ___ 10 10
1 19. Calvin bought a gallon of yogurt. He ate __ gallon 6 2 __ the first day, and 6 gallon the second day.
What fraction of the yogurt did he eat?
and white shirts. One-fifth of the class are wearing blue jeans and red shirts. One-fifth of the class are wearing brown pants and white shirts. What fraction of Mr. James’ class are wearing white shirts? 3 1 21. Reasoning What fraction would you add to __ to get __? 3 3
156 Intervention Lesson H36
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20. Three-fifths of Mr. James’ class are wearing blue jeans
Math Diagnosis and Intervention System Intervention Lesson
Name
H37
Subtracting Fractions with Like Denominators Materials crayons or markers
Tammy loves tuna bake. When she came home from school, she 6 1 found __ of a tuna bake on the stove. She ate __ of it. Find how 8 8
much of the tuna bake was left by answering 1 to 5. 6 1. Color __ of the rectangle on the right. 8 1 2. Cross out __ of the part you colored. 8
3. How much of the rectangle
you colored is not crossed out? ____
6 1 4. What is __ __? ____ 8 8
5. How much of the tuna bake
was left after Tammy ate? 3 Brad found __ of a submarine sandwich when he came home 4
1 from school. He ate __ of the sandwich. Find how much of the 4
sandwich was left by answering 6 to 12. 3 6. Color __ of the rectangle on the right. 4 1 7. Cross out __ of the part you colored. 4
8. How much of the rectangle
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you colored is not crossed out? ____
3 1 9. What is __ __? ____ 4 4 2 10. What is a fraction equivalent to __, but with smaller 4 2 numbers? Color the second rectangle to find out. __ ____ 4 3 1 2 11. So, __ – __ __ ____. 4 4 4
12. How much of the sandwich was left after Brad ate? Intervention Lesson H37
157
Math Diagnosis and Intervention System Intervention Lesson
Name
H37
Subtracting Fractions with Like Denominators (continued) 5 2 13. Reasoning Explain how to subtract ___ ___. 10 10
Subtract. 14.
1 __
1 __
6
6
1 __ 6
1 __
1 __
6
15.
5
3 5 __ __ 6
16.
4
1 __
1 __
5
5
5
1 __
1 __
4
17.
1 __
4
5
5
2 4 __ __
3 4 __ 18. __ 7 7
4 5 __ 19. __ 9 9
4
1 7 __ 20. __ 8 8
1 __
5
1 3 __ __ 4
1 __
1 3 __ __
6
1 __
1 __
6
5
The table shows the distances run by members of a track team. Use the table for Exercises 22 and 23.
23. How much farther did
Caro run than Tricia? 24. Reasoning Why would it be more difficult 2 1 2 1 to subtract __ __ than __ __ ? 3 6 3 3
158 Intervention Lesson H37
Runner
Distance in miles
Rosie
7 __
Tricia Amy Caro
8 4 __ 8 5 __ 8 6 __ 8
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Rosie run than Tricia?
5
5
1 4 __ 21. __ 6 6
22. How much farther did
1 __
5
Math Diagnosis and Intervention System Intervention Lesson
Name
H38
Adding and Subtracting Fractions with Like Denominators 3 3 Carlos spent __ hour writing email and another __ hour surfing the internet. 4 4
How much time did he spend on his computer in all? 3 3 __ by answering 1 to 4. Find __ 4 4 3 3 1. Show __ __ with fraction strips. 4 4 3 3 2. What is __ __ ? 4 4
1 1 __
1 __
1 __
1 __
1 __
1 __
4
4
4
4
4
4
6 3. Use the fraction strips to find __ as a mixed 4
number in simplest form. 3 3 6 __ __ __ 1____ 4
4
4
1
1
1
1 __
1 __
1 __
1 __
1 __
1 __
4
4
4
4
4
4
4
1 __
1
2
4. How much time did Carlos
spend on his computer in all? 9 7 5. Reasoning Explain how to find ___ ___. 10 10
5 Connie had __ hour to surf the internet. She finished with 6
1
1 hour. How much time did she have left? one site in __ 6
1 __ 1 __ 1 __ 1 __ 1 __
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5 1 Find __ __ by answering 6 to 11. 6 6
6 6 6 6 6
5 6. Show __ with fraction strips. 6 1 7. Take away __. 6 5 1 8. What is __ __? 6 6
1 1 __ 1 __ 1 __ 1 __ 6 6 6 6
4 9. Write the difference in simplest form. __ 6 5 1 4 10. So, __ __ __ 6 6 6
1 __
1 __
3
3
.
11. How much time did Connie have left to surf the internet?
Intervention Lesson H38
159
Math Diagnosis and Intervention System Intervention Lesson
Name
H38
Adding and Subtracting Fractions with Like Denominators (continued) 7 1 12. Reasoning Explain how to find __ __. 8 8
Add. Write the sum in simplest form. 1 5 13. ___ ___ 12 12
1 5 14. __ __ 9 9
8 4 ___ 15. ___ 15 15
4 3 16. __ __ 5 5
4 6 17. __ __ 7 7
2 2 __ 18. __ 3 3
9 7 ___ 19. ___ 10 10
5 7 __ 20. __ 8 8
5 11 ___ 21. ___ 12 12
Subtract. Write the difference in simplest form. 1 2 __ 22. __ 3 3
1 11 ___ 23. ___ 12 12
1 7 __ 24. __ 9 9
1 7 __ 25. __ 8 8
3 9 26. ___ ___ 10 10
1 3 27. __ __ 4 4
school gym, for the end of year party. The fifth grade class 9 7 has ___ of their chain finished. The sixth grade class has ___ 10 10 of theirs finished. How much more of the sixth grade chain is finished than the fifth grade chain? 7 29. Reasoning Richard gathered ___ of a dozen eggs and Karina gathered 12 5 ___ of a dozen. What part of a dozen did they gather in all? Explain. 12
160 Intervention Lesson H38
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28. Each class is making a friendship chain the length of the
Math Diagnosis and Intervention System Intervention Lesson
Name
H39
Adding and Subtracting Fractions on a Number Line Materials place-value blocks, for each student
9 1 _ or ___ Sarah walks ___ of the way to school. Then, she rides a bus _3 of 4 12 12 the way. Finally, she has to walk the rest of the way. When she gets off the bus, what part of the way to school is she? 9 1 Find ___ ___ by answering 1 to 4. 12 12 1 1. The number line below has an arrow from 0 to ___ to show how far 12
Sarah walks before she catches the bus. Draw another arrow that 9 1 is ___ units long, starting at ___ . 12 12
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2. At what fraction does your arrow end?
9 10 1 The two arrows show that ___ ___ ___ . 12 12 12 10 3. What is ___ in simplest form? 12 4. When Sarah gets off the bus, what part of the way to school is she?
When Sarah gets off the bus, how much farther does she need to walk to get to school? © Pearson Education, Inc.
10 12 ___ by answering 5 to 8. Find ___ 12 12 10 12 5. Draw an arrow that is ___ units long, from ___ or 1 back toward zero. 12 12
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6. At what fraction does your arrow end?
10 12 2 The number line shows that ___ ___ ___ . 12 12 12
Intervention Lesson H39
161
Math Diagnosis and Intervention System Intervention Lesson
Name
H39
Adding and Subtracting Fractions on a Number Line (continued)
2 7. What is ___ in simplest form? 12 8. When Sarah gets off the bus, how much farther
of the way
does she need to walk to get to school? Use the number line to add or subtract. Write answers in simplest form.
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4 3 9. ___ ___ 10 10 3 9 11. ___ ___ 10 10
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1 3 14. __ __ 8 8
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3 5 16. __ __ 8 8 2 4 17. Rodney mixed __ of a bottle of apple juice with __ of a bottle 9 9 1 15. _7_ __ 8 8
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4 2 1 18. Reasoning What is __ __ __? 9 9 9
162 Intervention Lesson H39
) .
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+ .
, .
.
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of cranberry juice. How much juice was in the mixture?
Math Diagnosis and Intervention System Intervention Lesson
Name
H43
Adding Mixed Numbers Materials fraction strips
Caroline is painting the ceiling border of her room. On Saturday, she 3 _ feet. How much did she painted 1__ feet. On Sunday, she painted 1_7 4 8 paint in the two days combined? 3 _ by answering 1 to 10. Find 1__ 1_7 4 8 3 7 1. Estimate. 1__ 1__ is about 4 8 3_ 7_ _ _ 2. Show 1 1 with fraction strips. 4 8
.
3 3. Put the ones together and the fractions together. Change __ to 4
eighths.
3 4. How many eighths equal __? Write the number in 4
the box at the right.
3 1__ 4 7 1__ 8
1____ 8 7 1__ 8
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5. Add the ones and write the sum at the right. Add 6 7 __ and __ and write the sum at the right. 8 8 13 6. Is ___ a proper fraction? 8 13 13 7. Since ___ is improper, simplify. What is ___ as a mixed number? 8 8
8
13 13 5 8. Fill in the blank. 2___ 2 ___ 2 1__ 8 8 8
3 7 9. What is 1__ 1__ ? 4 8 10. How much border did Caroline paint in the two days combined?
Intervention Lesson H43
169
Math Diagnosis and Intervention System Intervention Lesson
Name
H43
Adding Mixed Numbers (continued) 5 11. Is the answer 3__ close to the estimate of 4? 8 _ is close to the estimate of 4, 3_5_ is a reasonable answer. Since 3_5 8 8
Add. Write the sum as a simplified fraction. Estimate to check. 1 2__ 2
12.
3 5__ 8
1 6__ 9
17.
5 7 20. 6__ 1__ 8 6
3 1__ 4
14.
3 3___ 10
1 1__ 3
5 6__ 6
16.
1 1__ 5
13.
2 __ 5
3 4__ 4
18.
2 3__ 3
5 3__ 6
1 6___ 16
19.
5 7__ 6
3 1 21. 7__ 2__ 7 2
5 2___ 12
15.
3 4__ 8
5 1 22. 3___ 1__ 10 8
2 23. Ramona bought 1__ pounds of strawberries, 3 1_ _ _ pounds of oranges 24 pounds of apples, and 2_1 2
24. Reasoning Rhonda needs 4 gallons of green paint to decorate _ gallons of blue paint with 1_1_ gallons of her room. If she mixes 2_1 2 3
yellow paint, will she have enough? Explain.
170
Intervention Lesson H43
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at the store. What was the total weight of Ramona’s purchase?
Math Diagnosis and Intervention System Intervention Lesson
Name
H44
Subtracting Mixed Numbers Materials fraction strips
3 5 On Monday, Carmen swam 2__ miles and Katie swam 1__ miles. Answer 4 8 1 to 8 to find how much farther Carmen swam than Katie. 3 5 Find 2__ 1__ . 4 8 3 5 1. Estimate. 2__ 1__ is about 4 8 3 5 2. Show 2__ and 1__ with fraction strips. 4 8
.
3 3. How many eighths equal __? Write the number
in the box at the right.
4
3 2__ 2____ 4 8 5 5 1__ 1__ 8 8
4. Subtract the ones and subtract the fractions.
Fill in the boxes at the right.
8
3 5 5. What is 2__ 1__? 4 8 6. How much farther did Carmen swim than Katie?
1 7. Is 1__ close to the estimate of 1? 8 1 8. Is 1__ a reasonable answer? 8
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3 1 On Wednesday, Carmen swam 2__ miles and Katie swam 1__ miles. 4 8 Answer 9 to 18 to find how much farther Carmen swam than Katie. 3 1 Find 2__ 1__ . 4 8 3 1 9. Show 2__ and 1__ with fraction strips. 4 8
3 1 10. What is the least common denominator of __ and __? 4 8
Intervention Lesson H44
171
Math Diagnosis and Intervention System Intervention Lesson
Name
H44
Subtracting Mixed Numbers (continued) 3 11. How many eighths equal __? Write the number in 4
1 2__ 8
1 2__ 8
the box at the right. 3 ____ 1__ 4 1 8
6 1 __ 12. Compare. Write , , or . __ 8 8 6 1 __ __ Since 8 is less than 8 , you need to regroup. 1 13. What is 1__ as an improper fraction? 8 14. What is the missing number?
1 1 2__ 1 1__ 1 ____
8
8
8
Write this number at the right. 1 1 2__ 2__ 1____ 8 8 8
15. Subtract the ones. What is 1 1?
3 6 6 1__ 1__ 1__ 4 8 8
9 6 16. Subtract the fractions. What is __ __? 8 8
Write 3 at the right.
____
8
3 1 17. What is 2__ 1__? 8
4
18. How much farther did Carmen
swim than Katie on Wednesday? Subtract. Simplify, if possible. Estimate to check. 19.
2 2__ 3 1 1__ 6
4 2___ 10
20.
3 1__ 5
21.
1 5__ 4
22.
2 __ 5
of red material is needed. How much more blue material is needed than red material? 3 3 24. Reasoning If you have 7___ and you subtract ___, how much 16 16
do you have? 172 Intervention Lesson H44
5 1__ 6 © Pearson Education, Inc.
3 1 23. To make a dress, 1__ yards of blue material is needed and __ yard 4 6
7 6__ 8
Math Diagnosis and Intervention System Intervention Lesson
Name
J33
Make and Test Conjectures If a number n is a factor of a number m, what is true about the factors of n and m? Solve by answering 1 to 5. Start by looking at some examples and making a conjecture. 1. The table below has some examples for m and n. Notice each value
of n is a factor of the value of m in the same row. Complete the table. m 12
Factors of m
n
1, 2, 3, 4, 6, 12
6
28
14
24
12
36
12
36
18
Factors of n 1, 2, 3, 6
2. Complete the conjecture.
If a number n is a factor of a number m, then all the factors of are factors
.
A counterexample, is an example which proves a conjecture is not true. 3. Try to find a counterexample for your conjecture. List the numbers
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you try.
and
and
and
4. Could you find a counterexample?
A counterexample can prove a conjecture is false, but it cannot prove that a conjecture is true. 5. Is your conjecture proven false?
Is it proven true?
Intervention Lesson J33
103
Math Diagnosis and Intervention System Intervention Lesson
Name
J33
Make and Test Conjectures (continued) Make and test a conjecture about the factors of n and twice n by answering 6 to 9. 6. Complete the table. Look for a pattern.
n
Number of Factors of n
2n
Number of Factors of 2n
6
4
12
6
14
28
12
24
40
80
7. Complete the conjecture.
The number that is twice n has
more factors than n.
8. Try to find a counterexample for your conjecture. Either give the
counterexample or list at least 3 sets of numbers you try.
9. Is your conjecture proven false?
Is it proven true?
Write a conjecture to answer each question. 10. How are the patterns alike?
Benita’s pattern is: 2, 4, 6, 8, 10, 12, 14, … Carol’s pattern is: 1, 3, 5, 7, 9, 11, 13, … 11. How did Beth sort the shapes
12. Make another conjecture about how
Beth sort the shapes.
104 Intervention Lesson J33
Group A
Group B © Pearson Education, Inc.
into Groups A and B?
Exam Intervention Booklet
Math Diagnosis and Intervention System Intervention Lesson
Name
H36
Adding Fractions with Like Denominators Materials crayons or markers 2 1 Nur wove __ of a rug in February and __ of it in March. 5 5
Find what part of the rug she has finished in all by answering 1 to 4. 2 1. Color __ of the rectangle on the right. 5 1 __ 2. Color more of the rectangle on the right. 5 ____
3. How much of the rectangle
did you color in all? 3 2 1 2 1 This is the sum of __ and __ . So, __ __ __ . 5 5 5 5 5
4. What part of her rug has Nur finished in all? 2 2 Jamal wove __ of a rug in February and __ in March. 6 6
Find what part of the rug he has finished in all by answering 5 to 11. 2 5. Color __ of the rectangle on the right. 6 2 6. Color __ more of the rectangle on the right. 6
7. How much of the rectangle
____
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did you color in all? 2 2 8. What is __ __? 6 6 4 9. What is a fraction equivalent to __, 6
but with smaller numbers? Color the second rectangle to find out.
4 __ ____ 6
2 2 4 10. So, __ __ __ ____. 6 6 6
11. What part of his rug has Jamal finished in all? Intervention Lesson H36
155
Math Diagnosis and Intervention System Intervention Lesson
Name
H36
Adding Fractions with Like Denominators (continued) 1 4 12. Reasoning Explain how to add __ __. 9 9
Add. 13.
1 __
1 __
3
3
14.
15.
3
5
5
5
1 __
2 __
4
4
16.
4
5 2 __ 17. __ 8 8
1 __
1 __
1 __
1 __
1 __
6
6
6
6
6
3 2 __ __
2 1 __ __ 4
3 __
5
3 1 __ __
1 1 __ __ 3
1 __
6
6
2 3 ___ 18. ___ 10 10
1 19. Calvin bought a gallon of yogurt. He ate __ gallon 6 2 __ the first day, and 6 gallon the second day.
What fraction of the yogurt did he eat?
and white shirts. One-fifth of the class are wearing blue jeans and red shirts. One-fifth of the class are wearing brown pants and white shirts. What fraction of Mr. James’ class are wearing white shirts? 3 1 21. Reasoning What fraction would you add to __ to get __? 3 3
156 Intervention Lesson H36
© Pearson Education, Inc.
20. Three-fifths of Mr. James’ class are wearing blue jeans
Math Diagnosis and Intervention System Intervention Lesson
Name
H37
Subtracting Fractions with Like Denominators Materials crayons or markers
Tammy loves tuna bake. When she came home from school, she 6 1 found __ of a tuna bake on the stove. She ate __ of it. Find how 8 8
much of the tuna bake was left by answering 1 to 5. 6 1. Color __ of the rectangle on the right. 8 1 2. Cross out __ of the part you colored. 8
3. How much of the rectangle
you colored is not crossed out? ____
6 1 4. What is __ __? ____ 8 8
5. How much of the tuna bake
was left after Tammy ate? 3 Brad found __ of a submarine sandwich when he came home 4
1 from school. He ate __ of the sandwich. Find how much of the 4
sandwich was left by answering 6 to 12. 3 6. Color __ of the rectangle on the right. 4 1 7. Cross out __ of the part you colored. 4
8. How much of the rectangle
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you colored is not crossed out? ____
3 1 9. What is __ __? ____ 4 4 2 10. What is a fraction equivalent to __, but with smaller 4 2 numbers? Color the second rectangle to find out. __ ____ 4 3 1 2 11. So, __ – __ __ ____. 4 4 4
12. How much of the sandwich was left after Brad ate? Intervention Lesson H37
157
Math Diagnosis and Intervention System Intervention Lesson
Name
H37
Subtracting Fractions with Like Denominators (continued) 5 2 13. Reasoning Explain how to subtract ___ ___. 10 10
Subtract. 14.
1 __
1 __
6
6
1 __ 6
1 __
1 __
6
15.
5
3 5 __ __ 6
16.
4
1 __
1 __
5
5
5
1 __
1 __
4
17.
1 __
4
5
5
2 4 __ __
3 4 __ 18. __ 7 7
4 5 __ 19. __ 9 9
4
1 7 __ 20. __ 8 8
1 __
5
1 3 __ __ 4
1 __
1 3 __ __
6
1 __
1 __
6
5
The table shows the distances run by members of a track team. Use the table for Exercises 22 and 23.
23. How much farther did
Caro run than Tricia? 24. Reasoning Why would it be more difficult 2 1 2 1 to subtract __ __ than __ __ ? 3 6 3 3
158 Intervention Lesson H37
Runner
Distance in miles
Rosie
7 __
Tricia Amy Caro
8 4 __ 8 5 __ 8 6 __ 8
© Pearson Education, Inc.
Rosie run than Tricia?
5
5
1 4 __ 21. __ 6 6
22. How much farther did
1 __
5
Math Diagnosis and Intervention System Intervention Lesson
Name
H38
Adding and Subtracting Fractions with Like Denominators 3 3 Carlos spent __ hour writing email and another __ hour surfing the internet. 4 4
How much time did he spend on his computer in all? 3 3 __ by answering 1 to 4. Find __ 4 4 3 3 1. Show __ __ with fraction strips. 4 4 3 3 2. What is __ __ ? 4 4
1 1 __
1 __
1 __
1 __
1 __
1 __
4
4
4
4
4
4
6 3. Use the fraction strips to find __ as a mixed 4
number in simplest form. 3 3 6 __ __ __ 1____ 4
4
4
1
1
1
1 __
1 __
1 __
1 __
1 __
1 __
4
4
4
4
4
4
4
1 __
1
2
4. How much time did Carlos
spend on his computer in all? 9 7 5. Reasoning Explain how to find ___ ___. 10 10
5 Connie had __ hour to surf the internet. She finished with 6
1
1 hour. How much time did she have left? one site in __ 6
1 __ 1 __ 1 __ 1 __ 1 __
© Pearson Education, Inc.
5 1 Find __ __ by answering 6 to 11. 6 6
6 6 6 6 6
5 6. Show __ with fraction strips. 6 1 7. Take away __. 6 5 1 8. What is __ __? 6 6
1 1 __ 1 __ 1 __ 1 __ 6 6 6 6
4 9. Write the difference in simplest form. __ 6 5 1 4 10. So, __ __ __ 6 6 6
1 __
1 __
3
3
.
11. How much time did Connie have left to surf the internet?
Intervention Lesson H38
159
Math Diagnosis and Intervention System Intervention Lesson
Name
H38
Adding and Subtracting Fractions with Like Denominators (continued) 7 1 12. Reasoning Explain how to find __ __. 8 8
Add. Write the sum in simplest form. 1 5 13. ___ ___ 12 12
1 5 14. __ __ 9 9
8 4 ___ 15. ___ 15 15
4 3 16. __ __ 5 5
4 6 17. __ __ 7 7
2 2 __ 18. __ 3 3
9 7 ___ 19. ___ 10 10
5 7 __ 20. __ 8 8
5 11 ___ 21. ___ 12 12
Subtract. Write the difference in simplest form. 1 2 __ 22. __ 3 3
1 11 ___ 23. ___ 12 12
1 7 __ 24. __ 9 9
1 7 __ 25. __ 8 8
3 9 26. ___ ___ 10 10
1 3 27. __ __ 4 4
school gym, for the end of year party. The fifth grade class 9 7 has ___ of their chain finished. The sixth grade class has ___ 10 10 of theirs finished. How much more of the sixth grade chain is finished than the fifth grade chain? 7 29. Reasoning Richard gathered ___ of a dozen eggs and Karina gathered 12 5 ___ of a dozen. What part of a dozen did they gather in all? Explain. 12
160 Intervention Lesson H38
© Pearson Education, Inc.
28. Each class is making a friendship chain the length of the
Math Diagnosis and Intervention System Intervention Lesson
Name
H39
Adding and Subtracting Fractions on a Number Line Materials place-value blocks, for each student
9 1 _ or ___ Sarah walks ___ of the way to school. Then, she rides a bus _3 of 4 12 12 the way. Finally, she has to walk the rest of the way. When she gets off the bus, what part of the way to school is she? 9 1 Find ___ ___ by answering 1 to 4. 12 12 1 1. The number line below has an arrow from 0 to ___ to show how far 12
Sarah walks before she catches the bus. Draw another arrow that 9 1 is ___ units long, starting at ___ . 12 12
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2. At what fraction does your arrow end?
9 10 1 The two arrows show that ___ ___ ___ . 12 12 12 10 3. What is ___ in simplest form? 12 4. When Sarah gets off the bus, what part of the way to school is she?
When Sarah gets off the bus, how much farther does she need to walk to get to school? © Pearson Education, Inc.
10 12 ___ by answering 5 to 8. Find ___ 12 12 10 12 5. Draw an arrow that is ___ units long, from ___ or 1 back toward zero. 12 12
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6. At what fraction does your arrow end?
10 12 2 The number line shows that ___ ___ ___ . 12 12 12
Intervention Lesson H39
161
Math Diagnosis and Intervention System Intervention Lesson
Name
H39
Adding and Subtracting Fractions on a Number Line (continued)
2 7. What is ___ in simplest form? 12 8. When Sarah gets off the bus, how much farther
of the way
does she need to walk to get to school? Use the number line to add or subtract. Write answers in simplest form.
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4 3 9. ___ ___ 10 10 3 9 11. ___ ___ 10 10
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3 5 16. __ __ 8 8 2 4 17. Rodney mixed __ of a bottle of apple juice with __ of a bottle 9 9 1 15. _7_ __ 8 8
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1 7 ___ 10. ___ 10 10
) -
4 13. _1_ __ 8 8
, &%
%
& .
' .
( .
4 2 1 18. Reasoning What is __ __ __? 9 9 9
162 Intervention Lesson H39
) .
* .
+ .
, .
.
&
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of cranberry juice. How much juice was in the mixture?
Math Diagnosis and Intervention System Intervention Lesson
Name
H43
Adding Mixed Numbers Materials fraction strips
Caroline is painting the ceiling border of her room. On Saturday, she 3 _ feet. How much did she painted 1__ feet. On Sunday, she painted 1_7 4 8 paint in the two days combined? 3 _ by answering 1 to 10. Find 1__ 1_7 4 8 3 7 1. Estimate. 1__ 1__ is about 4 8 3_ 7_ _ _ 2. Show 1 1 with fraction strips. 4 8
.
3 3. Put the ones together and the fractions together. Change __ to 4
eighths.
3 4. How many eighths equal __? Write the number in 4
the box at the right.
3 1__ 4 7 1__ 8
1____ 8 7 1__ 8
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5. Add the ones and write the sum at the right. Add 6 7 __ and __ and write the sum at the right. 8 8 13 6. Is ___ a proper fraction? 8 13 13 7. Since ___ is improper, simplify. What is ___ as a mixed number? 8 8
8
13 13 5 8. Fill in the blank. 2___ 2 ___ 2 1__ 8 8 8
3 7 9. What is 1__ 1__ ? 4 8 10. How much border did Caroline paint in the two days combined?
Intervention Lesson H43
169
Math Diagnosis and Intervention System Intervention Lesson
Name
H43
Adding Mixed Numbers (continued) 5 11. Is the answer 3__ close to the estimate of 4? 8 _ is close to the estimate of 4, 3_5_ is a reasonable answer. Since 3_5 8 8
Add. Write the sum as a simplified fraction. Estimate to check. 1 2__ 2
12.
3 5__ 8
1 6__ 9
17.
5 7 20. 6__ 1__ 8 6
3 1__ 4
14.
3 3___ 10
1 1__ 3
5 6__ 6
16.
1 1__ 5
13.
2 __ 5
3 4__ 4
18.
2 3__ 3
5 3__ 6
1 6___ 16
19.
5 7__ 6
3 1 21. 7__ 2__ 7 2
5 2___ 12
15.
3 4__ 8
5 1 22. 3___ 1__ 10 8
2 23. Ramona bought 1__ pounds of strawberries, 3 1_ _ _ pounds of oranges 24 pounds of apples, and 2_1 2
24. Reasoning Rhonda needs 4 gallons of green paint to decorate _ gallons of blue paint with 1_1_ gallons of her room. If she mixes 2_1 2 3
yellow paint, will she have enough? Explain.
170
Intervention Lesson H43
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at the store. What was the total weight of Ramona’s purchase?
Math Diagnosis and Intervention System Intervention Lesson
Name
H44
Subtracting Mixed Numbers Materials fraction strips
3 5 On Monday, Carmen swam 2__ miles and Katie swam 1__ miles. Answer 4 8 1 to 8 to find how much farther Carmen swam than Katie. 3 5 Find 2__ 1__ . 4 8 3 5 1. Estimate. 2__ 1__ is about 4 8 3 5 2. Show 2__ and 1__ with fraction strips. 4 8
.
3 3. How many eighths equal __? Write the number
in the box at the right.
4
3 2__ 2____ 4 8 5 5 1__ 1__ 8 8
4. Subtract the ones and subtract the fractions.
Fill in the boxes at the right.
8
3 5 5. What is 2__ 1__? 4 8 6. How much farther did Carmen swim than Katie?
1 7. Is 1__ close to the estimate of 1? 8 1 8. Is 1__ a reasonable answer? 8
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3 1 On Wednesday, Carmen swam 2__ miles and Katie swam 1__ miles. 4 8 Answer 9 to 18 to find how much farther Carmen swam than Katie. 3 1 Find 2__ 1__ . 4 8 3 1 9. Show 2__ and 1__ with fraction strips. 4 8
3 1 10. What is the least common denominator of __ and __? 4 8
Intervention Lesson H44
171
Math Diagnosis and Intervention System Intervention Lesson
Name
H44
Subtracting Mixed Numbers (continued) 3 11. How many eighths equal __? Write the number in 4
1 2__ 8
1 2__ 8
the box at the right. 3 ____ 1__ 4 1 8
6 1 __ 12. Compare. Write , , or . __ 8 8 6 1 __ __ Since 8 is less than 8 , you need to regroup. 1 13. What is 1__ as an improper fraction? 8 14. What is the missing number?
1 1 2__ 1 1__ 1 ____
8
8
8
Write this number at the right. 1 1 2__ 2__ 1____ 8 8 8
15. Subtract the ones. What is 1 1?
3 6 6 1__ 1__ 1__ 4 8 8
9 6 16. Subtract the fractions. What is __ __? 8 8
Write 3 at the right.
____
8
3 1 17. What is 2__ 1__? 8
4
18. How much farther did Carmen
swim than Katie on Wednesday? Subtract. Simplify, if possible. Estimate to check. 19.
2 2__ 3 1 1__ 6
4 2___ 10
20.
3 1__ 5
21.
1 5__ 4
22.
2 __ 5
of red material is needed. How much more blue material is needed than red material? 3 3 24. Reasoning If you have 7___ and you subtract ___, how much 16 16
do you have? 172 Intervention Lesson H44
5 1__ 6 © Pearson Education, Inc.
3 1 23. To make a dress, 1__ yards of blue material is needed and __ yard 4 6
7 6__ 8
Math Diagnosis and Intervention System Intervention Lesson
Name
J33
Make and Test Conjectures If a number n is a factor of a number m, what is true about the factors of n and m? Solve by answering 1 to 5. Start by looking at some examples and making a conjecture. 1. The table below has some examples for m and n. Notice each value
of n is a factor of the value of m in the same row. Complete the table. m 12
Factors of m
n
1, 2, 3, 4, 6, 12
6
28
14
24
12
36
12
36
18
Factors of n 1, 2, 3, 6
2. Complete the conjecture.
If a number n is a factor of a number m, then all the factors of are factors
.
A counterexample, is an example which proves a conjecture is not true. 3. Try to find a counterexample for your conjecture. List the numbers
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you try.
and
and
and
4. Could you find a counterexample?
A counterexample can prove a conjecture is false, but it cannot prove that a conjecture is true. 5. Is your conjecture proven false?
Is it proven true?
Intervention Lesson J33
103
Math Diagnosis and Intervention System Intervention Lesson
Name
J33
Make and Test Conjectures (continued) Make and test a conjecture about the factors of n and twice n by answering 6 to 9. 6. Complete the table. Look for a pattern.
n
Number of Factors of n
2n
Number of Factors of 2n
6
4
12
6
14
28
12
24
40
80
7. Complete the conjecture.
The number that is twice n has
more factors than n.
8. Try to find a counterexample for your conjecture. Either give the
counterexample or list at least 3 sets of numbers you try.
9. Is your conjecture proven false?
Is it proven true?
Write a conjecture to answer each question. 10. How are the patterns alike?
Benita’s pattern is: 2, 4, 6, 8, 10, 12, 14, … Carol’s pattern is: 1, 3, 5, 7, 9, 11, 13, … 11. How did Beth sort the shapes
12. Make another conjecture about how
Beth sort the shapes.
104 Intervention Lesson J33
Group A
Group B © Pearson Education, Inc.
into Groups A and B?
