Topic 15 Solving Measurement Problems Exam Intervention Booklet
Topic 15 Solving Measurement Problems
Exam Intervention Booklet
Math Diagnosis and Intervention System Intervention Lesson
Name
H11
Counting Money Gary has a $1 bill, a quarter, 2 dimes, a nickel, and a penny. When you count money, start with the bill or coin of greatest value. Then count on to find the total. 1. Count Gary’s money.
$1.00
$1.35
2. How much money does Gary have? 3. Write $1.51 in words.
one dollar and
cents
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4. Ty has a $1 bill, a half-dollar, 2 quarters, and 3 dimes. Count Ty’s money.
$1.00
$2.10
5. How much money does Ty have? 6. Who had more money, Gary or Ty? Intervention Lesson H11
105
Math Diagnosis and Intervention System Intervention Lesson
Name
H11
Counting Money (continued)
Write the total value in dollars and cents. 7.
8. 1 five-dollar bill, 3 quarters,
9. 1 one-dollar bill, 1 half-dollar,
1 nickel, 2 pennies
4 nickels, 8 pennies
10. 1 one-dollar bill, 2 quarters,
11. 1 five-dollar bill, 1 one-dollar bill,
4 dimes, 3 nickels, 1 penny
1 quarter, 4 dimes, 3 nickels
Compare the amounts. Write ⬍, ⬎, or ⫽. 12. $1.17
4 quarters, 2 dimes $1.10
4 dimes, 1 nickel
15. 3 half-dollars, 3 nickels
$1.70
16. Reasoning Anita and Ted both have $1.49, but each have different coins.
What coins could each have?
106
Intervention Lesson H11
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14. 2 quarters, 6 dimes
13. $0.49
Math Diagnosis and Intervention System Intervention Lesson
Name
H12
Making Change Ivan bought a plastic dinosaur for $3.68. He paid with a $5 bill. Answer 1 to 10 to find how much change Ivan received. To make change, start with coins that will make it easier to skip count. Count up to the amount you paid. 1. Start with $3.68. Count on with pennies until you get to an
amount that ends in 0 or 5. $3.68,
$3.69,
2. How many pennies did you count? 3. How much are 2 pennies worth?
$0.
4. Count on from $3.70 with dimes.
$3.70,
,
,
5. How many dimes did you count? 6. How much is 3 dimes and 2 pennies worth?
$0.
7. Count on from $4.00 with one-dollar bills until you get to
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the $5.00 Ivan paid. $4.00,
8. How many dollar bills did you count? 9. How much is 1 dollar bill, 3 dimes
and 2 pennies worth?
$
. Intervention Lesson H12
107
Math Diagnosis and Intervention System Name
Intervention Lesson
H12
Making Change (continued) 10. How much change did Ivan receive?
List the coins and bills you would use to make change. Then write the change in dollars and cents. 11. Cost: $1.40
Amount paid: $2.00
12. Cost: $3.17
Amount paid: $4.00
13. Cost: $0.76
Amount paid: $5.00
14. Cost: $1.33
Amount paid: $5.00
She used three $1 bills. Give two ways to show the change. Circle the one that uses the fewest coins.
108 Intervention Lesson H12
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15. Reasoning Beverly bought a gallon of juice for $2.69.
Math Diagnosis and Intervention System Intervention Lesson
Name
I48
Rectangles with the Same Area or Perimeter Materials colored pencils or crayons.
Ms. Arellano’s class is making a sand box shaped like a rectangle for the kindergarten class. They have 16 feet of wood to put around the sand box. What length and width should the sand box be so it has the greatest area? Each of the rectangles in the grid at the right has a perimeter of 16 feet. Find which rectangle has the greatest area by answering 1 to 3.
8
7
9
1. Complete the table. The formula for
:
area of a rectangle is A ᐉ w. Rectangle
Length
Width
Area (square units)
W X Y Z 2. What are the length and width of the rectangle with
the greatest area? 3. What length and width should Ms. Arellano’s class
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use for the sand box? 4. Reasoning Tracy told Tomas that if a two rectangles have
the same perimeter, they have the same area. Is Tracy correct? Explain your reasoning.
Mr. Katz has 30 carpet squares to make a reading area in his classroom. Each square is one foot on a side. He wants to make the area in the shape of a rectangle with the least possible border. How should he arrange the carpet squares? Intervention Lesson I48
185
Math Diagnosis and Intervention System Intervention Lesson
Name
I48
Rectangles with the Same Area or Perimeter (continued)
Each of the rectangles on the grid at the right has an area of 30 square feet. Find which one has the least perimeter by answering 5 to 8.
2ECTANGLE
5. What is the perimeter of Rectangle 1? 2ECTANGLE
P 2ᐉ 2w 2(
) 2(5)
feet
6. What is the perimeter of Rectangle 2?
P 2ᐉ 2w 2(
) 2(3)
feet
7. What is the length and width of the rectangle with
the least perimeter? 8. How should Mr. Katz arrange the carpet squares?
Draw a rectangle with the same area as the one shown. Then find the perimeter of each. 0IN
9. IN
0CM
10. CM
0M
11. M
IN CM
M
© Pearson Education, Inc.
12. Reasoning Marco has 36 feet of fencing, what
is the greatest area that can he can fence? 186 Intervention Lesson I48
Math Diagnosis and Intervention System Intervention Lesson
Name
I62
Making Line Plots A year is sometimes divided into quarters, as show at the right. 1. Take a survey by asking, “Which
quarter of the year were you born?” Write the number of the quarter each person answers in the grid.
1st quarter: 2nd quarter: 3rd quarter: 4th quarter:
January to March April to June July to September October to December
Quarter of the Year You Were Born
2. What are all of the possible
quarters that can be said?
Answer 3 to 7 to make and use a line plot of the data. 3. Draw a line. Below the line,
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list in order, all the possible quarters that could be said.
4. Write “Number of Birthdays by Quarter” below the line plot. 5. For each quarter that was said, mark an X above that quarter
on the number line. If more than one X needs to be placed above a quarter, stack them in a single column. 6. Which quarter has the most number of birthdays? 7. How many birthdays are after the 2nd quarter? Intervention Lesson I62
213
Math Diagnosis and Intervention System Intervention Lesson
Name
I62
Making Line Plots (continued)
The nature club leader took a survey of the number of birdfeeders each member had made during camp. The results are shown in the table. 8. Make a line plot to show the data.
Birdfeeders Made During Camp Member
Ivan Chloe Stacey Victor Tony Manny
Made
4 4 3 6 5 6
Member
Luther Marco Victoria Chi Wesley Wendy
Made
5 5 6 7 5 5
9. How many members made 4 birdfeeders? 10. How many members made 2 birdfeeders? 11. What was the most number of
birdfeeders made by a member? 12. How many members made 5 or 6 birdfeeders? 13. How many members made less than 6 birdfeeders? 14. Did more members make more than
15. Reasoning By looking at the line plot, if one more person
attended camp, do you think that person would probably make 4 birdfeeders or 5 birdfeeders? Explain.
214 Intervention Lesson I62
© Pearson Education, Inc.
5 birdfeeders or less than 5 birdfeeders?
Math Diagnosis and Intervention System Intervention Lesson
Name
J18
Use a Simpler Problem, Table, and Pattern Materials color tiles, 10 for each student
Roger is putting up a row of mirror tiles in his entry way, as show at the right. The tiles are squares, 1 foot on each side. How many feet of wood trim does he need to go around 10 tiles in a row? Solve by answering 1 to 6. Answer 1 and 2 to understand the problem. 1. What do you know from reading the problem?
The tiles are square and each side is Roger is putting
long.
tiles in a row.
2. What do you need to find?
Answer 3 to 5 to plan and solve the problem. You can solve simpler problems, put the solutions in a table, and find a pattern to extend the table in order to solve the problem. 3. Find the feet of trim needed for 3 tiles, 4 tiles, and 5 tiles
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in a row. You may want to use the picture above. Write the answers in the table below. Number of tiles
1
2
Feet of trim
4
6
3
4
5
6
7
8
9
10
4. What is the pattern in the table?
5. Use the pattern to complete the table. How many feet of
wood trim does Roger need to go around 10 tiles in a row?
Intervention Lesson J18
73
Math Diagnosis and Intervention System Intervention Lesson
Name
J18
Use a Simpler Problem, Table, and Pattern (continued)
Answer 6 to look back at how you solved the problem. 6. Reasoning Was it easier to use simpler problems, a table, and
a pattern than it would have been to solve by drawing a picture of 10 tiles in a row? What if there were 50 tiles in a row?
Complete each table. Solve each problem. 7. Suppose Mr. Lange had a rope 50 feet long and wanted to
cut it into 25 equal pieces. How many cuts would it take? Pieces
2
3
Cuts
1
2
4
5
6
8. The Washington Stars signed up for a single elimination soccer
tournament. This means that 2 teams play and the loser is eliminated. There are 8 entries in the tournament. How many games must be played to determine the champion? Teams
2
3
Games
1
2
4
5
6
7
8
9. During the grand opening of a craft store, every fourth customer
Customers
4
8
10
Gifts
0
0
1
Coupons
1
2
3
74 Intervention Lesson J18
12
4
16
20
24
28
30
32
36
40
© Pearson Education, Inc.
was given a discount coupon. Every tenth customer was given a discount coupon and a gift. During the grand opening, 120 people visited the store. How many coupons and gifts were given away?
Exam Intervention Booklet
Math Diagnosis and Intervention System Intervention Lesson
Name
H11
Counting Money Gary has a $1 bill, a quarter, 2 dimes, a nickel, and a penny. When you count money, start with the bill or coin of greatest value. Then count on to find the total. 1. Count Gary’s money.
$1.00
$1.35
2. How much money does Gary have? 3. Write $1.51 in words.
one dollar and
cents
© Pearson Education, Inc.
4. Ty has a $1 bill, a half-dollar, 2 quarters, and 3 dimes. Count Ty’s money.
$1.00
$2.10
5. How much money does Ty have? 6. Who had more money, Gary or Ty? Intervention Lesson H11
105
Math Diagnosis and Intervention System Intervention Lesson
Name
H11
Counting Money (continued)
Write the total value in dollars and cents. 7.
8. 1 five-dollar bill, 3 quarters,
9. 1 one-dollar bill, 1 half-dollar,
1 nickel, 2 pennies
4 nickels, 8 pennies
10. 1 one-dollar bill, 2 quarters,
11. 1 five-dollar bill, 1 one-dollar bill,
4 dimes, 3 nickels, 1 penny
1 quarter, 4 dimes, 3 nickels
Compare the amounts. Write ⬍, ⬎, or ⫽. 12. $1.17
4 quarters, 2 dimes $1.10
4 dimes, 1 nickel
15. 3 half-dollars, 3 nickels
$1.70
16. Reasoning Anita and Ted both have $1.49, but each have different coins.
What coins could each have?
106
Intervention Lesson H11
© Pearson Education, Inc.
14. 2 quarters, 6 dimes
13. $0.49
Math Diagnosis and Intervention System Intervention Lesson
Name
H12
Making Change Ivan bought a plastic dinosaur for $3.68. He paid with a $5 bill. Answer 1 to 10 to find how much change Ivan received. To make change, start with coins that will make it easier to skip count. Count up to the amount you paid. 1. Start with $3.68. Count on with pennies until you get to an
amount that ends in 0 or 5. $3.68,
$3.69,
2. How many pennies did you count? 3. How much are 2 pennies worth?
$0.
4. Count on from $3.70 with dimes.
$3.70,
,
,
5. How many dimes did you count? 6. How much is 3 dimes and 2 pennies worth?
$0.
7. Count on from $4.00 with one-dollar bills until you get to
© Pearson Education, Inc.
the $5.00 Ivan paid. $4.00,
8. How many dollar bills did you count? 9. How much is 1 dollar bill, 3 dimes
and 2 pennies worth?
$
. Intervention Lesson H12
107
Math Diagnosis and Intervention System Name
Intervention Lesson
H12
Making Change (continued) 10. How much change did Ivan receive?
List the coins and bills you would use to make change. Then write the change in dollars and cents. 11. Cost: $1.40
Amount paid: $2.00
12. Cost: $3.17
Amount paid: $4.00
13. Cost: $0.76
Amount paid: $5.00
14. Cost: $1.33
Amount paid: $5.00
She used three $1 bills. Give two ways to show the change. Circle the one that uses the fewest coins.
108 Intervention Lesson H12
© Pearson Education, Inc.
15. Reasoning Beverly bought a gallon of juice for $2.69.
Math Diagnosis and Intervention System Intervention Lesson
Name
I48
Rectangles with the Same Area or Perimeter Materials colored pencils or crayons.
Ms. Arellano’s class is making a sand box shaped like a rectangle for the kindergarten class. They have 16 feet of wood to put around the sand box. What length and width should the sand box be so it has the greatest area? Each of the rectangles in the grid at the right has a perimeter of 16 feet. Find which rectangle has the greatest area by answering 1 to 3.
8
7
9
1. Complete the table. The formula for
:
area of a rectangle is A ᐉ w. Rectangle
Length
Width
Area (square units)
W X Y Z 2. What are the length and width of the rectangle with
the greatest area? 3. What length and width should Ms. Arellano’s class
© Pearson Education, Inc.
use for the sand box? 4. Reasoning Tracy told Tomas that if a two rectangles have
the same perimeter, they have the same area. Is Tracy correct? Explain your reasoning.
Mr. Katz has 30 carpet squares to make a reading area in his classroom. Each square is one foot on a side. He wants to make the area in the shape of a rectangle with the least possible border. How should he arrange the carpet squares? Intervention Lesson I48
185
Math Diagnosis and Intervention System Intervention Lesson
Name
I48
Rectangles with the Same Area or Perimeter (continued)
Each of the rectangles on the grid at the right has an area of 30 square feet. Find which one has the least perimeter by answering 5 to 8.
2ECTANGLE
5. What is the perimeter of Rectangle 1? 2ECTANGLE
P 2ᐉ 2w 2(
) 2(5)
feet
6. What is the perimeter of Rectangle 2?
P 2ᐉ 2w 2(
) 2(3)
feet
7. What is the length and width of the rectangle with
the least perimeter? 8. How should Mr. Katz arrange the carpet squares?
Draw a rectangle with the same area as the one shown. Then find the perimeter of each. 0IN
9. IN
0CM
10. CM
0M
11. M
IN CM
M
© Pearson Education, Inc.
12. Reasoning Marco has 36 feet of fencing, what
is the greatest area that can he can fence? 186 Intervention Lesson I48
Math Diagnosis and Intervention System Intervention Lesson
Name
I62
Making Line Plots A year is sometimes divided into quarters, as show at the right. 1. Take a survey by asking, “Which
quarter of the year were you born?” Write the number of the quarter each person answers in the grid.
1st quarter: 2nd quarter: 3rd quarter: 4th quarter:
January to March April to June July to September October to December
Quarter of the Year You Were Born
2. What are all of the possible
quarters that can be said?
Answer 3 to 7 to make and use a line plot of the data. 3. Draw a line. Below the line,
© Pearson Education, Inc.
list in order, all the possible quarters that could be said.
4. Write “Number of Birthdays by Quarter” below the line plot. 5. For each quarter that was said, mark an X above that quarter
on the number line. If more than one X needs to be placed above a quarter, stack them in a single column. 6. Which quarter has the most number of birthdays? 7. How many birthdays are after the 2nd quarter? Intervention Lesson I62
213
Math Diagnosis and Intervention System Intervention Lesson
Name
I62
Making Line Plots (continued)
The nature club leader took a survey of the number of birdfeeders each member had made during camp. The results are shown in the table. 8. Make a line plot to show the data.
Birdfeeders Made During Camp Member
Ivan Chloe Stacey Victor Tony Manny
Made
4 4 3 6 5 6
Member
Luther Marco Victoria Chi Wesley Wendy
Made
5 5 6 7 5 5
9. How many members made 4 birdfeeders? 10. How many members made 2 birdfeeders? 11. What was the most number of
birdfeeders made by a member? 12. How many members made 5 or 6 birdfeeders? 13. How many members made less than 6 birdfeeders? 14. Did more members make more than
15. Reasoning By looking at the line plot, if one more person
attended camp, do you think that person would probably make 4 birdfeeders or 5 birdfeeders? Explain.
214 Intervention Lesson I62
© Pearson Education, Inc.
5 birdfeeders or less than 5 birdfeeders?
Math Diagnosis and Intervention System Intervention Lesson
Name
J18
Use a Simpler Problem, Table, and Pattern Materials color tiles, 10 for each student
Roger is putting up a row of mirror tiles in his entry way, as show at the right. The tiles are squares, 1 foot on each side. How many feet of wood trim does he need to go around 10 tiles in a row? Solve by answering 1 to 6. Answer 1 and 2 to understand the problem. 1. What do you know from reading the problem?
The tiles are square and each side is Roger is putting
long.
tiles in a row.
2. What do you need to find?
Answer 3 to 5 to plan and solve the problem. You can solve simpler problems, put the solutions in a table, and find a pattern to extend the table in order to solve the problem. 3. Find the feet of trim needed for 3 tiles, 4 tiles, and 5 tiles
© Pearson Education, Inc.
in a row. You may want to use the picture above. Write the answers in the table below. Number of tiles
1
2
Feet of trim
4
6
3
4
5
6
7
8
9
10
4. What is the pattern in the table?
5. Use the pattern to complete the table. How many feet of
wood trim does Roger need to go around 10 tiles in a row?
Intervention Lesson J18
73
Math Diagnosis and Intervention System Intervention Lesson
Name
J18
Use a Simpler Problem, Table, and Pattern (continued)
Answer 6 to look back at how you solved the problem. 6. Reasoning Was it easier to use simpler problems, a table, and
a pattern than it would have been to solve by drawing a picture of 10 tiles in a row? What if there were 50 tiles in a row?
Complete each table. Solve each problem. 7. Suppose Mr. Lange had a rope 50 feet long and wanted to
cut it into 25 equal pieces. How many cuts would it take? Pieces
2
3
Cuts
1
2
4
5
6
8. The Washington Stars signed up for a single elimination soccer
tournament. This means that 2 teams play and the loser is eliminated. There are 8 entries in the tournament. How many games must be played to determine the champion? Teams
2
3
Games
1
2
4
5
6
7
8
9. During the grand opening of a craft store, every fourth customer
Customers
4
8
10
Gifts
0
0
1
Coupons
1
2
3
74 Intervention Lesson J18
12
4
16
20
24
28
30
32
36
40
© Pearson Education, Inc.
was given a discount coupon. Every tenth customer was given a discount coupon and a gift. During the grand opening, 120 people visited the store. How many coupons and gifts were given away?
