McGraw Hill My Math Grade 5 Chapter 12 Lesson 12 Answer Key Problem-Solving Investigation: Make a Model

All the solutions provided in McGraw Hill My Math Grade 5 Answer Key PDF Chapter 12 Lesson 12 Problem-Solving Investigation: Make a Model will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 5 Answer Key Chapter 12 Lesson 12 Problem-Solving Investigation: Make a Model

Learn the Strategy

Nick is helping his sister put away her alphabet blocks. To fill one layer. it takes nine blocks. If there are six layers, how many blocks would be in the box?
McGraw Hill My Math Grade 5 Chapter 12 Lesson 12 Answer Key Problem-Solving Investigation Make a Model 1
1. Understand
What facts do you know?
There are ___________ blocks in each layer and there are six layers.

What do you need to find?
The number of blocks in the box when there are ___________ layers.

2. Plan
I can solve the problem by making a ___________.

3. Solve
Arrange ______________ cubes in a 3 × 3 array. Stack the cubes until there are ____________ layers. There are a total of ____________ cubes. So, the box would have ___________ blocks.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 12 Answer Key Problem-Solving Investigation Make a Model 2

4. Check
Is my answer reasonable? Explain.
Multiply.
6 × 9 = ______________
Answer:
1. There are 9 blocks in each layer and there are six layers.
we need to find out: The number of blocks in the box when there are 6 layers
2. Plan:
we can solve the problem by making a model.
3. solve:
Arrange the 9 cubes in a 3 x 3 array. Stack the cubes until there are 6 layers. There are a total of 54 cubes. So, the box would have 54 blocks.
4. Checking whether the answer is reasonable or not.
Multiply the equation:
6 x 9 = 54
Therefore, the answer is reasonable.

Practice the Strategy

Evelyn wants to mail a package to her cousin. What is the volume of the package if it is 6 inches long, 4 inches wide, and 4 inches tall?
McGraw Hill My Math Grade 5 Chapter 12 Lesson 12 Answer Key Problem-Solving Investigation Make a Model 3
1. Understand
What facts do you know?

What do you need to find?

2. Plan

3. Solve

4. Check
Is my answer reasonable? Explain.
Answer:
1. The facts we know:
length = 6 inches
width = 4 inches
height = 4 inches
we need to find out the volume of the rectangular prism.
2. Plan: we can solve the problem by making a model.
3. solving the problem:
Arrange the 6 cubes in a 6 x 4 array. Stack the cubes until there are 4 layers. There are a total of 96 cubes. So, the box would have 96 blocks.
4. To check whether the answer is reasonable or not:
We know the formula for the volume of the rectangular prism:
V(RP) = length x width x height
V(RP) = 6 x 4 x 4
V(RP) = 96
Therefore, the volume of the rectangular prism is 96 cubic inches.

Apply the Strategy

Solve each problem by making a model.

Question 1.
On an assembly line that is 150 feet long, there is a workstation every 15 feet. The first station is at the beginning of the line. How many workstations are there?
Answer:
The above-given:
The length of the assembly line is 150 ft
The number of workstations for every 15 feet = 1
We need to find out the number of workstations. Let it be W.
W = 150 / 10
W = 15
Therefore, the number of workstations is 15.

Question 2.
Mathematical PRACTICE Use Math Tools A store is stacking cans of food into a rectangular prism display. The bottom layer has 8 cans by 5 cans. There are 5 layers. How many cans are in the display?
Answer:
The above-given:
The length of the prism in the bottom layer  is 8
The width of the prism in the bottom layer = 5
The number of layers = 5 (I think it should be the height)
We know that the volume of the rectangular prism = l x w x h
V = 8 x 5 x 5
V = 200
Therefore, 200 cans are on the display.

Question 3.
The distance around the centre ring at the circus is 80 feet. A clown stands every 10 feet along the circle. How many clowns are there?
McGraw Hill My Math Grade 5 Chapter 12 Lesson 12 Answer Key Problem-Solving Investigation Make a Model 4
Answer:
The above-given:
the distance = 80 feet
Clown stands = 10
Based on the given conditions, we can formulate:
80 / 10 = 8
therefore, the number of clowns is 8.

Question 4.
Martino wants to arrange 18 square tiles into a rectangular shape with the least perimeter possible. Perimeter is the distance around a figure. How many tiles will be in each row?
Answer:
I think the answer would be 9 because we put 9 in each row adding up to 18 but it would still be a rectangle.

Review the Strategies

Use any strategy to solve each problem.

  • Make a model.
  • Guess, check, and revise.
  • Look for a pattern.
  • Make a table.

Question 5.
Five friends are standing in a circle and playing a game where they toss a ball of yarn to one another. If each person is connected by the yarn to the other person only once, how many lines of yarn will connect the group?
Answer:
10 lines will connect them.

Question 6.
Mathematical PRACTICE Look for a Pattern In the figure below, there are 22 marbles in Box A. To go from Box A to Box B, exactly four marbles must pass through the triangular machine at a time. Exactly five marbles must pass through the square machine at a time. Describe how to move all the marbles from Box A to Box B in the fewest moves possible.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 12 Answer Key Problem-Solving Investigation Make a Model 5
Answer:
The above-given:
The number of marbles in box A = 22
The number of marbles that must pass through a triangle is 4
The number of marbles that must pass through the square is 5
To find: the fewest moves possible.
Here, exactly 5 marbles must pass through the square machine at a time.
So what we can do is, we can apply 2 times that is 2 x 5 = 10 marbles.
Now the remaining 22 – 10 = 12 marbles pass through the triangular machine.
we can pass 12 marbles 3 times.
3 x 4 = 12 marbles.
Hence, the total 2 moves + 3 moves = 5 moves.
Therefore, 5 moves are possible from box A to box B.

Question 7.
The volume of a rectangular prism is 5,376 cubic inches. The prism is 14 inches long and 16 inches wide. How tall is the prism?
Answer:
The above-given:
The length of the prism = 14
The width of the prism = 16
The volume of the prism = 5376
The height of the prism = h(prism)
We know that the volume of the rectangular prism = length x width x height
Now substitute the values:
5376 = 14 x 16 x h(prism)
5376 = 224 x h(prism)
5374 / 224 = h(prism)
24 = h(prism)
Therefore, the height of the rectangular prism is 24 inches.

Question 8.
The table at the right shows the number of minutes Danielle spent practising the trumpet over the last 7 days. If she continues this pattern of practising, in how many days will she have practised 340 minutes?
McGraw Hill My Math Grade 5 Chapter 12 Lesson 12 Answer Key Problem-Solving Investigation Make a Model 6
Answer:
The above-given:
7 days of data are given
overall 7 days, she practised total minutes are 20+ 20 + 35 + 20 + 20 + 35 + 20 = 170
for 7 days, he practised about 170 minutes.
for T days, he practised about 340 minutes
Now write the equation:
here we applied the cross-multiplication method:
T x 170 = 340 x 7
T x 170 = 2380
T = 2380 / 170
T = 14
Therefore, in 14 days he can practise 340 minutes.

McGraw Hill My Math Grade 5 Chapter 12 Lesson 12 My Homework Answer Key

Problem Solving

Solve each problem by making a model.

Question 1.
Nan and Sato are designing a coffee table using 4-inch tiles. Nan uses 30 tiles and Sato uses half as many. How many total tiles did they use?
__________________________
If the area of the table is 36 inches by 24 inches, will they have enough tiles to cover the table? If not, how many more will they need?
Answer:
The above-given:
The number of tiles Nan uses is 30
The number of tiles Sato uses 30 / 2 = 15
Therefore, Sato uses 15 tiles.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 12 Answer Key Problem-Solving Investigation Make a Model_1
Now we need to find out the number of total tiles they used. Let it be x.
x = 30 + 15
x = 45
Already given that the table is designed in 4 inches.
The number of columns = 36 / 4 = 9
The number of rows = 24 / 4 = 6
McGraw Hill My Math Grade 5 Chapter 12 Lesson 12 Answer Key Problem-Solving Investigation Make a Model_2
The total tiles = 9 x 6 = 54
Actually, they both had 45 tiles. So they didn’t have enough tiles.
designing the area of the table having dimensions 36 and 24 inches need 54 tiles completely.
Now the number of tiles needed for Nan and Sato to complete the table. Let it be T.
T = 54 – 45
T = 9
Therefore, they need 9 tiles more to complete the table.

Question 2.
The Jones family is landscaping their yard. Their yard is 160 square feet and one side is 10 feet long. What is the length of the other side of the yard?
__________________________
If they plant 3 bushes that need to be 3 feet apart and 3 feet away from the fence around the yard, will they have the space?
Answer:
The above-given:
Area = 160 square feet
width = 10 feet
length = l
We know that, the area of the rectangle = length x width
160 = l x 10
160 / 10 = l
16 = l
Therefore, the length is 16 yards.
yes, three bushes will need 3 x 4 = 12 feet of space and the length is already 16 feet.

Question 3.
Billy is organizing his closet. He has clothing bins that measure 20 inches high, 18 inches wide, and 14 inches long. How many bins can he fit in a 60-inch long closet that is 36 inches deep and 72 inches high?
Answer:
The volumes of the clothing bin and the closet can be calculated by multiplying the given dimensions.
Let it be the V(clothing bin).
V(clothing bin) = 20 x 18 x 14
V(clothing bin) = 5040 cubic inches.
Now coming to the closet, calculate the given dimensions and let it be V(closet).
V(closet) = 60 x 36 x 72
V(closet) = 155520 cubic inches.
To determine the number of clothing bins that can fit the closet, divide the volume of the closet by the volume of the clothing bin. Let it be N(fit).
N(fit) = 155520 / 5040
N(fit) = 30.85
We can say approximately 30 clothing bins can fit in the closet.

Question 4.
Mathematical PRACTICE Model Math Bob is organizing his pantry. If he has cracker boxes as shown, how many boxes can he fit on a 20-inch-long shelf that is 14 inches deep?
McGraw Hill My Math Grade 5 Chapter 12 Lesson 12 Answer Key Problem-Solving Investigation Make a Model 7
Answer:
The above-given:
length of the cracker box = 12 in
Width of the cracker box = 10 in
The height of the cracker box is 2 in
The area of the cracker box = length x width
area = 12 x 10
area = 120 square inches.
The given shelf dimensions:
Length = 20; width = 14
so, the area will be length x width
area = 20 x 14
area = 280 square inches
Therefore, the number of boxes that can fit on the shelf is given by 280 / 20 = 14
Hence, there are 14 boxes that can fit on a shelf.

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