All the solutions provided in McGraw Hill My Math Grade 3 Answer Key PDF Chapter 13 Lesson 10 Problem-Solving Investigation: Draw a Diagram will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 3 Answer Key Chapter 13 Lesson 10 Problem-Solving Investigation: Draw a Diagram
Learn the Strategy
Chloe’s father is building a rectangular sandbox. It has a width of 4 feet and a length of 6 feet. The wood that goes around the sandbox costs $2 for each foot. If they have $50, will that be enough to buy the wood?
1. Understand
What facts do you know?
- The sandbox is ____________ feet by 6 feet.
- The wood costs $____________ for each foot. They have $____________.
What do you need to find?
- if $50 is enough money to buy the wood
2. Plan
I can draw a diagram to solve the problem.
3. Solve
Draw a diagram to represent the sandbox.
The perimeter is 6 + 4 + 6 + 4, or ____________ feet.
Multiply the perimeter by the cost per foot, feet ____________ × $2 = $____________
Since $____________ < $50, they will have enough money.
4. Check
Is my answer reasonable? Explain.
Answer:
Given that,
The sandbox is 4 feet by 6 feet.
The wood costs $2for each foot. They have $50.
The perimeter is 6 + 4 + 6 + 4, or 20 feet.
Multiply the perimeter by the cost per foot, feet 20 × $2 = $40
Since $40 < $50, they will have enough money.
Practice the Strategy
A picture frame is 2 inches longer and 2 inches wider than the photo shown. What is the perimeter of the frame?
1. Understand
What facts do you know?
What do you need to find?
2. Plan
3. Solve
4. Check
Is my answer reasonable?
Answer:
Given that,
A picture frame is 2 inches longer and 2 inches wider than the photo shown.
The length of the picture frame shown is 6
The total length of the picture frame is 2 + 6 = 8 inches.
The width of the picture frame shown is 4.
The total width of the picture frame is 2 + 4 = 6.
The picture frame is in the shape of rectangle.
The perimeter of the rectangle is 2(l + w) = 2(8 + 6) = 28 inches.
Therefore the perimeter of the photo frame is 28 inches.
Apply the Strategy
Solve each problem by drawing a diagram.
Question 1.
Phil cut a piece of yellow yarn that was 7 feet long. Kendra cut a piece of red yarn that was 2 feet shorter. William cut a piece of green yarn that was 3 feet longer than the piece Kendra cut. How long was the piece of yarn that William cut?
Answer:
Given that,
Phil cut a piece of yellow yarn that was 7 feet long.
Kendra cut a piece of red yarn that was 2 feet shorter. It means Kendra cut 5 feet.
William cut a piece of green yarn that was 3 feet longer than the piece Kendra cut. It means 5 + 3 = 8 feet.
Therefore the piece of yarn that William cut is 8 feet.
Question 2.
Mathematical PRACTICE Use Math Tools Liseta is planting flowers around the outside edge of her rectangular garden. The garden is 12 feet long and 10 feet wide. She will place one flower at each corner and the remaining flowers will be placed 2 feet apart. How many flowers will she plant?
Answer:
Given that,
Liseta is planting flowers around the outside edge of her rectangular garden.
The length of the garden is 12 feet.
The wide of the garden is 10 feet.
He will place one flower at each corner and the remaining flowers will be placed 2 feet apart.
Therefore the number of flowers are 12.
Question 3.
A community center is organizing a dance. There are four large columns arranged at the corners of a square. The decorating committee will hang one large streamer from each column to every other column. How many streamers are needed?
Answer:
Given,
A community center is organizing a dance. There are four large columns arranged at the corners of a square. The decorating committee will hang one large streamer from each column to every other column.
As there are 4 columns she will need to connect the columns using 4 streams.
Thus 4 streamers are needed.
Question 4.
A cafeteria table has a length of 8 feet and a width of 3 feet. If three tables are pushed together, what is the combined area of the tables?
Answer:
Given that,
The length of the cafeteria table is 8 feet.
The width of the cafeteria table is 3 feet.
The table is in the shape of rectangle.
The formula for the area of the rectangle is l x b = 8 x 3 = 24 feet.
If the three tables are combined then 3 x 24 = 72 feet.
Therefore the area of the tables are 72 feet.
Review the Strategies
Use any strategy to solve each problem.
- Draw a diagram.
- Solve a simpler problem.
- Use logical reasoning.
- Make an organized list
Question 5.
Mathematical PRACTICE Use Math Tools Madeline has a pink dress, a blue dress, and a yellow dress. She has a black pair of shoes and a white pair of shoes. How many dress and shoe outfits can she make?
Answer:
Given that,
Madeline has a pink dress, a blue dress, and a yellow dress.
She has a black pair of shoes and a white pair of shoes.
The outfits can she make is
Pink dress, black pair of shoes.
Pink dress, white pair of shoes.
Blue dress, black pair of shoes.
Blue dress, white pair of shoes.
Yellow dress, black pair of shoes.
Yellow dress, white pair of shoes.
Therefore she has 6 outfits of shoe and dress.
Question 6.
Four friends are in line to see a concert. Greg is last in line. Melanie is before Greg and after Julie. Julie is after Dario. Who is first in line?
Answer:
Given that,
Four friends are in line
Greg is last in a line.
Melanie is before Greg and after Julie.
Julie is after Dario.
The sequence of the line is Dario, Julie, Melanie, Greg.
Therefore Dario is first in the line.
Question 7.
A restaurant has square dining tables. They will place table settings on each table so that there is a distance of 2 feet from each corner to a table setting. The 3 table settings on each side will be 3 feet apart. What is the perimeter of one table?
Answer:
Given,
A restaurant has square dining tables.
They will place table settings on each table so that there is a distance of 2 feet from each corner to a table setting.
The 3 table settings on each side will be 3 feet apart.
c² = a² + b²
2² = x² + 1.5²
4 = x² + 2.25
x² = 1.75
x = 1.323
P = 2x + 2x + 2x + x + x
P = 8x
8x = 8 × 1.323
= 10.583 ft
Thus the perimeter of each table is 10.583 ft
Question 8.
During one round of a game, Elio, Nida, and Geoffrey each scored 4 points. In round two, they each scored twice as many points. Find the total number of points scored.
Answer:
Given that,
The Elio, Nida, and Geoffrey each scored 4 points in a round 1.
They scored twice in round 2.
The total number pf points are 4 + 2(4) = 4 + 8 = 12.
Therefore the total number of points scored is 12.
Question 9.
Mathematical PRACTICE Make a Plan Lanetta will buy balloons for a party. She invited 6 friends from school, 3 friends from soccer practice, and 2 cousins. How many balloons will she need to buy if everyone gets two balloons?
Answer:
Given that,
Lanetta will buy balloons for a party.
She invited 6 friends from school, 3 friends from soccer practice, and 2 cousins.
The total numbers inverted to the party is 6 + 3 + 2 = 11
The total balloons she need to buy the if everyone get two balloons is 2 x 11 = 22.
Therefore she would to by 22 balloons.
McGraw Hill My Math Grade 3 Chapter 13 Lesson 10 My Homework Answer Key
Problem Solving
Solve each problem by drawing a diagram.
Question 1.
Mathematical PRACTICE Model Math Martina and Charlotte are sharing a pizza. The pizza is cut into eight pieces. Martina ate a quarter of the pizza. Charlotte ate 3 pieces. How many pieces are left?
Answer:
Given that,
Martina and Charlotte are sharing a pizza.
The pizza is cut into eight pieces.
Martina ate a quarter of the pizza
1 quarter = 1/4 part in 8 pieces 1 quarter = 2 pieces.
Charlotte ate 3 pieces.
The pieces left is 8 – 2 – 3 = 3 pieces.
Therefore there are 3 pieces left.
Question 2.
Five friends are having a tennis tournament. Each friend will play the other four friends once. How many matches will be played?
Answer:
Given that,
Five friends are having a tennis tournament.
Each friend will play the other four friends once.
Here 1 friend x 4 friends = 4 matches.
Therefore they will play 4 matches.
Question 3.
A rectangular bedroom floor has an area of 100 square feet and a length of 10 feet. What is the perimeter of the floor?
Answer:
Given that,
The area of the rectangular bedroom floor is 100 square feet.
The length of the rectangular bed room floor is 10 feet.
The formula for the area of the rectangle is l x b.
100 = 10 x b
b = 100 – 10
b = 90.
The perimeter of the rectangular bedroom floor is 2(10 + 90) = 200 square feet.
Question 4.
Alexander is riding his bicycle to school. After one mile, he is a third of the way there. How much farther does he have to ride?
Answer:
Given,
Alexander is riding his bicycle to school. After one mile, he is a third of the way there.
1 mile = 1/3 × (distance to school)
3 mile = 3 × 1/3 = 1
1 + remaining distance = 3
remaining distance = 3 – 1 = 2
Alexander has 2 miles more to ride.
Question 5.
Marjorie has 28 feet of trim to use as edging on a rectangular blanket she wants to make. What is the length and width of two blanket sizes she could make.
Answer:
Given,
Marjorie has 28 feet of trim to use as edging on a rectangular blanket she wants to make.
P = 2(l + w)
2l + 2w = 28
2(10) + 2(4) = 28 ft
The second blanket could be
2(7) + 2(7) = 28 ft