All the solutions provided in McGraw Hill My Math Grade 3 Answer Key PDF Chapter 11 Lesson 7 Problem-Solving Investigation: Work Backward will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 3 Answer Key Chapter 11 Lesson 7 Problem-Solving Investigation: Work Backward
Learn the Strategy
Billy’s picnic starts at 6:15 P.M. He needs to bake 3 dozen cookies. It takes 10 minutes to bake 1 dozen cookies. He will need another 20 minutes to get ready and 15 minutes to walk there. What is the latest time he can begin to prepare in order to be on time for the picnic?
1. Understand
What facts do you know?
the time the ___________ starts
how long it takes to bake cookies, get ready, and ___________ there
What do you need to find?
the latest time Billy can begin his preparations
2. Plan
Use the work backward strategy.
3. Solve
Use a number line. Mark everything in reverse order.
Billy needs to start preparing by ___________ P.M.
4. Check
Does your answer make sense? Explain.
Answer:
Given that,
Billy’s picnic starts at 6:15 P.M.
He needs to bake 3 dozen cookies. It takes 10 minutes to bake 1 dozen cookies.
For 3 dozen cookies he take 30 minutes.
He will need another 20 minutes to get ready.
15 minutes to walk there.
The total time to prepare is 30 minutes + 20 minutes + 15 minutes = 65 minutes = 1:05 minutes.
Here 1:15PM – 1 hour 5 minutes = 5:00 PM.
Therefore Billy needs to start preparing by 5:00 PM.
Practice the Strategy
It took Liam 80 minutes to complete a jigsaw puzzle. He finished at 2:40 P.M. What time did he start?
1. Understand
What facts do you know?
What do you need to find?
2. Plan
3. Solve
4. Check
Does your answer make sense? Explain.
Answer:
Given that,
Liam take 80 minutes to complete a jigsaw puzzle.
He finished at 2:40 P.M.
Therefore Liam started at 2:40 PM – 80 minutes = 1:20 PM.
Apply the Strategy
Solve each problem by working backward.
Question 1.
Ava added an additional 35 milliliters of water to a vase. She then poured out 10 milliliters of water. Now she has 26 milliliters of water left in the vase. How much water was in the vase to begin with?
Answer:
Given that,
Ava added 35 milliliters of water to a vase.
10 milliliters of water are poured out.
Now she has 26 milliliters of water in the vase.
The water in the vase at the begin is 35 – 10 = 25.
Vase has 26 milliliters 26 – 25 = 1
Therefore at the beginning the vase has 1 milliliter.
Question 2.
Kenya left home for her aunt’s house at 8:15 A.M. She arrived at her aunt’s house 2 hours 50 minutes later. What time did she arrive? Write the time in words and numbers.
Answer:
Given that,
Kenya left home for her aunt’s house at 8:15 A.M.
She arrived after 2 hours 50 minutes.
Here 8:15 + 2 hours 50 minutes = 11:10 AM.
Therefore Kenya arrived by 11:10 AM.
11:10 in words is eleven: ten.
Question 3.
Ciro played at the park with 5 friends for 30 minutes, 7 friends for 1 hour, and 2 friends for 15 minutes. He arrived at the park at 1:00 P.M. What time did he leave the park?
Answer:
Given that,
Ciro arrived the park at 1:00 PM.
Ciro played with his 5 friends for 30 minutes.
Ciro played with his 7 friends for 1 hour.
Ciro played with his 2 friends for 15 minutes.
Ciro played time is 30 minutes + 1 hour + 15 minutes = 1:45 minutes.
Therefore he leave the park by 1:00 PM + 1 hour 45 minutes = 2:45 PM.
Question 4.
Toya celebrated her birthday in March, 4 months after joining the swim team. Two months after joining the team, she swam in her first meet. What month did she swim in her first meet?
Answer:
Given that,
Toya celebrated her birthday in March 4 months after joining the swim team.
After two months she swan in her first team.
Therefore she swim in her month is after two months of march. It means May.
The may month she swim in her first meet.
Question 5.
Mathematical PRACTICE Keep Trying Work through this puzzle to find the number of minutes that it took Logan to clean his room. Add 8 to a number. When you subtract 10 from the sum, and double the difference you get 44. What is the number?
Answer:
Given that,
Add 8 to a number.
When you subtract 10 from the sum.
Double the difference you get 44.
Therefore the number is 24.
24 + 8 = 32
32 – 10 = 22
22 + 22 = 44
Review the Strategies
Use any strategy to solve each problem.
- Draw a diagram.
- Determine reasonable answers.
- Work backward.
- Use models.
Question 6.
Mathematical PRACTICE Model Math Blaine built a cube staircase. How many more cubes does he need to build 6 steps?
Answer:
Blaine need 21 cubes to build a 6 stair cases.
Question 7.
There are 3 children in line. Cami is right after Brock. Branden is third in line. What place is each child in line?
Answer:
Given that,
3 Childress are in a line.
Cami is after Brock.
Branden is third in line.
Therefore the place of the each child is 1 is Brock, 2 is Cami and the 3 is Branden.
Question 8.
Flora, Alonso, and Luz went fishing. Find how many fish each caught.
Answer:
Given that,
Flora, Alonso and Luz went for fishing.
Luz caught 5 fishes.
Flora caught 3 more fishes than Luz. It means 3 + 5 = 8.
Alonso caught 3 more fishes than Flora. It means 8 + 3 = 11.
Therefore The Luz caught 5 fishes.
Flora caught 8 fishes
Alonso caught 11 fishes.
Question 9.
Algebra A bottle of syrup has a mass of 560 grams. If the empty bottle has a mass of 305 grams, what is the mass of the syrup? Write an equation with a letter for the unknown. Then solve.
Answer:
Given that,
Algebra A bottle of syrup has a mass of 560 grams.
The empty bottle has a mass of 305 grams.
The equation for the mass of syrup is x – y = z
x = 560
y = 305
Then z = 560 – 305 = 255.
Therefore the mass of the syrup is 255.
McGraw Hill My Math Grade 3 Chapter 11 Lesson 7 My Homework Answer Key
Problem Solving
Solve each problem by working backward.
Question 1.
Selma finished her shift at work at 5:40 P.M. She had been working for 4 hours and 20 minutes. What time did Selma begin her shift?
Answer:
Given that,
Selma finished her shift at work at 5:40 P.M.
She had been working for 4 hours and 20 minutes.
Therefore Selma begin her shift by 5:40 – 4 hours 20 minutes. = 1:40 PM.
Question 2.
Riko has 3 kilograms of potatoes left. She sold 8 kilograms at the farmers’ market. She gave half that amount away to neighbors. How many kilograms of potatoes did Riko have to start with?
Answer:
Given that,
The Riko has 3 kilograms of potatoes left.
She sold 8 kilograms at the farmers’ market.
She gave half that amount away to neighbors.
Therefore Riko started with 22 kilograms of potatoes.
In 22 kilograms half of the potatoes are given to her neighbors.
Know she has 11 kilograms of potatoes. In 11 kilograms of potatoes 8 kilograms are sold to a farmer.
Therefore 11 – 8 = 3 kilograms has left with Riko.
Question 3.
Noah earned $24 last week by pet sitting. He worked 1 hour on Friday and 3 hours on Wednesday. He worked the most hours on Monday. Noah earns $3 per hour. How many hours did he work on Monday?
Answer:
Given that,
Noah earned $24 last week by pet sitting.
He worked 1 hour on Friday and 3 hours on Wednesday.
He worked the most hours on Monday.
Noah earns $3 per hour.
The total number of hours on Monday and Wednesday is 4 hours.
Therefore $3 x 4 = $12.
Here $24 – $12 = $12
Therefore Noah worked 4 hours on Monday.
Question 4.
Mathematical PRACTICE Be Precise It took Blake 20 minutes to walk home from school. He spent 35 minutes doing homework. Then Blake played basketball for 1 hour and 10 minutes. Now it is 5:45 P.M. and time for Blake to eat dinner. What time did he leave the school?
Answer:
Given that,
Blake 20 minutes to walk home from school.
He spent 35 minutes doing homework.
Then Blake played basketball for 1 hour and 10 minutes.
Now it is 5:45 P.M. and time for Blake to eat dinner.
Therefore the Blake leave the school at 5:47 + 20 minutes + 35 minutes + 1 hour 10 minutes = 7:52 PM.
Question 5.
Ms. Hirose filled a bucket with water. She used 3 liters of water to rinse her front porch. She used 2 liters of water to fill the bird bath. There are 3 liters of water left in the bucket. How much water did Ms. Hirose have to begin with?
Answer:
Given that,
She used 3 liters of water to rinse her front porch.
She used 2 liters of water to fill the bird bath.
There are 3 liters of water left in the bucket.
Therefore Ms. Hirose begin with 3 + 2 + 3 = 8 buckets of water.