my homework lesson 7 problem solving work backwards

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McGraw Hill My Math Grade 3 Chapter 11 Lesson 7 Answer Key Problem-Solving Investigation: Work Backward

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

2. Plan Use the work backward strategy.

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

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 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.

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 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

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.

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Fun teaching resources & tips to help you teach math with confidence

Math Strategies: Problem Solving by Working Backwards

As I’ve shared before, there are many different ways to go about solving a math problem, and equipping kids to be successful problem solvers is just as important as teaching computation and algorithms . In my experience, students’ frustration often comes from not knowing where to start. Providing them with strategies enables them to at least get the ideas flowing and hopefully get some things down on paper. As in all areas of life, the hardest part is getting started! Today I want to explain how to teach  problem solving by working backwards .

* Please Note : This post contains affiliate links which help support the work of this site. Read our full disclosure here .*

–>Pssst! Do your kids need help making sense of and solving word problems? You might like this set of editable word problem solving templates ! Use these with any grade level, for any type of word problem :

Solve a Math Problem by Working Backwards: 

Before students can learn to recognize when this is a helpful strategy, they must understand what it means. Working backwards is to start with the final solution and work back one step at a time to get to the beginning.

It may also be helpful for students to understand that this is useful in many aspects of life, not just solving math problems.

To help show your students what this looks like, you might start by thinking about directions. Write out some basic directions from home to school:

• Start: Home
• Turn right on Gray St.
• Turn left on Sycamore Ln.
• Turn left on Rose Dr.
• Turn right on Schoolhouse Rd.
• End: School

Ask students to then use this information to give directions from the school back home . Depending on the age of your students, you may even want to draw a map so they can see clearly that they have to do the opposite as they make their way back home from school. In other words, they need to “undo” each turn to get back, i.e. turn left on Schoolhouse Rd. and then right on Rose Dr. etc.

In math, these are called inverse operations . When using the “work backwards” strategy, each operation must be reversed to get back to the beginning. So if working forwards requires addition, when students work backwards they will need to subtract. And if they multiply working forwards, they must divide when working backwards.

Once students understand inverse operations , and know that they must start with the solution and work back to the beginning, they will need to learn to recognize the types of problems that require working backwards.

In general, problems that list a series of events or a sequence of steps can be solved by working backwards.

Here’s an example:

Sam’s mom left a plate of cookies on the counter. Sam ate 2 of them, his dad ate 3 of them and they gave 12 to the neighbor. At the end of the day, only 4 cookies were left on the plate. How many cookies did she make altogether?

In this case, we know that the final cookie amount is 4. So if we work backwards to “put back” all the cookies that were taken or eaten, we can figure out what number they started with.

Because cookies are being taken away, that denotes subtraction. Thus, to get back to the original number we have to do the opposite: add . If you take the 4 that are left and add the 12 given to the neighbors, and add the 3 that Dad ate, and then add the 2 that Sam ate, we find that Sam’s mom made 21 cookies .

You may want to give students a few similar problems to let them see when working backwards is useful, and what problems look like that require working backwards to solve.

Have you taught or discussed problem solving by working backwards  with your students? What are some other examples of when this might be useful or necessary?

Don’t miss the other useful articles in this Problem Solving Series:

• Problem Solve by Drawing a Picture
• Problem Solve by Solving an Easier Problem
• Problem Solve with Guess & Check
• Problem Solve by Finding a Pattern
• Problem Solve by Making a List

So glad to have come across this post! Today, word problems were the cause of a homework meltdown. At least tomorrow I’ll have a different strategy to try! #ThoughtfulSpot

I’m so glad to hear that! I hope you found some useful ideas!! Homework meltdowns are never fun!! Best of luck!

This is really a great help! We have just started using this method for some of my sons math problems and it helps loads. Thanks so much for sharing on the Let Kids Be Kids Linkup!

That’s great Erin! I hope this is a helpful method and makes things easier for your son! 🙂

I’ve not used this method before but sounds like a good resource to teach. Thanks for linking #LetKidsBeKids

I hope this proves to be helpful for you!

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• 3rd Grade Math
• Title: My Math
• Author: McGraw Hill
• Edition: Volume 1

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