Work BackwardsMA.7.A.5.2

1. Explain when you would use the work backwards strategy to solve a problem.

1. Describe how to solve a problem by working backwards.

Yesterday, I earned extra money by doing yard work for my neighbor. Then I spent $5.50 at the convenience store and four times that amount at the bookstore. Now I have $7.75 left.

Here’s another

method!

Draw a bar to help visualize the steps.

$7.75

Amount Miguel earned

$5.50

Amount Miguel has left

$5.50 $5.50 $5.50$5.50

Amount Miguel spent$5.50 x 5

Miguel

started with

$35.75

1. Leave the house

2. Get on the bus

3. Arrive at school

Explain the process of getting home from school.

Which step must we undo first?

Which step must we undo second?Which step must we undo last?

Steps for getting to school

€

10− 3+ 8

15

Fiona has a brother who is 8 years younger than her. Her younger sister is 10 years old and she is 3 years older than her

younger brother. How old is Fiona?Understand: We need to find out Fiona’s age. We know her sister

is 10 years old.

Plan: Start with 10 and work backwards.

Solve: Fiona’s sister is 10 Undo “3 years older”

Undo “8 years younger”

Check: Assume Fiona is 15.Her brother is 8 years younger than her which

makes him 7. His sister is 10 and she is 3 years older than her brother. Does this work?

Here’s another

method!Younger sister (10)

Brother (10 - 3 = 7)

+ 8

Fiona is 15 years old

Fiona has a brother who is 8 years younger than her. Her younger sister is 10 years old and she is 3 years older than her

younger brother. How old is Fiona?

Marisa spent $8 on a movie ticket. Then she spent $5 on popcorn and one half of what was left on a drink. She has $2 left. How much did

she have initially?

Understand: We need to find out how much money Marisa started with. We know that she has $2 left.

Plan: Start with $2 and work backwards.

Solve: Marisa has $2 Undo “one half”

Undo “spent $5” Undo “spent $8”

€

2× 2+ 5+ 8

17

Check: Assume Marisa has $17 initially.She spends $8 on a ticket and $5 on popcorn.

This leaves her with $4. She spends half of that on a drink. Does she end up with $2?

A number is multiplied by -3. Then 6 is subtracted from the product. After adding -7,

the result is -25. What is the number?

Understand: We need to find out what number we started with. The result is -25.

Plan: Start with -25 and work backwards.

Solve: Start with -25 Undo “add -7”

Undo “subtract 6” Undo “multiply by -3”

€

−25− (−7)+ 6

÷ −3

4

Check: Assume we start with 4.4 x (-3) – 6 + (-7)= -25

Last baseball season, Nelson had four less than twice the number of hits Marcus had. Nelson had 48 hits. How many hits

did Marcus have last season?Understand: We need to find out how many hits Marcus had.

Nelson had 48 hits.

Plan: Start with 48 and work backwards.

Solve: Nelson had 48 hits Undo “four less”

Undo “twice”

€

48+ 4÷ 2

26

Check: Assume Marcus had 26 hits. 26 x 2 – 4 = 48

What simple error can arise with this problem?

Angel Falls in Venezuela is 3,212 feet high. It is 87 feet higher than 2.5 times the height of the Empire State Building. Find the height of

the Empire State Building. Understand: We need to find out the height of the Empire State

Building. We know that Angel Falls is 3,212 high.

Plan: Start with 3,212 and work backwards.

Solve: Angel Falls is 3,212 Ft Undo “87 feet higher”

Undo “2.5 times”

€

3,212− 87

÷ 2.5

1,250

Check: Assume the Empire State Building is 1,250 ft tall.

1,250 x 2.5 +87 = 3,212

Joe forgot to check how much money he began the day with.  During the day, he spent $8.00 on

breakfast, made $40.00 washings cars, got his dry cleaning for $12.00, bought 5 shirts for $22.00 a piece

(plus 8% sales tax). At the end of the day, he had $100, how much did he start the day with?

Understand: We need to find out how much money Joe began the day with. We know that he had $100 at the end of the day.

Plan: Start with $100 and work backwards.

Solve: Joe has $100 Undo “bought 5 shirts for $22 each plus 8% tax” Undo “got dry cleaning for $12”

Undo “made $40” Undo “spent $8”

€

100 .00+ 118 .80 5(22 ×1.08)

+ 12.00

− 40.00

+ 8.00

198 .80

Joe forgot to check how much money he began the day with.  During the day, he spent $8.00 on breakfast, made $40.00 washing cars, got his dry

cleaning for $12.00, bought 5 shirts for $22.00 a piece (plus 8% sales tax). At the end of the day, he had $100.00, how much did he start the day with?

Solve: Joe has $100 Undo “bought 5 shirts for $22 each plus 8% tax” Undo “got dry cleaning for $12”

Undo “withdrew $40” Undo “spent $8”

€

100 .00+ 118 .80 5(22 ×1.08)

+ 12.00

− 40.00

+ 8.00

198 .80Check: Assume Joe started with $198.80He spent $8 on breakfast, which left him with $190.80. He made $40, which brought him to $130.80. He spent $12 on dry cleaning and $118.80 on his shirts. That leaves him with $100 at the end of the day.