## Tuesday, January 24, 2017

### Reverse Planning

Earlier this week, our class encountered this problem.

Chris paid \$3.60 for 3 colored pens. Each pen cost the same amount. How much did each pen cost? Solve the problem any way you choose.

Children all used some form of mental math to solve and were then asked to try another way.

Example strategies that worked.

Compatible numbers: 36 is a multiple of 3. The missing factor is 12. \$1.20 is the answer.

Breaking apart numbers into place values or expanded form: 3/1 = 3 and 60/3 = 20. \$1.20 is the answer.

This week, you need to choose a set of compatible numbers.  Then write a word problem for them. Finally, show two ways to solve, the first must be compatible numbers. The dividend must be a decimal number. The divisor cannot be a decimal number. The quotient must be a decimal number.

Compatible Numbers: 36 and 3

Word Problem: Chris paid \$3.60 for 3 colored pens. Each pen cost the same amount. How much did each pen cost? Solve the problem using compatible numbers. Solve one other way.

How to solve:

• Compatible numbers: 36 is a multiple of 3. The missing factor is 12. \$1.20 is the answer.
• Breaking apart numbers into place values or expanded form: 3/1 = 3 and 60/3 = 20. \$1.20 is the answer.

1. ChezMan paid \$426.60 for 6 desks. How much did he pay for each marble?
Compatible: 420 divided by 6 = 70.

Breaking Apart:420 divided by 6= 70.
6 divided by 6= 1.
0.6 divided by 6= 0.1.
70+1+0.1=71.1.

2. Du-hoy paid \$549.90 for 9 desk chairs. Each chair cost the same amount of money. How much did he pay for each desk chair?
Solve the problem using compatible numbers. Solve one other way.

Compatible Numbers: 540/9=60.

Breaking Apart: 540/9=60
9/9=1
0.9/9=0.1
60+1+0.1=61.1
Du-hoy paid \$61.10 for each desk chair.

3. Shadman paid \$120.56 for 4 shirts . How much did he pay for each shirt?

Compatible numbers: 12 is a multiple of 4. The missing factor is 3 so \$30.

Breaking apart numbers into place values or expanded form: 120/40=30 .56/4= 0.14 so \$30.14 is the answer.

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5. Word Problem: At the store Jeff bought 9 pens for \$7.20. Each pen cost the same amount. How much did each pen cost? Solve the problem using compatible numbers. Solve one other way.

Compatible numbers: 7.20 can be 72. 72 divided by 9 is 8. Since 72 divided by 10 is 7.20, 8 divided by 8 would be 0.8 and \$0.8 would be the answer.

Breaking apart numbers into place values or expanded form: 9 cannot go into 7 so go to the next place, 7.2/9 is \$0.8.

6. By: Jenna
Emily paid \$4.20 for 2 necklaces. How much did each necklace cost? Solve the problem using compatible numbers. Solve one other way.
4.20=42 is my compatible number
I know that 42/2=21
Each necklace will cost \$2.10
Breaking apart: 4/2=2 and 20/2=10 so it will be \$2.10

7. Evan has \$380.20 Evan wants to buy some pins, each pin cost \$7. How many pins can Evan buy? 350.00 divided by 7 = 50
Braking apart 350.00 7 = 50
35 is a multiple of 7 and 5 is the missing factor so it is \$50

8. Mr.Cheese has \$112.20. He wants to buy 4 footballs. Each football cost the same amount of money. How much money does each football cost?
Solve the problem using compatible numbers. Solve one other way.

Compatible numbers: 120/4=30

Breaking Apart:
100/4=25
12/4=3
0.20/4=0.05
25+3+0.05=\$28.05
Mr.Cheese paid \$28.05 for each football.

9. Prince Charming has 4.8 tacos. He has 4.8 tacos because he ate 0.2 of 1 of them. He wants to share them equally between himself and 3 math teachers. How many tacos did each teacher receive? Solve the problem using compatible numbers.

Compatible numbers: 48 is a multiple of 4. The missing 12. 1.2 tacos is the answer.

Breaking apart: 4/4=1 and 8/4=2. 1.2 is the answer.

Conclusion: The math teachers are proud because Prince Charming because he divided correctly, but angry because he did not do his math homework.

10. George paid 110.60 for 10 books. How much did George pay for each book? Solve two ways, one using compatible numbers.

Compatible Numbers: 110/10=11

Breaking Apart: 110/10=11 and 60/10=6 then put the decimal in the place right above it and the answer is 11.06

11. By Grace
Grace has \$2.55to buy 5 party favors. If each of the 5 things cost the same amount of money, how much money will each favor cost? Solve the problem using compatible numbers. solve one other way.

One strategy is to use _compatible numbers: 25.5/5=5.1. So that makes the real quotient.51.

Another strategy is breaking down the number: 5 can't go into 2 so see if 5 can go into 25. 25/5=5. Then 5/5=1. So that makes the quotient. .51.

12. Shreya has \$480.60. She wants to put it into 6 different groups. How much was in each pile? Solve the problem 2 ways. Use compatible numbers and breaking apart.

Compatible Numbers: 480/6=80.

Breaking Apart: 480/6=80 and 0.60/6=0.10.
80+0.10=80.10
\$80.10 in each pile.

13. Julia R. sold \$4.80 worth of girl scout cookies. If she sold them to 4 different people, and each person bought one box, how much does each box cost? Solve the problem using compatible numbers. Solve one other way.

Compatible numbers: 48 is a multiple of 4. The missing factor is 12, so \$1.20 is the answer. Each box costs \$1.20.
Breaking apart numbers into place values or expanded form: 4/4=1 and 80/4=20. \$1.20 is the answer. Each box costs \$1.20.

14. Julia earned \$360.60. She is donating an equal amount of money to 6 different fundraisers. How much money did each fundraiser get? Use compatible numbers and breaking apart to solve.

Compatible Numbers: 360/6=60
Breaking Apart: 360/6=60 and .60/6=0.10
60+0.10=60.10

Each fundraiser got \$60.10 from Julia.

-Julia B.

15. Boogus Wells bought a pack of 3 pencils for \$2.40. Each pencil cost the same amount. How much did each pencil cost? Solve the problem using compatible numbers. Solve one other way. Compatible numbers 24 and 3 I know 24 / 3 = 8 and since I started with 2.40 the quotient must be 80 cents. 8+8+8=24 So the quotient has to be correct. The quotient is 0.80 cents.

-Dillan

16. Compatible Numbers: 30 and 5

Word Problem: Reagan paid \$3.00 for 5 pieces of candy . Each piece of candy cost the same amount. How much did each piece of candy cost? Solve the problem using compatible numbers. Solve one other way.

How to solve:

* Compatible numbers: 5 is a multiple of 30. The missing factor is \$0.60. \$0.60 is the answer.
* Breaking apart numbers into place values or expanded form: 30/5 = 6. \$0.60 is the answer.
-Reagan

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18. Bella paid \$16.80 for 4 dozen eggs at 4 different stores. How much did she pay at each store? Solve two ways, one using compatible numbers.

Compatible Numbers: 16 is a multiple of 4 so the missing factor is 4 and the answer is 4.20

Breaking apart: 16/4=4
0.80/4=0.20

19. Emma S. (A.K.A. #1)

WORD PROBLEM: Emma paid 3 dollars for 5 guitar picks. Each pick costed the same amount. How much did each guitar pick cost? Solve the problem using compatible numbers. Solve one other way.

COMPATIBLE NUMBERS: 30 and 5 are the compatible numbers because, I know that 30 is a multiple of 5, so the missing factor is 60 cents. The answer is 60 cents.

BREAKING APART: I know that 30/5=6 so that means that the answer has to be 60 cents.

20. Shrek wanted to buy 9 taco`s from a store called “Caillou`s Taco`s”. Shrek had \$8.2. How much did each of the tacos from the store “Caillou`s Taco`s”? Solve using Compatible Numbers. Solve one other way.

The compatible numbers are 82 and 9. The missing factor is 9. The answer is \$.9

Another way is to do it is 9 / 1 = 9.

-Alec

21. Julie bought 5 pens for \$6.00. How much did each pen cost?
Compatible numbers:60/5=12

Breaking apart:
6/6=1
.80/4=.20
1+.20=\$1.20

22. Joe Smo paid \$5.40 for 6 bouncy balls. How much did each bouncy ball cost?
COMPATABLE NUMBERS: 54/6=9

1. 54/6=9 so you put 0.9 at the top.
2. 54-54=0 so the next thing we dive is 0.
3. 0/5=0 so you put a zero at the top.
4. your answer is 0.90 because 5.40/6 is a lot like 54/6=9 my problem just has decimals.

23. Emma paid \$4.40 for 4 erasers, they each cost the same. How much did each cost?

Compatible numbers: 44 is a multiple of 4. The missing factor is 11. \$1.10 is the answer.

Breaking apart numbers into place values or expanded form:
4/1 = 4 and 40/4 = 10.
24. 