Word Problems
Solve for the Variable
Estimation
Extended Responses
100

Ms. Blackburn, Ms. Kennedy, and Mrs. MacGill go to Kroger on Monday to buy ingredients to make a cake for Ms. Ciolek's birthday. Ms. Blackburn buys the milk for $3 and the icing for $4. Ms. Kennedy buys the flour for $12 and the sprinkles for $6. Mrs. MacGill buys the plates for $5, the forks for $12, and the napkins for $8. How much does Ms. MacGill spend at Kroger?  

$25

100
250+351=W

Solve for W. 

M=601

100
Samar bought pajamas for $38, slipper for $18, and a robe for $22. About how much did she spend. 


A. About $60

B. About $80

C. About $90

D. About $85

C. About $80

100

3,426+321=N

Solve for N. Explain how you solved for N.

N=3,747. 

*Explanations may vary. 

I solved for N by first putting the numbers in standard algorithm. I lined each place value up correctly by lining up the ones place, then the tens place, then the hundreds place, and the thousands place. I then began to solve to find the variable N. I began by adding the ones places together. I know that 6+1=7. I put a 7 in my ones place to represent 7 groups of one. I then added the tens place, 2+2=4. I put a 4 in the tens place to represent 4 groups of ten. I added the hundreds place, 3+4=7. I put a 7 in the hundreds to place to represent 7 groups of 100. I only had one digit in the thousands place, 3, I put a 3 in the thousands place to get the sum, 3,747.   

200

Raven and Chelsea went to the movies. They bought a large popcorn for $12, two waters for $5 each, a bag of Twizzlers for $4, and two tickets for $12 each. How much did they spend in all?  

$50

200

4,326+3,894=I

Solve for I. 

I=8,220

200

Round each number to find the estimated sum. 

45+21+10=

30

200

In 3rd grade, two students were solving the following problem. 4,351+2,361. 

Sally said the sum was 6,612

Danny said the sum was 6,712

Who found the correct sum? Explain what mistake the student who solved incorrectly made. 

Danny found the correct sum, 6,712. Sally made the mistake of not regrouping when adding. Sally added the digits in the ones places to get 2. She then added the tens places to get 11, but she forgot to regroup the 11 into one group of tens and one group of one hundred. Then when she added the hundreds place she only added 3 and 3 to get 6, when she should have added 3, 3, and 1 to get 7 groups of one hundred. 

300

Ms. Blackburn, Ms. Kennedy, and Mrs. MacGill go to Kroger on Monday to buy ingredients to make a cake for Ms. Ciolek's birthday. Ms. Blackburn buys the milk for $3 and the icing for $4. Ms. Kennedy buys the flour for $12 and the sprinkles for $6. Mrs. MacGill buys the plates for $5, the forks for $12, and the napkins for $8. How much do they spend all together? 

$50

300

43,168+31,174=N

Solve for N. 

N=74,342

300

What is the best estimate for the sum of 681 and 1,112?

A. 1,800

B. 2,000

C. 1,600

D. 700

A. 1,800

300

Kelly is going to the beach and wants to buy souvenirs for her friends. She only has $200 to spend. What 3 items can she buy to get as close to $200 without going over. 

Shells- $24

T-shirt- $36

Pillow-$16

Giant Teddy Bear-$156 

Explain how you decided what items she could choose. 

She can buy a Giant Teddy Bear, shells, and a pillow and spend $196. She will not go over $200 if she buys these three items. I decided she could buy these three items by using the standard algorithm. I first decided that if she bought shells, a t-shirt, and a pillow she would be below her budget of $200. I rounded each number and added to find the estimated sum to be $80, which I know is much less than $200. I then tried each different combination of three items to find that by buying the giant teddy bear, shells, and pillow would get her closest to $200 without going over. 

400

Rupp Arena is 3,346 feet tall. Kroger Field is 1,241 feet tall. What is the length of the two arenas together?  

4,587 feet tall. 

400

732+483=N

What is the value of N? 

A. Sum is greater than 1,500

B. Sum is less than 1,000

C. Sum is greater than 1,000

D. Difference is greater than 1,000

C. Sum is greater than 1,000

400

At the toy store the following toys are on sale. 

Uno- $8

Basketball-$22

Xbox- $248


Rylee bought 3 basketballs and an Xbox. About how much did she spend?  

About $310

*Answers may vary, must show work for points. 

500

Fourth grade students at Wayside Elementary are raising money for their field trip to the aquarium. On Monday, the students raised $342. On Tuesday, the students raised $444. On Wednesday, the students raised $875. On Thursday, the students raised $1,243. On Friday, the students raised $135. About how much money did they raise on Monday, Tuesday, and Thursday?

About $2,020.

*Answers may vary based on rounding. You must show your work to prove your answer. 

500

655,251+342,666=R

Solve for R. 

R=997,917

500

Mallory buys 6 cupcakes at the bakery and 1 large cake for Emily's birthday. Cupcakes cost $12 each, a small cake cost $25 and a large cake cost $44. About how much does she spend? 

About $100