6th Grade - Breaking Down A Complex Problem

Problem Solving
Breaking Down A Complex Problem
Determine when and how to break a problem into simpler parts.
Identify problems with multiple steps needed for a solution. Determine how to break the problem into smaller parts in a way that makes sense. Combine the parts of the problem to find a final solution.

Sample Problems


Felipe is on the track team. He runs 3 miles everyday before school. On weekend days Felipe runs 7 miles. How many miles does Felipe run each week?

(29 miles)


Mandy’s family went to the movies. They bought two adult tickets for $8.50 and three children’s tickets for $5.75. How much money did they spend in all?



Rob had 16 red marbles. He split them evenly with his brother. Then Rob bought 30 blue marbles. He gave away 1/3 of them. How many marbles does Rob have left?

(28 marbles)


Emily practiced playing soccer everyday after school for 1.25 hours. Her sister, Jenn, practiced on Monday, Wednesday, and Friday for twice the amount of time as Emily. Which sister spent the most hours practicing? Explain how you know.

(Jenn spent more hours practicing. She practiced for a total of 7.5 hours, while Emily practiced for 6.25 hours.)


Paul and Tisha are making candy-grams to sell as a school fundraiser. They made 25 on Monday and 31 on Tuesday. On Wednesday, they made half the sum of the amount made on Monday and Tuesday. How many candy-grams did they have completed by the time they finished on Wednesday?

(84 candy-grams)

Learning Tips


Mathematical reasoning is needed for problem solving. In general, sixth grade students should be able to problem solve by using 3 phases of a problem solving process. These phases allow children to think thorough a problem logically to determine a solution. The first phase of problem solving is to be sure to read and understand the problem. The second phase is to plan and solve the problem. The last phase is to look back at the problem and check work. The more children practice working through each of these phases, they better they will become at using mathematical reasoning to problem solve


Work with your child to help him/her successfully complete phase one of the problem solving process. Be sure that your child reads the problem a few times before attempting to solve it. In phase one, read and understand, sixth graders should be sure to identify and determine each of the following:

What exactly is being asked?

Children should underline the sentence or command in the problem and write a problem goal in their own words.

What do I know from the problem?

Children should highlight important, relevant facts that will help them to meet his/her goal from question one.

What do I know from personal knowledge?

When necessary, children will apply personal knowledge to add important facts to a problem.


In phase two of the problem solving process, 6th graders will use the information obtained in phase one to evaluate relationships and determine how to solve the problem. After choosing a strategy to solve a problem, children will use that strategy to find a solution. There are several strategies that can be used to solve problems. Help your child to use the list of all the options below to determine which could be used to reasonably solve each problem he/she encounters.

Problem Solving Strategies

Choose an operation: + , - , x,

Make an organized list

Make a table

Draw a picture

Make a graph

Look for a pattern

Guess and test

Write an equation

Work Backward

Solve a simpler problem

Act it out or use objects


Be sure that your child understands that phase 3 of the problem solving process is just as important and the first two phases. Many children get an answer and stop there. Going back to the original problem, re-evaluating the question and problem facts and comparing them to the solution will allow students to use mathematical reasoning to determine if his/her answer is reasonable. On phase 3, children should:

Compare work to the information in the problem.

Be sure all calculations are correct.

Estimate to see if the answer seems correct.

Make sure the question(s) has/have been answered.


Many students experience anxiety when asked to use mathematical reasoning to problem solve. Often times the become overwhelmed with the amount of information in the problem and the inability to use a standard algorithm to solve a math problem. If this is the case for your child, you can help him/her to overcome these fears by breaking the problem down into smaller parts. One way to do this is to come up with a system of color-coding or note taking for the solution of these sorts of problems. For example, you may want to have your child highlight important facts from the text in yellow and then underline the question being asked in green. This will greatly benefit the visual learner. In addition, the visual learner may need to transfer the information highlighted to a table, such as the one show below. Help your child to come up with a system that he/she will be able to remember and use independently.

Sample Problem Solving Table

My Goal

(Here, I restate the question in my own words)

Problem Facts

(Use this space to write in the important numbers and information the problem gives me)

Facts I Know

(This is where I tell any information I know from personal knowledge that needs to be added to the problem. I won’t always use this space.)

Solve It

(I will use this area to show my work on the strategy I used to solve the problem.)

Check It

  • ?

  • Facts

  • Calculations

  • Estimate

(Check off each box to make sure I check my work.)

Extra Help Problems


Julian read for 30 minutes 3 days a week and for an hour and a half 4 nights a week. How many hours in all does Julian read in a week?

(7-1/2 hours)


Tickets to an amusement park cost $42.50 for children 12 and up and adults and $25.50 for kids 12 and under. Lucia and her family are going to the amusement park. Her family includes; two sisters ages 6 and 17, two brothers ages 9 and 12, and her mom and dad. Lucia is 15. How much will it cost for Lucia and her family to get into the amusement park?



Juan is making copies of a school flier. The copy center is charging him $0.13 per copy for the first 100 copies and $0.08 cents for each copy after that. How much money will Juan have to pay for copies if he orders 300?



Eva’s cell phone company charges her $1.00 for the first minute and $0.10 for every minute after that. Anita’s cell phone company charges $2.00 for the first three minutes and $0.15 for every minute after that. The girls have been talking on their cell phones to one another for 30 minutes. How much will this call cost them collectively?



Nathan needs to calculate how much he will pay for his cell phone bill. His carrier charges him $0.10 a minute for weekday daytime calls, $0.06 a minute for weekday evening, and free weekend minutes. He’s used 286 weekday daytime minutes, 432 weekday evening minutes and 1,000 weekend minutes. How much will Nathan’s total bill be?



The table shows the cost of each item at the school store.







100 sheets notebook paper




Stephanie bought 3 pens, 2 notebooks 5 pencils and one erasure. How much money did she spend on school supplies?



Neil needs a pen and 5 notebooks. How much will this cost him? (Use the table from Extra Help Problem 6.)



Christine needs to buy 3 skirts. At Red Navy, she can buy 3 shirts for $25.85. At Forever 15, skirts are on sale for $8.05. At which store will Christine pay the cheaper price?

(Forever 15)


James has six pets. Maria has half as many pets as Kurt. How many pets do they have together?

(9 pets)


Holly’s tennis class meets twice a week for 1.5 hours. Holly practices tennis on her own for 2 hours a day on the weekends and one hour on Monday and Wednesday. How many hours does Holly spend practicing tennis each week?

(9 hours)


During a week in the dry summer months, the water level in a lake decreased by 5 inches per day for a week, except for two days when it decreased ½ that amount. How much water did the lake lose in one week?

(30 inches)


Kenny went to a concert with his big brother. The band played 8 songs that lasted 4.12 minutes long. They played 1 song that was twice that amount and 3 songs that were half a long. How long did the band play?

(47.38 minutes)


A rock band sold 330 CDs on Monday, twice that amount on Tuesday. On Wednesday they sold as many CDs as they did on Monday and Tuesday Combined. How many CDs had the bad sold by Wednesday?

(1,980 CDs)


A rock band sold 330 CDs on Monday, twice that amount on Tuesday. On Wednesday they sold as many CDs as they did on Monday and Tuesday Combined. They sold half as many CDs as Tuesday on Thursday and Friday. But, they tripled Friday’s sales on both Saturday and Sunday. How many CDs did the band sell during the week?



Mrs. Williams is buying supplies for a class party. She bought 3 quarts of ice cream for $4.98 each, 18 bananas at $.60 for two, 2 packs of chocolate cookies for $1.99 each, 3 canisters of whipped cream for $1.23 and chocolate syrup for half the amount of one ice cream. How much money did Mrs. Williams spend?



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