Grade Level: 6th Skill: Problem Solving Topic: Calculate and Check Your Answers Goal: Make precise calculations and check the validity of the results from the context of the problem. Skill Description: Find the exact answer to a problem, by using precise calculations. Re-read problems to check answers to make sure they make sense in relation to the problem.

## Building Blocks/Prerequisites

### Learning Tips

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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. The third phase is the focus of this skill.

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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:

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.

Sample–Phase 1: Identify the Question/Facts/Personal Knowledge

Gina gave Nico ½ of her gummy worms. Nico ate ½ of the gummy worms and gave the rest to Kyle. Kyle kept 5 of the gummy worms and gave the last 7 to Emily. How many gummy worms did Gina keep?

Question: How many gummy worms did Gina Keep

Facts:

Gina kept half

Nico took other half

Nico gave half of his half to Kyle

Kyle kept 5 and gave 7 to Emily

Personal Knowledge:

Kyle’s half was 5 + 7 = 12

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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

Sample–Phase 2: Choose a Strategy and Solve

Gina gave Nico ½ of her gummy worms. Nico ate ½ of the gummy worms and gave the rest to Kyle. Kyle kept 5 of the gummy worms and gave the last 7 to Emily. How many gummy worms did Gina keep?

Question: How many gummy worms did Gina Keep

Facts:

Gina kept half

Nico took other half

Nico gave half of his half to Kyle

Kyle kept 5 and gave 7 to Emily

Personal Knowledge:

Kyle’s half was 5 + 7 = 12

Strategy(s): Make an organized list and work backward

Gina – ½ of the total = 24

Nico – Kept ½ 12 – gave½ to Kyle = 12 – 12 + 12 =24 (original 1/2)

Kyle – ½ of Nico’s = 12 (Kyle kept 5 and gave 7 to Emily 5 + 7 = 12)

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Be sure that your child understands that phase 3 of the problem solving process is just as important and the first two phases. In fact, it is the focus of this skill. 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.

Sample–Check the Validity of the Results from the Context of the Problem

Gina gave Nico ½ of her gummy worms. Nico ate ½ of the gummy worms and gave the rest to Kyle. Kyle kept 5 of the gummy worms and gave the last 7 to Emily. How many gummy worms did Gina keep?

Question: How many gummy worms did Gina Keep?

Facts:

Gina kept half

Nico took other half

Nico gave half of his half to Kyle

Kyle kept 5 and gave 7 to Emily

Personal Knowledge:

Kyle’s half was 5 + 7 = 12

Strategy(s): Make an organized list and work backward

Gina – ½ of the total = 12

Nico – Kept ½ 12 – gave½ to Kyle = 12 – 12 + 12 =24 (original 1/2)

Kyle – ½ of Nico’s = 12 (Kyle kept 5 and gave 7 to Emily 5 + 7 = 12)

• Compare work to the information in the problem. *There is a problem here. The work shows that Gina kept 12. She and Nico originally had the same amount. Nico had 12 + the 12 he gave away to Kyle. So, Gina actually had 24.

• Be sure all calculations are correct. Correct.

• Estimate to see if the answer seems correct.

• Make sure the question(s) has/have been answered. Fix answer if needed. Gina kept 24 gummy worms.

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Many students experience anxiety when asked to use mathematical reasoning to problem solve. Often times they 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.)
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When solving division problems with remainders, your child will need to interpret the remainder to determine if the answer should be rounded down, up or written as a fraction or decimal. For example, if you’re asked to find the total number of busses needed to transport students and you get an answer with a remainder, it will be impossible to use this answer, because you can use a part of a bus. For this case, you would need to round up or hire one extra bus so that everyone can fit. However, if you’re dealing with a problem in relation to time you’ll be able to use a decimal or fraction, because time can be written as part of an hour. Logic will need to be used to determine if parts are acceptable or if a remainder needs to be rounded.

### Online Resources

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