Sample Problems From Every Major Math Category

Math is all about problem-solving skills. Children should be involved in problem-solving activities every day. One of the best ways to help children learn math is to present them with a problem in which they have to devise their own strategies to find the solution(s). Even if there's only one correct solution, there can actually be more than one way to figure out how to solve a math problem. Children need to be given the opportunity to discover their own shortcuts and create out their own algorithms to determine the appropriate answer—or answers.

In addition (no pun intended) they should also be able to justify the solution(s) they reach by explaining the choices they made to arrive at their answers. Students should be able to describe why their solutions work and how they know it's the right solution.

My favorite way to question children with regard to this is to ask them, "How do you know?" When they have to explain how they arrived at their answer, you immediately know the learning that has taken place and you can see the thought process they used to reach their conclusions.

Math problems for sixth-grade students should be read to them. The following math word problems are specific for children in the sixth grade and are divided into the main math categories: Number Concepts, Patterns and Algebra, Geometry and Measurement, and Data Management and Probability.

## Patterns and Algebra

• Kelly's classroom organized an e-Pal club. 11 people joined the club. Each of them sent an email to each of the members of the club. How many emails were actually sent? How do you know?
• Ticket sales for the bake sale were underway. Four people bought tickets on the first day of sales, twice as many people bought tickets on the second day, and each day after that, twice as many people bought tickets. How many tickets were sold after 16 days?

## Data Management and Probability

• Pet Parade: Mr. James has 14 pets: cats, dogs, and guinea pigs. What are all the possible pet combinations he could have?
• How many different types of pizza can you make with the following toppings: pepperoni, tomatoes, bacon, onions, and green peppers? Show your answer.

## Number Concepts

• Sam bought eight ball caps, one for each of her eight friends, for \$8.95 each. The cashier charged her an additional \$12.07 in sales tax. Sam left the store with only \$6.28 in change. How much money did she start with?

## Geometry and Measurement

• Watch your favorite television show from beginning to end. Time each of the commercials and determine the percentage of commercial time for the entire duration of the show. Now, determine the percentage of time the actual show is on the air. What fraction do the commercials make up?
• Two squares are next to each other. One square has six times the length of the other square. How many times greater in area is the larger square? How do you know?
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