Free 6th Grade Math Problems with Solutions

If your child is struggling with 6th grade math, he or she may benefit from additional at-home exercises. Most math problems can be solved by completing a specific series of steps; concentrated practice on these steps can help students improve in school. Have your child complete these problems after school and check the answers using the solutions provided.

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How to Help Your 6th Grader Solve Math Problems

In 6th grade, students learn to calculate ratios and rates and are introduced to statistical thinking. At home, you can help your child practice by providing additional worksheets. Repeated exposure to these concepts will help your child internalize the information. Use the problems below as examples when you're creating your own worksheets.

Additionally, use practical situations to deepen your child's understanding of concepts taught in school. For instance, recipes are good examples of ratios. If the recipe calls for two cups of tomatoes and three cups of cucumbers, then there's a 2:3 ratio of tomatoes to cucumbers. Mileage is another common example of how ratios are used in real life. Ten miles an hour can be written as 10:1, indicating that for every ten miles driven, one hour will have passed.

6th Grade Level Problems and Solutions

1. A recipe for fruit salad calls for eight cups of strawberries and four cups of bananas. What is the ratio of strawberries to bananas?

The ratio is 8/4, which can be reduced to 2/1. So, the proportion is two cups of strawberries for each cup of bananas.

2. Tom ate three hamburgers over the course of two hours. What is the rate at which Tom is eating?

Solve by setting up the ratio, which is 3/2. His rate of consumption is 1.5 hamburgers per hour.

3. It takes Francine three hours to paint a portrait. How long would it take her to paint 21 portraits?

Set up a proportion to solve this problem. Compare the given ratio (3:1) to the unknown ratio (x:21) like this: 3/1 = x/21. To solve for the unknown, cross-multiply: 3 x 21 = 1x. Since 3 x 21 = 63, it would take Francine 63 hours to complete 21 portraits.

4. In a group of friends, two are 11 years old, three are 12 years old and two are 13. What is the median age of this group?

Median means the middle number. To find the median, write the numbers out in numerical order like this: 11, 11, 12, 12, 12, 13, 13. There are seven numbers total, so the median number will be the fourth number, which is 12.

5. Last Halloween, Alex had 21 pieces of candy, Brian had 30 pieces of candy and Charlie had 15 pieces of candy. What was the mean amount of candy that the boys collected?

The mean is the average of the numbers. Add together all the pieces of candy: 21 + 30 + 15 = 66. Then, divide by the number of boys (3); so the boys had an average of 22 pieces of candy.
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