6th Grade Word Problems and Answers

In 6th grade, students learn to solve real-world problems using ratios, proportions, equations and statistics. These skills are used frequently in daily activities, like calculating gas mileage or measuring ingredients for cooking. Help your child make the connection between the classroom and real life by writing your own word problems at home. Read on to learn how.

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How to Create 6th Grade Word Problems

One of the more challenging aspects of 6th grade math is solving word problems. They integrate math concepts with real-world applications and can be tough because students must select the appropriate operations and write accurate expressions. Word problems also appear on most standardized tests.

Though your child's teacher is a valuable resource for extra practice, you can create your own word problems at home. There are just two things to remember. First, use the topics that the teacher covers in class. Your child will benefit the most from the extra practice if it supports what he is learning in class. In 6th grade, this can include ratios, expressions and statistics.

Second, use topics that appeal to your 6th grader. This means that the subject of your word problems should incorporate aspects from your son's life that he is passionate about, such as sports statistics or weather probability. If your daughter likes animals and nature, give her a few problems in which she uses ratios to compare the speeds of different animals.

Problems by Concept

Ratios and Proportions

1. For every hour that Nate played video games, Ted played three hours. What is the ratio of hours that Nate and Ted play games?

Because Nate plays one hour for every three hours that Ted plays, the ratio is 1 to 3. Ratios can also be written as a fraction, 1/3, or using a colon, 1:3.

2. A lion runs 50 miles per hour and a cheetah runs 75 miles per hour. Write the ratio comparing the lion's speed to the cheetah's speed.

The ratio is 50/75.

3. Lindsey's mom had a garage sale. After the first three hours, she made $100. At this rate, how much money will be made in nine hours?

This problem requires a proportion to solve. The proportion should compare the two sets of ratios: 100/3 = x/9. To solve, cross-multiply so that 3x = 900, and then divide both sides by three. After nine hours, Lindsey's mom should make $300.

Expressions and Equations

1. Anne has two dogs, Rex and Evie. Rex is seven years old, and he's one year older than twice Evie's age. How old is Evie?

An equation is needed to solve this problem. Begin by writing out what we know. In this case, Evie's age is the variable x. We know that Rex is seven years old, so 7 = 1 + 2x. To solve, isolate the variable by subtracting one from both sides: 6 = 2x. Then, divide both sides by two. As a result, we know that Evie is three years old.

2. Randy ate twice the number of pizza slices that Samantha ate, and Samantha ate one more slice than Madeline. If Madeline ate two slices, how many slices were there in all?

It is helpful to begin word problems by listing out the known facts. We know that Madeline ate two slices and Samantha ate three because she only ate one more than Madeline did. We can multiply 2 x 3 to figure out how many slices Randy ate because he ate twice the amount that Samantha ate. Add up the totals: 2 + 3 + 6 = 11, so there were 11 slices in all.

Probability and Statistics

When practicing probability at home, it can be fun to use hands-on activities. For instance, give your child a bag of colored candy that contains five red candies, three orange candies, one green candy and one blue candy. Then, ask your child to calculate the probability that she will pick out the blue candy. In this case, it would be 1/10, or 1%. This can similarly be done with other props, like a coin or a deck of cards.

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