Problem Solving and the Common Core

Appendix 2- Sample Problems

Below is a set of sample 6^th grade problems for ratios and proportions. These are problems that will be used for practice and assessment throughout the unit. They are not problems that will be used for the basis of structured problem solving-based lessons.

The ratio of the number of boys to the number of girls at a school is 4:5. If there are 120 boys, how many students are there all together?

Sam’s two new aquariums each hold exactly 200 gallons of water. One aquarium will hold small fish and the other will hold large fish. He will buy 5 small fish for every 10 gallons of water in the aquarium. He will buy 8 large fish for every 40 gallons of water in the aquarium. What is the total number of fish Sam will have? What will be the ratio of Sam’s small fish to large fish?

A total of 300 trees will be planted in a park. There will be 2 pine trees planted for every 3 maple trees planted. How many of each type of tree will be planted in the park?

A food company that produces peanut butter decides to try out a new version of its peanut butter that is extra crunchy, using twice the number of peanut chunks as normal. The company hosts a sampling of its new product at grocery stores and finds that 5 out of every 9 customers prefer the new extra crunchy version. If the company is planning to produce 90,000 containers of crunchy peanut butter, how many of these containers should be the new extra crunchy variety, and how many of these containers should be the regular crunchy peanut butter?

The producer of the news station posted an article about the high school’s football championship ceremony on a new website. The website had 500 views after four hours. Create a table to show how many views the website would have had after the first, second, and third hours after posting, if the website receives views at the same rate. How many views would the website receive after 5 hours? (It should be noted here that “same rate” means: in any two equal time periods, there are the same number of views.)

Hank bought 5 meters of ribbon for $10. How much does the ribbon cost per centimeter?

A runner ran 20 miles in 150 minutes. If she runs at that speed, how long would it take her to run 6 miles? How far could she run in 15 minutes? How fast is she running in miles per hour? What is her pace in minutes per mile?

Sally drives 66 miles in 3 hours and Molly drives 72 miles in 4 hours. What is the difference between their average speeds, in miles per hour?

A stand is selling 8 mangos for $10 at a farmers’ market. The grocery store is selling 12 mangos for $15. Which has a cheaper deal on mangos, the farmers’ market or the grocery store?

A line measures 30 centimeters long. A second line measures 500 millimeters long. Which line is longer?

Who walks at a faster rate: someone who walks 60 feet in 10 seconds or someone who walks 42 feet in 6 seconds?

During the winter of 2012–2013, Buffalo, New York received 22 inches of snow in 12 hours. Oswego, New York received 31 inches of snow over a 15-hour period. Which city had a heavier snowfall rate?

One math student, John, can solve 6 math problems in 20 minutes while another student, Juaquine, can solve the same 6 math problems at a rate of 1 problem per 4 minutes. Who works faster?