Middle school teachers often assign projects on ratios and proportions to help students learn how to compare and analyze information. Students might also choose to do their math fair projects on ratios and proportions. Ideas for projects should revolve around experimentation, data collection, data interpretation and comparisons.

## Population Comparisons With Crackers

Use small samples from larger populations to help students make multiplicative comparisons using proportional reasoning. Place 300 goldfish crackers in a large container and have students use a fish tank net to withdraw 24 or 25 crackers. Replace the withdrawn crackers with the same number of pretzel-style fish crackers and mix them up. Scoop out 24 or 25 crackers and count the number of goldfish and pretzel fish. Return the scooped fish before drawing again. Have students record the results and repeat the process six to eight times. Make a ratio comparing each fish type to the total in the scoop, such as 22 goldfish and two pretzel fish per 24 withdrawn. Students learn that the original 25-to-300 -- or 1- to-12 -- ratio holds true regardless of the total population size.

## Ratios and Cake

Pretend that a baker is promoting a contest and students must determine how he can cut a rectangular cake into eight equal slices using a different combination of slices each day. This project helps students use geometry, fractions and measurement to study proportions. The ratio is always one to eight, but there are many ways to cut the cake -- including curved slices. Divide your class into groups of two or three students each and give them rectangular pieces of paper to draw cake-cutting options to share with the class.

## Unit Prices for Pencils

Have students use proportions to calculate the unit price in a bulk package of goods. For example, a package of 15 pencils might cost $2.10, so students must determine the unit price of one pencil. You might say, "15 is to 210 as 1 is to 14 or each pencil costs 14 cents." Write the proportions on the board -- 15 over 210 and 1 over 14. Teach students how to cross-multiply to get the answer using a simple linear equation. Divide your class into pairs and provide other unit-price examples. Math fair participants can research actual items and prices and compare them on a trifold presentation board.

## Proportions With Baseball Bats

Compare a regulation-size baseball bat to a small souvenir baseball bat to examine scale factors using proportional reasoning. Divide your class into pairs and have each group measure the length of the regulation bat and the souvenir bat in centimeters. They should also measure the height of one person in the group. Pairs must determine how tall a person would need to be to use the souvenir bat as if it were regulation size. For example, the person might only be 2 feet tall. There will be some variation due to the different student heights, but the answers should be within a few centimeters of one another.

#### References

- PBS Mathline: The Middle School Math Project -- Something Fishy
- Ohio State University: Middle School Math and Science -- Learning Modules for Ratios and Proportions
- Math Blaster: The Price Is Right
- National Council of Teachers of Mathematics: Teaching Ratio and Proportion in Middle Grades
- University of South Florida: Baseball Proportion -- Teacher Notes

#### Photo Credits

- Ximagination/iStock/Getty Images