Give middle school students the opportunity to engage with integers through assigning projects involving timelines, money, calories or cube-building. As students apply integers to tangible goods or to real-world circumstances, the once- abstract mathematical concepts will become second nature.

## Integer Timeline

Reinforce for students that zero is a marker, dividing negative numbers from positive numbers in an amount before and amount after system of measuring, similar to a timeline. For this project, have students brainstorm 10 important events -- five that occurred before their birth, and five that occurred after their birth. Students will create a timeline, setting their birth year as zero, and all other events measured in integers. For example, an event occurring 25 years before the student’s birth would be marked as -25 on the timeline. Each event should be described and illustrated. This project connects the familiar timeline system of organization to the number line format, converting years to positive and negative integers.

## Budgeting Money

Students apply adding integers to spending and earning money in this budgeting project. Have students plan a monthly budget allowing for earnings and expenses. Have students begin a worksheet adding a \$10 weekly allowance. Students document and add positive integers to the balance for additional earnings each week, such as a part-time job, or they can add negative integers to the balance for expenses such as an outing to the movies. After the four-week period, students analyze their balance and create a written explanation of how and why they budgeted well, or how they could revise their budget to manage expenses. This project focuses on integers in monetary form, and teaches students the valuable life skill of tracking expenses and budgeting money.

## Tracking Calories

As students add and subtract integers to track the calories they consume and burn over a week, they learn to apply integers to real-world scenarios as a tool of measurement. Have students track the foods they eat and the physical activities they partake in for a week. For each food, have students look up the estimated number of calories they ate. Keep track of this number. For each physical activity, have students look up the estimated number of calories they burned, given their age and weight. Students should convert the calories consumed to positive integers and the calories burned to negative integers. At the end of each week, they will be able to find out the total number of calories remained.

## Integer Rules Cube

Assess the students’ understanding of the rules of adding, subtracting multiplying and dividing integers via a cube project that reinforces the concepts students have learned about integers. Have your students create a large origami cube, with each face providing different information. On four of the faces, have your students write the rule for the addition, subtraction, multiplication, or division of two integers, providing a numerical example and a word problem example. On the fifth face, students should write the definition of absolute value and provide a numerical example and a word problem example. The final face contains the student’s name, date, and class information. The final product becomes a resource or study tool for students in the future.