Algebra concepts may seem abstract -- and largely are -- but projects that get students moving and thinking create multimodal ways of learning that make these concepts more concrete. Engage your students with projects that illuminate the real-world applications of algebraic concepts and increase understanding. You can tailor these projects to a variety of mastery levels, addressing the needs of any learner.

## Linear Functions Projects: Finding Slope

Students begin finding slope and graphing linear equations in middle school and continue throughout high school. To investigate the real-world applications of slope, create an assignment in which students measure an incline. Highlighting the relevancy of this concept, students at an Alabama school measured the slope of ramps and compared the steepness with the standards for wheelchair ramps.

Your class can also use steps to measure rise over run and calculate the rate of change of a staircase or bleachers on campus. Instruct students to explain how rise over run and rate of change are the same, as well as how to represent this information in an equation and a graph.

## Projects for Writing Equations

Design a project on writing linear equations from a graph or data collected from observations of the real world. Students can record real scenarios in their own lives over a defined period of time that include a constant and a rate of change.

To help students write an equation from a graph, instruct them to design an image on a coordinate plane and then identify the equation of each line and parabola. Algebra teachers at Piedra Vista High School in New Mexico assigned a project in which students designed a logo for a company with a set number of lines, circles and quadratics. Students identified the equation of each line, circle and parabola in the logo. Work with students to include creative ways to present their findings.

## Systems of Equations Projects

Instruct students to take data for two variables and write an equation to represent the data. Students then solve to find the solution of the system. These variables may be payments for services that add up to a total cost, such as a monthly cable bill plus individual charges for on-demand movies, or a rental car fee plus daily insurance. Instruct students to represent the data in a graph to illustrate the solution.

One school project in the Northwest Independent School District in Texas had students compare two different plans by keeping track of cell-phone bills that included the monthly fee and price per text message, or the cost of two different cars based on the car payment and gas costs in miles per gallon. Students wrote the equations that represented the total cost for the cell-phone bill or monthly car expenses and graphed them to find out when the cost would be the same.

## Real-Live Quadratic Equations

Design a project in which students analyze of a real-life object shaped like a parabola to make quadratic equations less abstract. Emphasize how students should determine the axis of symmetry of the real object, both by drawing it in and transposing it onto a coordinate plane. Also emphasize how to identify the equation that represents the object.

An Algebra 2 class at Malden High School in Massachusetts designed a project around a diagram of the Golden Gate Bridge. Other possibilities include the McDonald's golden arches or the path of water from a hose. Students might also build a physical object using a quadratic equation, with an accurate axis of symmetry and corresponding ordered pairs.