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Linear System Student Activities

In Algebra 2, we spend a fair bit of time on understanding and solving linear systems. In task 2-2, I designed a student task about solving a linear system by substitution. Finding ways to keep students to keep students motivated and interested in creating, solving, and graphing linear systems can be challenging! This student activity is a linear systems game which is designed to make linear systems "fun". Here are a couple of interactive games using linear systems:

Make Your Own Linear EquationDivide students into pairs. Have each pair choose three possible values of x and use each one to make an equation. For example, if x is supposed to equal 3, they can discover what 3x + 7 equals; their final equation will be 3x + 7 = 16. Have them write three of these equations on notecards and trade them with another pair of students. Challenge the pairs to solve their classmates' linear equations and see if the answers match up. Each matching answer wins a point for both pairs. Repeat this process with pairs trading with different pairs each round, and count up the points at the end to determine the winning pair. This game gives students the option of deciding which method they will use to solve a linear system and keeps it fun.

Graphing Linear Equations with Pictures

Most of my students cringe when they hear the word "graph". This game attempts to make graphing fun by using linear equations to create simple pictures on graph paper. Students will be asked to figure out ways to make various patterns or pictures, such as stripes (parallel lines--vertical, horizontal, and diagonal), a square, a triangle, a checkerboard pattern, and a diagonal checkerboard pattern. The lines will extend beyond the shapes. Each group can then write out the equations they discovered on a piece of paper and trade with another group.

Assessment

This will be graded as an alternative assessment task. For the first game, students will be hand in their note cards and be assessed based on the number and accuracy of the equations they created. They will also receive points based on their performance within the game. For the second game, students will be assessed based on the number and accuracy of the patterns they created. They will be assessed based on creativity and "neatness" of their patterns. And, they will be assessed based on identifying the correct linear equations corresponding to their drawing.

One way to help students understand the ins and outs of linear equations is to have them make their own. Divide students into pairs. Have each pair choose three possible values of x and use each one to make an equation. For example, if x is supposed to equal 3, they can discover what 3x + 7 equals; their final equation will be 3x + 7 = 16. Have them write three of these equations on notecards and trade them with another pair of students. Challenge the pairs to solve their classmates' linear equations and see if the answers match up. Each matching answer wins a point for both pairs. Repeat this process with pairs trading with different pairs each round, and count up the points at the end to determine the winning pair.
I really like the "picture graph" activity. Kids can do it by hand or use graphing software. One thing I would change is offering them to make some "representational art" such as a cat or a car, the first letter of their name, or something else "more concrete" as an option. Some will still go with abstract patterns. This is also a good time to refresh the "domain and range" idea, because kids will want to use pieces of lines, and possibly "functions vs. non-functions" may come up.

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