Math Concepts: Coefficients, Variables, Like Terms

What You Can Do: Students have likely been exposed to variables in familiar contexts, even if they have never given the concept a name. For instance, students know that if a widget costs $2, then two widgets will cost $4, three widgets will cost $6, and, in general, the total cost is equal to two times the number of widgets, or 2*n*.

Students may have also seen variables in common formulas, such as *P* = 2*b *+ 2*h*. From these formulas, students know that variables can represent values. Students can use or create other formulas based on their daily experiences. For instance, they can determine the average speed on a car trip using the formula distance = rate × time (d = *rt*), or they might realize that there are 12 inches per foot, which leads to the formula inches = 12 × feet (i = 12ƒ).

A variable machine can be used to introduce kids to variables. The idea is to assign a value to each letter in the alphabet, for instance, A = 1, B = 2, C = 3, and so forth. (An alternate assignment of values could be to use the keypad on a phone, where A, B, C = 2; D, E, F = 3; G, H, I = 4; and so on.) Students can then use those values to find the value of their name or other words by adding the values of the individual letters. You can then challenge students with questions such as, “What three-letter word has the highest value? ”

Students can use the variable machine to learn about combining like terms. For instance, students can find the value of the word *banana* by first realizing that the word contains three *a*'s, two *n*'s, and *a b*. This leads to the equation 3*a* + 2*n* +* b*, and the value of the word can be found by substituting values for each of the three variables.

Math in the Game: Students are forced to practice combining like terms to free up space in their holding bin. Strategy comes into play as students apply power coins to the treasure chests to change the value of the variables. An understanding of coefficients and how they will affect the student's overall score is a key to winning the game.

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