## Functions and Graphing: Tips and Tricks

• To turn graphing into a kinesthetic experience, make a set of axes on the school grounds by laying down two perpendicular axes with some tape. Mark off units from -6 to +6 on both axes. Place students on the points (-6, 0), (-5, 0), … ,(0, 0), …, (6, 0). Whisper to them an algebraic expression such as, “Double your number and add 1.” Then have them walk the appropriate number of steps forward or backward, depending on whether the number they have is positive or negative. Together, the students should form the graph of the equation y = 2x + 1 by doing that. Have the rest of the class try to guess the equation that was graphed. After doing this several times, switch roles and have other members of the class graph the equation and the other students guess what it is.
• Sometimes it is easier to remember rules by remembering certain phrases. To help students remember the rules for order of operations, have them remember “Please excuse my dear Aunt Sally.” The p from please stands for “simplify the parentheses.” The e from excuse stands for “evaluating the exponents or powers.” The m from my and the d from dear stand for “doing multiplication and division from left to right.” And the a from Aunt and s from Sally stand for “doing addition and subtraction from left to right.”
• Instead of having students evaluate expressions you create, have them create an expression using at least four different numbers equal to a given number. For example, have them create an expression using any four different numbers and a set of parentheses which are equal to -7. Solutions might be -1(8 x 2 − 9) or 2³ − 8 x 3 − 1 + 2 x 5.
• A good activity to help students acquire number sense and an understanding of the order of operations is to play the game “Find Me.” In this game, 5 one-digit numbers are selected and each number has to be used just once to get a target number. For example, you may select the numbers 2, 4, 5, 8, and 9 and have a target number of 17. Ask students to create an expression using any operations and/or parentheses they would like, using all the numbers just once, and creating an expression equal to 17. Some examples are given below.
 8 + 9 x (5 − 4)² = 17 4 x 5 − 2 − 9 + 8 = 17 9 + 8(4 + 2 − 5) = 17 2 9 − (4 − 8 + 5) = 17 (8 − 2) x 5 − (4 + 9) = 17 59 − (84 ÷ 2) = 17
• Graphing often takes time, so be sure to give students ample time in class or allow them to take home their graphing work.
• When subtracting x-coordinates or y-coordinates to find distances between points when finding the lengths of line segments on a coordinate graph, some students may get negative values. Be sure to remind them that distance is always positive, so they want the absolute value of that difference.