The purpose of this Warm-up is for students to practice solving an equation for an unknown value while thinking about a coordinate pair, (x,y), that makes the equation true. While the steps to solve the equation are the same regardless of which value of x students choose, there are strategic choices that can make solving the resulting equation simpler.
Give students 2–3 minutes of quiet work time followed by a whole-class discussion. If necessary, encourage students to not pick 0 for x each time.
For each equation choose a value for x and then find the corresponding y-value that makes that equation true.
Sample responses:
The goal of this discussion is to reinforce the idea that the solutions to a given equation will all lie on the same line, and that line represents the set of all possible solutions to the equation. Begin by collecting the pairs of x’s and y’s students calculated and graphing them on a coordinate plane. It may be useful to graph each set of points in a different color. Here are some questions for discussion:
“How did you pick your x-values?” (For the first problem, choosing x to be a multiple of 7 makes y an integer. For the last problem, picking x to be a multiple of 3 makes y an integer.)
“What do you notice about all the points?” (The points collected for each equation form a different line.)
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The purpose of this Warm-up is for students to practice solving an equation for an unknown value while thinking about a coordinate pair, (x,y), that makes the equation true. While the steps to solve the equation are the same regardless of which value of x students choose, there are strategic choices that can make solving the resulting equation simpler.
Give students 2–3 minutes of quiet work time followed by a whole-class discussion. If necessary, encourage students to not pick 0 for x each time.
For each equation choose a value for x and then find the corresponding y-value that makes that equation true.
Sample responses:
The goal of this discussion is to reinforce the idea that the solutions to a given equation will all lie on the same line, and that line represents the set of all possible solutions to the equation. Begin by collecting the pairs of x’s and y’s students calculated and graphing them on a coordinate plane. It may be useful to graph each set of points in a different color. Here are some questions for discussion:
“How did you pick your x-values?” (For the first problem, choosing x to be a multiple of 7 makes y an integer. For the last problem, picking x to be a multiple of 3 makes y an integer.)
“What do you notice about all the points?” (The points collected for each equation form a different line.)