In this Warm-up, students write equations representing linear relationships. While the relationships can be represented by any form of linear equation, these two situations lend themselves to using equations of the form y=mx+b and Ax+By=C. This activity encourages students to think about strategies for writing linear equations.
Tell students to close their books or devices (or to keep them closed). Reveal one situation at a time and ask students to write an equation that represents the relationship. For each problem:
Give students quiet think time and ask them to give a signal when they have an answer and a strategy for how they came up with their equation.
Invite students to share their equations and strategies and record and display their responses for all to see.
Write an equation to represent each relationship.
The purpose of this discussion is for students to hear and explain strategies for writing equations to represent situations. Consider discussing:
“How are the equations for the two situations similar? How are they different?” (Both equations have two variables. Both equations include numbers used in the descriptions. Both equations describe a linear relationship. One equation has both variables on one side while the other equation has variables on both sides. The slope and vertical intercept are indicated in one of the equations but not the other.)
“What are some strategies that helped you to write your equations?” (Make a table of possible values; find an initial value and a rate of change; compare the situation to similar situations from previous lessons and activities.)
“Is the slope for each of these equations positive or negative? Why does that make sense with the situation?” (For the fruit, the slope is negative, which makes sense because if more of one fruit is bought, less can be bought of the other. For the savings account, the slope is positive, which makes sense because the more weeks go by, the more money will be in the account.)
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In this Warm-up, students write equations representing linear relationships. While the relationships can be represented by any form of linear equation, these two situations lend themselves to using equations of the form y=mx+b and Ax+By=C. This activity encourages students to think about strategies for writing linear equations.
Tell students to close their books or devices (or to keep them closed). Reveal one situation at a time and ask students to write an equation that represents the relationship. For each problem:
Give students quiet think time and ask them to give a signal when they have an answer and a strategy for how they came up with their equation.
Invite students to share their equations and strategies and record and display their responses for all to see.
Write an equation to represent each relationship.
The purpose of this discussion is for students to hear and explain strategies for writing equations to represent situations. Consider discussing:
“How are the equations for the two situations similar? How are they different?” (Both equations have two variables. Both equations include numbers used in the descriptions. Both equations describe a linear relationship. One equation has both variables on one side while the other equation has variables on both sides. The slope and vertical intercept are indicated in one of the equations but not the other.)
“What are some strategies that helped you to write your equations?” (Make a table of possible values; find an initial value and a rate of change; compare the situation to similar situations from previous lessons and activities.)
“Is the slope for each of these equations positive or negative? Why does that make sense with the situation?” (For the fruit, the slope is negative, which makes sense because if more of one fruit is bought, less can be bought of the other. For the savings account, the slope is positive, which makes sense because the more weeks go by, the more money will be in the account.)