Sign in to view assessments and invite other educators
Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.
Give students 2–3 minutes of quiet work time followed by a whole-class discussion. If necessary, encourage students to not pick 0 for each time.
For each equation choose a value for and then find the corresponding -value that makes that equation true.
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 ’s and ’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 -values?” (For the first problem, choosing to be a multiple of 7 makes an integer. For the last problem, picking to be a multiple of 3 makes an integer.)
“What do you notice about all the points?” (The points collected for each equation form a different line.)
In this activity, students are given graphs of lines and asked to consider statements about solutions to the equations that define each line. While there is not enough information to accurately find the equations for these lines, some students may try to find them. The important understanding of this activity is that a coordinate pair lies on a line if it is a solution to the equation of that line, and points not on the line are not solutions.
In this activity, students critique a statement or response that is intentionally unclear, incorrect, or incomplete and improve it by clarifying meaning, correcting errors, and adding details (MP3).
Arrange students in groups of 2. Give students 4–5 minutes of quiet work time followed by a partner discussion. If partners disagree on an answer, encourage them to work to reach an agreement before continuing with a whole-class discussion.
Graph, origin O, no grid. Lines l, m, n. Line l, y intercept -2. Line m, y intercept 4, labeled D. Line n, y intercept 0, labeled E. Point A on line l. Point H on lines l and n. Point E on line n. Point G on lines n and m. Point K on line m. Point J not on any line plotted at 2 comma 0.
Decide if each statement is true or false. Explain your reasoning.
Discuss your thinking with your partner. If you disagree, work to reach an agreement.
The purpose of this discussion is to reinforce the idea that solutions to equations with two variables are a pair of numbers. Use Critique, Correct, Clarify to give students an opportunity to improve a sample written response to the last question by correcting errors, clarifying meaning, and adding details.
Display this first draft:
Yes, is a solution of the equation for line because line passes through the point .
Ask, “What parts of this response are unclear, incorrect, or incomplete?” As students respond, annotate the display with 2–3 ideas to indicate the parts of the writing that could use improvement. (The answer is incorrect because is not a solution. defines a vertical line but the solution to an equation with two variables is a point. A solution to an equation with two variables is a pair of values, and is only a single value. The values and are a solution to the equation for line .)
Give students 2–4 minutes to work with a partner to revise the first draft.
Select 1–2 individuals or groups to read their revised draft aloud slowly enough to record for all to see. Scribe as each student shares, then invite the whole class to contribute additional language and edits to make the final draft even more clear and more convincing.
Consider the graph of the linear equation .
Since is a point on the graph of the equation, is a solution to the equation. Any point not on the line is not a solution to the equation.
Sometimes the coordinates of a solution cannot be determined exactly by looking at the graph. For example, when , the -value is somewhere between -2 and -3. If we have a value for one of the variables, we can use the equation to figure out the value of the other variable.
The equation can also be used to check whether a pair of values is a solution to the equation by seeing if the values make the equation true. For example, since the values and do not make the equation true, then the point is not a solution and does not lie on the line.
Your teacher will give you a set of cards. One partner has 6 cards labeled A through F and one partner has 6 cards labeled a through f. Cards with the same letter, for example Cards A and a, have an equation on one card and a coordinate pair that makes the equation true on the other card. Take turns asking your partner for either the - or -coordinate value and using it to solve your equation for the other value.
The partner with the equation asks the partner with a solution for either the -value or the -value.
The partner with the equation uses this value to find the other value, explaining each step as they go.
The partner with the coordinate pair checks their partner’s work. If the coordinate pair does not match, both partners should look through the steps to find and correct any errors. Otherwise, both partners move onto the next set of cards.
Keep playing until you have finished all the cards.