Writing multiple equations for the same relationship and doing so in context prepares students to later consider more rigorously what makes equations equivalent.Īs students write equations for the first relationship, identify students who use all numbers and those who use both numbers and variables.įor the second question, students may explain Tyler's claim concretely (using values of \(m\) and \(y\)) or more abstractly (using the structure of the equations).
In this activity, students examine simple relationships that can each be expressed with many equations. For example, they know that \(3(x + 5)\) is equivalent to \(3x + 15\) by the distributive property (without trying different values of \(x\)).Įxplain to students that they'll learn more about how to identify or write equivalent expressions and about equivalent equations in this unit. Remind students that in middle school they had seen simpler equivalent expressions. We call expressions that are equal no matter what value we use for the variable equivalent expressions. There are, however, ways to show that these expressions must have the same value for any value of \(n\). Tell students that it would be impossible to check every value of \(n\) to see if the expressions would give the same value. "Do you think that the two expressions will have the same value no matter what value of \(n\) is used? How do you know?"."If (or when) you tried using other values of \(n\), what did you find?"."Were you surprised that these expressions have the same result for different values of \(n\)?".If time permits, consider allowing students to try evaluating the expressions using a value of their choice. If they noticed that all the given values of \(n\) are odd numbers, they might wonder if even values of \(n\) would give the same result. Students are likely curious if the values of the two expressions will be the same for other values of \(n\). Then, ask students what they wonder about the results. Ask a few students from each group for their results.
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