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# Which Goes with Which?

Alignments to Content Standards: 6.EE.B

Decide which of the following equations best represents each situation.

 $$x + 2= 10$$ $$x=10+2$$ $$2\cdot10=x$$ $$x+10=2$$ $$10x=2$$ $$2x=10$$
1. After Lou poured 2 liters of water into a large jug, the jug contained 10 liters of water. How many liters were in the jug to start?
2. Clara ran 10 miles, which was twice as far as Nina ran. How far did Nina run?

## IM Commentary

In grade 6, students should have ample opportunities to translate between mathematical equations and verbal statements. Sometimes when algebraic equations are introduced in grade 6, students are just asked to write an equation for a problem that they could easily solve numerically. This task takes the focus off of the answer and offers an opportunity to focus on, for example, how we write the product of $2$ and an unknown quantity.

To help students write equations to represent stories more naturally and fluently, they should also be asked to do the opposite, which is to come up with a story to go with an equation. This task provides stories to choose from, but students should also tackle a more open-ended task like, “Write a sentence about a real-life situation that could be described with the equation $\frac13x = 4$."

These statements were written to discourage reasoning based on "key words," but teachers still may need to watch for guessing or superficial reasoning.

For students who struggle, a few modifications may be helpful:

• Reduce the number of choices; eliminate two or three of the incorrect equations.
• Ask them to say or write what $x$ could represent in each situation. For example in part (a), students may benefit from explicitly clarifying that they are looking for an equation where $x$ means "the water in the jug before Lou poured 2 liters into it."
• Suggest students solve each story first using numbers, and then consider which equations are consistent with their solution. For example, a student might reason for (a), "Lou added water and got $10$ liters. So I know there was less than $10$ liters to start. If he added two liters, there must have been $8$ liters to start. So I know that I'm looking for an equation where the value $8$ in place of $x$ would make the equation true."

For students who finish early, an extension could be to ask students to write a sentence describing a situation that could go with each equation they did not choose.

## Solution

1. $x+2=10$
2. $2x=10$