# Reversals

In this video, we disrupt the routine by expanding your possibilities for practice problems using an idea that’s been around for a while, but you may not have heard of. Reversals.

### Relevant Standards

CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.

CCSS.MATH.CONTENT.8.EE.C.7 Solve linear equations in one variable.

CCSS.MATH.CONTENT.8.EE.C.8Analyze and solve pairs of simultaneous linear equations.

Dougherty, B., Bryant, D. P., Bryant, B. R., & Shin, M. (2016). Helping students with mathematics difficulties understand ratios and proportions. Teaching Exceptional Children, 49, 96-105.

Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren (J. Kilpatrick & I. Wirszup, Trans.). Chicago, IL: University of Chicago Press.

### Video Transcript

If you’re an algebra teacher, you’ve probably searched for practice problems for your students. And you’ve probably found lots of things like this — worksheets and textbooks that have the same type of problem over and over again.

In this video, we disrupt the routine by expanding your possibilities for practice problems using an idea that’s been around for a while, but you may not have heard of. Reversals.

The concept is pretty simple: When there’s a typical problem format, just reverse it.
No really, that’s it.

##### Example 1. Equation and Solution

Let’s try it out with those algebra problems. All of them start with an equation and ask students to find the solution. So the reversal would be: give students a solution and ask them to find an equation.

##### Example 2. System and Solution

Here’s another one. For systems of equations, students are typically given a system and asked to find the point of intersection. The reversal is to give students a point and ask them to find a system of equations that have that point as the solution.

##### Example 3. Operation and Difference

And one more: If students are still practicing integer operations, they might be given a numerical expression and asked to compute the difference. A reversal would be to give students a difference and ask them to find two integers that could’ve produced it.

##### Reasons to Do Reversals

Although reversals are a great way to come up with additional practice for students, there are even more reasons to incorporate reversals.

##### Reason 1. Disrupt the Monotony

First of all, reversals can disrupt the monotony of practice problems. This is good because it allows students to think about the same topic in a slightly different way.

##### Reason 2. Promote Flexible Thinking

Reversals also promote flexible thinking as students do and undo problems. This leads to a deeper understanding of the procedures students are practicing.

##### Reason 3. Provide Discussion Ideas

Finally, because reversals often have many solutions, students can get creative. This means you could have a discussion comparing and contrasting their ideas.

So be brave, try it out, and let us know how it goes in the comments.