# Math Misconceptions and Productive Discourse

We have a great Algebra warm-up (or instructional) task for you and your students this week! It highlights how Woot Math helps you quickly and efficiently address potential math misconceptions. We also show how to promote productive discourse about those misconceptions in your classroom. Best of all, it’s 100% free to use.

## Assessing Math Misconceptions

The first problem is a tap-on-the-mistake type. Students need to analyze the projected procedure and find the mistake (if there is one). Recognizing math misconceptions is a great exercise.

## – Task 1: Tap on the Mistake –

With tasks like this, everyone has the opportunity to do productive mathematics. If a student don’t know how to solve an inequality or where to start, they can evaluate the projected work. Everyone gets to apply their prior understandings of mathematics to this problem.

The fact is, your students might not catch this mistake. It is a subtle and often forgotten rule that dividing or multiplying an inequality by a negative requires flipping the inequality. If your students ask why this rule is true, you can tell them to think of it as multiplying each side by -1 and then dividing each side by 4. Inequalities are like unbalanced scales. One side is heavier than the other. When you multiply each side by -1, you are changing all negatives to positives and all positives to negatives, this means the scale will reverse. If one side weighed 10lbs and the other weighted 2 lbs the side with 10lbs is lower. Multiplying each side by -1 means the low side now weighs -10lbs (think of it as 10lbs worth of upward force from balloons). The other side is now -2lbs. 10lbs up will pull more than 2lbs so the side with 10lbs up is now higher. The scale has flipped so the inequality needs to flip.

Some of your students will likely choose the correct answer, and some will likely “choose no mistake was made. Now is when the sneaky and magical power of Woot Math shines! Deselect the reveal answer button to reveal student responses as a heatmap without revealing who was correct.

Some of your students might no think there is an answer, some (hopefully) got it right, and some may have chosen another place in the work. Those who got it wrong may have been guessing or may be going off of a juicy misconception… aka: a productive learning moment. For more on the value of learning from mistakes, check out Woot Math’s CEO, Krista Marks, Ed Surge article on Aha moments.

After you click show results, your heatmap might look a little something like this:

## Small Group Discussions

This is a great opportunity for students to discuss the problem, either as a whole class or in small groups. You can ask the students to come to a consensus as a group. This is where another one of our favorite features comes in handy. With the “assign groups” button, Woot Math automatically groups of 2-6 students. You can choose to generate these groups based on if they put the same answer (homogeneous), a different answer (heterogeneous) or at random

## – Student Grouping –

With heterogeneous grouping by answer, each group should have someone who got it right (as long as you have enough students getting it right). Now, each of the groups is set up for success. Woot!

Get started by previewing the activity right now with the link below. Or, login to wootmath.com and search for Warm Up: Modeling with Linear Systems in the Shared Gallery.

Visit our page on formative assessment for more on how to use these strategies in your classroom.