Solving Two-Step Equations Visually

In this series of Math Is Visual Prompts, we slowly introduce the idea of Solving Two-Step Equations Using Partitive Division Scenarios.

 

In this series of Math Is Visual Prompts, students are given the opportunity to start solving two-step equations with partitive division through the use of cups to hide “squares” or connecting cubes where the cups are acting as the “parts” or “groups” in partitive division.

We also do our best to model this using the linear model of a number path (precursor to the number line) as well as abstractly using numbers and symbols.

As always, the visuals provided as a consolidation are useful AFTER students are given the opportunity to work with these ideas concretely and after consolidating in the classroom through student work.

Let’s get started…

 

Sparking Curiosity: Conceptual Subitizing Number Talk

First, we introduce this series of visual prompts with a really low floor by showing these squares before quickly covering them up:  

Post 42 - Solving Two-Step Equations - Part 1.006 Question 1 squares

Covered up:

Post 42 - Solving Two-Step Equations - Part 1.011 15 squares covered up

Students are then tasked with convincing their partners of how many squares they observed and how they know.

Then, we “slide in” a couple of red solo cups and reveal:

Post 42 - Solving Two-Step Equations - Part 1.014 how many squares are under each cup

 

The question now becomes:

How many are under each cup if the squares were divided (partitively) amongst the cups evenly?

When you actually provide the concrete manipulatives for students to use, this is a pretty easy activity and all students can access this task. 

When you ask students, everyone will say “4”, which is great!

Post 42 - Solving Two-Step Equations - Part 1.018 question 1 reveal

However, we want to make sure that they are clearly articulating what is happening here. 

Something students (and teachers) can easily miss is that this is a specific type of division known as partitive division

Want to learn more about partitive and quotative division? Check out my post on tapintoteenminds.com about the progression of division here.

Challenge #2: Another Partitive Division Scenario

Here we go:

Post 42 - Solving Two-Step Equations - Part 1.024 question 2

Students are then asked to determine how many squares before we cover them up and to say how they “saw” the squares.

Then, they are tasked to determine how many squares are under each of the cups now:

Post 42 - Solving Two-Step Equations - Part 1.031 how many under each cup

 

With the use of manipulatives or mental math strategies, students will be able to come up with “7” as the result:

Post 42 - Solving Two-Step Equations - Part 1.034 question 2 reveal

 

Challenge #3: 

Here’s the last challenge:

Post 42 - Solving Two-Step Equations - Part 1.039 question 3

Again, students will be able to come up with “6” as the result:

Post 42 - Solving Two-Step Equations - Part 1.042 reveal

 

Now, let’s tie this to a linear model using a number path (or concrete number line using connecting cubes):

 

Post 42 - Solving Two-Step Equations - Part 1.050 question 3 using number line

 

This becomes pretty intuitive when we see it this way.

Now, let’s connect it to algebra:

Post 42 - Solving Two-Step Equations - Part 1 Question 3 Algebraic GIF

 

Post 42 - Solving Two-Step Equations - Part 1.062 question 3 algebraic

 

Be sure to check out the visual prompts video at the top of the post to get the FULL EFFECT including “pause bars” to allow you to pause the video and let kids have think / discussion time.

 

How’d It Go?

Thanks for watching and reading!

Did you use this in your classroom or at home? How’d it go? Post in the comments!

Math IS Visual. Let’s teach it that way.

kylepearce3

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