Distributive Property by Expanding Lesson Plan- 7th Grade Math

Overview

In this lesson, we’ll introduce the concept of distributive property for `7`th graders with a warm-up that will allow students the opportunity to visualize a few representations for the distributive property by seeing what is the same and different between representations. Students will explore how the representations all end up with the same answer. You can expect this lesson with practice to take one `45`-minute class period.

Grade 7

Expressions, Equations, And Inequalities

7.EE.A.1

How to Teach Distributive Property by Expanding

Warm-up

Start the lesson on slide `1` of the teacher slideshow by giving students a warm-up on identifying what is the same or different between the three given representations. This is a link to the warm-up.

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What is same? What is different?

Here are some points that are likely to come up:

All three models are different ways of showing the same thing.
Model B shows repeated addition. Multiplication is the same as repeated addition.
Model C shows the area model - they might call it the box model. That you an find the total area of the rectangle by adding the individual areas.
Model A shows distributive property - quite possibly students have forgotten the term but know how to do it. They might talk about a rainbow going from the number outside to the numbers inside.
All the expressions have the same value - a good time to reintroduce the vocabulary word “equivalent”.

This exercise is a great way to gauge student understanding and builds on their knowledge of distributive property developed in `6`th grade.

Distributive property with negative numbers

The first problem looks at using the distributive property with a negative factor outside the parentheses. This builds on their skills of multiplying signed numbers.

Usually students are quite successful in expanding this expression. Move onto slide `2` where students will see an expression where the term is negative and the operation is subtraction. We are deliberately using the word “Simplify” to make students familiar with this term in this context.

Students are likely to come up with answers like `-6a - 15b` or `-6a - (-15b)` and, of course `-6a + 15b`. You are likely to have a conversation about which is the right answer. Have students explain to each other which makes the most sense. Acknowledge that `-6a - (-15b)` is equivalent but is not in the simplest form.

Formalize the process

Students will develop their own ways of applying the distributive property. Some will want a process that they can refer to in the future. Share this slide with them.

Scaffolding with the area model

Some students might benefit from having an area model template always accessible. Over time, they are likely to stop using them but it is great tool for conceptual understanding and accurately applying the distributive property.

Understanding a negative sign outside the parentheses.

In one last example that you do as a class, introduce a problem with just a negative sign as parentheses. Let students try it on their own.

I have heard two different explanations from students. Encourage students to adopt whatever makes sense to them.

You have to write a `-1` instead of just a negative sign.` -(2k-5m)` will become `-1(2k-5m)`. Then simplify as usual.
A negative sign outside the parentheses means you have to take the opposite of everything inside the parentheses. This explanation goes really well with the meaning of a negative sign as “negation”.

Distributive Property by Expanding Practice

After students have completed their lesson, it’s time for some independent practice! ByteLearn gives you access to tons of distributive property by expanding activities. Check out the online practice and assign them to your students for classwork and/or homework!