# Inquiry-Based Lesson on Arithmetic Property

Below is a slide show I plan on using for my lesson on properties (commutative, associative, identity, and inverse) for my 7th grade Pre-Algebra class.  They will answer a couple questions, I’ll have them share their thought process and drawings, asking them probing questions and having them convince the rest of us of their thinking.  The questions will be as follows:

Does the order of you multiply numbers matter? Why or why not? Explain and draw a picture.
Does the order you add numbers matter? Why or why not? Explain and draw a picture.

[HERE I SHARE THAT THIS IS THE COMMUTATIVE PROPERTY]

How would you do the following in your head: 10 + 7 + 30 + 6. Once you’ve done it in your head, write down what you did.
How would you do the following in your head: 3 * 4 * 2 * 10. Once you’ve done it in your head, write down what you did.

[HERE I SHARE THAT THIS IS THE ASSOCIATIVE PROPERTY]

Can you add something to a number that keeps the number the same? Explain and draw a picture.
Can you multiply a number by something that keeps it the same? Explain and draw a picture.

[HERE I SHARE THAT THIS IS THE IDENTITY PROPERTY]

Can you add something to a number that gives you a sum of 0? Explain and draw a picture.
Can you multiply a number by something that gives you a product of one? Explain and draw a picture.

[HERE I SHARE THAT THIS IS THE INVERSE PROPERTY]

Afterwards, I will have them create a Frayer model for each property and place it in their journals.  A Frayer model template is found on the last slide.