# How to Teach Algebraic Thinking with the Distributive Property

Last year was the first year I had to teach under the Common Core math standards.  Under the Common Core standards for third grade math is this doozy of a standard:  CCSS.MATH.CONTENT.3.OA.B.5  Teaching the Distributive Property of Multiplication to third graders was something completely new to me as a teacher.  How as I going to teach it?  Well, last year I did and I wrote about it HERE.  Using foam tile as manipulatives was probably the biggest factor (no pun intended) to help my students understand the Distributive Property of Multiplication (DPM).

What did I do this year differently than last year?  How did I get my students to think “algebraically” with multiplication? First lesson learned from last year:  this takes more than one day!

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## Day 1

First, I presented some word problems to my students: Word problems for the Distributive Property of Multiplication

I asked them to use an array to solve these problems.  The students were comfortable with arrays since we had been using them for quite a while with multiplication.  What they did not know were the facts for 6s, 7s, 8s, and 9s.  When I asked them how to solve to get the answer, they knew they had to multiply 7 x 6 for the first problem and 6 x 9 for the second problem. Using an array to solve a word problem.

So then I posed a question:  Is there an easier way to solve this array?  About 3-4 students immediately chimed in that we could just split the array.  Great!

But then what do you do with the 2 smaller arrays, I asked?  Silence. Until one student spoke up and said we could add them.  Brilliant!

From there, I had them split the arrays anywhere they wanted to, then solve for each smaller array.  Then we took the one student’s suggestion and added the 2 products.  So we kept practicing those steps:  1) split the array  2) solve for each smaller array  3) add the 2 products.  We did this all with manipulatives and some scratch paper (in case they could not add the 2 products in their heads).  I presented a total of 4 problems this way.  At the end, I told my students that they had just learned a new property of multiplication.  So as a wrap up, I explained how the Distributive Property of Multiplication is very important to break down complex problems and they they would be using this property frequently in the next grade levels, especially when they start Algebra in Middle and High School.  One thing I did not do on the first day was introduce writing the distributive multiplication sentence.  That would be day 2.

## Day 2

On day 2, we started with a review of the Distributive Property of Multiplication.  I really like making my own PowerPoints to teach math.  Our current adopted math text is a hot mess, and it just confuses the kids more than anything.  In the PowerPoint I start out with a review of what the word distributive means.  Then I present an new word problem like the one below: PowerPoint to review the Distributive Property of Multiplication

What I really wanted to emphasize was following the steps when using the DPM:

1. split the array
2. solve for each smaller array
3. add the 2 products from the smaller arrays PowerPoint to review the Distributive Property of Multiplication

Then I had the students practice with several problems.  I showed them how to write a distributive sentence using the split array.  They were given an array to split and then had to follow the steps, including now writing the DPM sentence.  This is where it gets interesting.  Though the students knew how to split an array and write the 2 multiplication sentences, putting that all into an equation proved more difficult! Writing a Distributive Property of Multiplication sentence proved difficult.

So this day, I guided them through the process.  Over the next week, we practiced daily taking a multiplication fact like 8 x 7 and using the distributive property to solve it.  They eventually got better at it.  When it came time to take a quiz, 70% of my students were able to answer the DPM questions correctly such as the one below:

Overall, I as a teacher am getting better at teaching this very difficult property to 8 year olds.  In these past 2 years, I have learned a great deal about how 8 year olds interpret and see this property as well as, where the confusions lie.  Next year it will only be better!

UPDATE 11/24/15:  I JUST UPLOADED THE COMPLETED POWERPOINT TO MY TPT STORE!  You can see it HERE.

Click below to read about how other teachers tackle Operations and Algebraic Thinking.