## Distributive

Property of Multiplication…oh, my!

Yes, captain. Shields up and ready to fire on the Distributive Property of Multiplication. |

Root canal

without Novacaine. Pins under my

fingernails. Sitting through an

insurance seminar. Those all seem

preferable to teaching the Distributive Property of Multiplication (DPM) to

third graders. Seriously, didn’t my

generation learn that sometime in MIDDLE SCHOOL? I know, stop with the whining and just teach

it.

Here’s the

rub. I have never had to teach this

property! I met with my team and we

talked about how to teach this. Should

we break it down into steps? Should we

do only hands on first? Should we use

the Go Math book? We decided that we had

to start with the concrete. Get the

students to use manipulatives to build arrays that could then be broken apart

and make the connection to the DPM. So here’s

what I did.

I presented the problem/question then highlighted key words. |

First I

introduced the problem:

*How can we break apart the array 3 x 7 to make it easier to solve?*

If you have

read my previous posts about Lesson Study and bansho, then you know I always

start with a question that begins the lesson.

We read the question together, we underlined important key words (break

apart, easier). I explained to the

students that I would give them the bag of foam tiles and a blank paper. They were to use the tiles to build the array

first and the paper was to record their solutions with drawing and words and

numbers.

I began to

walk around the room interested in how the students interpreted “break

apart.” Some students literally

scattered their tiles around leaving no semblance of an array. Some students

broke apart the array by putting the tiles into equal groups (hey at least they

were equal groups!). Some students broke apart the array into 2 smaller

arrays. I saw that one student was

already recording his solution so I went to see what he had done. He had broken the array into 2 smaller

arrays, counted the tiles in each array, then added. Not bad!

I had the student go up to the board and copy his solution and then

explain to the class what he had done. This was an excellent opportunity for me

to step in after his explanation (which by the way I wish I had recorded

because he used the correct vocabulary and his explanation was worthy of any

common core question!) to talk about what it means to “break apart.”

Student used tiles to find a solution, then recorded answer then shared it with classmates. |

I like to

tell stories, so I told the students this story about my backyard. In my backyard, I had to move a lot of bricks

from one location to the other. There

were more than 30 bricks. I said that

there was no way I could move all the bricks at once. So I decided to move about half of them at a

time using a hand dolly. This way I

divided or divvied up the work to make the task easier. I kept referring back to this idea of

breaking up a hard task into easier tasks.

I guided the

students to understand that breaking apart the array meant that after you broke

it apart, you still had to have an array!

Not groups, no piles, not unequal shapes. So once that was cleared up, I gave them

another array to make and break apart: 3

x 8.

Another student found a solution for 3 x 8. |

This time,

the students understood that they had to end up with 2 smaller arrays made out

of the bigger array but keeping the same amount of rows or columns. Most of the students I observed broke apart

the array into 2 arrays of 3 x 4. Then

they added the two arrays (12 + 12). I didn’t

see any multiplication sentences yet, so I had to make sure I encouraged using

multiplication sentences when labeling.

However, I did find one student who had written multiplication sentences

so I picked the student to come up and record the solution while the others

continued to work.

After the

student explained what she had done, I then asked the students:

*Where is the best place to break up an array?*

I guided the

conversation by asking them which factors were easiest to multiply. They came up with 0, 1, 2, 5 and 10. Great!

I kept guiding the conversation by saying pointing out that you’re not

going to break up an array by 0 or 1. Since we are working with large arrays, I

pointed out that 5 would be a better choice.

Once that was established, I asked the students to turn their paper over

and take notes. A very quick lecture

followed introducing them to the DPM. We

brainstormed synonyms for the word distribute and we talked about WHY they had

to learn this property.

From there,

I gave them another array to break apart:

4 x 9. Most of them began by

breaking apart the array at 4 x 5 and 4 x 4.

From there I saw them write their multiplication sentences and added the

partial products to get the total product.

Success! For now at least.

I did

quickly explain to them how their 2 multiplication sentences needed to be

combined into one multiplication sentence 4 x (5 + 4) so they could see where

we were going with this whole process.

That’s tomorrow’s lesson. Stay

tuned.