## Monday, December 10, 2012

### Demystifying the Distributive Property

Okay, raise your hand if you're an elementary teacher and just the mention of the distributive property makes you break out in a cold sweat.  Go ahead...no one can see you.  Hmmmm, that's what I thought. :)

The common core standards are all about the properties, and that's very new to most elementary teachers.  It's okay to admit that you had to go back and brush up on "big" math.  Last week I got an email from Terry, a reader in New Jersey.  Before I get into her request, I want to let you know that Terry is the director of a wonderful organization, Free Military Child Tutoring.  Be sure to check out her website!  So, Terry was working with her third graders on the distributive property, and she wanted some activities that would help her kiddos develop a deep understanding of the distributive property.

CCSSM 3.OA.5 reads, in part: Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56.  Whew!  That's a mouthful!  To put it in elementary terms, you split 7 (one of the factors) into 5 + 2 (friendlier numbers), multiply 8 x 5 and 8 x 2, and add the products together.  Not so bad, really.  Now I don't know about you, but 8 x 7 was a hard fact for me, and maybe this strategy might have helped!

As with any other math concept, it's important to take this skill through the concrete (manipulatives) and representational (drawing) stages before the abstract (purely symbolic) stage.

So, first there is a mat that kiddos can use to build their array and then split it in two parts.  This is the concrete learning.  They write equations for both the original array and the split array (requires parenthesis).  This connects the concrete to the abstract. Please note that there is no right way to split the array.  For example, I split the 8 x 3 array into (4 x 3) and (4 x 3).  Another student might split it into (6 x 3) and (2 x 3). That's the cool thing!  Students will see that the array can be split more than one way.

Next, I have a little game that students can play to practice representing arrays and connecting them to equations.

1. Hi Donna!
Thank you so much for these activities :)
With the common core standards being as rigorous as they are, I find that my students lack the basic number sense to tackle newer, more difficult problems. Your activities really help students dig deeper into the concepts and provide students with a deeper mathematical understanding! I really appreciate all the freebies and so do my students :)
--jen
teaching, life, and everything in between

1. You are so right about number sense! So many kiddos are really lacking it. I'm glad my activities help. :)

2. Oh my goodness....thank you so much for posting this tonight. You must have been reading my mind because I was struggling with a way to make this kid friendly...your activity fits the bill. Looking forward to using this with my class soon!

1. Ha ha...I LOVE it when my mind-reading powers kick in! So glad this is timely for you. :)

3. Thank you so much Donna! It's exactly what I needed!

1. So glad to hear it, Terry. :)

4. This is what I have been reading about as a better way to teach multiplication facts. I was also trying to think of a way to make this kid friendly and accessible to my third graders, but you have done a better job than my attempts. Thank you for sharing.

1. You are so welcome, Michele! Glad you find it useful. :)

5. Thanks so much for sharing this! I am teaching this very concept next week so your timing was perfect!

1. Perfect! I hope it works well for you! :)

6. Thank you, I teach 4th grade and have been teaching this concept for a couple weeks. I still have some that aren't quite getting this. I am going to put this in my game/manip center for rotations.

1. Sounds like a great idea, Jennifer!

7. Great post (and yes, I know, I am late to the party)! Just think of all the other things students can do by understanding the distributive property! This is actually one of my favorite things to teach in upper level math. And I love the moment when they are able to use this for doing mental math and discuss it during our number talks! :)

Janaye

1. No such thing as late in the blogoshpere! I totally agree with how exciting the "ah ha" moment can be!

8. This is adult and student friendly! Your resources and teaching strategies amaze me! Is it to early to nominate you for Blogger of the Year?

1. How did I miss this comment? Ha ha. So sweet!

9. What a great activity! Thanks! I'm a new follower!
Jenn

1. Welcome, Jenn! Glad to hear you're finding some information that's useful to you. :)

10. Thanks for sharing, Donna! I plan to do this tomorrow to help my kiddos really "get" it.

Farrah

1. Awesome, Farrah! I hope it went well! :)

11. You got a really useful blog I have been here reading for about an hour.

1. Glad you're finding it useful!

12. Thanks for sharing! I look forward in viewing more of these articles.

13. Thank you! I will share this with my grade level and your great blog! So many teachers worry about students knowing the name of the property instead of knowing how the properties can help them.

14. What a great resource you are! Thank you for everything you have shared with me. My students love the games.

1. Always nice to hear that kids are loving math, Chaya! :)

15. You came to my rescue! I am working after school with a group of our t risk 5th graders who lack a fundamental number sense. I was beginning to sense that the properties were the way to reach them and you have given me a valuable tool that will be used this week. THANKS!

1. Oh, perfect, Roberta! I hope it helps them out! :)

16. Perfect timing in more ways than one. First, we're just now getting to the the larger, more difficult factors where my third graders can benefit from decomposing one of them into friendlier numbers. And secondly, I'm watching my Seahawks on Monday Night Football tonight!

1. Ha ha, too funny, Liz!

17. Oh my goodness, I teach 6th grade and we still are on regular state standards until next year but the district is full throttle common core. Since we aren't going to be tested on common core this year we have to fill in the gaps. This is one of them. I have had a hard time presenting this to students in the past but I think your activities will help a lot!

18. This is such a great activity! Thank you so much for sharing!

19. Fabulous! Thank You!

20. Thank you for providing an activity that students can do independently that requires mathematical thinking!

21. Your game is excellent! It really helped my students get a better feel for the Distributive Property! Thanks for sharing!

22. Hi I'm not a teacher technically. I pulled my 4th grader out mid year because common core was kicking his bottom and the Teacher just couldn't get though to him. Anyway I do not remember him being taught this at all. Can you tell me what grade common core introduces the distributive property concept?

23. I teach 6th grade math and I am so using this!! Just what I was looking for...something fun and visual for the kids! Thank you SOOO much for sharing!

1. You're welcome, Kendra! :)

24. Thank you for a great resource! I'm using it as extra practice for my 9th graders taking a Math 180 course!

25. Glad to see someone (above) using this for higher grades. I don't know what's happened before hand to my 8th graders but I am certainly going to use this for some of my strugglers. Thank you!

26. I'm new to teaching Math/Science at my school. In fact, I have a degree in History! Looking at our year at a glance and where were supposed to be. I was thinking how in the world do I even begin to explain the distributive property. I think of algebra as soon as see this in action. This will definitely help! thank you!

27. This is excellent!! Thank you for sharing

28. This is great! Thanks! Keep posting 3rd grade stuff. I need all the help I can get! My students have a hard time with math!

29. I'm just about to move on to area models for multiplication... great timing to find another way to do it! Thanks so much for sharing. You have such awesome ideas and activities that you present here. =)

30. Thank you for sharing! Great activity.

1. My pleasure, Melissa! :)

31. Thanks for sharing. I am doing this lesson for my evaluation and I needed a graphic organizer that would assist my ELL's grasp and organize the process. I can't wait to try it!