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.
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 into 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.
Click here to grab your copy of this activity.