I love finding new ways to use the multiplication chart to tie concepts together for my students. I created an activity to reinforce area and connect area to the distributive property…and I love it!!! Many students find it difficult to know exactly what numbers to put inside the parentheses and which operational symbols to use to demonstrate the distributive property. This fun activity demonstrates the math that is actually happening in all of those symbols. Let’s get started!!!
1st: Cut out the arrays. I colored mine so they would really stand out on the multiplication chart, but that isn’t necessary.
2nd: This is where the magic happens! Place the first rectangle, labeled “B” in the top left corner of the multiplication chart. Make sure that students don’t cover up the column and row for the factors being multiplied, but instead cover the products inside the multiplication table. The two factors being multiplied can be seen in the pink column and blue row.
The big reveal: The area of that rectangle is revealed when you lift up the bottom right corner. My students all think it is “magic.” I love watching my students flip out when they see how this works. It is pretty awesome that the number of unit squares in the rectangle is listed under that corner. It works every single time!!! This is a powerful activity for students to see how arrays are related to area of a rectangle. Finding the total number of unit squares in an array is concrete, while finding the area of a rectangle with only the dimensions labeled is abstract.
Once students build a good foundation with the concept of area on the multiplication table, we can extend their understanding by introducing the distributive property. You are going to LOVE this.
DISTRIBUTIVE PROPERTY ON THE MULTIPLICATION TABLE
1st: Color and cut out all of the rectangles on the page. This is a great opportunity to remind your students that squares are rectangles, since they have four 90° angles. We often call squares special rectangles. 🙂
2nd: Cut out the rectangles. We can also call them arrays.
3rd: Place the array labeled “A” on the multiplication chart. I labeled the first factor and second factor on the multiplication chart so that students will enter the numbers correctly on their recording sheet. It is important for the numbers to be in the right order to see the pattern. The multiplication expression for an array is reported in __ rows of __, corresponding to __x__. I followed that same pattern. Note that 4×4 is an expression that is part of a larger equation. This is where I start to get giddy….scroll down to see what happens next.
4th: Students can cut the array horizontally or vertically one time, creating two smaller arrays. It is important to point out to students that the two parts contain all of the unit squares from the 4×4 array. This drives the point home that the two sides of the equation they are building are in fact equal. One side is merely decomposed, or broken apart.
5th: Place one of the pieces back into the multiplication table. Students must keep the orientation the same. The multiplication chart shows that this part is 4 rows of 3, or 4×3,which should be recorded in the equation. Put parentheses around this expression to show that these two numbers are multiplied before adding on the other part.
6th: Repeat the same process with the other part of the array. The numbers on the multiplication chart guide students as they fill in the equation representing the distributive property.
7th: Quality questions are the key to this lesson. Here are some good ones to guide your students to discovering the pattern on their own:
- Do you see 3 multiplication expressions in the equation? Name them. (4×4, 4×3, 4×1)
- What is the first digit in each of the expressions? (4)
- What is the second digit in each expression? (4, 3, 1)
- What would happen if we covered up everything other than the second digits in each expression and the equal and plus signs?
We see 4=3+1. Wow! When we guide students to mini-discoveries, we show them that math is full of patterns. When the patterns are revealed, that is when the mathematics peaks through. I always want my students to see math as the uncovering of patterns, not the memorization of random rules. That is the essential difference between teaching conceptually and teaching procedurally.
Let me show you one more thing:
If you always do a vertical cut, then the second factor in each multiplication expression will follow this pattern. If you do a horizontal cut, the same pattern applies to the first factor in each multiplication expression. It may sound confusing but your kids will just see this: One factor always stays the same. Sometimes it is the first. Sometimes the second. The other set of factors will make an addition sentence: __ = __+__.
Here is an example of a horizontal cut:
There are 5 pre-made arrays to work through and then a sheet with grid paper for students to create their own arrays.
Area. Distributive Property. A little bit of wonder. A perfect math lesson. 🙂
You can find the FREE printables for this lesson in my TPT store