MATH: Using Arrays to Represent Division

In Lesson 4-3, we worked hard on using arrays to represent division stories. Here was our learning target:

We worked on two types of division stories: equal sharing (where a number of items are shared equally between a given number of people) and equal grouping (where a number of items are put into a groups of a given amount).

I wanted to show how students worked through these two types of division stories. While these aren't the only strategies that will get to a correct answer, I know sometimes it's helpful to see how your children are practicing in class.

Equal Sharing
Here's an example of an equal sharing number story, and the steps we would go through, along with exactly what we would record:

First we made a "tick mark" to represent how many people we had (or how many groups we would need.)

Then we started distributing our 14 counters by drawing circles (or Xs), in an equal way. (We had to give each person one before we gave any person a second one.) We kept track of how many counters we were giving out.

As we gave out the counters by drawing the circles, we made sure to keep the array organized. We stopped after our 14th circle.

We then drew a line to separate the "leftovers," since we know that each person has to have an equal number. Then we counted how many each person received.

We counted up our leftovers, and recorded our answer: "4 counters each, with 2 remaining."

Equal Grouping
Here's an example of an equal grouping number story, and the steps we would go through, along with exactly what we would record:

This time, we don't know how many groups (or people) we need: that's what we're trying to figure out. But we do know that each person will get 5, so we go ahead and make the first row of 5 in our array:

We continue to make groups of 5, keeping track of how many counters we have given out. We stop after 16.

Then we draw our line horizontally, to show that the 16th counter would be a leftover. Now we can draw the "tick marks" as we count how many people we would have.

We count up our remainder, and can write our answer as: 3 people with 1 counter remaining.

While working on homelink 4-3, encourage your child to record their arrays on the opposite page. Let me know if you have any questions!