We typically think of beginning multiplication as memorizing your math facts for 2’s, 3’s, 4’s and 5’s. But in my new job, things aren’t so typical. So I’m trying something new.

### Sieve of Eratosthenes

It started with a brilliant idea to teaching the Sieve of Eratosthenes.

I began by asking the students to color in (or cross out) each of the multiples of 2, 3, 5 and 7. Alas, the plan went awry quickly.

Students got confused when they needed to cross out a number that was previously crossed out (like 6). So they moved to the next number and crossed it out: 7. Which threw off the counting and made a huge mess.

### Do over – SEPARATE PAGES!

So in the next class, I decided they should do the multiples on *separate sheets*. This turned out to be a *much* better idea.

Most of them figured out the pattern for 2’s rather quickly. Although it did take some into the 40’s before they saw it.

The pattern for 5’s was just as obvious. But the patterns for 3 and 7 are a little more obscure.

In fact, many copied the pattern for 2’s for 3’s!

Once I would get them straight on that, I asked about the pattern for 3’s. They would use skip counting and show me the numbers on the chart – clearly the “pattern” was the counting. But I was hoping to have them see the visual pattern too.

So I had them color a *blank* Hundreds Chart in the same way. My hope was they could see the pattern without being distracted by the numbers.

### Connecting the Coloring to the Math

The next thing was giving them worksheets that used the charts they made. With this, they could connect the coloring exercise with skip counting and the word “multiples.”

So far it’s been a big success. Many students have completed the “Multiples of 2” and “Multiples of 3” worksheets. After 5 and 7, I’ll try out some worksheets for *common* multiples of two primes.

Then we’ll use this for multiplication and least common multiples (LCM). But we haven’t gone there yet.

### Try it with your students!

Here’re the instructions:

1. Get a Hundreds Chart and write on it “Multiples of 2.”

2. Color all multiples of 2. (Start with 2 and then count and color every 2 after that.)

3. Compare your sheet with a friend to see if you have the same numbers colored. If not, figure out what went wrong and help each other fix it.

4. Get a blank grid and color the same squares as you just did on the Hundreds Chart. How could you describe the pattern to someone else?

5. Do the worksheet “Multiples of 2.”

Cycle through the steps with other prime numbers.

Here are the worksheets and charts you need for the Multiples of 3. You can get the full pack of multiples of 2, 3, 5 and 7 on my Teachers Pay Teachers page, or create your own with a generic hundreds chart.

And do share with your PLN on Twitter, Facebook and Pinterest!

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