It’s been on my TO DO list for a long time. Years, in fact. But I’ve finally checked it off and I’m thrilled with the results.

As many of you know, for each of my Family Math Night events I include a

*What Do You Notice?* poster. These posters are designed to get kids and parents thinking about math on a deeper level. Although each poster has been included on our website, there has never been details…until now. I’ve taken each of the posters and written a thorough description of the math involved. I’ve also included the specific skills by grade span, K-2 and 3-5, and given several examples of student responses.

Here’s an example:

**What Do You Notice? ***Rectangular Arrays*

**Skills**

Primary students (K-2): shapes, counting, repeated addition, area

Intermediate students (3-5): classifying quadrilaterals, area model of multiplication, multiplication, prime, composite, and square numbers

**Mathematical Background**

For this one, I represented each number as a rectangular array. I also color-coded the arrays hoping that students would notice the relationship between the colors and the arrays that went with them. Notice how the orange arrays are square numbers. The red arrays are our prime numbers. Then I used blue for arrays that were non-square and had a length of two. Purple was non-square with a length of three.

I was also hoping that students would notice that some numbers were represented by more than one array (composite numbers). Prime numbers had only one array. Note: ‘1’ is not a prime number which is why I colored it orange – the color of the square numbers.

This activity does a nice job of visually reinforcing the area model of multiplication: L x W = A

**Sample Student Responses**

“The long grid before the square and/or rectangle grid(s) have the same number of blocks.”

“None of them are the same.”

“There is a color pattern.”

“Some numbers are on there more than once.”

The idea is to make it easier for you to include these posters at your events. But it’s not just limited to Family Math Night events. Teachers have written me about how they include them in their classroom learning and some are even displaying them in the school hallways to give students something to think about as they walk the halls.

However you decide to use them, I know they’ll help your students explore math in new and exciting ways.