Paint Splatter Arrays

This isn’t Splat!

Paint Splatter Arrays (.key)
Paint Splatter Arrays (.pdf)

In Steve Wyborney’s Splat!, the total number of dots is given and the number of dots under each splat is unknown. In my Paint Splatter Arrays, the total number of dots is unknown. My paint splatters do cover some dots but how many is beside the point. Also, Steve’s dots are scattered; mine are arranged in arrays. (More on that below.) Steve’s splats splat. My splatters are there from the get-go. See? Not the same.

h/t Andrew Stadel

Here’s why I created this activity…

Number Talks -- Dot Cards

T: “How many do you see?”

S: “Twenty-five.”

T: “How do you see them?”

S: “Two, four, six, …”

Every. Single. Time.

Not all students. Most students do see and use groups or arrays to figure out how many. Those strategies are described in this post. But some students don’t seem to make sense of others’ ideas. That’s a greater challenge than I’ll tackle here. (Recommended: Intentional Talk by Elham Kazemi and Allison Hintz.) Instead, I designed the activity above to (gently) shove students towards looking for and making use of arrays.

The first three are softballs. For example, the second:

Paint Splatter Arrays.004

Students can still see each dot and count all by ones or twos. But a more efficient strategy is to see 3 × 5 (3 rows, 5 columns).

The next several slides completely cover at least one dot, so students can’t count all by counting what they can see. In each, at least one complete row and one complete column is visible. For example:

Paint Splatter Arrays.010

4 × 6

Paint Splatter Arrays.028

6 × 6

I had some fun with the last two. In the next-to-last one, the middle column is completely concealed.

Paint Splatter Arrays.030

3 × 7

In the last one, most of the dots are hidden. A bit of estimation. How many?

Paint Splatter Arrays.032

How confident are you?

Paint Splatter Arrays.033

<shrinks> 6 × 8

What about now?

I test-drove these on my daughters. (Keira likes Booger Math! over Paint Splatter Arrays, by the way. It is catchier.) I’m looking forward to trying this out in Surrey classrooms. Feedback welcome!

And mine goes ding ding ding di di ding ding DING ding ding ding di di ding ding.

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Math Picture Book Post #6: Fika

For fans of arrays (and those with OCD), there’s much to like about Fika, the Ikea cookbook. Each recipe spans two pages: the ingredients on the first, the finished product on the second.

A sample:

Fika 1

Fika 2

My daughters and I have been talking skip counting, equal grouping, repeated addition, arrays, multiplication, etc. “How many? How do you know?”

We got in on the act:

Cookies 1

Cookies 2

Our “family recipe”