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# Basic Arithmetic

Please Excuse My Dear Aunt Sally (PEMDAS), she has the hardest time remembering how to make sense of these arithmetic rules...

This is a series called Step Up which goes through the process of problem solving. Our goal is to solve this problem:

**Justify visually that 258 is divisible by 3.**

We'll start by **analyzing** the problem. Since the goal is a visual representation, we should try to represent 258 visually. Which of these is 258?

This is a series called Step Up which goes through the process of problem solving. Our goal is to solve this problem:

Justify visually that 258 is divisible by 3.

Now we'd like to **explore** the problem; which often is an experiment with a simpler case. Based on the diagram, why is 111 divisible by 3?

Goal: Justify visually that 258 is divisible by 3.

You should **explore** and try an experiment with a number other than 111 (like 333) before answering this question (that is, make a diagram like in problem #2 and see if it justifies divisibility by 3). Usually one experiment is not enough!

(Seriously, experiment a little! Then come back to this problem.)

Based on those experiments, **plan** which approach would aid justifying why 258 is divisible by 3?

Represent the number out of blocks of size 100, 10, and 1, then ...

**Carry Out**: Which of these will justify visually that 258 is divisible by 3?

After solving a problem, it's good to **look back**; not just to verify your answer, but to think about more general cases.

Since 99 and 9 are always divisible by 3, the thing that makes a number not divisible by 3 are the red squares. If the red squares count to something divisible by 3, the whole number is divisible by 3. The red squares are also:

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