SWBAT create a picture or diagram that represents the division and multiplication fact families for 6, 7, 8 and 9.

Students don't always transfer their understanding of addition and subtraction fact families to multiplication and division. This activity gives them concrete practice with the idea.

3 minutes

I give students the current statistics on their mastery of the basic multiplication and division facts required for 3rd grade. I remind them that this is on of the areas in which fluency is essential to their progress. To that end, I show them that in today's focus, multiplication equations with factors of 6 7 and 8.mp4, they already know 18/30 required facts!

I explain to them that fluency with math facts is in many ways analogous to fluency in a language. It doesn’t mean you know everything all the time but it means that you have an efficient understanding, you know the facts (or words) enough of the time to function well, and you usually don’t have to think through to the detriment of comprehension.

12 minutes

In order to emphasize the facts they already know, as presented in the opener, as a class we list the 6, 7 and 8 fact families and circle the facts that are held in common. Then we underline the “1 facts” (identity) and “2 facts” (doubles). We count the facts held in common only once and look at the number of facts that they actually need to learn within this set, which is a smaller number than it might first appear.

I draw something very simple to show them how to use the math facts as lines. For example, I might draw a circle or a square and draw the lines as math facts. The danger in showing students teacher created examples is that this then sometimes stifles their creativity because they emulate the teacher example because they believe that is the only correct way, or because they want to please the teacher. I have found that it is generally more effective to find a few students examples (there are always some students who start in on this more quickly, as if they had a drawing in their head that was just waiting to escape) and hold them up to show the class. Here are a few teacher created examples if you would like to use them: an example fact picture in which the facts are written once and then the objects counted out, and this fact picture in which the outline of the shapes are drawn from facts themselves.

40 minutes

Students create their drawings. They may integrate all the multiplication and division facts on one page or may separate out the six facts, the seven facts and the eight facts. They can also separate out the 1 facts and 2 facts for 6, 7 and 8.

7 minutes

The students count themselves out in a 1, 2, 1, 2 pattern. Ones walk, twos stay.

"Ones" are expected to ask questions of the mathematical artists. Both groups are using sentence frames:

- "What made you choose this design?"
- I chose this design because...

- "What do you like best about your picture?"
- What I like best about my picture is that.... (I chose, I used, I created...)

- "Which facts were the easiest, most difficult, most interesting to represent?"
- The most interesting facts to represent were the ________________ because __________.

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