For each expression, draw two unique Circles of Evaluation.
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In the column on the left, draw a Circle to illustrate evaluating from left to right.
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In the column on the right, draw a Circle to illustrate evaluating division first, followed by multiplication.
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Evaluate each Circle and make a note of whether or not they produce the same result. We’ve done the first one for you.
| Expression | Divide First | Solve Left-to-Right | |
|---|---|---|---|
1 |
3 × 8 ÷ 2 |
(/ (* 3 8) 2)
|
(* 3 (/ 8 2))
|
2 |
4 × 50 ÷ 2 |
||
3 |
5 × 3 ÷ 3 |
||
4 |
5 × 6 ÷ 3 |
||
5 |
Come up with an example of your own! See if you can come up with an unusual expression. |
6 What did you Notice? What do you Wonder?
7 Can you change the groupings or the order in which you evaluate an expression like this one: 100 ÷ 20 ÷ 5? On the back of your paper, sketch out a few possible Circles. Which one is correct? Why do we need to use the left-to-right rule here?
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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