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 subtraction first, followed by addition. In other words, evaluate from right-to-left.
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In the column on the right, draw a Circle to illustrate evaluating from left to right.
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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 | Subtract First | Solve Left-to-Right | |
|---|---|---|---|
1 |
20 + 8 − 5 |
(+ 20 (- 8 5))
|
(- (+ 20 8) 5)
|
2 |
4 + 3 − 2 |
||
3 |
12 + 9 − 8 |
||
4 |
64 + 92 − 91 |
||
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? Do you get the same answer when you solve left-to-right and right-to-left? Which way is correct?
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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