1 Open Variables & the Commutative Property Starter File. On the table below, record your Noticings and Wonderings about what you see there.
| Notice | Wonder |
|---|---|
2 Hit "Run." A message appears that says, "Looks shipshape, all 4 tests passed, mate!"
3 Click "Show Details" on the right side of the green examples-block-1 rectangle. Describe what you see.
4 In lines 4-5 of the Definitions Area (left side of the screen), change the variable definitions. This time, use a = 6 and b = 10. What do you predict will happen when you hit "Run"?
5 Was your prediction correct? In your own words, explain what happened and why. If you need help, click "Show Details".
6 Give three additional pairs of values for a and b that will cause both example 3 and example 4 to fail. Try them out!
a = b =
a = b =
a = b =
7 Are there any pairs of values for a and b that will cause example 1 or example 2 to fail? If so, list them here:
8 Are any of the examples true every time, no matter what values we use for a and b? If so, which ones?
9 Are any of the examples true some of the time, depending on what values we use for a and b? If so, which ones?
10 Maria says, "The Commutative Property applies for every operation. I know because sometimes I can change the order of the numbers being subtracted or divided and the result remains the same." Is she correct? Explain.
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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