@fawnpnguyen A different bar model approach. Since the number of bananas didn’t change, 3 parts had to become 2 parts without changing the boxes - so each part is now 1.5 boxes. Making the kiwis into 3 parts of the same size showed the fraction made up by the 3 eaten kiwis.
@pwharris C, but I think of it less formally. I recognize 144 as twelve 12s. Half of that is six 12s. Six 12s are 72. (If I don’t remember that six 12s are 72, I add a 12 to 60. I know that five 12s are 60 because twelve 5s are 60 - I see them in the 12 numbers on a clock.)
My nephew just turned 8. These are his thoughts on math:
"The reason I like math is there's no right or wrong way to do it. The only wrong way to do math is not to do math."
#ANNMath
@JMV_Jaramillo@mathladyhazel I don't think there should be symmetry. The circles along the top determine the x's and the circles down the side determine the y's. Since the graphs of cos and sin are different, we get different graphs when we double the argument of one vs the other.
@jamestanton Rearranging the groups can help you see why the total stays the same. Make each new group by taking one from each of the original groups. If we get used to visualizing and playing with numbers, these ideas make sense. They may not be immediately obvious, but they become clear.
@jamestanton The standard algorithm hides the sense of what is going on. With partial products (especially if developed from area models), you can see why the product comes out the same regardless of the order of the factors.
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