For example, picture an 8-by-10 pool with a single block of black as border. Adding the border creates a 10-by-12 rectangle.

Pool (white): 80 tiles

Border (black): 40 tiles

So, an 8-by-10 pool with a single block of black border is not a solution. Hope this helps!

]]>I was not directing the questions at you, but rather suggesting them as possible questions for a student who is learning about the importance of decomposing numbers by place value in the context of using the Arrow Way.

]]>In computing 18 + 12, my son will usually do 8 + 2 = 10 then add that ten to the total of the other tens to get 30. Other times he will break the 12 and do 18 + 2 = 20 then 20 + 10 = 30.

]]>How does he compute 18 + 12?

Suppose you suggest a new method, called the Squiggly Way.

In the arrow way, you can add or subtract:

1, 10 (which is 10*1), or 100 (which is 10*10).

In the Squiggly Way, you can add or subtract:

1, 6 (which is 6*1), or 36 (which is 6*6).

Is the Squiggly Way better than the Arrow Way?

Is the Arrow Way better than the Squiggly Way?

Are they both equally good?

How can you tell?

Why x4?

Interestingly he’ll solve 49 + 23 as 49 + 1 + 22, using a strategy to make a ten, but isn’t tying that or previous number-line work to The Arrow Way.

]]>I’m actually thinking of the proof analysis strategies provided in CME geometry. There are definitely problems in there that say “use a reverse list to plan this proof”. I actually did not force students to use proof blocks and flowcharts this year as many times as I should have and now I think some students who could really benefit from that organization system have missed the opportunity to really see how powerful the strategy can be.

At the same time you are absolutely right that we don’t want students losing the forest for the trees. I definitely had some students trying to use proof blocks and flow charts far longer than they should have despite the strategy not really working for their thought process. Those I had to assure that the strategy itself didn’t matter. It is a tricky balance.

]]>If you used the word ones you’d be saying part of a whole one, or I now have one whole one which I don’t think helps.

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