Kay is working on money in her math class. She had homework that required her to compute two people's money based on the coins they have, decide who has more and by how much.

She incorrectly calculated the amount of the difference for the two people. I asked her how she decided who had more money, since there were some markings on the paper. Using the comparison strategy, she explained, she was able to show that one person had an extra dime and penny. But there was a mistake that she was able to catch. One of the coins in her comparison was a nickel, not a dime. She then totaled the two and came up with 36 and 42 cents. She came up with an answer of 16 initially.

Standard response, "How did you get that?" She thought a moment, then said she did it wrong and it should be 6.

"How did you get that?"

"I know that 6 plus 4 is 10, and another 2 makes 42." Content she settled down and moved on. 30 seconds later...

"I could have done that so much easier I had just remembered my doubles facts...6 plus 6 is 12!"

Love this kid! She's making sense of problem, developing and evaluating strategies, and coming up with alternate paths to solutions. She is not, however, using the standard algorithm.

When is the right time for this introduction? She had a good conceptual grasp. Looking back to my post, she can use models to explain her thinking. She uses strategies that make sense to her. I'm torn on deciding if standard algorithm well become just one more tool for her or become a confusing abstract tool. How do you know 5 right time for the algorithm?

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