# Number Strings: Addition with Doubles, Make Ten and Doubles + 1: Sort n' Solve

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One of the chief critiques I have heard about math instruction is that our students know all about how to do a procedure; they just don’t know when it applies. This is an activity that tries to correct this by having students cut out 15 different number strings of 3, 4 and 5 numbers (all single digits), and then “classify” them into one of three groups: “make 10,” “doubles” and “doubles + 1” (also known as near doubles.”) They then paste them into the chart and solve them using the strategy that they identified.

From there, they go on to create number strings of their own using a set of constraints, and then write a number strong problem about it. For example:

They paste this problem down on a recording sheet, and then write a number string that would apply to that. You’ll notice that this is “open ended” enough to give students a lot of “mathematical creativity” (when have you ever seen the words “mathematical” and “creativity” in the same sentence, more or less adjacent to one another?) For example, they could write “5 + 10 + 5 + 1” or “6 + 6 + 5 + 0” or, well, you could figure that out.

Finally, since this should not be just for the sake of nothing, I have included an activity where they take one of the “clue” questions and then write a word problem which would require that number string to solve it. For example, if you used the one shown above, it could be “Therese and Laurent saw 5 stoats on Monday morning, 10 on Monday afternoon, 5 on Monday evening, and then none on Tuesday. How many stoats did they see on Monday and Tuesday?” They can then share these stories, figure out what the number string should look like and solve it!

The point of all this is that your students need more than isolated practice doing addition strings. You’ll notice that I put the equal sign on different sides of the equation so that they learn that an equation can have the operations on either (or both) sides. They also work on strings with 3, 4 and 5 numbers, because I wanted them to understand that they could have different numbers of numbers. We should refer to these as “addition number strings,” because some have subtraction, and some are “mixed” in that they use both addition and subtraction. I’ll release an activity with those varieties another time.

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