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I make the problems too difficult, the children don’t listen to each other.

February 22nd, 2005

Today we worked on double-digit addition and subtraction problems involving multiples of 10. Both Sunny and Daniella had some trouble with the pennies problem (Join Change Unknown: 22 pennies, how many more to have 50). What I find fascinating is that Sunny and Daniella both used unifix cubes in sticks of 10 to build 22:

Using unifix cubes to show 2 tens plus 2.
But after this auspicious start, they were stumped about how to build on to 22 to get to 50. I wonder if the tens structure of the unifix cubes got in the way? When I changed the 50 pennies in the problem to 30 pennies, Daniella quickly solved it by counting up by ones.

Next time, I’ve decided to write problems with numbers that are more conducive to using tens in the strategy. For example, if the problem is something like 20 pennies and how many more pennies to have 45, it will be easier to build up from 20 pennies to 45 using unifix cubes in sticks of ten. (Of course! I now say to myself.)

Jack solved this problem handily although his strategy made no use of tens. He counted up by ones from 22 using tallies to keep track.

I have noticed several of the children writing vertical double-digit problems for the Separate Result Unknown problem (40 chocolate chips, eat 15) but not making use of tens in their solutions. For instance, Jack wrote a vertical number sentence for 40-15, but actually solved the problem by modeling it with individual “chips”:

Jack's work for 40 - 15.
Daniella wrote something similar for 60 – 26 and got 86 – a classic “bug�? which suggests she does not understand (or is at least not making use of) base-10 concepts.

I will continue to write problems like these and provide children with materials that are structured in tens (e.g., unifix cubes in sticks of tens or base-10 blocks). I want to urge all of the children to use these materials to solve problems, and – perhaps just as important – to record their strategies using numbers (not words) to help them connect the base-10 structure of the materials with their symbols. I expect that developing an understanding of base-10 concepts in a way that these conepts are usable in their strategies will take some time.

Finally, I must lament that I have not been very successful getting the children to listen to each other’s strategies! Each child is perfectly willing to tell me – and whoever WILL listen for that matter! – about what they have done. There is, truth be told, a lot of noise as they solve problems. So for now, I have the children spread out to solve their problems and I talk to them individually.

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