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Thinking Mathematically: A Hands-on Take on Place Value and Multi-Digit Numbers

by Kate Minear, Lower School Math Specialist


Many of us remember a teacher saying “and then just carry the one,” when we were learning how to add multi-digit numbers.  There may have been little explanation or exploration of why that would work.

At Brooklyn Friends, we want our young mathematicians to make sense of the math they are doing.  Our number system has a structure, and the rules governing each operation stem from that structure.  So as third graders begin to learn addition and subtraction stacking, we provide them with a context that helps them really understand the steps and how place value organizes numbers.

We begin by reading a picture book about the Masloppy family, who has piles of t-shirts scattered all over their house.  Nicholas, the one neat family member, organizes the t-shirts by gathering them into rolls of ten and loose ones.

The third graders then use colored index cards to represent t-shirts, and organize them into rolls of ten and loose ones.  They quickly see that 64 will be 6 rolls of ten and 4 loose ones, while 136 will be 13 rolls of ten and 6 loose ones.  Actually building the numbers helps them to understand place value more deeply, giving them a stronger foundation for the paper and pencil work they will soon be doing.

The next day, they find all the different ways to organize a number using rolls of ten and loose ones.  So 36 could be 3 rolls and 6 loose or 2 rolls and 16 loose or 1 roll and 26 loose.  Understanding that all of these are ways to reorganize the same number helps them to understand trading (or “carrying the one”) in the addition and subtraction algorithms.

They are then ready to start combining t-shirts.  They combine two or three amounts, and then “Nicholas” them– or make them as organized as possible.  We hear kids saying, “That’s 17 loose– but we can put 10 of them into a roll.  So 1 roll and 7 loose,” or “20 loose!  We can make 2 new rolls.”

Soon they will begin using bags of 100 and also start addition stacking with just pencil and paper (and maybe some mental t-shirts).  After that, they will begin “selling t-shirts” as they take on subtraction stacking.

Jan. 19, 2018