Actually Helping Jack with his Subtraction Problem

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You may have seen this purported parent response to a homework question on Facebook or even the Colbert Report.

I thought it was time to help Jack and explain what the teacher was probably thinking when he or she assigned this problem.


Dear Jack,

You did a great job using the number line to figure out this subtraction problem.  It looks to me like you forgot about the tens jump.  Remember 316 means 3 hundreds, 1 ten,  and 6 ones.  I see you took away 3 hundreds jumps and 6 jumps of one, but missed the 1 jump of ten.

I hope this helps.

A Math Teacher

The Frustrated Parent is exactly right about this being an inefficient method of subtracting.  Procedural fluency is an important part of the Common Core State Standards (CCSS), so the teacher wants the student to be able subtract those two numbers quickly and efficiently.  However, another important part of the CCSS is building conceptual understanding.   One of the reasons we need the Common Core State Standards is because for many years students were only taught procedural fluency without any understanding of the concept behind it.  That is to say, the trouble Frustrated Parent had figuring out the problem is exactly the reason it was assigned.  The math teacher wanted the student to understand what subtraction and place value mean so that they can do the problem and understand the problem.  This new shift will require parents and teachers to relearn many of the mathematics they thought they knew.
Another aspect of the Common Core this teacher was working towards was Mathematical Practice 4: Construct viable arguments and critique the reasoning of others.  Whether or not you agree with Jack’s method, being able look at someone else’s work, figure it out, and help them fix the errors, is an important skill.
While many of us are not familiar with the particular models that are being used to develop students’ conceptual understanding, those of us who have seen the shift in student comprehension of mathematics agree that these models can serve as a very important bridge between just “doing” math and actually understanding it.


Need more Common Core Math help?  Visit our Common Core Math Help page and get your answers today!

By Jim Town – Mathematics Specialist at ACOE Core Learning

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