Common Core Math: Using a Number Line for Subtraction

If you have a child in elementary school, you are likely noticing that your children are learning to do math VERY differently than you and I did. In this post, I wrote about what your child’s common core multiplication homework. I wrote about what your child's homework might look like, why, and what you can do to help at home.

Today I want to address different math content and another math assignment that has gone viral. This time with a note from a parent who’s clearly unhappy about the homework!

Image Source: Facebook

Image Source: Facebook

I feel for this parent. I can understand the frustration of not being able to help your child with what seems to be a very simple subtraction problem. I can just picture this parent and child sitting at their kitchen table, pouring over this assignment, brainstorming, frustrated, and stressed. And that is what makes me frustrated. Because math doesn’t have to feel that way. It shouldn’t feel that way. Even common core math.

Again, the purpose of this post is not to get into the politics of common core, or argue for or against the teacher or parent involved in this homework assignment. It's simply to help you in your home. I want you to know more about this type of problem so that you can best help your child with their math work at home.

The problem on the assignment above was likely written to target this Common Core standard. Brace yourself, it's a long one....  "Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds."

Basically, we want our 2nd grade children to be able to add and subtract within 1,000, using varied strategies to show they truly understand what it means to subtract. We want them to understand place value and how it relates to subtraction, not rely solely on a subtraction algorithm or prescribed method for solving a problem.

When you and I learned how to subtract and borrow from the neighbor number, most of us didnt know why we were borrowing. I didnt. And educators now know that when children dont know WHY they are doing what they are doing in math, things can go South fast.

In teaching common core math standards, teachers are allowing their students to use many different strategies in solving a subtraction problem with the purpose of making sure that kids know the WHY in math. This can look pretty messy and confusing in homework form, but under the guidance of an artful teacher in the classroom, it is amazing to see children invent and use their own strategies, formed on the foundation of a true understanding of mathematical principles. Pretty cool stuff. But I get that it doesnt look cool at all when it comes home on a worksheet. It just looks confusing.

In writing this assignment question, the teacher wanted his or her students to understand how to count backwards using a number line as a representation for subtraction. Why? When children are exposed to strategies that allow them to mentally “picture” a problem, we know that their understanding of algorithms will be stronger and computation skills more accurate.

So, basically, this number line problem is being assigned to students with the goal of helping them picture this subtraction problem.

Going back to the specifics of the problem…

427 – 316

Solving this on a number line, we would start at 427.

We would take away 300 (100 three times).

Then we would count back 16.

(Some students would jump back by 10, then 6. Some students would count back 16 by ones. Both ways are correct, they just show different developmental stages of mathematical understanding.)

Either way, it would look something like this...


“Jack” in this assignment’s question was correct in the beginning when he took away 300 from 427. His mistake came when he only took away 6 instead of 16.

This is the answer (I imagine) this teacher was looking for.

If your child encounters problems similar to this in their homework, here are some tips on how you can help.

Quick Tips:

-       You can help your child form a deep understanding of subtraction by encouraging them to draw representations of subtraction problems. If number lines are challenging for them at this stage, find a different representation. They can draw a picture of 427 cookies (maybe representing them in packages of 100, then plates of 10, then singles). Have them take away the 316 cookies by crossing off cookies until they find the amount remaining, their answer. (I understand this feels tedious – just remember this is an investment in their future mathematical accuracy! They will get to the quick algorithm soon!)

-       After your child is able to draw pictures representing their thinking, move toward using a number line. Make a number line at home. I’ll post more about exactly what that can look like next time. Use a popsicle stick or spoon to physically count backward or forward as you and your child solve addition and subtraction problems together.

-       Help your child see subtraction in the real world. You may think about starting to give your child an allowance so that they can begin buying things at the store. While there, have conversations to get their mathematical thinking going. You may start by encouraging them to make estimations, an extremely valuable mathematical skill. Later, as their mental math capabilities grow stronger, you may ask for exact numbers. You may say…

o   Are you sure you can buy that?

o   About how much money will you have left over?

o   Will you be able to buy anything else with that money?

o   Are you sure you got the right amount of change back?

o   How much more money do you need to save in order to get that? How long do you think that will that take you?

Later this week I'll post examples of physical number lines you can quickly make at home to help your child form a mental picture of math problems. In the meantime, just remember, all this representing that feels like it's pointless and taking a ridiculous amount of time? It will pay off later. Really.