Hundreds charts, or 120 charts, are used a lot in early elementary to help kids with a lot of mathematical concepts. In particular, they are often used for addition and subtraction. However, I have seen kids struggle way too much with this model, and they aren’t learning the conceptual understanding through the model, and often I see kids using it as a crutch instead of actually thinking through the addition and subtraction.

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• Graham Fletcher’s post about Bottoms Up Hundreds Chart: https://gfletchy.com/2014/10/10/bottoms-up-to-conceptually-understanding-numbers/
• Brown Bag Teacher – https://brownbagteacher.com/a-lightbulb-moment-transforming-120s/

Hundreds Charts Have A Place

Now, don’t get me wrong, I really actually love hundreds charts, just not for addition and subtraction. Hundreds charts build some really cool mathematical concepts for our young kids. They get to count, they get to see patterns, they get to do sequencing. What comes next, what comes before, what comes after. All of those kinds of things. The hundreds chart is really great for building those ideas.

The problem starts to become when we try to use that model to help our kids model addition and subtraction on the hundreds chart, and there are some good reasons why kids are really struggling with it.

This is a typical hundreds chart. It starts at one, goes to 100. Yours might look a little different. You might start at zero and go to 99. You might have one that goes to 120. So, whatever you typically use, just replace it with this image. This is just for us to use as an example, but typically, they are set up to start with the small amounts at the top, and then we work our way down to the larger amounts.

This was done to basically mimic the way that we read. We read from top to bottom, left to right. It’s helping us read the numbers, but when we go through and try to add and subtract on this, it becomes super confusing for kids. Here is a great post by Graham Fletcher that talks about flipping this, and that leads into our next part about why this is so darn confusing.

Why Kids Are Confused-Numbers Seem Backwards To Kids

Let’s just take a look at what it would look like if kids tried to add or subtract. I’m gonna use an addition example here. Let’s go to 27 plus 20.

This is one of the typical ways that we want kids to add is when they’re doing multiples of 10 because they can hopefully easily jump by multiples of 10. You’ve got some kids who might have to count one by one.

I get that, but for this example, if a kid is doing a jump of 10, it might look like this, and then another jump of 10, but the problem is, this seems backward to them, and Graham talks about it in his blog post a bit more extensively than I’m going to here, but basically, kids don’t get why they’re going down a chart when the number is actually getting bigger.

To them, when something gets bigger, we should go up, when something’s getting smaller, we should go down, and this model, the hundreds chart this way, does not mimic that idea. And yes, I get that we should have kids understand that it doesn’t matter which direction we’re going, right, on this hundreds chart. It’s just like on a number line. You could go either way, really.

But, we want kids to first have that conceptual building that when we go up when we’re adding, the numbers are getting bigger and the quantities are getting bigger. But, it doesn’t feel like that when they’re using a hundreds chart because they’re going down the hundreds chart.

So, Graham suggests that we should move into helping kids see that by going bottoms up with our hundreds chart.

You start at the bottom with your hundreds chart, and then you move up the chart. You can still look at a lot of those patterns and stuff, but as they’re moving and adding by multiples of 10, so if we looked at the 27, and we wanted to add 20 to it, you can see those hops of 10 are now going up the chart, which just conceptually feels better to those young kids, that we’re going up because the number is getting bigger.

And, if I was subtracting, we would be going down that chart, and that just feels better to the kids. I know it doesn’t seem like a big thing, but, you guys, it really is. When you switch your hundreds chart and do this, it just feels better to the kids. It may seem awkward to us because we’re so used to the hundreds chart starting at the top and going down, but I’ll tell you, the kids love it.

Why Kids Are Confused About What To Do At The End Of A Line

Now the other hard part is that kids aren’t too sure about the transitions. What happens when we’re adding just small amounts, and maybe kids are counting one by one? So, 27 and they have to add seven. They add one, two, three, but then they get to the end of the line.

This is often a sticky point for kids because they just aren’t sure what to do next. Do they just drop down, do they go to the front of the next line, do they go to the one above it? It’s just really weird for kids.

An example of why I prefer a number path and a number line over this is a post by The Brown Bag Teacher, which is here. Basically, she took the 120s chart, she was using a 120s chart, and had the students cut it up and glue them together to create this big, long number path that went from one to 120. That linear model is just way better for addition and subtraction. When things are in a line, it just flows nicer for kids, but it also connects to that number path and number line that we’re gonna be having kids use later.

I hope that this has given you some insights into why your students are struggling to do addition and subtraction on the hundreds charts, and again, I don’t dislike hundreds charts. Use hundreds charts for counting, sequencing, pattern building, looking for patterns, and investigating patterns. They’re really great for that, but I just don’t see kids using hundreds charts in a conceptual way that builds great number sense and thinking strategies.

And remember, the models that we have kids use should be a model of their thinking. They shouldn’t have to do more thinking to use the model than they are to focus on the actual mathematical content. So if the students are taking more time, and you’re spending more of your time actually teaching how to use the hundreds chart versus how to add and subtract, then it’s the wrong model. The focus should be on addition and subtraction strategies, not using that particular model.

I hope that this has helped build your math mind so that you can go build the math minds of your students.

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