## Resources mentioned in this episode:

A Bottom-Up Hundred Chart? article by Jennifer Bay-Williams and Graham Fletcher

My favorite hundred pocket chart from Hand2Mind

Welcome fellow Recovering Traditionalists to Episode 23. Today we are looking at creating a Bottoms Up Hundred Chart

As you start to prepare for school to start back up, a common thing in elementary classrooms is the Hundred Chart. There are things I don’t like about using a hundred chart (like how kids rely on them too much and they still count one-by-one when adding and subtracting), but one thing they are great for is investigating patterns.

However, the traditional way that a hundred chart is set up actually causes confusion for students instead of insights which is why so many kids might get stuck counting one-by-one. So, I thought I’d share with you an article by my friend Graham Fletcher and Jennifer Bay-Williams entitled A Bottom-Up Hundred Chart?

On page e2, they write

*“…as students talk about adding and subtracting (conceptual talk) and how this relates to moves on the hundred chart (directional talk), a problem arises. Listen to this child share her strategy for adding 16 + 23: ‘I found sixteen on the hundred chart. I added twenty more, so I went down two rows, then added three by going over three. The total is thirty-nine’.*

*Notice that as the student connects her reasoning to the chart, she increases her quantity by twenty, but moves down the chart. In other words, her quantitative statement (add twenty) does not match her directional statement (move down). This apparently opposite language can cause a ‘directional conflict’ for students, in particular, students with disabilities (Randolph and Jeffers 1974, p. 203).*

*The language issue has nagged at us for years because it seems to be counterintuitive. Children have asked, ‘Why do you go down [the chart] when you are going up [in quantity]?’”*

So I want to ask you, do your students ever struggle with that conflict? Even if they don’t say it out loud, I bet many of them are thinking it to themselves: Why do I go down when I’m adding? The quantities are getting higher but they are physically moving down the chart.

This may seem like a trivial piece of your students’ mathematical understandings, but it is one more place where kids see mathematics as not making sense. You just go through the motions and you get an answer.

As you prepare your hundred chart for this year, I’d like you to consider putting the 1 in the bottom-left corner instead of the top-left corner. Jennifer and Graham give lots of activities using this new form of a hundred chart in the article. I’ll also put a link to my favorite hundred pocket chart. It’s a great resource to have because you can put the numbers into the chart in any order you want. After kids learn the patterns of the numbers it’s fun to mix it up more and put the 1 in the upper-right corner and then have them figure out where other numbers would be in the chart.

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Yeah! I am listening to you. Great ideas!! I agree , get away from the text. I haven’t used the text for years and my students really flourish and are more open minded to math strategies.

Always listening, always learning! Thank you!

This makes sense, however, our standard for First Grade is to 120. Any bottom-up chart for that?

I’m a veteran teacher (teaching since 1973) and I learn something every single time I read, listen to, or watch anything on Building Math Minds. .Please continue to help us one concept, one day, one student at a time. Thank you! We are listening.

Brilliant, and so easy to do!

I love it! Going to give it a try this year.

Whe can I find a poster- sized version for my classroom? I want to hang one up.

I like this idea. I also would like to suggest starting at 0 instead of 1 to really see number patterns and how a new groups of numbers starts after we get to 9 because we make a new ten group.

I really like the idea of starting at the bottom! Thank you for sharing this.

Great idea regarding the “directionality”. Looking forward to using this as an intervention.

Love this! I will be changing the numbers tomorrow and thank you for such a great idea. I also like the idea of mixing up the numbers to see if they can put it together again.

I am listening as an administrator in an elementary school. Thank you for that unique and totally relevant issue with our 100s charts. I am sharing with our faculty.

We co-created one as a class.

In turn, the kids wrote numbers on post it notes and stuck them up on the wall. We talked about things we noticed as we put them up.

The post-it notes had poor stickability and kept falling down, which turned out to be great as they had to find where they belonged and tape them back up.

Also, if you already have a top-down 100 chart printed up, don’t just throw it in recycling! We cut each row and used it as a giant number line (kids could then see the relationship between the number line and the chart) and used it for various activities.

I’m wondering if there would be any benefit in making a connection to snakes and ladders – snakes go down and ladders go up.

Loving it. Thank you.

I am left wondering if we should be using the MathRack 100 the same way? The language would make sense, the number of beads would “get taller” as they increased, and students could make contextual connections to things in their lives that go up as they get bigger and down as they get smaller.