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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