- Episode Highlights
- Transcript
The hundred chart is a classroom staple, but what if a small change could make it an even more powerful tool? In this episode, we explore the bottom-up hundred chart, a lesser-known version that could help students build stronger connections between number, language, and direction.
We’ll unpack what makes this twist on a familiar tool so useful, why it might be especially supportive for multilingual learners and students with disabilities, and how you can introduce it in your classroom without tossing out your tried-and-true hundred chart. Get ready to see this classic math tool in a whole new light!
Links mentioned in this episode:
✅ ”A Bottom-Up Hundred Chart?” by Jennifer M. Bay-Williams and Graham Fletcher
Hello, Meaning Makers! Jillian here from Team Meaningful Math and welcome to this week’s episode of the podcast. Today we’re examining a common tool used in math classrooms – the hundred chart. But there’s a twist. We’re going to talk about a BOTTOM-UP hundred chart. Feeling curious? Maybe a little confused? Perfect. Let’s get started!
The Ubiquitous Hundred Chart
I don’t think I’ve ever been in a primary classroom that didn’t have a hundred chart hanging on the wall. In fact, this tool is so versatile and popular that students typically even have their own copy to use as a tool during math class.
Having a hundred chart hanging in your classroom and ACTUALLY USING IT, not just displaying it, makes it a public tool that students learn to reference as they explain their reasoning to others. When students have their own copy of the hundred chart to utilize, it creates a sense of ownership and develops students’ independence with using the chart.
From Early Numeracy to Place Value
The hundred chart is fantastic for developing early numeracy concepts, from rote counting to number recognition to place value and so much more – this chart truly does it all!
The structure of the chart is what makes it so powerful. The hundred chart helps students see that a ten is made up of 10 ones. That is unitizing!
They count ten ones across the chart and arrive at a multiple of ten.
They also see that a hundred is made up of 10 tens. As they count each group of ten moving down the chart, they see that 10 rows of ten make one hundred. This builds an understanding of our base-ten place value system.
The way the chart is set up also supports students by connecting place value to addition and subtraction. They notice how the digits in a number change as they add by counting forward on the chart and when they subtract by counting back. For example, students may observe that when they add 10 to a number, the digit in the ones place stays the same, and the digit in the tens place increases by one.
An Argument for a Bottom-Up Hundred Chart
If the hundred chart is so great, why consider another version of it? Well, there is a fantastic article titled “A Bottom-Up Hundred Chart?” by Jennifer M. Bay-Williams and Graham Fletcher.
In this article, the authors reference another article published 45 years ago that focused on supporting students with special needs by recommending a different structure for the hundred chart, by, you guessed it, making the chart from the bottom up.
Bay-Williams and Fletcher argue that the justification for a bottom-up hundred chart STILL stands all these years later because as students talk about how they navigate the hundred chart, a conflict surfaces.
How Movement on a Hundred Chart Poses a Directional Conflict
Consider a student explaining their strategy for adding 24 + 15: “I went to 24 on the hundred chart and added 10 more by moving DOWN one row to get to 34. Then I added 5 by moving across 5 spaces to get to 39.” The student explained that they moved DOWN the chart, but as they did this, their amount INCREASED.
The same conflict arises when we use the chart to count backwards, or count DOWN. We start at a number and count back, but we are actually moving UP on the chart. The opposite is also true: when counting forward, or UP, we are actually moving DOWN on the chart.
These scenarios feel and sound contradictory. When students’ language doesn’t match the actions they are describing, this creates a “directional conflict”. This is problematic for all students, but especially for students with disabilities and multilingual learners.
This is why a bottom-up hundred chart was proposed to support these students in the article Bay-Williams and Fletcher referenced from 45 years ago. And, as we know, considerations that are made for students with special needs are often ideal for ALL students.
Bottom-Up Hundred Chart From a Student Perspective
Fletcher writes in the article that he visited a first grade classroom and observed students interacting with a traditional hundred chart.
After the lesson, the teacher asked Fletcher, “Why does the chart go down when it’s increasing in quantity?” He didn’t have a good answer, but he returned the next day with a bottom-up hundred chart to show the class.
He asked what they noticed about this “upside-down” hundred chart, as he called it, and uncovered two themes in their responses:
- Students’ descriptions of the chart matched how they were using it. Students explained that as they moved UP the chart the numbers “got bigger” and as they moved DOWN the chart the numbers “got smaller”.
- Students made connections to the real world where something became bigger or there was more of it as it went up and became smaller or there was less of it as it went down. For example, a student said that the bottom-up hundred chart was like a carton of milk because when they drink some, the amount of milk in the carton goes down, and if they were to pour it back in, the amount of milk would go up.
Key Benefits of Using a Bottom-Up Hundred Chart
Based on their research and work with students, Bay-Williams and Fletcher establish some key benefits of using a bottom-up hundred chart:
- Students’ language while explaining their moves on the hundreds chart clearly matches what is happening to the quantity. As we mentioned, this is helpful for all students, but exceptionally helpful for students with learning disabilities and multilingual learners.
- The bottom-up hundred chart allows students to use tools, such as cubes, to physically see increases as more cubes are stacked. They actually SEE the stack getting taller as the quantity increases. The same is true as cubes are taken away and the stack decreases.
- The movement on a bottom-up hundred chart mirrors movement on a vertical number line. On a vertical number line, the quantity increases when you move up and decreases when you move down, just like on the bottom-up hundred chart. This movement is similar to how some other tools are used in our world, such as measuring cups, beakers, thermometers, and even graphs and coordinate planes.
Now, I know what you might be thinking – should I get rid of my traditional hundred chart? Not necessarily. I think students’ ability to utilize both charts helps develop their ability to think flexibly.
However, since the bottom-up hundred chart has all the benefits of a traditional hundred chart and MORE, I think it’s fair to say that that would be the chart I would utilize most often. Since your students have probably only experienced a traditional hundred chart at this point, consider introducing them to this “upside down” version now.
Introducing a Bottom-Up Hundred Chart
Here are some ideas to get you started:
- Display the chart and have a discussion about what students notice and wonder. Annotate students’ ideas on the chart and encourage them to look for patterns.
- Use the bottom-up hundred chart for choral counting. Decide how you would like students to count (such as by 1s, 2s, 5s, 10s, etc. and backwards or forwards). Begin the count and circle the numbers as students’ count. Stop to examine the patterns that are created as you move through the count.
- Cut a bottom-up hundred chart into various pieces and have students put it back together like a puzzle.
- Gather number cards from 1-00 and an empty pocket chart with at least 10 rows. Place some cards in their correct locations as if the pocket chart were a bottom-up hundred chart. Have students work together in a small group to fill in the rest of the chart.
- Finally, take a look at the hundred chart activities that you already have and consider how they might work with the bottom-up version. You’ll be surprised to find that most activities can work with the bottom-up hundred chart too!
Meaning Makers, I hope this episode gave you some new ideas to think about. I would love to hear your thoughts about using a bottom-up hundred chart, and I would love to know if you try it out with your students.
If you enjoyed this episode, please take a few seconds to leave us a review! We’d love to hear from you, and your review will help bring this information to even more teachers and impact even more students. Thank you for tuning in! Until next time, Meaning-Makers, have a great one!
