Research shows that using multiple representations of an idea is a powerful approach to promote deeper mathematical thinking and conceptual understanding for your students. Not only do you reach different types of learners this way, but you also highlight different aspects of complex topics with each new representation.
At Happy Numbers, we apply this research by presenting math skills using various representations of numbers and procedures. Some tried-and-true representations we offer students are real objects (tennis balls, strawberries, etc.), base-10 blocks, number lines, 10-frames, and the hundred chart. These manipulatives and tools are dispersed throughout the different topics to build familiarity and to reinforce understanding through multiple representations.
We recently blogged about the teaching potential of base-10 blocks and of the number line. Now, we would like to share with you the power of the hundred chart and how you can use it to create meaning with your students.
So how, exactly, does the hundred chart help students build number sense?
While the number line helps with the concept of sequencing, and base-10 blocks reinforce place value, the hundred chart combines these skills on a grander scale. Students see number lines, organized in groups of 10. They also observe patterns of tens and ones both horizontally and vertically. Those who internalize these patterns gain a distinct advantage in learning more advanced skills.
With that in mind, we present exercises that use the hundred chart to help your students deepen their understanding of place value and composition of 2-digit numbers.
All of the exercises mentioned here are part of the HappyNumbers.com course and are presented along with exercises using other representations.
Number Sense: Place Value and 2-Digit Number Structure
1. Missing numbers
We begin slowly by having students provide a missing number when all other numbers on the chart are present. They have many cues to rely on, and almost any student who can count into the double digits can complete this task successfully. You can recreate this activity on a hundred poster by covering a number with a Post-It Note.
One benefit of using Happy Numbers is the immediate feedback and differentiation. If a student makes an error during this exercise, we provide a visual hint (red coloring and highlighting of tens or ones in the row or column):
We also prevent students from continuing until the error is corrected. Our exercises differentiate by adjusting the number of problems students must complete to show mastery.
2. Number composition
To reinforce the meaning behind the organization of the hundred chart, we present students with an exercise decomposing numbers into tens and ones. First, students fill in the missing number on the chart:
Then, students identify the number of tens and the number of ones corresponding to this cell:
Again, we support the student who makes a mistake by giving immediate feedback:
This activity helps students understand that 13 and 31 are not the same number and why.
As soon as students show mastery of this exercise, we increase the challenge by removing an intermediary step. Now, students identify how many tens and ones without first completing the hundred chart:
Once students understand how the hundred chart is organized, the following activity is great to challenge their thinking. Cover all of the numbers on the chart and ask students to choose a window. The window opens to reveal the number, and students must fill in the missing neighbors above, below, left, and right:
To practice this skill on a hundred poster, cut a window out of a piece of paper. Have students hold it over the poster to reveal just one number and write in the neighbors (laminate the paper to use with dry erase markers).
4. Count by tens
Another great activity is to have students complete a column of missing numbers to connect it with counting by tens. Here, we remove the neighboring numbers to the left and right to keep the focus on the pattern within each column.
Again, there is immediate feedback in case of an error, and students may not progress until they correct it:
We keep students engaged and challenged by removing more and more numbers as their proficiency increases:
Our constant monitoring and adjusting is another benefit of using Happy Numbers. We move students to more advanced types of problems as soon as we see proficiency with a previous task. This scaffolding ensures that students are not bored by something too easy or stuck on something too difficult.
We have found these many exercises to be very effective and engaging for primary students. You can try all of our exercises by visiting HappyNumbers.com or by adapting them for off-screen use as described throughout the post. Whichever approach you take, we would like to support your teaching on this topic with a bonus gift: get your free copy of printable worksheetsfree copy of printable worksheets based on exercises from this post!
Evgeny at HappyNumbers.com