How the Hundred Chart Helps Students Add & Subtract
In Part 1 of this post (found here), we examined how the hundred chart helps students build number sense and understand composition of 2-digit numbers. Here, we continue the conversation as we share our tips for using the hundred chart to teach 2-digit addition and subtraction.
The hundred chart is, as research shows, most powerful when it is presented as one of several representations of numbers and operations. This approach to math promotes critical thinking and conceptual understanding. At Happy Numbers, we do not see the hundred chart as a separate topic, but present it along with the number line, base-10 blocks, 10-frames, and real objects across multiple topics for maximum results.
The benefits of the hundred chart, as compared to other tools and manipulatives, are many. It functions much like a number line, but in a more condensed space that highlights place value and patterns. It allows for more advanced 2-digit operations, which can become cumbersome with manipulatives such as base-10 blocks. Adding this tool to your shed will give you one more way to reach learners in your class and will help them in ways that other tools can’t.
How can the hundred chart help students add & subtract 2-digit numbers?
Students learning to add and subtract 2-digit numbers must rely on a solid foundation of place value understanding. Few resources emphasize place value as well as the hundred chart. Throughout all of Happy Numbers’ exercises, we provide students with immediate feedback on errors. With the hundred chart, this usually means highlighting all of the ones digits in a column or all of the tens digits in a row. As students become familiar with these patterns and relationships, they more easily create an internal hundred chart, allowing them to perform mental math and estimate answers quickly and accurately. These skills lay the groundwork for more advanced operations of multiplication and division in the future.
Our goal is to enhance your teaching with insights, tips, and resources that you can apply in a practical way, making the work you already do more effective and efficient! The exercises below show how Happy Numbers approaches 2-digit addition and subtraction using a hundred chart.
All of the exercises mentioned here are part of the HappyNumbers.com course and are presented along with exercises using other representations.
1. Add 1 or 10:
Here, our friend the bunny helps students begin using the hundred chart to add and subtract. We start simply with moves right and down, which represent +1 and +10. Students will feel like they are playing a video game, while you know they are actually preparing to tackle challenging addition problems!
An off-screen adaptation of this exercise would be to have partners lead one another to a designated number on the hundred chart by calling out “Add 1” or “Add 10.” A toy or game piece can be the “bunny” and a counter or sticky note the “carrot.”
2. Add a round number:
A smart next step to take in teaching addition or subtraction of 2-digit numbers is to break down a round number into tens. Students rely on their prior learning about counting by tens on the hundred chart to arrive at an answer. Here, they begin with an equation and work it out using the hundred chart:
3. Correlate the hundred chart to equations:
Happy Numbers also reverses the process to have students move along the chart first and then determine the correlating equation:
Both activity 2 and 3 lend themselves well to whole-group warm-ups using a hundred chart poster. Have students count aloud by tens as you or a student leader move a pointer along the chart to illustrate an equation.
With Happy Numbers, technology allows us to increase the difficulty in steps, first by removing more numbers from the hundreds chart:
Then, we remove the intermediary step of filling in the missing number on the chart and go directly to the expression. We also ask students to determine two numbers in the equation instead of just one:
The steps we take to increase difficulty are carefully determined based on each student’s individual performance. Happy Numbers monitors and adjusts the number of exercises a student must complete accurately to show mastery. Those who answer correctly are moved more quickly into more challenging tasks, while those who make errors receive more remediation and practice before moving on.
4. Add and subtract 2-digit numbers without regrouping (step 1):
We reinforce the connection between different representations by having students solve equations in parallel with using the hundred chart.
Students add on the round number first, determine what still needs to be added, and then find the result using the hundred chart:
In another activity, students complete the same task using subtraction.
5. Add and subtract 2-digit numbers without regrouping (step 2):
Once students are confident with the exercises above, we increase the difficulty by asking them to show 2-digit addition on the hundred chart without decomposing the addend into tens and ones.
Identify the first addend on the hundred chart:
Use columns and rows to add the second addend:
Enter the answer:
If students have internalized the hundred chart, then it’s a good idea to remove all numbers except the first row and the first column and try this activity again:
Once students master this step, they are probably ready to “remove the training wheels” and work exclusively with equations. No doubt, the hundred chart has played a big part in bringing them this far. Keep in mind that these exercises are presented throughout different lessons that gradually lead students to this point over time.
Evgeny at HappyNumbers.com
Evgeny at HappyNumbers.com
P.S.: If you missed it, our post Number Sense with the Hundred Chart shares more basic concepts using the hundred chart.