Have you looked at your child’s homework and wonder how much concepts and tools used in math education have changed since you were a child yourself? Today, we’re going to talk about two of these tools that are introduced for building the foundation of number sense in early elementary levels – Ten Frames and Number Bonds.

## Why?

Mastery of basic facts in addition and subtraction is a developmental process. Kids start with counting, then learn more efficient reasoning strategies, and finally move to quick recall. Both Ten Frames and Number Bonds were introduced to help kids with the reasoning strategies phase.

## Ten Frames

The ten frame is a visual tool that helps kids break numbers apart to make ten. It consists of two rows (or columns) of five squares stacked against each other to form a box of spaces. Students can fill in the squares with shapes and symbols to help them see the relationship between numbers.

For example, in the above, kids can visually see the number 8’s relationship to the numbers 5 and 10, the two key landmark numbers.

## Number Bonds

After students mastered using ten frames to visualize number relationships, we have another tool to connect their visual understanding to more abstract numerical notations – Number Bonds. The number bond is a visual tool to understand the concept of “part-part-whole”. It consists of three circles, the main circle contains the “whole” (the number to break apart), while the two other circles contain the “parts” (numbers that make up the whole).

In combination with ten frames, the number bond can be used to introduce basic addition and subtraction facts, especially in cases where regrouping is required, e.g.

## Middle Elementary

Ten frames and number bonds, or more importantly, the conceptual understanding of breaking numbers apart to make tens can be extended to higher place values in later years, e.g.

## More Resources

Here’s a sample worksheet to illustrate the use of ten frames and number bonds to develop a child’s basic facts in addition and subtraction. Sign up for our newsletter to get the free worksheet.

## Related Resources

For more related resources, please see our Number Sense, Addition and Subtraction page.