For some people and classrooms, it just isn’t feasible to purchase high-quality number bond flash cards like you can obtain through Crystal Springs Books. I came across a site where you can download your own, print them and cut them out. These are addition and subtraction cards appropriate for grades K-3. You can download them for free after registering at Teachers Pay Teachers.

A caveat: While the free cards by William Hughes cover the basic principles of number bonding for addition and subtraction for numbers to 10, the Crystal Springs cards are better because they do not rely on just one position of the whole vs. part numbers. In other words, on the Hughes cards, the “whole,” or total number, is always on the left, while the two smaller numbers, or “parts”, are always on the right. On the Crystal Springs set, the whole can either be the top number, the left number or the side number.

I think this is an important teaching tool for students to understand that an equation is not directional, but must have equal parts no matter which direction the equation goes. When students are taught that equations always go from left to right (which actually happens in some elementary classrooms), for instance 2 + 2 = 4, then they often flounder when they encounter pre-algebra and are expected to solve problems like 6y + 6 = y + 26.

So the earlier we teach that equations are like a balance scale and not like a one-way street, the better our students will be equipped when they encounter concepts like these in algebra.