Focus on Math

Helping children become mathematicians!

Ten Frames for Learning Math: Basic Facts +1, +2, +9, +8 February 17, 2011

Basic facts are just that: basic. They are the foundation for a lot of other kinds of mathematical thinking including estimating, doing mental math, and doing other, more sophisticated kinds of computations.

Basic facts are generally defined as the set of addition and multiplication problems that are one digit +/x one digit, along with the “reversals”of those questions for subtraction and division. Thus 6 + 7 = 13 is a basic fact, as is 13 – 7 = 6. However, 13 – 2 = 11 is not, because its reversal, 11 + 2 = 13 begins with a double-digit number.

Ten frames (click for download) are a powerful tool for helping children learn the basic facts. They give children a way to visualize the numbers, to “see” their thinking with the card(s) until they are able to “see” the thinking in their minds. Once they own the images the empowerment happens.

So to start off, I recommend you download the 10 frames, cut the cards apart, and begin having your children learn the images. You can play games such as “war” or “concentration” to help them.

The facts that are +1/-1 and +2/-2 (which flow out of the “Big Ideas for Little People” workshop) can be visualized. I have often talked with kids about adding or removing dots on the cards with a “magic eye”. Thus 6 + 1 can be visualized by seeing the 6 card and adding another dot mentally. Children who have worked on the big ideas mentioned above will find these facts easy.

Several other kinds of addition and subtraction facts are supported by the ten frame visuals. Consider the +9 facts. 7 + 9 = 16 is one of the “hard” facts in the eyes of most children, but if they learn to visualize the ten frames, the fact can be quite easy. By looking at the 7 card and the 9 card, they can visually move a dot from the 7 card to fill the 9 card, turning it into 6 + 10 – 16, a much easier fact! Alternately, a child can look at 7 + 9 and think 7 + 10 is 17, but since I added one to the nine I must remove it (which is using the “zero principle” — adding and removing the same amount). Both strategies can be used on the +9 facts with great success! The +8 facts can be done in a similar manner, just moving  two dots mentally or by adding 10 and then removing 2 from the result.

Most children learn their addition basic facts in the primary years (grades 1-3) but if yours did not master them early, it is never too late! In fact, if children are older and do not know them, it is usually because they are not good memorizers — and if no strategies for learning are taught, memorization is the only route. Older students can benefit from the ten frames, too! If you haven’t used ten frames with your children, now is a great time to start! Mathematically yours,



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