“I just don’t understand, Amy! How can he pass a test on fractions, multiply two digits by two digits in his math workbook, and solve word problems on his homework, yet if I ask him, ‘What’s 2 less than 9?’ he has to think about it for several seconds and count on his fingers to get the right answer?” Sound familiar? This woman’s frustration with her grandson’s inability to do something as “basic” as mentally solving 9 minus 2 is not uncommon. In fact, it’s an aggravation often expressed by grandparents, parents, teachers, and the like—basically anyone who’s had the baffling experience of dealing with a child who typically makes good grades in school and may even score well on standardized tests, but can’t seem to solve a simple addition or subtraction fact without the use of his fingers. And if the child is struggling to work with small numbers, he can all but kiss success with larger numbers goodbye! Ask any teacher, and she’ll tell you–it’s a universal issue. And an impartial one. Afflicting the academically high-achieving, as well as those deemed most at risk, the inability to compute mentally with fluency is fast becoming the norm.

Lest I am instantly berated for being “old-fashioned,” allow me to say that there’s nothing inherently wrong with using one’s fingers to add and subtract. And in this age of technology, when virtually everyone has ready access to a cell phone calculator, some may feel that I am making too big a deal out of this, but I would beg those people to reconsider. A cursory examination of our everyday lives reveals that we most frequently depend on mental computation when we use arithmetic: calculating a waitress’s tip, figuring the sale price of an item, doubling a recipe, etc. Possessing a good sense of numbers is essential to life!

Enter the ten-frame. It’s a tool as old as the hills within the walls of academia, but its use in the public-school classroom generally declines markedly after the primary years. “Why is that?” you may ask. Tragically, the majority of the answer can be summed up with just two words: standardized testing. While superior teachers recognize the importance of continually working with students to develop their number sense and fluency with mental computation, they don’t always have the opportunity to spend an adequate amount of classroom time on this endeavor. In other words, if it isn’t likely to be a test question, it isn’t likely to be granted much time in the classroom. Sad, isn’t it?

While I could (and eventually *will*) spend an inordinate amount of time lambasting the current testing trend forced upon educators by the powers-that-be who’ve never taught, I am going to use this post to focus on something that doesn’t induce vomiting. And that, my friends, brings me back to the purpose of this post: the ten-frame and how to use it.

Five-, ten-, and twenty-frames are fantastic tools for helping children gain a conceptual understanding of working within those numbers which, in turn, enables them to work mentally with much larger numbers, as well. The frames are basic and look like this.

Five-frame

Ten-frame

Twenty-frame

Dots or counters are placed on the frame to provide a visual representation of a certain number, specifically as it relates to the total number of blanks in the frame. For example, the number 3 on a five-frame would look like this.

Five-frame

The number 7 on a ten-frame would look like this.

Ten-frame

And so on.

The beauty of these little gems is that they give children a visual for how much *three* is in relation to *five* or how close *seven* is to *ten*. The strategy is simple, but the benefits are ENORMOUS. Students who possess a firm grasp of 5, 10, and 20 usually will not need to use their fingers to count forward or backward, even when dealing with numbers that contain 2, 3, and 4 digits. In addition, children who have used these frames extensively are much less likely to be fooled by “absurd” answers when solving problems. For example, a child who finds the difference of 45 – 39 to be 14 will promptly see her error, even if it takes her a few moments to make the necessary corrections. She will realize that she has made a mistake in calculating because she has a solid understanding of numbers; she knows without even contemplating it that 14 is greater than 10, and that 10 added to 39 would equal 49, which is already larger than 45, even without the additional 4. Consequently, she will know (without being told) that her answer cannot be correct. And isn’t that what we want—to enable today’s children, and tomorrow’s leaders, to be successful *independently*?

If you’re a teacher who is fortunate enough to work under an administration that believes in high-quality instruction meant to improve students’ lives, not just their test scores, perhaps it’s time for you to dust off your old ten-frames and introduce them back into the daily life of your classroom. If you’re a parent who can relate to the scenario described at the beginning of this post, or if you just want to give your child a leg up in developing his or her number sense, here are a few things to remember when using five-, ten-, or twenty-frames.

1. Only one counter is allowed in each frame.

2. The top row of frames is filled first.

3. The frames are filled from left to right.

4. Like anything else, practice makes perfect! Repeat, repeat, repeat!

5. Following are a few activities to get you started:

• Begin with a complete set of five-frame cards. (You can purchase my pirate-themed pack of five-, ten-, and twenty-frames with activities here.) Have the child show any number on his five-frame. For example, say, “Show me 2.” The child can place two counters on a five-frame, or he can pick up the five-frame with the pre-printed two dots. Next, ask the student to tell you what he notices about the number 2. Any response at this point has merit, but remember that the ultimate goal is to focus the child’s attention on how many more dots or counters are needed to make 5 or how far away from 5 that number is. Again, repetition is your friend! Building a concept takes time, but it’s well worth it!

• The above activity should be repeated with the ten- and twenty-frame cards. “Show me 8. What do you notice about the number 8? How far is it away from 10? How many more dots are needed to make 10?” Also, talk about 8 in relation to 5 since a complete five-frame is half of a ten-. “The number 8 is three more than 5. The number 8 is closer to ten than it is to 5.”

• Once the student has spent a sufficient amount of time making observations and has grown familiar with numbers’ visual representations, use the pre-printed frames like flash cards. Hold one up in front of the child and have her identify the number shown as quickly as possible. Needing to count the dots every now and then is not a huge issue, but if counting is required more than once or twice per ten or fifteen cards, don’t sweat it—just go back to getting to know the numbers and save this activity for later!

• If your child has mastered the above and is ready to move on to something more challenging, you can use the frames like you would employ addition flash cards. Hold one up in front of the student and have him identify the addition fact represented there. For example, a ten-frame that has 6 dots and 4 blanks would be identified as 6 + 4 = 10. And so on.

• The above activity then may be adjusted to provide practice with subtraction. “10 – 4 = 6.” Et cetera.

Ten-frame cards (and their five- and twenty-frame cousins) are inexpensive and highly effective tools for helping children develop number sense and increase fluency with mental computation. Give them a try; you’ll be glad you did!

Until!

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