What is six?

“Well, it’s a concept that means six things,” you might say, and you wouldn’t be wrong. You could define “six” by gathering six beans and counting them and saying: “There, that’s six.”

But six is something else, too. It’s the product of many different mathematical procedures. For example:

5+1 is 6

4+2 is 6

3+3 is 6

In the realm of subtraction, 7-1 and 10-4 both produce 6.

In the realm of multiplication, 2X3 produces 6.

And so on. Six is a concept but it is also the product of many different procedures.

## Develop number sense with number talk

The capacity to switch between understanding “6” as a concept and also the product of different procedures is what children need in order to develop number sense, or a “feel” for numbers.^{1} People with numbers sense can use numbers flexibly, decomposing and recomposing numbers in order to solve problems more easily.

You can help your child develop number sense by playing around with numbers together at the right level of challenge. If you have a younger elementary school child, you could start with a one-digit number like six.

“Let’s see how many ways we can think of to say “six,” you could offer, while walking or driving somewhere. “How about five plus one? Can you think of other ways to say six?” Then encourage your child to think of many different ways of expressing six through addition or subtraction. Then try another number.

## Adapt the game to your child’s ability

To adapt the game to your child’s mathematical ability, use small or large numbers, and whatever combination of addition, subtraction, multiplication, and division that works best for your child.

For example, if your child is pretty good with multiplication and division, you can use larger numbers. You might take turns expressing 24 in different ways. 4 times 6. 48 divided by 2. 96 divided by 4. Then try 240.

You can play this game cooperatively, or you can take turns coming up with answers. If it motivates your child, you can one-up each other with ever more wild and crazy answers.

Don’t emphasize speed, however. You want to give your child the time to make sense of what they’re doing, and you don’t want them to be self-conscious about whether they’re fast enough. And don’t push them to play if they’re not in the mood; wait and try another time.

This kind of playful conversation about numbers is exactly what your child needs to develop number sense, a foundation of mathematical ability. Keep it fun and keep them coming back for more!

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- For more insight into number sense and how to help kids develop it, I recommend
*What’s Math Got to Do With It*, by Jo Boaler, Professor of Mathematics Education at Stanford University. Professor Boaler also shares insights on youcubed.org