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# News from Mathnasium of Waterloo

### Number Sense Part 1

May 3, 2018

Ever hear your child or another student talk about math class and say, “That stuff doesn’t make sense to me!”? That’s pretty typical, and it’s because children don’t get enough context when they learn material. Providing context helps students integrate new ideas and information in a way they understand. Unfortunately, children often experience “fragmented learning” (learning without a sense of context) rather than “integrated learning.” To fill in the gap between fragmented and integrated learning, students need to establish Number Sense.

So, Number Sense … what is it?

Number Sense is the ability to appreciate the size and scale of numbers in the context of the question at hand.

What does Number Sense involve? We’ll explain.

There are three major elements that fall under number sense:

countingwholes and parts, and proportional thinking.

The basis of Number Sense begins with counting, so we’ll focus on that today. (We’ll do wholes and parts and proportional thinking in future articles.)

Counting, simply put, is the ability to count from any number, to any number, by any number, both forward and backward.

When asked to explain what counting is, many students will respond by counting from 1 (1, 2, 3, …), though counting should technically start at 0 instead of 1.

After learning to count by 1s, kids need to learn to count starting from other numbers, for instance, beginning at 28 (28, 29, 30, …). How about counting by 2s? Starting from 2 (0, 2, 4, 6, …) is easy to understand. But can our kids count by 2s when starting from the number 3 (3, 5, 7, …)?

After a good deal of practice, an experienced counter will be able to count to 250 by 1s forward and backward; to 300 by 2s, 5s, and 10s; and to 3,000 by 100s—starting at any point.

As children become experienced counters, they should also learn how to group the numbers they count. Ask your child questions such as:

• How much altogether is a group of 9 balls and a group of 7 balls?
• If you have a group of 10 and take away a group of 7, that leaves how many?
• If I give you 5 groups of 10 pennies, how many pennies will you have?
• How many groups of 4 does it take to make 12?

The importance of thinking about counting this way is its connection with the basic math operations: addition (counting how much altogether), subtraction (counting how much is left or how far apart), multiplication (counting in equal groups), and division (counting how many of these are inside of that).

As children learn to think in larger and larger groups, several good things happen.

• Being able to see one group of 24 as 1 group of 24 … 2 groups of 12 … 3 groups of 8 … 4 groups of 6 … 8 groups of 3 … 12 groups of 2 … or 24 groups of 1 allows students to almost effortlessly transition to knowing their times tables.
• Thinking in groups of 10 is the foundation of understanding place value in the decimal number system, as well as our monetary system (10 pennies make 1 dime …) and the metric system (10 centimeters make 1 decimeter …).
• Seeing the relationship between the size of two groups is the foundation of proportional thinking (literally “reasoning in groups, according to amount”—seeing in groups).

Once children learn the basis for counting, they can progress with confidence to wholes and parts and proportional thinking. At Mathnasium™, we’ve developed a method that teaches these fundamentals so that children can finally understand math in a way that makes sense to them.

Remember, children don't hate math; they hate being confused, frustrated and embarassed by math. Once they understand math, a passion will follow naturally.
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