Number Sense
By Michael Naylor

Numbers are the building blocks of mathematics, and developing number sense is important for children at all grade levels. Number sense is a feel for the size and meaning of numbers, the relationships between numbers, the ways numbers can be put together and taken apart and the connections between numbers and the world around us. Here are some activities to help your students develop number sense.

Number hunt (Grades K-1)
Look around your room and find examples of numbers, either written numerals or objects that exhibit a number, such as four legs on a chair, six window panes, three apples on a bulletin board, etc. Make a list of these and have your students go on a number hunt to find the numbers.

Operation connections (Grades 2-5)
Give your class a number such as eight, and ask them what comes to mind. For example: the number of legs on an octopus, the number of fingers (not counting thumbs) on their hands, the number of hamburger buns in a bag and so on. Next, have each student choose a favorite number and come up with at least five connections.

Number connections (Grades 1-4)
Extend the previous activity by having your students draw or print out pictures of objects showing their favorite number and then making a poster showing multiples of that number. For example, a student could draw a row of ants across the paper, and then write two rows of numbers showing the running total of the number of ants and the number of legs, as shown here.

Younger kids will be developing counting and adding skills; with older kids you can emphasize multiples and multiplication.

Fill in the numbers (Grades 2-8)
Give your students scenarios in which the numbers have been removed and listed separately. Ask the students to place the numbers in the appropriate blanks.

In the following example, students must consider what are reasonable numbers for each of the measurements:

Numbers: 610, 5, 75, 10
"Janna is ___ feet tall and weighs ____ pounds. Every day, she rides her bike ___ minutes to get school. She lives at ____ Maple Avenue."

You can easily create examples that fit with other subjects. Suppose you're studying sharks in science – just take a few shark facts from the encyclopedia and remove the numbers:

Numbers: 8, 41, 80, 2400
"There are about ___ different kinds of sharks. Sharks can range in size from the hand-sized pygmy shark, which is only ___ inches long, to the whale shark, which can reach ___ feet – that's longer than a school bus! Sharks can have as many as ___ teeth, which they constantly lose. A tiger shark can grow as many as ___ teeth every year!"

Encourage your students to write their own examples. They should try to write them so that each number fits only in one blank. example, the numbers 3 and 5 could go in either blank in this example: "Jon has ___ brothers and ___ goldfish." If the numbers were instead 3 and 100, the problem would have just one reasonable answer.

Could be, couldn't be (Grades 4-8)
Write a chart on the board with columns labeled "Number," "Could Be" and "Couldn't Be." Provide some examples of things that could and couldn't be represented by a particular number, like the examples below:

Working in pairs, have students come up with their own examples. They should try to make the examples conceptually related, so if their "could be" is about spiders, for instance, their "couldn't be" should also relate to spiders. Have each pair pick their favorite one to share with the class.

With older kids, once they have the hang of the activity, ask them to use greater and greater numbers. Can they come up with an example using a number greater than 1,000? A million?

Michael Naylor is a professor of math education at Western Washington University, Bellingham, WA.

February, 2007, Vol.37, No.5