Strong number sense is the foundation for all the building blocks of mathematics that follow. Despite its importance, number sense can be difficult to define. It may be because many of the concepts of number sense are acquired through everyday life and not through formal learning. In general, young children arrive at school already knowing what it means to have two turns at a game or to have five grapes to eat. But for some children, especially those with disabilities, those concepts must be explicitly taught. In this article we will define number sense as well as offer strategies to strengthen it in students.

NUMBER SENSE is the ability for students to:

1. Count with one to one correspondence: As preschoolers, students learn to count by rote: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. They may even count to 50 before they develop the concept of one-to-one correspondence. For example, counting five cookies means counting each cookie once and only once and understanding that the last number you say (5) is the amount or quantity.

How to help: Count the room.: Get students up and out of their chairs to: count the windows in the room, touching each one as they count. Count the chairs, the desks, the books in a stack, the bins on a shelf, the bulletin boards. Count Actions: Students stand next to their desks. Teacher calls out numbers + actions: stamp your foot 8 times, clap 4 times, touch your toes 6 times. Count Objects: Place open containers with a number on one side. Student must count out and place the manipulatives given (buttons, bears, counters, erasers, etc.) in the opposite side of the container.

Count Objects Bins: Supply student with 10 containers, number cards 1-10, and 55 small items.

2. Put numbers in correct sequence: Understanding number sequence is an important part of number sense. For example: 8 always follows 7 in number sequence. It never changes.

How to Help: 100 Chart Activities: When students are invited to frequently interact with a 100 chart, sequence becomes visual, auditory and tactile. Try cutting up a 100 Chart Poster into strips: 1-10, 11-20, 21-30 etc. Mix them up and have students place them in linear order on the floor. Number Cups: This is a super easy and fun activity. Take 10 cups and write a number (1-10 or any sequence you are teaching) on each one. Ask student to put the cups in sequence from 1-10. Ask questions such as “what number comes before 3?” and “what number comes after 3?” A fun way to mix it up is to use seasonal or holiday paper cups. It’s always a popular center activity! Chutes and Ladders: Playing this game is a fun way to teach number sequence. Number Sequence 1-10 Activity: Sign up for this FREE activity ABOVE!

3. Connect abstract symbols to actual quantity:

For example: eight, 8, and o o o o o o o o

How to help: Number the Room: Students are given sticky notes and instructed to label bins, jars, and boxes with the number of items it contains. For example if a book bin has six books, the student would write “SIX 6” on a sticky note and attach it to the bin. Ten Frame Activity: Download the ten frame activity below or make your own. You will need 55 small objects (pom-poms, counters, mini erasers, counting bears, buttons). Student chooses a number card and then places that number of items on the ten-frame. When done, all of the objects will be used.

CLICK HERE for a FREE Ten Frame Activity

Apple Counting Activity: Download this free activity that matches numbers, number words and quantities. Use counters, buttons, erasers, or play dough for apples.

CLICK HERE for a FREE Apple Counting Activity

4. Compare numbers: Number sense allows a student to compare numbers. Which group has more? Which group has less? Which group has the same?

How to Help: Counting Beans: Fill a large bowl with dried beans. Set out two small, empty bowls. Student scoops one handful of beans for the first bowl. Repeats the action for the second bowl. Now the student must compare amounts to decide which bowl has MORE. A sticky note that says MORE is attached. Another sticky note that says LESS is attached to the second bowl. Challenge: student adds or removes beans so that each bowl has the SAME number of beans.

5. Compose and decompose numbers in flexible ways: For primary students it might mean counting on fingers, using a number line, or drawing a part-part-whole chart to solve 2 + 5. A third grader may create an array, use repeated addition, or draw equal groups to find the product of 3 X 7. In short, a student with strong number sense chooses strategies beyond standard algorithms to solve mathematical problems.

How to help: As teachers we teach these alternative ways to look at numbers, but more importantly we should encourage students to use them. Have scrap paper, ten squares, part-part whole mats, number lines, small white boards and manipulatives available when students are working independently.

6. Estimate: Number sense includes the ability to reasonably estimate quantity. Do you have about 10 crayons or about 100 crayons?

How to help: Estimation Jar: Teacher (or assigned “estimation helper”) fills the jar on Monday with small items. Students note their estimate on a folded paper with their name and place in a second jar. On Friday, the class counts the items and sees who came in the closest with their estimate. Estimate NO COUNTING Activity: Click below to download for FREE or make your own with photographs.