Number sense is essential for math, but not everyone knows what it is. Number sense is the ability to use numbers and math processes flexibly and in a variety of ways. Mental math or mental computation is one piece of number sense as is estimating, being aware of patterns and relationships, predicting, and being able to tell if results are reasonable.
Here are some signs a student has good number sense:
- They calculate in their head or solve problems without a calculator or paper and pencil
- They know different approaches to solving calculations and choose an appropriate approach
- They know how to estimate and how to use estimates to get a rough answer.
- They know different ways to check their answers to see if they are reasonable and if calculations are correct.
- They recognize patterns in numbers and understand different relationships between numbers.
- They generally feel comfortable working with numbers.
What if a student doesn’t have good number sense?
Students with poor number sense often feel uneasy and dislike numbers and math. They rely on calculators and paper and pencil. Even with these tools they may be at a loss as to how to approach a problem and don’t or don’t know how to check their responses. The good news is, students can build better number sense and math intervention can help.
Build number sense with math intervention
Numeracy skills start with number sense and also includes counting strategies, procedural knowledge or how to go about solving a problem, number fact development and recall, and understanding math language. Math intervention can help students develop more solid foundational skills that they will need as they continue to build other numeracy and math skills.
Working (and playing) with numbers in a variety of ways helps develop number sense and confidence over time. When you are modeling or demonstrating, talk aloud your thought process.
Representing numbers. Give students counters of any sort. Ask them to show different ways to represent a number, such as ten. For example, they could have ten counters together to represent 10. They could also have 9 and 1, 8 and 2, 7 and 3, and so on.
You can do something similar with multiplication. Have students color an array on graph paper 2×6 and then 6×2. Show students that the same number of squares are colored even though the shape is different. Have them color in 1×12 and 3×4. Help students see that all of these come to the same number.
Patterns. Use 100s charts to help students see patterns in numbers and to practice skills. For example, students might see that multiples of 10s always end in zero and multiples of 5s alternately end in zero or five. You can use hundreds charts with missing numbers for students to fill in or have students practice skip counting or adding on. You can find more ideas for using 100s charts for number sense here.
You can also have students practice their doubles facts and skip counting without hundreds charts.
Relationships between numbers. Which is bigger 17 or 21? What about ½ or ⅓? Have students answer greater than/less than questions. Or give a set of numbers and have students order them from smallest to largest. You can also ask students to express other relationships between numbers like 5 is half of 10.
Resources for number sense math intervention
As suggested above, 100s charts can be used for math intervention around number sense along with any kind of counters that help students see and manipulate numbers in different ways.
One of the most useful things is repeated practice (even for small amounts each day). For this purpose, I like task cards. Number sense task cards might be focused on multiplication or time or place value and each time students work on them, they approach it a slightly different way. The repeated practice on a skill with different types of activities helps students see from different angles and develop foundational skills.
Try these FREE Multiplication Task Cards
And if you want more task cards to develop number sense, add these to your math intervention tool kit: