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Strategies for Teaching Elementary Math Students Number Sense

Updated on January 23, 2017

Simple, yet effective tips and strategies for helping elementary mathematics students develop number sense

After a few years of teaching in elementary and middle school mathematics classrooms, I soon discovered that a majority of my students, year after year, suffered from a common math condition called 'lack of number sense' . This is not an insult to the students. It is basically their inability to understand numbers, their meanings, and how they relate to each other. The problem arises when students are expected to, but have not developed number sense by a certain grade or stage of their learning and development.

There are several factors that are attributed to this condition, and they vary depending on what grade the child is in. Therefore, I will not focus on those factors in this article. Instead, I will share tips and strategies for curing this condition. Yes, there's good news! This common math condition is curable!

I have identified strategies, vocabulary, and rules to help you successfully develop number sense in your students. Each strategy is easily adapted to upper elementary grade levels by using larger numbers. The principles and rules are the same and work regardless of how large or small the numbers are.


Operations - addition, subtraction, multiplication, and division

Inverse Operations - two operations that are opposites of each other yet can be used to check each other

Commutative Property - the ability to reverse the order of numbers in addition and multiplication operations and still get the same answer

  • IMPORTANT RULE: Make a conscious effort to NOT teach mathematics skills and concepts in isolation. Connect new skills to a related skill or to prior knowledge. ·

STRAGEGY 1: Teach students addition and multiplication facts using the Commutative Property. Regardless of the grade level, children are able to apply this property to make important connections.


2 + 4 = 6 is the same as 4 + 2 = 6

4 x 2 = 8 is the same as 2 x 4 = 8

Teachers often use timed drills to build fluency. From the onset of teaching facts, use the Commutative Property. You will save students precious time from computing same facts when the order is reversed.


STRATEGY 2: Teach students the related division facts for multiplication facts, and the related subtraction facts for addition facts.

Examples: Multiplication/Division

4 x 2 = 8

2 x 4 = 8

8 ÷ 2 = 4

8 ÷ 4 = 2


4 + 2 = 6

2 + 4 = 6

6 – 4 = 2

6 – 2 = 4

STRATEGY 3: Show students how to check their work by using inverse operations. This will develop their number sense and confidence. (NOTE: The inverse of subtraction is addition and the inverse of division is multiplication.)


6 – 2 = 4 Check by adding 2 + 4 = 6, or 4 + 2 = 6.

8 ÷ 2 = 4 Check by multiplying 2 x 4 = 8, or 4 x 2 = 8.

Manipulatives and models may be used for helping early learners to see and understand these concepts and show how they are connected.


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