How to Teach Number Permanence (or When Is a 3 Not a 3?)

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Number permanence is so obvious to almost anyone who has made it past their 5th birthday, that we might take this concept for granted. But for the youngest learners, explicit instruction of number permanence is vital to working with larger numbers, operations, and place value later on.


Corresponding Common Core Standards: K.CC.A.3, K.CC.B.4, K.CC.B.5


Step 1: Start with paired digits and objects

So how do we teach number permanence? To begin, students identify a numbered set of cubes to match a given numbered set of cubes. At first, the digits remain identical while the arrangement of cubes is different.


Once they’ve mastered that, both the digit and the arrangement of cubes differ. Presenting digits in different fonts and colors helps ensure conceptual understanding that goes beyond simple recognition.


Step 2: Same skill, new look

As part of our scaffolded approach to building number fluency, we use different exercises to present one key concept. We build upon the familiar by changing one element at a time and providing immediate feedback.


This next exercise uses familiar images to present a new task – selecting one or more numbered sets of cubes that match a given digit. Again, the style of the digits and the arrangement of the cubes differ. Additionally, students now have to find more than one correct response.


After students show success with this, we lead them to rely more heavily on counting skills by obscuring some of the digits. This prepares them for the next step as well.


Step 3: Separate digits from objects

Next, we separate the digits from the sets of cubes and ask students to match them.


We present the digits and the cubes both sequentially and non-sequentially and even change the character associated with each number.


Step 4: Introduce a new representation

As a final step in teaching this concept, students match numbers to positions on a number line. We don’t yet use the term “number line” but simply add sequence to the task by presenting numbers 0-10 in order, along with dot patterns. Multiple representations (digits, sets of cubes in different arrangements, a number line, dot patterns) help ensure conceptual understanding. In addition, students practice fluent responses and basic skills without the monotony of doing the same thing over and over again.


Here, students slide a given digit along the number line to its position.


How can you implement these strategies?

1. Get online: ←

At, you’ll find this lesson and more. The exercises above are all part of our kindergarten curriculum.


So start your students off on the right foot with this targeted exercises that solve the problem:


Evgeny & Happy Numbers Team


P.S.: Questions or comments about this lesson or about Happy Numbers? Shoot us an email at — we would love to hear from you!

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