## Counting by Tens Matters: A Next Step in Place Value Understanding

How can you help your primary students make the leap from working with small numbers to becoming fluent with larger ones? One way they can start thinking in larger ‘chunks’ is by counting by tens. More than just an oral exercise, counting by tens is an essential skill that builds number sense, encourages thinking about number structures, and economizes counting and operations. Students with a strong conceptual understanding of round numbers, a ‘ten’, and ‘the tens place’ are better prepared to work with two-digit numbers and beyond.

In this post, we will share the ideas behind our exercises in the topic Counting by Tens (available in your  Happy Numbers’ account) and some additional tips on reinforcing counting skills using Unifix cubes.

## 1. Using Base-10 Blocks – First Steps

A great way to start counting by tens is to model numbers using manipulatives. We begin by building the 10 rod using cubes:

Once students build a rod, we ask them to count the total number of cubes in the rod:

At Happy Numbers, we first use animation to give students a clue for the answer:

Then we guide students to do it independently:

The activity above models the relationship between counting by tens and counting by ones.

## 2. Using Base-10 Blocks – Advanced

Next we present several rods at the same time and ask students to count the total number of cubes.

We begin by guiding students in finding the total by asking them to count the number of cubes in one rod:

Then the number of rods:

And then the total number of cubes:

Once students demonstrate mastery with guidance, we convert to asking for only the total number of cubes:

Happy Numbers customizes the number of exercises students complete based on their responses. This ensures that they master each skill before moving on to the next and are truly working at their own pace. It also makes classroom management easier, as teachers are not juggling multiple ability levels while bored students build castles out of cubes!

## 3. Using 10-Frames

Another great model to use for counting by tens is the 10-frame:

We follow a systematic approach (similar to what students have done with cubes and rods) to guide students through counting the apples in one box:

Then counting the boxes:

And finally counting the total:

Once they master these steps, the guided steps are removed and they simply report the total:

As always, Happy Numbers responds immediately to student input and provides remediation for any errors:

By reinforcing the concept of ‘ten’ with both rods and 10-frames, students acquire the understanding that it doesn’t matter how the group of 10 is made. They can easily count the total by just knowing there are 10 objects inside!

## 4. Regrouping into Tens to Count

Once students can fluently count by tens, they advance to an exercise that requires them to create groups of ten before counting the total. They have already mastered counting full boxes of fruit, and now they see how it is easier to count totals with round numbers.

First we demonstrate the task with animation:

And then we let them create groups of ten themselves:

This activity is great as it provides students with a strategy on how to count a scattered array of objects – by simply organizing it into tens and counting groups of tens as they did in the previous exercises.

It also pairs well with ‘carpet exercises’ using objects. Provide students with a round number of small objects (such as buttons) and have them count the objects two different ways: one by one and then by making groups of tens and counting tens. That will clearly show the difference in efficiency to your students!

Head back to the carpet with your buttons for another approach to counting by tens – counting out. Give students a collection of buttons and ask them to count out a round number of them. They will see that counting by tens is a fast and efficient strategy!

## 5. Bonus – Ideas on Skip Counting

We found this video interesting and think you will, too. It shares ways to use Unifix cubes to help model counting by tens as well as some other classroom strategies for skip counting:

The idea of letting students build a long “snake” composed of tens (at 1:00) and then count the total is just terrific!

As you work to move your students from working with small numbers to understanding larger ones, try some of these strategies either online at HappyNumbers.com or with manipulatives. Please share with us any other activities you use to reinforce counting by tens – leave a comment below or write us an email! We are looking forward to your feedback!

Yours,
Happy Numbers Team