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Unitizing? Yes! It’s an Important Big Math Idea

Unitizing is not only a mathematical term, but it’s also a business term.  Have you ever wondered when businesses ship hundreds of boxes, how do they keep track?

Unitizing is a big math idea!

By unitizing!  The shipping company will unitize the boxes into groups or pallets.  That means they will organize boxes together into a certain quantity then shrink wrap or tie them together.  Now it’s easier to count pallets than individual boxes.

Marines stacking boxes into groups.

So Why do our Students Need Unitizing?

Unitizing the foundation for place value.  When students count and group objects they internalize this mathematical concept of bundling units into a set (10s, 100s, 1000s, etc.).

It’s also a big developmental shift in thinking for 6 and 7-year-olds.  Students have been learning to count by one and develop one to one correspondence.  Now, they shift to thinking of a group of 10 as 1.  It’s very abstract to show this with drawings or a place value chart.

What six and seven-year-old children need is to count real objects while developing counting strategies.  As their counting becomes more accurate and sophisticated, they will develop a more efficient counting strategy known as unitizing.  Rather than count by one each object, students will see that grouping objects by a set number results in faster and more efficient counting.

Unitizing is a developmental shift from 1:1 correspondence to a one set of 10

Teachers need to guide their students to see that grouping by 10 is a very efficient counting strategy.  Students can then also use the rote skill of counting by 10 to count large quantities grouped by ten.

This practice of counting groupings of ten internalizes for the student the concept of 1 ten is the same as 10 ones.

Planning Instruction for Unitizing

Think of unitizing as a Big Math Idea.  It is such a big idea, that students shouldn’t leave first grade without this understanding.  Check out this video on the progression of addition and subtraction to better understand why it’s important!

Unitizing as a big idea for teaching and learning based on standards

As the graphic above shows, from this big math idea, we go to the standards, specifically the standards for place value in first grade.  Place value receives even more emphasis in second grade when students must work within 1,000.  It continues in third grade when students expand their understanding of place value to round whole numbers to the nearest 10 or 100.

Let’s look more carefully at the place value standards for first grade relating to unitizing.

As you can see the standards make specific references to bundles of 10 ones, amounts of 10, based on meanings of 10s and 1s.  Students will need lessons designed around this concept of unitizing into bundles of 10s.

Common Core State Standards for Math for first grade that are based on unitizing

Fortunately, students have also had exposure to making a ten.  Most kindergarten and first-grade students practice making a ten on a ten frame.  Ten frames help students develop and understand the benchmark of 10.

Unitizing through Counting Collections

If you’re not familiar with counting collections, here’s a good resource:  Teacher Education by Design.

Recently, in a first-grade class, I taught a lesson using counting collections.  Keep read to learn how to sign up for my FREE newsletter and receive the lesson plan in your email.

I started the lesson by showing a picture of a bunch of gummy bears so I could ask this question:  What do you notice?

counting gummy bears

It’s a simple question, but it’s a great entryway for all students to engage in a math problem.  Most students saw that the gummy bears were different colors.  They wondered what they tasted like or if they talked or sang, but most importantly, they recognized that there seemed to be more of one color than the others.

Then I wondered out loud, “I wonder how many there are?”  Students immediately began estimating that there were 20 or 50 or 100.  “How could we find out?” I asked.  Counting!

Bags of Objects to Count

Earlier I had scoured through our math bins to find objects to count such as two-sided counters, linker cubes, unit cubes, square foam tiles, pattern blocks, and the like. I also checked out the 99 Cent Store and found aquarium rocks!  We had a bag full of empty plastic water bottles so I took off each cap and made a counting collection of those.

I specifically chose these quantities:  27, 32, 33, 34, 35, 36, 37, 38, 39.

Bags of objects for counting collections

I put the students into groups of three to work together to count the objects in their bags. When each group had determined how many, I had them keep their groupings and record on a sheet how they counted.

Several groups counted by 5s, some by 10s, and some, one by one.

Discussion about Groupings

Once all the students had recorded their quantities, we stopped to come back to the whole group.  We talked about the different ways they had grouped their objects.  I asked, “Which way do you think might be more efficient or easier?” I steered away from “faster way” because I don’t want to give the impression that math is only about speed.

Recording sheet for students to show how they counted the objects

The consensus was that grouping by 10 was more efficient.  “Did that remind you of anything?” I asked. A ten frame! BINGO!

Showing how a ten frame is the same as a base 10 rod

I gave each group 3 ten frames to go back and fill in with their objects.  Now they made a connection to previous learning. Now they visually saw a group of ten.  Once they had their objects in groups of 10 on a ten frame, I had them recount by counting by 10s and then 1s. If their total was correct, I handed the group a card with their number on it.

Once all groups had their number, it was time for the trade.

Trading for a Tens Rod

The idea of unitizing has to be practiced many times through lots of opportunities to count. But for today’s lesson, I wanted to show how the 10 frame with 10 objects could be represented by a base ten rod. So I went around and we traded each ten frame for one base ten rod.

Just to drive home the point, I had the groups count the individual unit cubes that made up the base 10 rod.  They had to count each unit cube.  Most said it would be easier to just count it as a ten.  Exactly! Lesson learned.  Well not quite.  More practice would be needed over the weeks and during the school year repeating this same lesson but with increasingly larger quantities up to 120.

From Concrete to Representational to Abstract Unitizing

With six and seven-year-olds, it is NOT developmentally appropriate to approach unitizing as an abstract concept.  Students might be able to parrot back that 10 ones make one 10, but conceptually they will not understand what is happening.  That will lead to difficulties later when students are taught to regroup for addition and subtraction.

Concrete to Representational to Abstract

A better approach is to teach the concept in a concrete manner, using real objects hence counting collections.  Students need to be counting real objects. Later, once they’ve had practice counting and grouping objects in bundles of ten, they can represent their thinking in concrete/abstract or representational/abstract models as shown below.

Final Thoughts on Unitizing

The Common Core State Standards for Mathematics in first grade make it clear that unitizing is not be overlooked but to be taught explicitly and understood by the end of first grade.  Second-grade math CCSS continues the progression of place value with students understanding that the three digits of a three-digit number represent hundreds, tens and ones.  These are critical understandings for conceptually understanding why and when to regroup for addition and subtraction.

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How do you teach your students to unitize? Share your ideas in the comments!

Unitizing? Yes! It\'s an Important Big Math Idea
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