Unitizing Groups of 10

Introduction

This lesson plan will introduce your learner to unitizing groups of 10. They will practice grouping objects into sets of ten and recognizing each set as "one ten." This develops the concept of unitizing which can later be applied to solving various types of problems.

Before beginning the lesson, your learner should be able to confidently count sets of objects.

Key Concepts for Unitizing Groups of 10

Here are a few concepts that are helpful to know for the lesson:

• Unitizing: Unitizing is the process of grouping individual units into a single, larger unit to simplify counting and calculation. This concept helps learners understand, count, and manage larger quantities.
• Examples of Unitizing: Counting ten individual blocks and grouping them into one "stick" of ten. Collecting ten single pennies and exchanging them for one dime. Recognizing ten fingers as one complete set of fingers.
• Models for Unitizing: This lesson plan includes identifying and counting groups of ten in various representations such as sticks of cubes, pictures of ten objects, and tens frames.

Teaching Plan

The following activities will help your learner become confident with unitizing groups of 10. Remember to go at a pace that is comfortable for your learner.

Examples and visuals to support the lesson:

1. Recognizing Groups of Ten

In this activity, we'll use multilink cubes to create and recognize groups of ten.

• Ask your learner to count out a set of ten cubes and join these to make a stick of ten. Make sure that the cubes are the same color so that the color does not distract from the idea of it forming one group of ten.
• To reinforce the equivalence between the stick of ten cubes and ten ones, ask your learner to break up their stick of ten into individual cubes and count them again. Use variation to explore the idea of a group of ten begin composed of ten individual cubes.
• Use the following generalized statements to demonstrate the idea of unitizing: "Ten ones are equal to one ten. We have one group of ten. We have one ten."

Emphasize that neither the orientation, arrangement, nor color affect that there are ten cubes forming one group. Here are a few ways to demonstrate this concept:

• Introduce a stick of cubes of another color and a stick of cubes made of a mix of colors.
• Show ten cubes in an arrangement other than a stick.
• Compare ten cubes in a cup with a stick of ten cubes of the same color. compare ten cubes in a cup with a stick of ten cubes of a different color.

Skill Check
I know that a group of ten ones is the same as 1 ten.

2. Modeling Groups of Ten

Next, show your learner pictures of ten objects represented as a single group.

• Here are some examples for showing 10 objects as a group: ten fingers, packs of ten pencils, a vase of ten flowers, a bag of ten apples, or a bundle of ten sticks.
• Reinforce the concept that we can prove that these are groups of ten because we can separate the objects and count them individually.
• When the objects are grouped into ten, ask your learner if they can still see ten ones. Continue to use the generalized statements to reinforce the concept of unitizing.
• To check your learner's understanding, present them with a concrete representation that does not show ten such as a box of eleven pencils or a stick of nine multilink cubes.
• Ask your learner whether they have a group of ten and have them explain their answer. They may say, for example, "This is not one group of ten, because when you separate the sticks there are not ten sticks."

Skill Check
I can tell if a group of objects is or is not one ten.

3. Using Fixed Groups of Ten

• Once your learner has developed a good understanding of a group of ten using objects that can be separated, progress to using representations that cannot be broken apart. This can include pictures of ten frames, number boards, or a ten-rod from a base ten set.
• Although these tens cannot be separated into ones, the cardinality of ten is still clear since the individual ones can be counted. Continue to use the generalized statements to help your learner see the objects as groups of ten.
• Next, progress to exploring representations of ten that give no indication of cardinality other than showing a word (ten) or numeral (10). Examples include tens counters, ten-cent coins, ten-dollar bills, or game pieces with 10 written on them.
• Some learners find difficulty understanding that a ten-cent coin has the same value as 10 one-cent coins. Provide plenty of opportunities for your learner to physically swap 10 one-cent coins for a ten-cent coin. You can also demonstrate this concept using place value counters or base ten cubes and rods.

Skill Check
I know that some things represent a group of 1 ten even if I can't see each item.

Summary

By the end of this lesson plan, your learner will have a solid understanding of the concept of unitizing, recognizing that ten individual objects can be grouped to form one ten. They will be able to create groups of ten using multilink cubes, identify groups of ten in various representations, and understand the importance of unitizing in mathematics. This knowledge will serve as a building block for more complex mathematical operations and problem-solving skills.

Teaching Plan adapted from NCETM under OGL license v3.