Composing the Number 100

Introduction

In this lesson, your learner will explore composing the number 100 with tens and ones, and other common groupings like 20s, 25s, and 50s. These foundational concepts will support their understanding of place value, number relationships, and real-world math like measuring and graphing.

Before starting, your learner should be able to count fluently to 100 by tens and ones.

Key Concepts

• Ten Tens in One Hundred: 100 is made up of ten tens. This can be shown using Dienes rods, place value charts, coins, or number lines.
• One Hundred Ones in One Hundred: Learners will count all the way to 100 by ones and see how it connects to their everyday experience—whether it’s 100 pennies, 100 steps, or 100 puzzle pieces.
• Other Groupings That Compose 100: 100 can also be made with groups of 50, 25, or 20—common divisions seen in measuring tools and graphs.
• Bar Model and Equations: Learners will use bar models and write both additive and multiplicative equations to show how 100 is composed.

Teaching Plan

The following activities will help your learner become confident with composing the number 100. Remember to go at a pace that is comfortable for your learner.

Examples and visuals to support the lesson:

1. Reviewing Counting and Writing to 100

Begin with a quick review of how numbers are written.

• Show 10 on a place value chart and ask what each digit represents. Then show 100 and ask the same.
• Reinforce that although the tens and ones digits in 100 are zero, they still contribute to the full value through their position.

Next, review counting in tens from 0 to 100 out loud:

• "No tens, one ten, two tens... up to ten tens."
• "Zero, ten, twenty... up to one hundred."

Skill Check
I can explain each digit in the number 100. I can count by tens up to 100.

2. Showing Ten Tens Equals One Hundred

Show your learner the connection between counting by tens and using groups of 10 to compose 100.

• Use tools like: Dienes rods, ten-pence (ten-cent) coins, bead strings, number lines, printed hundred grids, Gattegno charts
• Encourage your learner to touch or trace each group of ten as they count. Reinforce: "There are ten tens in one hundred."

Now summarize what your learner has just done by writing equations. You can also represent them with bar models.

• Additive: 10 + 10 + 10 + ... (10 times) = 100
• Multiplicative: 10 × 10 = 100

Skill Check
I can show and explain that 10 tens make one hundred.

3. Counting One Hundred Ones

Now switch to counting in ones. Use:

• Penny coins
• Measuring sticks with all centimeters marked
• Loose cubes or counters
• Jigsaws with 100 pieces

Let your learner count by ones to 100 using real or pictured objects. Then write:

• Additive: 1 + 1 + 1 + ... (100 times) = 100
• Multiplicative: 100 × 1 = 100

Skill Check
I can show and explain that 100 ones make one hundred.

4. Composing 100 with 50s and 25s

Guide your learner to discover other groupings within 100 including 2 groups of 50 and 4 groups of 25.

• Use printed hundred grids or Dienes squares.
• Count together in 50s and 25s: "50, 100"; "25, 50, 75, 100"
• Encourage your learner to tap or trace each group as they count.

Skill Check
I can show and explain that 100 can be made with 25s and 50s.

5. Composing 100 with 20s

Now introduce the idea that five groups of 20 also make 100. Use bar models, counting tools, or real-world examples like 20p coins.

• Help your learner count aloud: "20, 40, 60, 80, 100"
• Relate this to counting in twos—just with a unit of 10!

Skill Check
I can show and explain that five 20s make one hundred.

6. Practice and Apply

Now mix it all up! Give your learner a variety of tasks:

• Complete bar models with missing parts
• Fill in number sequences that count by 10s, 20s, 25s, or 50s
• Solve missing number equations
• Read real-world scales on rulers, measuring tapes, or thermometers

Encourage reasoning with this stem sentence: “One hundred is divided into ___ equal parts, so each part has a value of ___.”

Skill Check
I can show 100 in different ways and use it to solve real-life problems.

Summary

By the end of this lesson, your learner will understand that 100 isn’t just a big number—it’s a powerful number made of smaller parts! Whether using 10s, 20s, 25s, 50s, or 1s, they’ll be able to flexibly compose and decompose 100 for place value, measures, and more. Let your learner explore these ideas at their own pace and celebrate their growing number sense!

Teaching Plan adapted from NCETM under OGL license v3.