Counting and Writing Multiples of 10

Introduction

In this lesson plan, your learner will explore counting and writing multiples of 10 up to 100. We will start by skip-counting using objects like coins, pencils, and multilink cubes, and gradually introduce numerals and multiples of ten. This approach will help your learner see the connections between numbers, names, and quantities, providing a strong foundation for understanding larger numbers and place value.

Before beginning the lesson your learner should be familiar with unitizing groups of 10.

Key Concepts for Counting and Writing Multiples of 10

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

• Skip-Counting by Tens: Skip-counting is a method of counting forward by a number other than one. When skip-counting by tens, we count as follows: 10, 20, 30, 40, and so on.
• Unitizing Groups of Ten: Unitizing involves grouping individual objects together and recognizing them as one unit. For example, ten individual cubes can be grouped to form one unit of ten.
• Dual-Counting Multiples of Ten: Dual-counting involves naming numbers using both their standard names and their place value structure. For instance, the number 25 can be dual-counted as "twenty-five" and "two-ten five." This method helps learners understand how numbers are composed and introduces the concept of place value.
• Subitizing Groups of Ten: Subitizing is the ability to instantly recognize the number of objects without counting them individually. Just as learners can quickly subitize up to 5 individual objects, they can learn to recognize up to 5 groups of ten. This skill makes counting more efficient and supports quick mental calculations.

Teaching Plan

The following activities will help your learner become confident in counting and writing multiples of 10. Remember to go at a pace that is comfortable for your learner.

Examples and visuals to support the lesson:

1. Skip-Counting by Tens

• Begin by demonstrating how to count groups of ten by skip-counting. Use a variety of real-life contexts such as coins, fingers, bags of ten toys, packs of ten pencils, tens frames, or sticks of ten multilink cubes.
• Incorporate dual counting to help your learner identify the groups of ten with their proper name. For example, count ten-cent coins by saying, "0 ten-cent coins, 1 ten-cent coin, 2 ten-cent coins," etc.
• You can also use a ruler that is labeled by tens to count "0 centimeters, 1 ten-centimeter, 2 ten-centimeters," etc. In each instance, follow up with the proper number names, "zero, ten, twenty," etc.
• Start to use numerals to represent multiples of ten. As your learner gains confidence you can begin to use the term "multiple of ten" to describe the numbers.
• Continue with using skip-counting alongside pictures and numerals as you introduce each multiple of ten.
• Use dual counting as before so that your learner can see, for example, three groups of ten along with the numeral 30. At this stage, encourage them to say both "thirty" and "three tens."

Skill Check
I can skip-count by tens up to 100.

2. Writing Numerals for Multiples of 10

• Next, progress to a more detailed exploration of how multiples of ten are written as numerals. Your learner is likely very familiar with the fact that 10 represents the number we call ten, but may not know why ten is represented as 1 followed by 0.
• Show them a picture of one ten (such as a vase of ten flowers) labeled as "10" alongside a picture of two tens (two vases of ten flowers) labeled as "20." Ask your learner what the 1 in 10 represents and what the 2 in 20 represents. Make sure that they understand that the 1 represents one ten and the 2 represents two tens.
• Repeat with other multiples of ten, asking questions to point out the pattern in the numbers. For example: "What do you notice about the way the numbers are written? How do we write five tens? How do we write six tens? What's the pattern?"
• Encourage your learner to use the following stem sentence: "This is the number ___. The ___ represents ___ tens." For example, "This is the number sixty. The six represents six tens."
• When writing multiples of ten, children sometimes reverse the numbers, for example, writing 02 for twenty. Use the following generalized statement to address the misconception: "All multiples of ten end with zero."

Skill Check
I know that all multiples of ten end with zero and the first digit tells you how many tens there are.

3. Recognizing and Writing Multiples of 10

Once your learner understands the pattern for writing multiples of 10, provide them with additional practice. Here are some examples:

• Show a representation of a multiple of ten and ask your learner to write the number. Note, that when showing more than five groups, arrange them so that 5 are in one row with the others in a second row. This will help them to subitize (recognize the quantity without having to count) the groups.
• Show a number written in digits without saying it. Have your learner represent the number either with objects or pictures. Provide them with prepared groups of tens (or copies of pictures) so that they can focus on the multiples of ten rather than having to draw or count individual items.
• In both tasks, ask your learner to explain their reasoning. For example, when shown a picture of 70 items, they may say, "There are seven groups of ten so we write seven-zero." Or when shown the numeral 40, they may say, "I know the number is a multiple of ten because it ends in zero. That means I can make it out of groups of ten. The four tells me there are four groups of ten."

Skill Check
I can write numbers that represent objects grouped in sets of tens.

4. Exploring Number Names

• Next, focus on the number names. Using a familiar representation, such as pictures or coins, start with the number sixty since it is the first "regularly" named multiple.
• Discuss how the name sixty can be broken down into "six-ty" and how it relates to "six tens." Examine the name of each of the multiples of ten up to ninety, exploring how they do or don't relate to the structure of the number.
• The names sixty, seventy, eighty, and ninety contain the number of tens followed by "-ty." In twenty, thirty, forty, and fifty, the start of the name has some connection to the number of tens, but not as closely as the other numbers.
• Link each multiple to the number of tens using the stem sentence: "We have ___ tens. We call this number ___." For one hundred, show your learner the numeral 100 and ask them how many tens it represents (10 tens). Explain that it has a special name called "one hundred." Ensure they say "one hundred" rather than "a hundred."
• Summarize the connections between the names, digits, and composition of each multiple of ten. For example, "twenty, 20, and 2 tens."
• Provide your learner with practice using each representation by counting objects and explaining their answers in full sentences ("I have five groups of ten cubes. That means I have fifty cubes.").

Skill Check
I know the names of multiples of ten up to 100.

5. Challenge Activities

• Next, show pictures of multiples of ten and have your learner represent each number as an expression of repeated addition of tens. For example, thirty cubes can be written as 10 + 10 + 10.
• You can also have them fill in missing numbers of equations that show multiples of ten as sums of ten. For each set of tasks, be sure to include problems that show 100 as 10 tens to reinforce their understanding of one hundred.
• If your learner shows interest in more challenging tasks, provide questions such as: Each piece of fruit costs ten cents. If I spent sixty cents, how many pieces of fruit did I buy? How many children are needed to show seventy fingers?
• While these questions are early examples of division, it is not necessary for your learner to know what division is to solve them. They can use their understanding of multiples of ten along with models to find the solutions.

Skill Check
I can solve math problems that have multiples of ten broken down into groups of tens.

Summary

Through this lesson plan, your learner explored various activities, including skip-counting, using visual aids, and practical applications for counting multiples of ten. They also learned how multiples of ten are written and the patterns in their names and numerals. This knowledge provides your learner with a foundation for more advanced math concepts including place value.

Teaching Plan adapted from NCETM under OGL license v3.