Counting Tens and Ones

Introduction

In this lesson plan, your learner will explore the concept of counting tens and ones by using a variety of base-ten tools and models. This hands-on approach helps them understand grouping ones into tens, helping them to count efficiently and write two-digit numbers properly. Counting tens and ones will also introduce your learner to the concept of place value.

Key Concepts for Counting Tens and Ones

• Efficient Counting with Groups of Ten: Counting objects can be made more efficient by grouping them into sets of ten. This method reduces the likelihood of losing count and makes it easier to handle large quantities. Using physical items such as sticks, straws, or beads grouped into tens helps learners visualize and understand the concept of grouping.
• Understanding the Value of Digits: The digits in two-digit numbers tell us about their value. For example, in the number 42, the '4' represents four tens (or forty), and the '2' represents two ones. Understanding that the position of a digit in a number determines its value introduces learners to the concept of place value.
• Unitizing Ten: Unitizing groups of ten involves grouping ten of one thing into one of something else. By physically grouping items into sets of ten, learners can better grasp the idea of tens and ones, making it easier to work with larger numbers and understand their structure. This concept also helps learners understand place value in the decimal system.

Teaching Plan

The following activities will help your learner become confident with counting tens and ones. Be sure to work at a pace that is comfortable for your learner.

Examples and visuals to support the lesson:

1. Exploring Base-Ten Tools

Begin by having your learner make their own base-ten tools. This will give them practical experience with grouping some ones into tens and leaving others as ones.

• Use a range of resources such as fingers, sticks or straws grouped into bundles of ten, small cups each containing ten counters, strings with ten beads, small net bags containing ten objects, multilink cubes in stacks of ten, index cards with ten clothespins attached.
• Prompt your learner with tasks such as: "Show me 1 ten. Show me 1 one. Show me 10 ones." When showing you 10 ones, encourage your learner to show you one group of ten, although it is correct if they show you ten separate ones. Encourage your learner to use the generalized statements: "This is 1 one." "This is 10 ones. It is also 1 ten."

Skill Check
I can use different math tools to count groups of ten.

2. Counting Large Groups Efficiently

To introduce the idea of using groups of ten for efficiency, show your learner a picture of many objects and ask, "How many are there?"

• First, model counting in ones and being distracted or losing count during the process, having to start again at the beginning. Then count again, this time counting ten at a time, circling each group of 10 as you go.
• Emphasize that by organizing into groups of ten, it doesn't matter if you lose count. You can even pretend that you lost count again and only have to go back to the start of the current group of ten.
• Remind your learner that 10 ones is the same as 1 ten. Then count the total by saying, "I have one, two, three, four groups of ten. And one, two extra ones."
• Finally, count the images in ones again, confirming that the total is 42, for example.
• Summarize the activity by saying, "We can figure out how many there are by counting in ones, or by counting the groups of ten and the extra ones."

Skill Check
I can count sets of objects by making groups of ten.

3. Writing and Reading Two-Digit Numbers

Continue with the previous example by recording the groups of ten and the extra ones in a table.

• First, use descriptive headings in the table such as "Groups of Ten" and "Extra Ones." Then progress to writing "Tens and Ones" or "10s and 1s."
• Finally, write the number again but not on the table. Emphasize that this is the correct way of writing the number 42, for example.
• Emphasize that the numbers are read starting at the left. Point to each digit while repeating, "forty-two... forty-two."
• Note that the teen numbers do not follow the left-to-right reading format, so this is likely the first time your learner is reading numbers this way.

Next, spend some time examining the number names in more detail.

• Remind your learner of the number names for the multiples of ten before demonstrating how the numbers are written when the number of ones is not zero.
• For each number you explore, show the connections between the number name, the digits that represent it, and the tens-and-ones structure.
• Emphasize that the digits are written in the order that the parts of the name are spoken. Try using this stem sentence: "This is the number ___. We write the ___ then the ___." For example, "This is the number forty-two. We write the four then the two."
• Repeat the process several times using different numbers. Note that for numbers such as 63, you can hear the "six" in "sixty." But in 36, the connection between "thir-" and "three" is less clear for learners.
• Be sure to include numbers with all the irregularly named multiples of ten (twenties, thirties, and fifties).

Skill Check
I can say the names of two-digit numbers properly.

4. Counting and Writing Practice

Provide opportunities for your learner to practice counting sets of items then expressing the number name verbally and with written digits.

• Encourage your learner to use the "groups of ten" strategy first, then count by ones to check their answers.
• Be mindful that your learner writes the digits correctly in the table. For example, they may write 20 in the tens column instead of just 2.
• If such a mistake is not corrected early on, it can lead them to writing 27 as 207, for example. You can help them correct their misunderstanding by saying, "There are two tens which have a value of twenty."

Next, start to take steps to prioritize unitizing groups of ten.

• Return to using the groups of sticks or straws. Place a number of them on the table, then bundle them into groups of ten. Show how we can find out the total number of sticks by counting the groups of ten then counting the extra ones.
• Then ask your learner to pick up a given number of sticks, by saying and writing the number. For example, tell them to pick up thirty-eight sticks as you write the number 38.
• Work through checking the total by counting in ones, and emphasize how the task is completed more easily by working with bundles of ten.
• This process is similar to an earlier activity; however, this time, your learner is able to manipulate each group of ten as a single unit instead of circling groups of ten on a picture.

Skill Check
I can use what I know about tens and ones to write two-digit numbers properly.

5. Exploring More Representations

This activity will allow your learner to explore more ways to represent two-digit numbers.

• Provide your learner with Dienes rods (or base-ten rods and cubes) that represent a number such as 34. Have them practice writing the numerals using place-value charts then without the charts.
• Vary the ways that you present the rods. For example, present the rods with the ones and tens mixed up, with the ones on the left and tens on the right, or in a linear arrangement.
• Also, practice using pictures of real-world objects that are grouped into tens. For example, bags of ten fruits or boxes of ten crayons reinforce the idea that although we may not be able to see the individual pieces, there are still ten items inside.
• To help them make connections between different representations of the same number, have your learner sort pictures and numerals into groups based on their number. For example, sorting all the representations of 63 into one pile and all the representations of 36 into another pile.
• To deepen their understanding, ask them to describe how the representations are the same and how they are different.

Skill Check
I can represent two-digit numbers in many ways, including rods, charts, and objects.

6. Additional Practice

Once your learner is confident writing numerals for different quantities that you provide them, have them work in the opposite direction.

• For example, say a number name or write a numeral and have them represent the number with a base-ten model.
• Emphasize that the number represented is the same no matter how the model is arranged, however arranging the tens on the left and the ones on the write corresponds to how the digits are written.
• Make sure that you learner is not just picking up "four of the big things and five of the little things," for example.
• Reinforce the connection between the model and the number by counting: "Ten, twenty, thirty, forty... forty-one, forty-two, forty-three, forty-four, forty-five."
• You can also have them color in squares on hundred grids to represent the number. Encourage them to count the squares as groups of tens and ones rather than counting them all by ones.

Finally, have your learner practice moving between digits, pictures, objects, number names, and tens-and-ones structures.

• For example, give them a number to write as a numeral, as tens and ones, and color in a hundred grid.
• You can also provide tasks for additional challenge such as giving them three single-digit cards (for example, 0, 2, and 4) and having them see how many different two-digit numbers they can make.

Summary

With this lesson plan, your learner engaged in various tools and representations to help them understand two-digit numbers. By engaging in activities focused on counting tens and ones, they will develop a strong understanding of place value and efficient counting strategies. This foundational knowledge is crucial for their future math skills, making numbers more manageable and comprehensible. Keep practicing these techniques to reinforce their learning and boost their confidence in math.

Teaching Plan adapted from NCETM under OGL license v3.