Adding Three Numbers by Making 10

Introduction

In this lesson plan, your learner will explore adding three numbers by making 10. They will review pairs of numbers that have a sum of ten and apply them to adding three numbers efficiently. This lesson also builds on their understanding of other addition strategies such as the associative property.

Key Concepts for Adding Three Numbers by Making 10

Here are a few concepts that are helpful to know for this lesson.

• Associative Property of Addition: The associative property states that the way addends are grouped does not change the sum. For example, we can find the sum of 2, 3, and 5 by adding 2 and 3 first, adding 3 and 5 first, or by adding 2 and 5 first: (2 + 3) + 5 = 2 + (3 + 5) = (2 + 5) + 3
• Make Ten: Using pairs of numbers that sum to ten to simplify addition. For example, in 3 + 5 + 7, recognizing that 3 + 7 = 10 can make the calculation easier.
• Applying Different Strategies: It's important that learners practice a variety of strategies for adding numbers. This not only helps them develop a deeper understanding of numbers, but encourages them to find strategies that are the most useful to them.

Teaching Plan

The following activities will help your learner review the associative property of addition and apply make ten as a strategy for adding three numbers.

Examples and visuals to support the lesson:

1. Reviewing the Associative Property

• Begin by exploring different ways of calculating the sum of three addends using the associative property. For example: "I have 3 red cars, 5 blue cars, and 2 yellow cars. How many cars do I have? (3 + 5) + 2 = 3 + (5 + 2)."
• Use concrete materials to represent the addends and discuss how the total remains the same regardless of the order in which the addends are grouped.
• Introduce the generalized statement: "When we add three numbers, the total will be the same whichever pair we add first."

Skill Check
I know that when I add three numbers, the sum is the same no matter which two numbers I add first.

2. Connecting Different Representations

• Use tens frames to represent different orders of addition. For example, show how 3 + 5 + 2 can be grouped to make ten first: "Three plus seven is equal to ten, then ten plus five is equal to fifteen."
• Move to the part-part-part-whole model and continue using symbolic representations, including expressions and equations, alongside the models to help your learner make connections.
• Emphasize the correct use of the equals symbol when writing equations. The equation 3 + 5 + 2 = 10 + 2 = 12 is written correctly. However, 3 + 5 = 8 + 2 = 10 does not represent a true equation.
• Ensure that the connection between the context, pictorial, and abstract representations is made explicit. Ask your learner: "What does the 3 represent?" "What does the 5 represent?" "What does the 2 represent?" "What does the 10 represent?"
• Encourage responses in full sentences, such as "The 3 represents the three red cars."

Skill Check
I can use models and equations to show each step of adding three numbers.

3. Introducing the Make Ten Strategy

• Next, introduce a context where the total is greater than ten. Begin with calculations where two of the addends sum to ten such as 3 + 5 + 7. Demonstrate that two of the numbers (3 and 7) have a sum of ten so adding them first can make the calculation simpler: "Three plus seven equals ten. Adding two more equals twelve."
• Use tens frames to represent the problem pictorially and make a clear link to the tens frame representation. Emphasize to your learner that they can add the addends in any order, focusing on finding pairs that sum to ten.
• Once your learner is confident in making tens using tens frames, move on to symbolic representations alone. Encourage recalling number bonds to ten to find the most efficient calculation strategies.
• Provide missing number problems for practice in identifying efficient strategies and correct symbolic notation. For example: "Three plus seven equals ten. What number, when added to ten, equals twelve?"

Skill Check
When I add three numbers, I can start with the numbers that make ten.

4. Varied Practice

• Present a mix of calculations and ask your learner to sort them into two groups: those for which the "making ten" strategy can be applied and those for which it can’t. For example: "Sort these problems: 7 + 3 + 4; 2 + 6 + 8; 1 + 9 + 5."
• For an additional challenge, give your learner four-addend problems that include: Two pairs of number bonds to ten (2 + 4 + 6 + 8 = ?) and three addends that sum to ten (8 + 3 + 6 + 1 = ?).
• Use a pictogram-based question to provide opportunities to apply the strategy in different contexts. For example: Give your learner a pictograph that shows how many sweets different children have and ask your learner how many three of them have altogether. (How many sweets do Jayesh, Sam, and Sara have together?)

Skill Check
I can solve many types of math problems by making ten first.

5. Communicating Mastery

• By the end of the lesson, your learner should be able to describe their answers in full, using consistent language. For example: "Seven plus three is equal to ten, then ten plus four is equal to fourteen."
• Use a stem sentence with the structure: "___ plus ___ is equal to ten, then ten plus ___ is equal to ___."

Summary

By the end of this lesson, your learner will master adding three numbers by making 10 and incorporating other addition strategies. They will understand the associative property and efficiently use the make ten strategy to solve addition problems, making math both engaging and intuitive.

Teaching Plan adapted from NCETM under OGL license v3.