Mathematics · Grade 2 · Additive Thinking and Mental Strategies · Term 2

Addition Strategies: Making Ten and Doubles

Students will practice mental math strategies like making ten and using doubles to solve addition problems within 20.

• Ontario Curriculum Expectations
• 2.OA.B.2

About This Topic

Understanding the inverse relationship between addition and subtraction is a key milestone in the Ontario Grade 2 Algebra strand. Students move beyond seeing these as isolated skills and begin to see them as two sides of the same coin. By exploring 'fact families' and the part-part-whole model, students learn that if they know 8 + 2 = 10, they also know 10 - 2 = 8. This flexibility reduces the 'memory load' for basic facts and builds a stronger foundation for solving equations.

This topic also touches on the commutative property (order doesn't matter in addition) and how it differs from subtraction. In a classroom setting, this can be linked to social concepts like reciprocity and sharing. Students grasp this concept faster through structured discussion and peer explanation where they 'prove' how one operation can undo the other using concrete tools.

Key Questions

1. Analyze how 'making ten' simplifies addition problems.
2. Compare the efficiency of using doubles versus counting on for certain sums.
3. Explain why knowing 6+6 helps you solve 6+7.

Learning Objectives

• Calculate sums up to 20 using the 'making ten' strategy, demonstrating the process.
• Apply the 'doubles' strategy to solve addition problems within 20, explaining the connection to near doubles.
• Compare the efficiency of 'making ten' versus 'doubles' for solving specific addition facts.
• Explain how knowing a double fact, such as 7+7, can help solve a related fact, like 7+8.

Before You Start

Counting to 100 by Ones, Twos, Fives, and Tens

Why: Students need to be proficient with counting to effectively break apart numbers and make tens.

Number Bonds to 10

Why: Understanding how numbers can be composed and decomposed to make 10 is fundamental to the 'making ten' strategy.

Introduction to Addition

Why: Students should have a basic understanding of what addition means and how to represent it, often using manipulatives or drawings.

Key Vocabulary

Making Ten	A mental math strategy where one addend is broken apart to make a ten, then the remaining part is added to the ten. For example, to solve 8 + 5, think 8 + 2 = 10, and 10 + 3 = 13.
Doubles	An addition fact where two identical numbers are added together, such as 6 + 6. Knowing these facts helps with related sums.
Near Doubles	Addition facts that are close to a double fact. For example, 7 + 8 is a near double because it is close to 7 + 7 or 8 + 8.
Part-Part-Whole	A visual model or concept where a whole amount is made up of two or more parts. Addition problems can be seen as combining two parts to find the whole.

Watch Out for These Misconceptions

Common Misconception

Thinking that 5 - 3 is the same as 3 - 5.

What to Teach Instead

Students often try to apply the commutative property of addition to subtraction. Active modeling with physical objects shows that if you have 3 candies, you cannot give away 5, helping them realize that order matters in subtraction.

Common Misconception

Seeing addition and subtraction as completely unrelated tasks.

What to Teach Instead

This leads to students struggling with 'missing addend' problems. Using a 'Think-Pair-Share' where students solve 8 + ? = 12 by using subtraction (12 - 8) helps them bridge the gap between the two operations.

Active Learning Ideas

Role Play: The Number Reverser

One student acts as the 'Adder' and creates a problem with blocks (e.g., 5+3). The partner acts as the 'Undoer' and must physically take away the added blocks to show the subtraction fact. They then switch roles to see how many facts they can 'undo' in five minutes.

20 min·Pairs

Inquiry Circle: Fact Family Houses

Small groups are given three numbers (e.g., 12, 7, 5). They must work together to find all four equations that live in that 'house.' They present their house to the class, explaining why no other numbers are allowed to move in.

25 min·Small Groups

Think-Pair-Share: The Subtraction Mystery

Ask students: 'If I have a total and I take away one part, what am I left with?' Pairs use part-part-whole mats to test this with different numbers and then share their 'rule' for subtraction with the class.

15 min·Pairs

Real-World Connections

• Cashiers at a grocery store use mental math strategies to quickly calculate the total cost of items, often making tens to simplify their calculations. For example, if a customer buys items costing $8 and $5, the cashier might think 8 + 2 = 10, then add the remaining $3 to get $13.
• Construction workers might use doubles facts when estimating materials. If they need 7 beams for one section and know they need a similar number for another, they might quickly calculate 7 + 7 = 14 beams, then adjust if the second section needs one more or one less.

Assessment Ideas

Quick Check

Present students with a series of addition problems (e.g., 9+3, 7+7, 8+5, 6+7). Ask them to write down the strategy they used for each problem (Making Ten, Doubles, or Near Doubles) and the answer. Review their choices to see if they are applying the strategies appropriately.

Discussion Prompt

Pose the question: 'How does knowing 5+5=10 help you solve 5+6?' Facilitate a class discussion where students explain their reasoning, using terms like 'making ten' or 'near doubles'. Encourage students to share their thought processes with a partner before sharing with the whole group.

Exit Ticket

Give each student a card with an addition problem, such as 7+5. Ask them to write two different ways to solve it: one using the 'making ten' strategy and one using the 'doubles' or 'near doubles' strategy. They should also write the final sum for each method.

Frequently Asked Questions

What is a fact family in Grade 2?

A fact family is a group of related addition and subtraction facts using the same three numbers. For example, 3, 4, and 7 make: 3+4=7, 4+3=7, 7-4=3, and 7-3=4. It helps students see the connection between operations.

How does the part-part-whole model work?

It is a visual way to see that a whole number is made up of smaller parts. A rectangle is divided into a top bar (the whole) and two bottom boxes (the parts). If you know the two parts, you add to find the whole. If you know the whole and one part, you subtract.

Why is it important for kids to know that addition can undo subtraction?

It allows them to check their work and solve more complex problems. If a student solves a subtraction problem and isn't sure, they can add their answer to the amount taken away to see if they get the starting total. It builds mathematical confidence.

How can active learning help students understand the relationship between operations?

Active learning strategies like role-playing 'The Undoer' make the abstract concept of an 'inverse relationship' concrete. When students physically move objects to build a sum and then remove them to return to the start, they are seeing the math in action. This kinetic experience makes the logic of fact families much more memorable than just writing them on a worksheet.