Addition Strategies: Making Ten and Doubles

Active learning helps students connect abstract number relationships to concrete experiences, which is essential for grasping the inverse relationship between addition and subtraction. This topic benefits from hands-on exploration because students need to physically manipulate numbers to see how making ten and doubles strategies simplify calculations and reduce memory load.

• Grade 2
• Mathematics
• 3 activities
• 15 min–25 min

Learning Objectives

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

Role Play

⏱ 20 min·Pairs

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.

Prepare & details

Analyze how 'making ten' simplifies addition problems.

Facilitation Tip: For The Subtraction Mystery, circulate and listen for students who justify their missing addend solutions by referencing known addition facts, as this indicates they are bridging operations.

Setup: Open space or rearranged desks for scenario staging

Materials: Character cards with backstory and goals, Scenario briefing sheet

• Apply
• Analyze
• Evaluate
• Social Awareness
• Self-Awareness

Inquiry Circle

⏱ 25 min·Small Groups

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.

Prepare & details

Compare the efficiency of using doubles versus counting on for certain sums.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Think-Pair-Share

⏱ 15 min·Pairs

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.

Prepare & details

Explain why knowing 6+6 helps you solve 6+7.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Teaching This Topic

Teachers should avoid presenting addition and subtraction as separate skills. Instead, use consistent language like 'parts' and 'whole' across all activities so students see the operations as interconnected. Research suggests that students who verbalize their strategies while solving problems develop stronger number sense and retention.

What to Expect

Successful learning looks like students confidently applying making ten and doubles strategies to solve addition problems. They should also articulate how these strategies connect to subtraction using terms like 'fact families' and 'part-part-whole'. By the end, students will fluently switch between operations to find unknown values.

Watch Out for These Misconceptions

Common Misconception

During the Number Reverser role play, watch for students who reverse the order of numbers when acting out subtraction scenarios, such as giving 3 candies when the problem is 5 - 3.

What to Teach Instead

Prompt students to use the counters to model the starting amount first, then physically remove the second amount, emphasizing that the order of removal matches the problem.

Common Misconception

During the Think-Pair-Share activity, watch for students who see addition and subtraction as unrelated and rely only on addition facts to solve missing addend problems like 8 + ? = 12.

What to Teach Instead

Have students use the counters from the Fact Family Houses to model 12 as the whole, then separate 8 as one part to find the missing part, explicitly naming it as subtraction (12 - 8).

Assessment Ideas

Quick Check

After the Number Reverser role play, present students with a quick set of problems (e.g., 9+3, 7+7, 8+5, 6+7) and ask them to circle the strategy they used for each, then write the answer.

Discussion Prompt

After the Think-Pair-Share activity, ask students how knowing 5+5=10 helps them solve 5+6, then have them explain their reasoning to a partner before sharing with the class.

Exit Ticket

During the Fact Family Houses activity, give each student an exit ticket with a problem like 7+5 and ask them to show two ways to solve it: one using making ten and one using near doubles, with the final sum for each.

Extensions & Scaffolding

• Challenge students to create their own word problems using the fact families they built in the Fact Family Houses activity.
• For students who struggle, provide number lines during the Number Reverser activity so they can visualize the movement forward for addition and backward for subtraction.
• Deeper exploration: Ask students to generate a rule for when making ten is the most efficient strategy compared to using doubles or near doubles.

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.