Adding and Subtracting within 20 Fluently

Active learning works for fluency within 20 because automaticity grows from repeated, purposeful practice with immediate feedback. When students explain their reasoning aloud, compare strategies, and test ideas through games, they move from counting to flexible thinking. This topic demands more than memorization, so hands-on and social activities create the mental pathways needed for quick recall.

• 2nd Grade
• Mathematics
• 3 activities
• 15 min–35 min

Learning Objectives

1. Compare the efficiency of 'making a ten' versus 'counting on' for addition problems within 20.
2. Explain how the commutative and associative properties of addition support flexible strategy use.
3. Justify the relationship between addition and subtraction facts within 20 by demonstrating inverse operations.
4. Calculate sums and differences within 20 using at least two different strategy-based methods.

Think-Pair-Share

⏱ 15 min·Pairs

Think-Pair-Share: Strategy Sort

Display a set of addition problems (e.g., 7+8, 6+6, 9+4) on the board. Each student privately selects a strategy and solves, then pairs compare which strategy each used and why. Pairs share one disagreement or insight with the whole class.

Prepare & details

Explain how knowing doubles facts can help solve near doubles addition problems.

Facilitation Tip: During Think-Pair-Share: Strategy Sort, circulate and listen for precise vocabulary, gently modeling language like 'I used the make-a-ten strategy because...'.

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

Gallery Walk

⏱ 35 min·Small Groups

Gallery Walk: Strategy Posters

Groups of three create a poster illustrating one strategy (doubles, near-doubles, make-a-ten, count on) with two example problems solved step by step. Post around the room; students rotate with sticky notes to leave a question or a 'this works for me because...' comment on each poster.

Prepare & details

Justify why different strategies lead to the same result if the logic is sound.

Facilitation Tip: During Gallery Walk: Strategy Posters, position yourself so you can observe which strategies students linger on, noticing which methods are becoming automatic.

Setup: Wall space or tables arranged around room perimeter

Materials: Large paper/poster boards, Markers, Sticky notes for feedback

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Collaborative Problem-Solving

⏱ 20 min·Pairs

Partner Game: Fact Family Flip

Each pair gets a deck of cards (1-10). Flip two cards, and both partners race to state the addition fact and its related subtraction fact. The partner who gives a strategy name (not just the answer) earns a bonus point. Debrief: which strategy came up most often?

Prepare & details

Differentiate between counting on and making a ten as strategies for addition.

Facilitation Tip: During Partner Game: Fact Family Flip, watch for pairs who quickly verbalize the fact family relationship before flipping cards, indicating growing fluency.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Teaching This Topic

Experienced teachers approach this topic by balancing strategy instruction with repeated practice. Avoid rushing to memorization before students can explain why 8 + 7 = 15 without counting. Use routines that require students to verbalize their thinking, such as explaining a strategy to a partner or labeling their work with the method used. Research shows that students who articulate their reasoning develop stronger connections between facts and can transfer strategies to new problems.

What to Expect

Successful learning looks like students choosing efficient strategies without counting by ones, explaining their reasoning using terms like doubles, near-doubles, and making a ten, and recognizing relationships between facts. They should move smoothly between addition and subtraction, showing confidence and speed in their work.

Watch Out for These Misconceptions

Common Misconception

During Think-Pair-Share: Strategy Sort, watch for students who incorrectly describe near-doubles as adding an extra whole sum, such as saying 6 + 7 equals 12 + 2 = 14.

What to Teach Instead

Prompt them to revisit their doubles fact first: 'What is 6 + 6? Now, what is one more than that?' Have them model this on their sorting mat with counters to see the correct near-double pattern.

Common Misconception

During Gallery Walk: Strategy Posters, watch for students who believe making a ten only works with numbers like 9 or 8.

What to Teach Instead

Ask them to test their idea with combinations like 7 + 6 or 5 + 8 on their ten-frame, physically moving counters to see that any sum over 10 can use this strategy.

Common Misconception

During Partner Game: Fact Family Flip, watch for students who default to counting on for every problem.

What to Teach Instead

Challenge them to solve the same card using a different strategy, such as making a ten, and compare which method was faster. Discuss why counting on is less efficient for larger numbers.

Assessment Ideas

Quick Check

After Think-Pair-Share: Strategy Sort, present a problem like 7 + 6 and ask students to write the strategy they used and show their work on a sticky note. Review responses to identify students who rely on rote counting versus those who use a strategy.

Discussion Prompt

During Gallery Walk: Strategy Posters, pose the question: 'How does knowing that 8 + 8 = 16 help you solve 8 + 9?' Circulate and listen for explanations using the term 'near doubles' and the idea of 'one more', noting who can articulate the relationship.

Exit Ticket

After Partner Game: Fact Family Flip, give students two problems: 13 - 5 and 6 + 8. Ask them to solve each and write one sentence explaining how the two problems are related. Look for understanding of inverse operations in their responses.

Extensions & Scaffolding

• Challenge: Give students a set of ten mixed facts within 20 and time them solving them with their chosen strategy. Ask them to find a more efficient path for any they count by ones.
• Scaffolding: Provide ten-frames and counters for students who still count on fingers, guiding them to visualize making a ten or using near doubles.
• Deeper: Invite students to create their own 'strategy guide' poster that explains when to use each method, using examples they choose.

Key Vocabulary

doubles facts	Addition facts where both addends are the same number, such as 5 + 5 = 10. Knowing these helps solve similar problems.
near doubles	Addition facts that are close to doubles facts, like 5 + 6. You can solve them by using the known doubles fact (5 + 5) and adding one more.
making a ten	A strategy for addition where you break apart one addend to make a ten with the other addend, then add the remaining part. For example, 8 + 5 becomes 8 + 2 + 3, which is 10 + 3 = 13.
counting on	A strategy for addition where you start with the larger number and count up the amount of the smaller number. For example, to solve 7 + 4, you start at 7 and count 8, 9, 10, 11.
inverse operations	Operations that undo each other, like addition and subtraction. For example, 7 + 3 = 10 and 10 - 3 = 7 show this relationship.