Mathematics · 2nd Grade

Active learning ideas

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.

• Common Core State Standards
• CCSS.Math.Content.2.OA.B.2

• 15–35 min
• Pairs → Whole Class
• 3 activities

Activity 01

• 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.

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...'.

What to look for

Present students with a problem like 7 + 6. Ask them to write down the strategy they used to solve it (e.g., doubles, near doubles, making a ten, counting on) and show their work. Review responses to identify students who rely on rote counting versus strategy use.

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

Activity 02

• 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.

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.

What to look for

Pose the question: 'How does knowing that 8 + 8 = 16 help you solve 8 + 9?' Facilitate a whole-class discussion where students explain their reasoning, encouraging them to use vocabulary like 'near doubles' and 'one more'.

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

Activity 03

• Think-Pair-Share
• 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?

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.

What to look for

Give students two problems: 13 - 5 and 6 + 8. Ask them to solve each problem and then write one sentence explaining how the two problems are related. Look for understanding of inverse operations.

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

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

• 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.

  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.

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

  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.

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

  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.

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Methods used in this brief

• Think-Pair-Share
• Gallery Walk