Mathematics · 2nd Grade · The Power of Ten: Building Place Value and Fluency · Weeks 1-9

Adding and Subtracting within 20 Fluently

Developing flexible strategies for adding and subtracting within 20 using properties of operations and mental math.

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

About This Topic

Fluency with addition and subtraction within 20 is one of the most important computational goals of second grade in the US K-12 framework. Students are expected to go beyond counting on fingers and develop genuine automaticity through flexible, strategy-based thinking. This topic targets that shift: rather than memorizing isolated facts, students build a web of relationships among numbers so they can choose the most efficient path to an answer.

Key strategies include doubles facts (6+6=12), near-doubles (6+7 is one more than 6+6), making a ten (8+5: move 2 from 5 to make 10+3=13), and counting on from the larger number. Students also begin to see that addition and subtraction are inverse operations, which deepens both sets of facts simultaneously. The CCSS standard 2.OA.B.2 sets the expectation that students know all sums to 20 from memory by end of second grade.

Active learning accelerates this fluency because students articulate strategy choices aloud, compare approaches with partners, and defend their reasoning. When classmates explain why near-doubles work, the relationship between quantities becomes far more durable than repeated drill.

Key Questions

1. Explain how knowing doubles facts can help solve near doubles addition problems.
2. Justify why different strategies lead to the same result if the logic is sound.
3. Differentiate between counting on and making a ten as strategies for addition.

Learning Objectives

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

Before You Start

Counting and Cardinality

Why: Students need a solid understanding of number sequence and quantity to develop addition and subtraction strategies.

Introduction to Addition and Subtraction Concepts

Why: Students should have prior experience with the basic meaning of addition as joining and subtraction as separating quantities.

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.

Watch Out for These Misconceptions

Common Misconception

Near-doubles means adding one more to the whole sum, so 6+7 = 12+2 = 14.

What to Teach Instead

Near-doubles means one addend is one more, so the sum is one more than the doubles fact: 6+6=12, so 6+7=13. Pair-sharing reveals this error quickly because students hear each other's reasoning and notice the step that went wrong.

Common Misconception

Making a ten only works when one number is 9 or 8.

What to Teach Instead

Any pair where the numbers sum to more than 10 can use make-a-ten. Students discover this through hands-on ten-frame work with various combinations.

Common Misconception

Counting on is the best strategy for every problem.

What to Teach Instead

Counting on from 4 to get to 4+9 means nine counts, which is slow and error-prone. Strategy fluency means choosing the most efficient path. Gallery Walk discussions make this trade-off visible and concrete.

Active Learning Ideas

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.

15 min·Pairs

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.

35 min·Small Groups

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?

20 min·Pairs

Real-World Connections

• Cashiers at a grocery store use addition and subtraction facts within 20 to quickly calculate change for small purchases, like buying two items costing $7 and $6.
• Construction workers might need to add or subtract lengths of materials up to 20 feet, for example, determining if they have enough of a 15-foot pipe to cut two 7-foot sections.

Assessment Ideas

Quick Check

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.

Discussion Prompt

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'.

Exit Ticket

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.

Frequently Asked Questions

What does math fluency mean in 2nd grade?

Fluency means students can solve addition and subtraction facts within 20 accurately, efficiently, and flexibly. It goes beyond memorization to include knowing why strategies work and choosing the best approach for a given problem. CCSS 2.OA.B.2 expects students to know all sums to 20 by the end of second grade.

How do near-doubles help kids add faster?

Near-doubles use a doubles fact students already know as a shortcut. If 7+7=14, then 7+8 must be one more: 15. This reduces a new problem to a quick adjustment rather than a full calculation. It is one of the fastest strategies once doubles facts are secure.

What is the make-a-ten strategy for addition?

Make-a-ten involves decomposing one addend to complete a group of ten, then adding the remainder. For 8+6, move 2 from the 6 to the 8 to get 10+4=14. The strategy works because tens are easy to add mentally and reflects the structure of our base-ten number system.

How does active learning help students become fluent with math facts?

When students explain strategies to partners, defend choices in discussions, and compare approaches in games, they engage with the reasoning behind facts rather than rote repetition. This builds durable, flexible recall. Research consistently shows that strategy-based practice produces stronger long-term fluency than timed drill alone.