Addition Strategies: Counting On

Active learning lets students move beyond abstract symbols to see addition as a real process they control. When they physically count on with tools like number lines or counters, they build number sense that paper-and-pencil drills alone cannot provide.

• Grade 1
• Mathematics
• 3 activities
• 15 min–30 min

Learning Objectives

1. Demonstrate the 'counting on' strategy to solve addition problems within 20.
2. Compare the efficiency of 'counting on' versus 'counting all' for addition problems.
3. Explain the commutative property of addition using the 'counting on' strategy.
4. Calculate sums within 20 by applying the 'counting on' strategy from the larger addend.

Peer Teaching

⏱ 20 min·Pairs

Peer Teaching: Strategy Share-Out

After solving a problem like 8+7, students pair up to show two different ways to find the answer (e.g., one uses 'doubles plus one' and the other 'makes ten'). They then teach their partner's method to a second pair.

Prepare & details

Explain how counting on is more efficient than counting all objects for addition.

Facilitation Tip: During Peer Teaching: Strategy Share-Out, circulate and prompt students to ask clarifying questions like, 'How did you decide to start counting from the larger number?'

Setup: Presentation area at front, or multiple teaching stations

Materials: Topic assignment cards, Lesson planning template, Peer feedback form, Visual aid supplies

• Understand
• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

Stations Rotation

⏱ 30 min·Small Groups

Stations Rotation: The Strategy Lab

Set up stations focused on different strategies: a 'Doubles' station with dice, a 'Make Ten' station with ten-frames, and a 'Number Line' station. Students rotate and practice the specific strategy at each stop.

Prepare & details

Compare counting on from the first number versus counting on from the larger number.

Facilitation Tip: In Station Rotation: The Strategy Lab, set timers so each group rotates before attention fades, ensuring all students engage with multiple tools.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Think-Pair-Share

⏱ 15 min·Pairs

Think-Pair-Share: Fact Family Triangles

Give students three numbers (e.g., 3, 7, 10). They must work with a partner to find all the addition and subtraction sentences they can make, then share their 'family' with the class.

Prepare & details

Predict how knowing 3 + 7 helps you solve 7 + 3.

Facilitation Tip: For Think-Pair-Share: Fact Family Triangles, assign specific roles (e.g., 'explainer,' 'recorder') so all students contribute, especially those who hesitate to speak.

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

Teach counting on by modeling it aloud first, then gradually shifting responsibility to students. Avoid rushing to abstract symbols; let them verbalize the steps ('I start at 7, then add 5 more: 8, 9, 10, 11, 12'). Research shows this verbal rehearsal cements understanding. Also, rotate between visual, auditory, and kinesthetic approaches to reach all learners.

What to Expect

Successful learners will explain why counting on from the larger number is efficient, use visual or physical models to demonstrate the strategy, and show flexibility by applying the same method to different problem types like near-doubles and making ten.

Watch Out for These Misconceptions

Common Misconception

During Peer Teaching: Strategy Share-Out, watch for students who insist subtraction only means 'taking away.'

What to Teach Instead

Ask the pair to model a subtraction problem like 12 - 8 on a number line by jumping from 8 to 12, and have them explain the distance as the answer.

Common Misconception

During Station Rotation: The Strategy Lab, watch for students who memorize facts without understanding the 'counting on' process.

What to Teach Instead

Have them recount aloud with counters while a peer watches, then discuss why the method works for both 5 + 5 and 5 + 6.

Assessment Ideas

Quick Check

After Station Rotation: The Strategy Lab, present students with a series of addition problems (e.g., 7 + 5, 9 + 3) and ask them to show their work using the 'counting on' strategy on mini whiteboards.

Discussion Prompt

During Peer Teaching: Strategy Share-Out, pose the question, 'Is it faster to count on from the smaller number or the larger number? Why?' Have students discuss with a partner using examples like 4 + 9 and 9 + 4, then share reasoning with the class.

Exit Ticket

During Think-Pair-Share: Fact Family Triangles, give each student a card with two addition problems: 6 + 8 and 8 + 6. Ask them to solve both using 'counting on' and write one sentence explaining if the strategy helped them solve the second problem faster than the first.

Extensions & Scaffolding

• Challenge: Ask students to create their own word problems where counting on is the best strategy, then swap with a partner to solve.
• Scaffolding: Provide number lines with pre-marked starting points to reduce cognitive load for students still building automaticity.
• Deeper exploration: Introduce missing addend problems (e.g., 7 + _ = 12) where students must use counting on to find the unknown.

Key Vocabulary

counting on	An addition strategy where you start from one number and count up the amount of the second number without recounting the first number.
addend	The numbers that are added together to find a sum.
sum	The answer to an addition problem.
commutative property	The property that states that the order of addends does not change the sum (e.g., 3 + 7 = 7 + 3).