Mathematics · Grade 1

Active learning ideas

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.

• Ontario Curriculum Expectations
• 1.OA.C.5

• 15–30 min
• Pairs → Whole Class
• 3 activities

Activity 01

• 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.

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?'

What to look for

Present students with a series of addition problems (e.g., 7 + 5, 9 + 3). Ask them to solve each problem by showing their work using the 'counting on' strategy, either by drawing jumps on a number line or writing the sequence of numbers they count.

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

Activity 02

• 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.

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.

What to look for

Pose the question: 'Is it faster to count on from the smaller number or the larger number? Why?' Have students discuss with a partner and then share their reasoning with the class, using examples like 4 + 9 and 9 + 4.

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

Activity 03

• 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.

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.

What to look for

Give each student a card with two addition problems: 6 + 8 and 8 + 6. Ask them to solve both using the 'counting on' strategy and write one sentence explaining if the strategy helped them solve the second problem faster than the first.

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

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

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

  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.

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

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

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Methods used in this brief

• Peer Teaching
• Stations Rotation
• Think-Pair-Share