Mathematics · Grade 1 · Operations and Algebraic Thinking · Term 2

Addition Strategies: Counting On

Moving from counting all to using the 'counting on' strategy for addition within 20.

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

About This Topic

Addition and subtraction in Grade 1 move beyond simple counting to more efficient mental strategies. The Ontario curriculum encourages students to use 'derived facts,' such as using doubles (5+5=10) to solve near-doubles (5+6=11) or 'making ten.' These strategies help students develop computational fluency and a flexible understanding of how numbers work together. It is about building a toolkit of methods rather than just memorizing facts.

In our multicultural classrooms, we can use stories and games from various traditions to practice these operations. For example, using a Rekenrek (an abacus-style tool often used in Canadian schools) allows students to see the 5-and-10 structure clearly. This topic comes alive when students can physically model the patterns and share their unique 'math secrets' for how they solved a problem with their peers.

Key Questions

1. Explain how counting on is more efficient than counting all objects for addition.
2. Compare counting on from the first number versus counting on from the larger number.
3. Predict how knowing 3 + 7 helps you solve 7 + 3.

Learning Objectives

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

Before You Start

Counting to 20

Why: Students need to be able to accurately count forwards to at least 20 to apply the 'counting on' strategy.

Addition: Counting All

Why: Students should have prior experience with finding sums by counting all objects to understand the transition to a more efficient strategy.

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).

Watch Out for These Misconceptions

Common Misconception

Students believe subtraction always means 'taking away' and cannot be solved by 'counting on.'

What to Teach Instead

Use a number line to show that subtraction is also the 'difference' or distance between two numbers. Active games where students jump from 8 to 12 help them see that 12 minus 8 can be solved by adding 4.

Common Misconception

Students may try to memorize facts without understanding the underlying relationship.

What to Teach Instead

When a student gets an answer wrong, ask them to model it with counters. Peer discussion often helps surface the error, as students explain the logic of the strategy rather than just the result.

Active Learning Ideas

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.

20 min·Pairs

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.

30 min·Small Groups

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.

15 min·Pairs

Real-World Connections

• When a baker is decorating a cake with 8 candles and needs to add 5 more, they can count on from 8 (9, 10, 11, 12, 13) to quickly find the total of 13 candles.
• A construction worker building a wall might lay 12 bricks and then need to add 6 more. They can count on from 12 (13, 14, 15, 16, 17, 18) to know they have laid 18 bricks.

Assessment Ideas

Quick Check

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.

Discussion Prompt

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.

Exit Ticket

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.

Frequently Asked Questions

What are 'derived facts' in Grade 1 math?

Derived facts are when a student uses a known fact to solve an unknown one. For example, if a student knows 10 + 10 = 20, they can derive that 9 + 10 = 19. This is a key focus of the Ontario curriculum.

Is it okay if my student still counts on their fingers?

Finger counting is a natural developmental stage. However, we want to gently move them toward more efficient strategies like 'counting on' from the larger number or using doubles, as these are faster and more reliable for larger numbers.

How can I help my child understand the connection between addition and subtraction?

Use 'fact families.' Show them that 3, 4, and 7 are related. If they know 3 + 4 = 7, they also know 7 - 4 = 3. Using physical objects like blocks to build and then break apart a tower makes this relationship visible.

How can active learning help students understand addition and subtraction?

Active learning strategies like 'Strategy Share-Out' encourage students to move beyond rote memorization. By explaining their thinking and hearing how others solve the same problem, they build a more flexible 'mental map' of numbers, which leads to better long-term retention.

From the Blog

15 Active Learning Strategies for Elementary School: A Teacher's Guide to Engagement

Discover 15 research-backed active learning strategies for elementary school that boost engagement, retention, and critical thinking in K-5 classrooms.