Mental Maths: Quick Adding and Subtracting

Active learning helps students build speed and confidence in mental math by engaging multiple senses and movement. For quick adding and subtracting to 20, physical games and partner work make abstract strategies visible and memorable, turning calculations into something students can see, hear, and do together.

• 1st Class
• Foundations of Mathematical Thinking
• 4 activities
• 15 min–30 min

Learning Objectives

1. Calculate the sum of two single-digit numbers using a counting-on strategy.
2. Identify the strategy used to add 10 to any single-digit number.
3. Demonstrate how to use doubles facts to solve near-double addition problems.
4. Explain the relationship between addition and subtraction using fact families within 20.
5. Compare the efficiency of different mental addition strategies for numbers up to 20.

Think-Pair-Share

⏱ 20 min·Pairs

Pairs: Make Ten Snap

Partners hold cards with numbers to 10. They snap pairs summing to 10 and explain the strategy, like '8 needs 2'. Switch roles after 10 rounds and record three new pairs.

Prepare & details

How can you add small numbers quickly in your head?

Facilitation Tip: During Pairs: Make Ten Snap, circulate and listen for students verbalizing the ‘make 10’ step aloud as they play.

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

Think-Pair-Share

⏱ 30 min·Small Groups

Small Groups: Doubles Relay

Form lines of 4-5 students. Teacher calls a double fact; first student solves aloud and tags next for a near double. Group celebrates correct chains and discusses strategies used.

Prepare & details

What trick can you use when adding any number to 10?

Facilitation Tip: For Doubles Relay, position yourself near the back of the line to quickly observe and correct any missteps in doubling.

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

Think-Pair-Share

⏱ 25 min·Whole Class

Whole Class: Counting On Chant

Students stand in a circle. Teacher starts a problem like 12 + 4; class counts on chorally: '13, 14, 15, 16'. Rotate leaders to model from larger number.

Prepare & details

Can you use doubles, like 4 + 4, to help you work out 4 + 5?

Facilitation Tip: Lead the Counting On Chant by modeling strong, rhythmic counting and pausing to let students echo back the next number.

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

Think-Pair-Share

⏱ 15 min·Individual

Individual: Strategy Journal

Each student solves 10 problems on a worksheet, notes the strategy used (e.g., make 10), and draws a quick picture. Share one with a partner afterward.

Prepare & details

How can you add small numbers quickly in your head?

Facilitation Tip: When students complete their Strategy Journal, read their written strategies and add brief, encouraging feedback in the margin.

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 strategies explicitly, then embed them into games where speed and accuracy matter. Use partner talk and peer modeling to normalize flexible thinking. Avoid teaching counting from one as the default, as it slows down fluent calculation. Research shows that children who learn to use derived facts and known relationships become more confident and accurate over time.

What to Expect

Successful learning looks like students using efficient strategies such as counting on, making 10, or doubling without relying on counting from one. They explain their thinking clearly and apply these strategies flexibly across different problems, showing fluency and confidence in their calculations.

Watch Out for These Misconceptions

Common Misconception

During Pairs: Make Ten Snap, watch for students counting both cards from one instead of scanning for pairs that make ten.

What to Teach Instead

Prompt pairs to say the two numbers aloud, then decide together if their sum is ten before snapping. Model this language during the first round.

Common Misconception

During Doubles Relay, watch for students believing that doubles facts only produce even totals.

What to Teach Instead

Ask each group to show 5 + 6 on their fingers and talk through how it equals double 5 plus one, reinforcing near doubles with concrete models.

Common Misconception

During Counting On Chant, watch for students always counting back to subtract instead of using related facts.

What to Teach Instead

Pause the chant to ask, ‘What plus 6 equals 14?’ and have students respond with 8, linking subtraction to known addition facts during the activity.

Assessment Ideas

Quick Check

After Pairs: Make Ten Snap, present three problems on the whiteboard (e.g., 6 + 7, 9 + 3, 8 + 5). Ask students to write the answer and the strategy they used on mini-whiteboards. Review responses to identify who still counts from one or struggles with near doubles.

Exit Ticket

After Doubles Relay, give each student a card with a problem like ‘Use doubles to solve 8 + 7’. Ask them to write the doubles fact (8 + 8 = 16) and the answer (15), then collect these to check understanding of near doubles.

Discussion Prompt

During Counting On Chant, pose the question, ‘What is the quickest way to add 9 to any number?’ Facilitate a class discussion where students share strategies, focusing on ‘add 10, subtract 1’. Record their ideas on the board and ask volunteers to explain why it works.

Extensions & Scaffolding

• Challenge early finishers to create their own ‘make 10’ or ‘doubles’ cards for a class set.
• Scaffolding for struggling students: provide ten-frame mats or number lines during Doubles Relay to support visual tracking.
• Deeper exploration: invite students to invent their own ‘tricks’ for adding 9 (e.g., ‘add 10, subtract 1’) and share them in Counting On Chant.

Key Vocabulary

Counting On	A strategy where you start with the larger number and count up the smaller number of steps to find the sum.
Making Ten	A strategy that involves breaking down one number to make a ten with another number, then adding the remainder.
Doubles	Addition facts where both numbers being added are the same, like 5 + 5.
Near Doubles	Addition facts where the two numbers are close to each other, like 5 + 6, which can be solved using a doubles fact.
Fact Family	A set of related addition and subtraction facts that use the same three numbers, for example, 7 + 3 = 10, 3 + 7 = 10, 10 - 7 = 3, and 10 - 3 = 7.