Foundations of Mathematical Thinking · 1st Class · Addition of Numbers to 20 · Autumn Term

Mental Maths: Quick Adding and Subtracting

Develop a repertoire of mental strategies for addition and subtraction of larger numbers, decimals, and simple fractions.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Number - N.1.1
• NCCA: Junior Cycle - Strand 3: Number - N.1.2

About This Topic

Mental Maths: Quick Adding and Subtracting builds fluency in addition and subtraction to 20 for 1st Class students. They master strategies like counting on from the larger number, making 10 (such as 7 + 5 by thinking 7 + 3 = 10, then +2 more), and doubles with near doubles (6 + 6 = 12, so 6 + 7 = 13). These connect to unit key questions on head calculations, tricks with 10, and using doubles, supporting NCCA Number strand standards N.1.1 and N.1.2 in the Autumn term.

Within Foundations of Mathematical Thinking, this topic fosters number sense and flexible strategies, essential for progressing to larger numbers, decimals, and simple fractions. Students gain confidence in part-whole relationships and fact families, skills that underpin problem-solving across maths strands.

Active learning suits this topic perfectly. Partner games and group relays provide repeated practice in a fun, social setting, embedding strategies through play. Movement-based tasks and strategy-sharing discussions offer immediate feedback, helping students choose and refine methods independently.

Key Questions

1. How can you add small numbers quickly in your head?
2. What trick can you use when adding any number to 10?
3. Can you use doubles, like 4 + 4, to help you work out 4 + 5?

Learning Objectives

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

Before You Start

Number Recognition and Counting to 20

Why: Students must be able to recognize numbers up to 20 and count accurately to use strategies like counting on.

Addition to 10

Why: A solid understanding of basic addition facts within 10 is foundational for extending to numbers up to 20 and using strategies like making ten.

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.

Watch Out for These Misconceptions

Common Misconception

Always count fingers from 1 for addition.

What to Teach Instead

Model counting on from the larger number with pair talks. Students compare times for 1+8 versus 8+1, seeing efficiency gains through timed partner challenges.

Common Misconception

Doubles only work for even answers.

What to Teach Instead

Use near doubles visuals like ten frames in small groups. Hands-on manipulation shows 5+6 as double 5 plus one, building flexible thinking via group sharing.

Common Misconception

Subtraction means always count back.

What to Teach Instead

Introduce related facts (14-6=8 since 6+8=14) in games. Active relay races pair addition and subtraction, helping students connect operations.

Active Learning Ideas

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.

20 min·Pairs

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.

30 min·Small Groups

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.

25 min·Whole Class

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.

15 min·Individual

Real-World Connections

• A shopkeeper calculating the total cost of two items, like a €5 toy car and a €3 teddy bear, by quickly adding them in their head.
• A child counting the total number of sweets they have if they have 7 red sweets and 5 blue sweets, using a strategy like making ten (7 + 3 = 10, plus 2 more).
• A baker checking if they have enough ingredients for two batches of cookies, where one batch needs 6 eggs and the second needs 7 eggs, using near doubles (6 + 6 = 12, so 6 + 7 = 13).

Assessment Ideas

Quick Check

Present students with a series of addition problems on a whiteboard (e.g., 8 + 5, 7 + 7, 9 + 10). Ask students to write down the answer and the strategy they used to solve it on a mini-whiteboard. Review responses to identify students needing more support with specific strategies.

Exit Ticket

Give each student a card with a problem like 'Use doubles to help you solve 6 + 7'. Ask them to write the doubles fact they used and then the answer. Collect these to gauge understanding of the near doubles strategy.

Discussion Prompt

Pose the question: 'What is the quickest way to add 9 to any number?' Facilitate a class discussion where students share their strategies, focusing on the 'add 10, subtract 1' method. Encourage them to explain why it works.

Frequently Asked Questions

How do you teach making 10 for mental addition?

Start with ten frames or bead strings to visualise complements to 10. Practice with flashcards where students call the pair (e.g., see 7, say 3). Extend to problems like 8+6 by partitioning 6 as 2+4, making 10+4=14. Daily 5-minute partner quizzes reinforce automaticity.

What are common mental math errors in 1st class?

Errors include starting from zero or ignoring larger addend. Address with explicit modelling and error games where pairs spot mistakes in sample work. Visual aids like number lines help, and choral responses build consensus on correct paths.

How does active learning help mental maths strategies?

Games like snap and relays make practice joyful and repetitive, embedding facts without rote drill. Partner explanations during activities clarify thinking, while movement boosts engagement and memory. Class data from challenges shows progress, motivating students to refine methods collaboratively.

How to extend mental strategies to subtraction?

Link via fact families: if 9+7=16, then 16-7=9. Use part-whole boxes in pairs for decomposition. Games reversing addition problems build subtraction fluency, preparing for decimals by emphasising partitioning.