Mathematics · Primary 2 · Advanced Number Concepts · Semester 2

Mental Addition and Subtraction Strategies

Students develop and apply mental strategies for adding and subtracting 2- and 3-digit numbers, including making tens, compensating, and using known facts.

• MOE Syllabus Outcomes
• MOE: Numbers and Algebra - P2
• MOE: Whole Numbers - P2

About This Topic

Mental addition and subtraction strategies help Primary 2 students compute with 2- and 3-digit numbers without writing. They learn making tens, for example 38 + 7 becomes (40 - 2) + 7 = 43, compensation such as 65 + 49 as 65 + 50 - 1 = 114, and linking subtraction to known addition facts like 72 - 28 by finding what adds to 28 to make 72.

These methods fit the MOE Numbers and Algebra strand for whole numbers. Students build fluency in partitioning, place value, and number bonds, skills vital for daily tasks like handling money or estimating quantities. Regular practice develops quick thinking and confidence in multi-step problems.

Classroom number talks encourage students to share approaches, revealing efficient paths. Active learning benefits this topic greatly. Pair games with manipulatives make strategies visible and fun, while group challenges promote peer teaching. This turns abstract mental work into concrete, collaborative practice that sticks.

Key Questions

1. How does making a ten or hundred make addition easier?
2. What is the compensation strategy, and when is it useful?
3. How can we use known addition facts to solve subtraction problems mentally?

Learning Objectives

• Calculate the sum or difference of two 2-digit numbers using the making tens strategy.
• Apply the compensation strategy to mentally add or subtract 2-digit numbers efficiently.
• Explain how to use known addition facts to derive answers for subtraction problems involving 2- and 3-digit numbers.
• Compare the efficiency of different mental addition and subtraction strategies for a given problem.
• Solve word problems involving 2- and 3-digit addition and subtraction using mental strategies.

Before You Start

Addition and Subtraction within 100

Why: Students need a solid foundation in basic addition and subtraction facts and concepts within 100 before applying mental strategies to larger numbers.

Place Value to Hundreds

Why: Understanding place value is crucial for strategies like making tens or hundreds and for compensating correctly.

Number Bonds

Why: The ability to see numbers as parts and wholes is fundamental to strategies like making tens and partitioning numbers.

Key Vocabulary

Making Tens	A strategy where you adjust one number to make a multiple of ten, then add or subtract the remaining part. For example, 47 + 5 becomes 47 + 3 + 2.
Compensation	A strategy where you adjust one number to make it easier to calculate, then adjust the answer to compensate for the change. For example, 65 + 49 becomes 65 + 50 - 1.
Known Facts	Addition or subtraction facts that students have memorized or can quickly recall, such as doubles (e.g., 7 + 7) or facts that make ten (e.g., 6 + 4).
Mental Math	Performing calculations in your head without using written methods or a calculator.

Watch Out for These Misconceptions

Common Misconception

Always start with ones column like written addition.

What to Teach Instead

Mental strategies prioritize flexible partitioning, such as making tens first for speed. Pair discussions during games help students test and compare approaches, seeing why rigid steps slow them down.

Common Misconception

Compensation only works with 9s or 1s.

What to Teach Instead

It applies to any compatible pairs, like 47 + 28 as 47 + 30 - 2. Small group sorting tasks reveal broad patterns, building confidence through shared examples.

Common Misconception

Subtraction requires counting back each time.

What to Teach Instead

Relating to known addition facts is quicker, like 50 - 19 as 19 + 31 = 50. Number talks in whole class expose this, as peers model efficient thinking.

Active Learning Ideas

Pairs: Strategy Swap Game

Partners draw problem cards like 56 + 37. One solves mentally, explains the strategy used, such as making tens. Switch roles after three problems and compare methods. End with partners creating their own problem.

20 min·Pairs

Small Groups: Compensation Hunt

Provide cards with addition problems suited for compensation. Groups sort them into 'easy to compensate' and 'other strategies,' solve each, and justify choices. Share one group example with the class.

30 min·Small Groups

Whole Class: Mental Math Number Talk

Pose problems like 81 - 29 on the board. Students use signals to share strategies silently, then volunteers explain aloud. Record multiple methods on chart paper for reference.

25 min·Whole Class

Individual: Strategy Journal Reflection

Students solve five mixed problems mentally, note the strategy chosen and why. Draw quick sketches if needed, like tens frames. Share one entry with a partner.

15 min·Individual

Real-World Connections

• Cashiers at a supermarket use mental math to quickly calculate change for customers, often using compensation strategies when dealing with prices like $4.95.
• Parents planning a family trip might mentally estimate travel times or costs, using strategies like making tens to quickly add distances or expenses.

Assessment Ideas

Quick Check

Present students with a series of addition and subtraction problems (e.g., 58 + 7, 92 - 19). Ask them to write down the strategy they used for each problem (e.g., 'making tens', 'compensation', 'known facts') and their answer.

Discussion Prompt

Pose the problem: 'Sarah has 35 stickers and buys 18 more. How many does she have now?' Ask students to share how they would solve this mentally. Prompt them with: 'Could you use compensation? How would that work? What if you made a ten instead?'

Exit Ticket

Give each student a card with a problem like '63 - 27'. Ask them to write the answer and then explain in one sentence how they found it using a mental math strategy.

Frequently Asked Questions

How do you teach making tens for mental addition?

Start with concrete tools like tens frames or base-10 blocks to show partitioning, such as 28 + 6 as (30 - 2) + 6. Progress to visuals, then pure mental practice in pairs. Number talks let students share real examples, reinforcing the 'why' behind easier tens.

What is the compensation strategy for Primary 2?

Compensation rounds numbers to friendlier ones then adjusts, like 34 + 29 as 34 + 30 - 1 = 63. Teach it for additions near tens or hundreds. Practice with word problems involving shopping totals, helping students see its real-world speed over counting all.

How can active learning help students master mental strategies?

Active methods like pair relays and group card sorts make strategies tangible through talk and movement. Manipulatives visualize partitioning, while peer sharing during number talks builds confidence and exposes varied paths. This engagement reduces anxiety, boosts retention, and turns practice into play over rote drills.

How to address errors in mental subtraction?

Use known facts first, like 64 - 27 by thinking 27 + 37 = 64. Quick checks with manipulatives correct place value slips. Daily choral responses in class normalize mistakes as learning steps, with students self-correcting through partner feedback.