Mental Strategies in Maths for Grade 1 Students

Complete guide to mental strategies in maths: counting back, number bonds, compensation, doubles facts, and decomposing numbers with detailed explanations and examples.

Mental Strategies in Maths Overview
1 Introduction to Mental Maths
Mental Strategies in Maths Introduction
Five core mental maths strategies for addition and subtraction:
Definition:

Mental Strategies in Maths: Efficient methods for performing mathematical calculations in your head without using external tools or writing anything down

Counting Back
Move backward on number line from starting number
Number Bonds
Use addition facts to solve subtraction problems
Compensation
Adjust numbers to make calculation easier
Doubles Facts
Use known doubles for related problems
Decomposing
Break apart numbers into smaller parts
Core Mathematical Concepts:

Addition: Combining numbers to find a total

Subtraction: Taking away to find the difference

Inverse Operations: Addition and subtraction are opposite operations

Number Sense: Understanding how numbers relate to each other

Strategy Selection Process:
  1. Analyze the numbers: Look for patterns and relationships
  2. Choose the best method: Select the most efficient strategy
  3. Apply the technique: Follow the steps for chosen strategy
  4. Verify the answer: Check by adding or using another method
Key Mathematical Principles:

• Flexibility: Different problems may require different strategies

• Practice: Regular practice builds fluency and confidence

• Verification: Always check your answers

• Confidence: Start with easier problems and progress gradually

2 Counting Back Strategy
Counting Back Strategy
Moving backward on the number line to solve subtraction
Definition:

Counting Back: Starting from the minuend (first number) and counting backward by the number of steps equal to the subtrahend (second number)

Simple Example
8 - 3 = ?
8
←
7
←
6
←
5
Answer: 5
Advanced Example
15 - 6 = ?
15
←
14
←
13
←
12
←
11
←
10
←
9
Answer: 9
Counting Back Method:
  1. Start at the first number (minuend)
  2. Count backward one number at a time
  3. Count the same number of steps as the second number (subtrahend)
  4. The final number is your answer
Best for: Small numbers (1-5) being subtracted
Tip: Use fingers or mental imagery to keep track of steps
3 Number Bonds Strategy
Number Bonds Strategy
Using addition facts to solve subtraction problems
Definition:

Number Bonds: Understanding that addition and subtraction are inverse operations; knowing that if a + b = c, then c - a = b and c - b = a

Simple Example
9 - 4 = ?
Think: 4 + ? = 9 → Answer: 5
Advanced Example
13 - 7 = ?
Think: 7 + ? = 13 → Answer: 6
Number Bonds Method:
  1. Identify the subtraction problem: minuend - subtrahend = ?
  2. Rewrite as an addition problem: subtrahend + ? = minuend
  3. Solve the addition problem using known facts
  4. The answer is the same for both problems
Best for: Problems with known addition facts
Tip: Practice addition facts regularly to strengthen number bonds
Advanced Mental Strategies in Maths
a + b = c ↔ c - a = b
Inverse Relationship
4 Compensation Strategy
Definition:

Compensation: Adjusting numbers to make calculation easier, then adjusting the answer accordingly

Simple Example
12 - 9 = ?
Think: 12 - 10 = 2, then 2 + 1 = 3
Answer: 3
Advanced Example
16 - 8 = ?
Think: 16 - 10 = 6, then 6 + 2 = 8
Answer: 8
Compensation Method:
  1. Round the subtracted number up to the nearest ten
  2. Subtract the rounded number from the first number
  3. Add back the difference between the rounded number and the original
  4. The result is your answer
Best for: Numbers close to 10 (8, 9, 11, 12)
Tip: Remember to add back the difference!
5 Doubles Facts Strategy
Definition:

Doubles Facts: Using known doubles (like 6 + 6 = 12) to solve related subtraction problems

Simple Example
10 - 5 = ?
Think: 5 + 5 = 10, so 10 - 5 = 5
Answer: 5
Advanced Example
14 - 7 = ?
Think: 7 + 7 = 14, so 14 - 7 = 7
Answer: 7
Doubles Facts Method:
  1. Recognize if the subtraction involves a double
  2. Recall the corresponding addition fact
  3. Apply the inverse relationship
  4. The answer is the same as the double number
Best for: Doubles subtraction (like 12-6, 16-8, 18-9)
Tip: Memorize doubles facts (1+1 to 10+10) for quick recall
6 Decomposing Strategy
Definition:

Decomposing: Breaking apart the number being subtracted into smaller, easier-to-manage parts

Simple Example
13 - 6 = ?
Think: 6 = 3 + 3
So: 13 - 3 - 3 = 10 - 3 = 7
Answer: 7
Advanced Example
15 - 8 = ?
Think: 8 = 5 + 3
So: 15 - 5 - 3 = 10 - 3 = 7
Answer: 7
Decomposing Method:
  1. Break the subtracted number into smaller parts
  2. Subtract each part one at a time
  3. Continue until you reach the final answer
  4. Combine the results
Best for: Complex subtraction problems
Tip: Choose parts that are easy to subtract (like 5s and 2s)
Complete Mental Strategies in Maths Guide
Mental Maths = Understanding + Practice + Confidence
Success Formula
Key Mathematical Definitions:

Mental Maths: Calculating in your head without external tools

Number Bonds: Pairs of numbers that add up to a given total

Compensation: Adjusting numbers to make calculations easier

Decomposing: Breaking numbers into smaller parts

Mathematical Fluency: Ability to perform calculations quickly and accurately

Strategy Selection Guide:
  • Subtracting 1-3: Use counting back
  • Subtracting 4-5: Counting back or number bonds
  • Subtracting 6-7: Number bonds or decomposition
  • Subtracting 8-9: Compensation (think 10 and adjust)
  • Doubles: Use doubles facts (12-6, 16-8)
Mathematical Properties:

Commutative Property: a + b = b + a (applies to addition)

Associative Property: (a + b) + c = a + (b + c) (applies to addition)

Inverse Operations: Addition and subtraction are opposite operations

Identity Element: a + 0 = a, a - 0 = a

Key Insight: Mental maths builds number sense and computational fluency.
Strategy Selection: Choose the method that feels easiest for each problem.
Tip 1: Practice daily with simple problems before moving to harder ones.
Tip 2: Use visual aids like fingers or objects when learning new strategies.
Tip 3: Always verify your answer by adding the result to the subtracted number.
Tip 4: Focus on accuracy before trying to go faster.
Important Mathematical Rules:

• Commutative Property: Does NOT apply to subtraction (a - b ≠ b - a)

• Associative Property: Does NOT apply to subtraction

• Identity Property: a - 0 = a

• Inverse Operations: Addition and subtraction undo each other

Success Habits in Maths:
  1. Consistent Practice: 10-15 minutes daily
  2. Start Simple: Master basics before advancing
  3. Visualize: Use mental images or physical objects
  4. Check Answers: Verify by adding back
  5. Build Confidence: Celebrate small improvements
Weekly Practice Schedule:
  • Week 1-2: Focus on counting back strategy
  • Week 3-4: Introduce number bonds
  • Week 5-6: Practice compensation
  • Week 7-8: Work on doubles facts
  • Week 9-10: Combine all strategies
Understanding + Practice = Fluency
Mathematical Growth Equation
Common Mistakes in Mental Maths:

• Counting Errors: Miscounting steps when counting back

• Compensation Confusion: Forgetting to add back the difference

• Wrong Strategy: Using a complex method for simple problems

• No Verification: Not checking answers

Questions & Answers

Question: I get confused when doing 14 - 7. Should I use number bonds or counting back? Which is better for mental maths?

Answer: Both methods work well in mental maths, but 14 - 7 is a perfect example of a doubles fact! Since 7 + 7 = 14, then 14 - 7 = 7. This is often faster than counting back 7 steps. However, let's compare:

  • Counting Back: 14 → 13 → 12 → 11 → 10 → 9 → 8 → 7 (7 steps)
  • Number Bonds: 7 + ? = 14, so ? = 7
  • Doubles Fact: 7 + 7 = 14, so 14 - 7 = 7

The doubles fact is the quickest for mental maths! As you practice more, you'll recognize when problems involve doubles and can solve them instantly.

Question: How can I help my child develop mental maths strategies at home?

Answer: Here are effective ways to develop mental maths strategies at home:

  • Daily Routine: 10-15 minutes of focused practice each day
  • Real-Life Scenarios: "If we had 12 cookies and ate 5, how many are left?"
  • Games: Flashcards, dice games, or online math games
  • Physical Objects: Use toys, blocks, or fingers to visualize problems
  • Encouragement: Praise effort and celebrate progress

Keep sessions short and positive. The goal is building confidence and fluency in mental maths!

Question: What are the most important mental maths strategies for grade 1 students to master?

Answer: The most important mental maths strategies for grade 1 students are:

  • Number Bonds: Understanding addition and subtraction relationships
  • Counting Back: For subtraction with small numbers
  • Doubles Facts: Building fluency with known facts
  • Compensation: Making calculations easier by rounding
  • Decomposing: Breaking numbers into manageable parts

These foundational strategies prepare students for more complex mathematical thinking in later grades.