Mental Math Strategies
Use compensation, doubling, splitting and friendly numbers to calculate in your head.
Key idea
Use compensation, doubling, splitting and friendly numbers to calculate in your head.
In depth
Mental math uses structure: break numbers apart, make tens, double and halve, compensate. These work because of the properties of addition and multiplication.
Worked example
49 + 37: take 1 from 37 to make 50 + 36 = 86.
Real-world uses
- Working out 99 × 4 quickly
- Calculating tips and discounts without a calculator
- Checking change in a shop
Common mistake
Trying to hold too many digits in your head at once. Break the problem into parts.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Mental Math Strategies?
Use compensation, doubling, splitting and friendly numbers to calculate in your head. It is a topic at the beginner level in Arithmetic & Number Sense.
Where is Mental Math Strategies used in real life?
Real-world examples: Working out 99 × 4 quickly; Calculating tips and discounts without a calculator; Checking change in a shop.
What should I learn before Mental Math Strategies?
Make sure you are comfortable with Estimation, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Mental Math Strategies?
Trying to hold too many digits in your head at once. Break the problem into parts.
How can I practise Mental Math Strategies?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Mental Math Strategies?
Move on to Order of Operations next.
Related beginner topics in Arithmetic & Number Sense
- Counting & Cardinality – Assigning one number word to each object to find how many there are.
- Place Value – The value of a digit depends on its position: ones, tens, hundreds and so on.
- Number Line – A line where numbers are placed in order at equal spacing to compare and add them.
- Comparing Numbers – Use <, > and = to say which number is smaller, larger or equal.
- Ordering Numbers – Arranging numbers from least to greatest or the reverse.
- Even and Odd Numbers – Even numbers divide by 2 with no remainder; odd numbers leave remainder 1.