Mental Math

Research (from various studies in UK, US, New Zealand and Australia as wellclassroom

as a worldwide math survey in the 1990’s) shows better elementary maths

standards occur when:

  • the foundations of mental calculation and recall of number facts are established thoroughly before written methods are introduced
  • there is opportunity for daily oral and mental work to develop and secure students’ calculation strategies and rapid recall skills
  • involving students and maintaining their interest through appropriately demanding work including non-routine problems that require them to think for themselves

Teaching written procedures too early can prejudice learner’s chances of developing efficient ways of working with numbers ‘in their heads’. Mental calculation is founded on understanding place value and the knowledge of number facts. The vocabulary associated with mental maths is an important part of gaining understanding and confidence.

Skills of mental calculation are:

  • remembering number facts and recalling them without hesitation
  • using facts that are known by heart to figure out new facts
  • drawing on a repertoire of mental strategies to work out calculations (with some thinking time), eg rounding
  • understanding and using relationships between the ‘four rules’ (add, subtract, multiply, divide)to work out answers and check results
  • approximating calculations to judge whether or not an answer is about the right size
  • solving problems and judging whether the answers are reasonable.



Learning Styles

We are all very aware of how difficult maths seems to be for some learners. You will have a good idea of your child’s preferred learning style. Here are some strategies, which use different senses and learning styles. The examples given show how they can be applied to the 9 x table.

Learning Style  Strategy
Visual Make a set of cards with the question on one side (9 X 5) and the answer on the other. (45). The learner keeps the cards in order and practices to see if they know the answer, turning the card over. They then repeat having shuffled the cards. They then test themselves by turning the cards over and asking how many 9s go into that number.
Pattern Use a multiplication square to highlight the 9 times table. Look for patterns in the numbers e.g. the tens go up by one as the ones go down, or add the digits together and they make 9.
Written Again, look at the written numbers in a multiplication square.
Aural Make recordings of the tables and listen back or listen to tables set to music.
Kinaesthetic Hold your hand in from of you and number your fingers 1,2…10 from left to right. To calculate 4 X 9, bend down finger 4. There are 3 fingers to the left and 6 fingers to the right so the answer is 36. etc

Ideas for using Math Equipment and Resources

There are many useful resources that can help when learning about number. Some of these are:

Place value cards, arrow cards, 10-sided dice, whiteboards and markers, tens and ones blocks, number fans, counting sticks, number lines, dominoes etc.

Here are some suggestions for how you could use some of these resources in your maths topics.


Resources  Possible Math Concepts 
Number Fans ·        reading and writing numbers·        place value·        Estimating

·        facts practice

·        decimals·

Counting Stick ·        counting by ones, twos, tens, hundreds, tenths·        counting on and back·        multiplication facts

·        addition and subtraction facts

·        comparing and ordering numbers

Number Lines / Tracks ·        counting reliably·        comparing and ordering·        fractions/decimals

·        addition and subtraction

Dominos ·        facts practice·         organizing and using data·        mental calculation strategies
Dice ·         facts practice·        mental calculation strategies·        probability

·        operation dice

Whiteboards ·        place value and ordering·        problem solving·        pencil and paper procedures (non-threatening)

·        organizing and using data



Using games when learning maths can be a fun, non-threatening, way of practicing concepts and building confidence. The following are just a few suggestions for games that can be used to reinforce a number of mathematical ideas:

The Apple Tree Game

You will need: a gameboard – a large tree with 12 ‘apples’ on, counters, dice (1-6 or 1-9)

Throw 2 dice. Add the numbers. If the answer is even, put a counter (apple) on the tree. If it is odd do not put a counter on the tree. When the tree is full, the player with the most apples wins.


Variations – multiply or subtract the two numbers together instead; throw 3 dice; both throw dice and the highest number gets the apple; use the two dice to show tens and ones and make the highest number

Addition War

You will need: a pack of playing cards

Take approximately half a pack of cards each. Take it in turns to turn over two cards and add them together. The player with the highest number wins and keeps all 4 cards. If there is a tie, then war is declared and each player turns over 3 cards each at the same. The players add the numbers together and again, the highest number wins. The winner collects all 6 cards. When all cards have been used, the player with the most cards is the winner.

Variations – multiply the numbers; subtract the numbers and the lowest number wins

Number Ladders

You will need: 1-100 cards, a gameboard for each player with a ‘ladder’ on it with 10 spaces

Have a pile of 1-100 cards. Each player has a ladder with 10 spaces. The object of the game is to try and fit as many cards on as possible. The first player picks a card and puts it on his ladder. If the number is low, she should put it near the bottom and the reverse if the number is high. The next player does the same thing. Each player has 10 turns and must try and place their cards on in order, from lowest to highest. If there is no space then the player loses that go and cannot place the card.

Variation –  throw 2 dice and make a 2-digit number using each dice as the tens and ones – play is the same.

Hundreds, Tens and Ones


You will need: a gameboard with 3 sections marked Hundreds, Tens and Ones, dice, counters (or hundreds, tens and ones pieces)


Use the HTO game board. Throw a dice and collect that number of ones. Take it in turns. When a player has 10 ones, they can exchange (regroup) it for a ten. The winner is the first to get one hundred.

Variation – Start with 100 and subtract, regrouping to take away the number shown on the dice. The winner is the first one to get to 0.

Race to 100


You will need: a gameboard with squares numbered 0-100 (as in snakes and ladders without the sakes and ladders!), dice, counters


Use the Race to 100 gameboard. Throw a dice and move that number of spaces. Predict what number you will land on. Take it in turns. The first to 100 wins.

Variation – Race from 100. Start from 100 and subtract the numbers. First to 0 wins. Throw 2 dice and add/multiply first before moving.

Emma Binder 2006

Some useful websites for mental maths practice and ideas:

a site with several online, interactive activities

a list of online math activities

A list of ‘math on the go’ fun activities

a list of websites with online math games and activities

a school website with interactive numeracy resources

more interactive activities

containing activities, puzzles, worksheets, tips and strategies for learning the tables

online activities to support all areas of the curriculum, especially maths


See also:

Candy Land Addition and Subtraction

Candy Land Multiplication


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