Mental arithmetic refers to working maths problems out in your head without having to write anything down.
Although we live in a world full of technology and gadgets, having mental strategies at your fingertips is really helpful for day-to-day life, such as working out change and figuring out how long you need to wait for the next bus. It is also a key element of SATs tests for maths in England in Year 6.
- adding and subtracting multiples of 10, 100 and 1000;
- doubling and halving numbers up to 100;
- recalling times tables facts and related division facts up to 12 x 12;
- multiplying any number by 10 and 100.
Confidence and fluency (recalling known facts or methods and using these flexibly, accurately and quickly) are key here and practice is essential!
Here are a few ideas to support your child’s mental arithmetic.
Write down a mix of questions on times tables up to 12 x 12, doubling and halving numbers up to 100, and multiplying any number by 10 and 100. Read out the questions and see how many your child can answer correctly in 30 seconds. Can they beat their score with similar questions the next day? If they are getting any wrong, go back and discuss what they’d do next time to work it out.
Get eleven Post-it notes or similar-sized pieces of card. On the first Post-it or card, write a question, e.g. 12 x 12. On the second Post-it, write the answer (144), and the next question, e.g. what is half of 78?. The third Post-it should have the answer (39) and the next question. Carry on until you have written ten questions. The final Post-it will just have the answer to question ten.
Mix up all the Post-its, and ask your child to stick them in the correct order, to make one long chain of questions and answers. How long does it take them, and can they beat their time tomorrow? Can they make a set of linking cards for you or a friend to try?
Many of the times tables have patterns in their answers. For example, all the answers in the 5 x table end in 5 or 0. And in the 9 times table, the digits of each answer add up to 9 (e.g. 2 x 9 = 18. 1+ 8 = 9). Help your child spot patterns in the times tables, for example by looking for repeating digits, as this should help them with recall.
You can find more ideas for practising times tables with your child in my times tables blog post.
What the hack?
Ask your child to write some tips for someone who is trying to learn some mental arithmetic skills. For example, what tips do they know for multiplying numbers by 10 or 100? They may have noticed that the digits stay the same, but a zero has been added to the ‘ones’ (or units) place for example.
When doubling a two-digit number they can partition into tens and ones and double both and then recombine the result. E.g. 27 doubled is 20×2 (40) and 7×2 (14) = 54.
What other hacks do they know/can they find?
Remember, practice makes perfect – work together to vary the questions and numbers, and challenge each other to see how quickly you can answer and how many patterns or hacks you can spot!
Activity books and flashcards
Progress with Oxford | Age 9–10
This activity book will help your child to progress with core maths skills while having fun!
The books in our Progress with Oxford series are focused on the skills your child will need at each stage of the school curriculum.
Bond SATs Skills | Age 10–11
Bond SATS Skills Arithmetic for age 10–11 has been developed by Bond to develop the arithmetic skills expected by the National Curriculum, preparing for SATs, as well as selective school exams. This workbook focuses on the arithmetic agility needed for success.
Bond SATs Skills | Age 8–11
This activity book will help your child to progress with times tables while having fun!
These flashcards provide rapid recall practice in all the times tables from 1 to 12, helping children to meet the curriculum expectations for Key Stage 2 maths and prepare for the Year 4 multiplication tables check.
Bond | Age 8–11
It’s time to train your brain! Some monkeys are stuck in the maze – are you able to help them escape? From Sudoku grids to number riddles, switch on your puzzle powers to solve all sorts of challenges.
- Over 100 fun number puzzles, including maths mazes, algebraic enigmas, and fraction fun.
- Solve sudokus and real-life maths problems.
- Untangle number riddles and clever patterns.