Resources needed: whiteboards and pens
- Explain to the children that you are going to show them a variety of maths tricks with numbers. They can try the tricks out themselves on their friends or family to amaze them!
- TRICK 1: Think of any number – if it is even, divide it by 2. If it is odd, multiply by 3 and add 1. Keep going with this process and write down the numbers as you go – you will inevitably end up with a number 1!
E.G: 6 –> 3 –> 10 –> 5 –> 16 –> 8 –> 4 –> 2 –> 1
- TRICK 2: To find the square of any number which ends in 5, use this process: Ignore the 5 in the units place. Take the digit in the tens place and multiply it by the next number in number order i.e. 8+1 = 9. The result is 72. Now place 25 at the end of the result, so 7225 is the square of 85.
- TRICK 3: To multiply a two-digit number by 11, for example 11 x 35. Write 35 as 3 5 (with a space in between for a new digit. This digit is the sum of the two digits on either side – so 385 is the answer. If the sum of the two numbers results in a two-digit number, add the tens digit to the first digit. So, 65 x 11 = 6(6+5)5 = 6(11)5 = 715.
- TRICK 4: Multiplying by 5 is the same as multiplying by 10 and then halving the answer. It works exactly the same if you do this the other way round: half the number to be multiplied, and then multiply the answer by 10. For example, 346 x 5 = 173 x 10 = 1730.
- TRICK 5: To multiply a number by 25, first multiply it by 100 and then half your answer and half it again. For example, 86 x 25 = 8600. 8600 halved is 4300. 4300 halved is 2150.
- TRICK 6: To subtract any number from 1000, firstly subtract the digit in the units place from 10. Then subtract the digit in the tens place from 9 and do the same for the digit in the hundreds place. So 1000 – 352 would be 9 – 3, 9 – 5, 10 – 2 = 648.
- TRICK 7: To divide a number by 5, for example 565 by 5, double the number: 1130 and divide the answer by 10: 113. This works with any number, even decimal numbers.
Ask the children to create their own rule or trick for one of the four number operations. Can they prove it works? They should think about using facts which they already know, for example multiplying by 20 is double multiplying by 10, or dividing by 20 is dividing by 10 and then halving the answer.
Curriculum Areas covered:
(Y5)Pupils should be taught to:
- Add and subtract numbers mentally with increasingly large numbers
- Multiply and divide numbers mentally drawing upon known facts
- Solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign
(Y6) Pupils should be taught to:
- Perform mental calculations, including with mixed operations and large numbers § identify common factors, common multiples and prime numbers
- Use their knowledge of the order of operations to carry out calculations involving the four operations
- Solve problems involving addition, subtraction, multiplication and division