Number Play
Class 8 · Mathematics
5 ideas in Class 8 Mathematics, explained in plain words, with games and quizzes to practise.
Parity of Sums and Expressions
Even and odd are called the parity of a number. Odd ± odd and even ± even are even, while odd ± even is odd. So when four numbers are joined by plus and minus signs in any way, every result has the same parity, because changing a sign changes the value by twice a number, which is even. An expression like 4m + 2n is always even since both parts are even, but x² + 2 is even only when x is even.
Why it matters. Parity reasoning lets children make sure about a fact without trying every case, which is the heart of proof. It is also a quick way to catch mistakes in calculations.
Try it in two minutes
- Pick four numbers, say 2, 5, 7, 8. Put plus and minus signs between them in a few ways and check whether each result is even or odd.
- Ask what happens to the answer's parity when you change one sign.
- Ask whether 6x + 4 is even for every whole number x, and why.
Try at home. Ask your child to write three expressions that are always even and one that is not, and to explain their choices.
Multiples, Remainders and Sums
Numbers that leave a remainder 3 when divided by 5 are all of the form 5k + 3. If two numbers are multiples of a, then their sum and difference are also multiples of a. A number divisible by 12 is divisible by every factor of 12, and a number divisible by two numbers is divisible by their LCM. But divisibility by 4 and 6 does not give divisibility by 24, because the LCM of 4 and 6 is 12.
Why it matters. These ideas let us predict remainders without dividing and help children test statements with examples and non-examples, a key habit in mathematics.
Try it in two minutes
- Ask your child to list numbers that leave remainder 2 when divided by 5 and spot the pattern (2, 7, 12, 17...).
- Ask how to write all of them in one expression (5k + 2).
- Ask if the sum of two multiples of 3 is always a multiple of 3.
Try at home. Ask your child to find a number that leaves remainder 1 when divided by 2, 3 and 4, and to explain how they found it.
Divisibility by 3 and 9 and Digital Roots
Every place value 10, 100, 1000 is one more than 9, 99, 999 which are multiples of 9. So a number leaves the same remainder on division by 9 as its digit sum. A number is divisible by 9 if its digit sum is, and by 3 if its digit sum is divisible by 3. Adding digits again and again until one digit is left gives the digital root, which is 9 for multiples of 9.
Why it matters. These shortcuts let children check multiplication, spot errors in sums and see how place value connects with divisibility. They also build confidence in explaining why a rule works.
Try it in two minutes
- Ask your child to add the digits of 4,518 (18) and decide whether the number is divisible by 9.
- Check with a division. Try 4,519 and see the remainder (1).
- Find the digital root of 7,359 by adding the digits repeatedly.
Try at home. Ask your child to find the digital roots of the numbers 1 to 20 and notice the pattern.
Divisibility by 11 and by Larger Numbers
Place values alternate between being 1 more and 1 less than a multiple of 11. So to test a number for 11, start from the units digit, add and subtract the digits alternately, and see if the result is 0 or a multiple of 11. To test for larger numbers such as 6 or 24, split them into factors that share nothing, like 2 and 3, or 3 and 8. Checking 4 and 6 is not enough for 24.
Why it matters. Divisibility shortcuts speed up simplifying fractions and factorising, and they show children how place value links with remainders.
Try it in two minutes
- Write 2849 and ask your child to add and subtract its digits alternately from the right (9 − 4 + 8 − 2 is 11).
- Ask whether 2849 is a multiple of 11 and check by dividing (259 × 11).
- Ask why a number divisible by 4 and by 6 need not be divisible by 24 (12 is an example).
Try at home. Ask your child to build a three-digit and a four-digit number that are divisible by 11 using the alternating rule.
Cryptarithms: Digits in Disguise
In a cryptarithm, each letter stands for one digit, different letters stand for different digits, and the first digit of a number is never 0. To solve one, use place value, how many digits the answer has, and the units digit of products. For instance, a 2-digit number times 8 gives a 2-digit answer only when the number is at most 12.
Why it matters. Cryptarithms train logical thinking and careful checking of arithmetic. Children learn to use clues and eliminate possibilities rather than guess.
Try it in two minutes
- Write a puzzle like A + A = 14 and ask what digit A is (7).
- Try a harder one: AB × 4 = CBA is too hard, but 4K + K4 is 99 is doable. Ask your child to try values for K.
- Remind them: different letters, different digits; no number starts with 0.
Try at home. Ask your child to make up their own cryptarithm from a sum they like and test whether it has only one answer.
What your child will practise
- Cryptarithms: Digits in Disguise: Desert Quick Fire (Quick Fire)
- Divisibility by 11 and by Larger Numbers: Ocean Puzzle (Clue Puzzle)
- Divisibility by 3 and 9 and Digital Roots: Ocean Quick Fire (Quick Fire)
- Multiples, Remainders and Sums: Number Quest (Collect the Answer)
- Parity of Sums and Expressions: Lab Explorer Sort (Sort It Out)
- Quiz: Cryptarithms: Digits in Disguise (8 questions)
- Quiz: Divisibility by 11 and by Larger Numbers (8 questions)
- Quiz: Divisibility by 3 and 9 and Digital Roots (8 questions)
- Quiz: Multiples, Remainders and Sums (8 questions)