Algebra Play
Class 8 · Mathematics
5 ideas in Class 8 Mathematics, explained in plain words, with games and quizzes to practise.
Think of a Number Tricks
Part of: Algebra tricks and puzzles
In a think-of-a-number trick, you follow steps on a secret number and the result does not depend on the number. To see why, call the number x and write each step as an expression. For example: double it (2x), add 10 (2x + 10), halve it (x + 5), subtract the number (5). The x cancels out, so everyone ends up with 5. Changing a step changes the final answer in a predictable way.
Why it matters. This is a first taste of how algebra explains and proves patterns instead of only checking examples. It also makes maths fun to share.
Try it in two minutes
- Ask your child to think of a number and double it, add 10, halve it and subtract the starting number.
- Try a second number and see that the answer is the same.
- Ask your child to write the same steps with x and see why the number disappears.
Try at home. Invent a new trick together that always ends in 7 and test it on the family.
Decoding a Date Trick
Part of: Algebra tricks and puzzles
In a date trick, your friend does steps on the month number M and the day number D and tells you the answer. If the steps are: multiply the month by 4, add 3, multiply by 25 and add the day, the answer is 100M + 75 + D. Subtract 75 to get 100M + D. Since the day is at most 31, it fills the last two digits and the month is in front of them, so you can read the date.
Why it matters. Decoding a trick shows how algebra can be used to undo steps. This helps with working backwards in equations.
Try it in two minutes
- Ask your child to choose a date and do the steps: month times 4, add 3, times 25, add the day.
- Tell the answer to you and subtract 75.
- Read the date from the digits and check with them.
Try at home. Create a trick with different numbers, work out the expression, and ask the family to try it.
Number Pyramids
Part of: Algebra tricks and puzzles
In a number pyramid, each number is the sum of the two numbers just below it. For a pyramid with three rows and bottom numbers a, b and c, the middle row is a + b and b + c, and the top is a + 2b + c. So the middle number of the bottom row counts twice. With four rows and bottom numbers a, b, c and d, the top is a + 3b + 3c + d.
Why it matters. Pyramids train children to use rules to find unknown numbers and show how letter-numbers describe a pattern for all cases at once.
Try it in two minutes
- Draw a pyramid with bottom row 6, 2, 3 and ask your child to fill in the rest.
- Do another pyramid with a different bottom row and ask which bottom number matters most for the top.
- Ask your child to find the top using a + 2b + c and check against the full pyramid.
Try at home. Ask your child to make a pyramid with the top number 50 and figure out a bottom row that works.
Calendar and Algebra Grids
Part of: Algebra tricks and puzzles
On a calendar, each row has 7 days, so the date below a date a is a + 7. A 2 by 2 block with top left date a holds a, a + 1, a + 7 and a + 8, and the sum is 4a + 16. From the sum, you can find a. In an algebra grid, shapes stand for numbers, and the total of a row gives an equation that we solve to find the value of the shape.
Why it matters. These puzzles show how algebra can describe a layout and then be solved. They are also good for building confidence in handling expressions.
Try it in two minutes
- Look at a calendar page. Pick a 2 by 2 block and ask your child to add the four dates.
- Show that the sum is 4a + 16, where a is the top left date.
- Ask your child to find the block if the sum is 52.
Try at home. Challenge your family: tell the sum of a 2 by 2 block on a calendar and see who finds the four dates first.
Digit Tricks and Divisibility
Part of: Algebra tricks and puzzles
To make the largest product of a two-digit and a one-digit number from three digits, use the largest digit as the multiplier and write the other two in decreasing order. A two-digit number with digits a and b equals 10a + b. Reversing and subtracting gives 9(b − a), so it is always divisible by 9. Adding a two-digit number and its reverse gives 11(a + b), which is divisible by 11.
Why it matters. Writing numbers with place values in algebra shows why number tricks always work, and helps in divisibility and mental maths.
Try it in two minutes
- Take the digits 2, 4 and 7 and ask your child to try different pairings to get the largest product.
- Ask your child to choose 83, reverse it to 38, subtract and divide by 9.
- Ask them to add 83 and 38 and divide by 11.
Try at home. Ask your child to try the reverse-and-subtract trick on three different numbers and say what they notice.
What your child will practise
- Calendar and Algebra Grids: Candy Quick Fire (Quick Fire)
- Decoding a Date Trick: Jungle Puzzle (Clue Puzzle)
- Digit Tricks and Divisibility: Space Quick Fire (Quick Fire)
- Number Pyramids: Desert Puzzle (Clue Puzzle)
- Think of a Number Tricks: Mission Control Quest (Collect the Answer)
- Quiz: Calendar and Algebra Grids (8 questions)
- Quiz: Decoding a Date Trick (8 questions)
- Quiz: Digit Tricks and Divisibility (8 questions)
- Quiz: Number Pyramids (8 questions)