Finding the Unknown
Class 7 · Mathematics
4 ideas in Class 7 Mathematics, explained in plain words, with games and quizzes to practise.
Turning balances and patterns into equations
Part of: Seeing the unknown
An equation says two expressions hold the same value, with a letter standing for the hidden number. A scale with three 4 kg packs on one pan and two bags on the other becomes 12 balances 2 bags. A stick pattern that grows by 3 each step with 2 extra becomes 3n plus 2. LHS is the left side, RHS the right side.
Why it matters. It turns picture puzzles into sentences that maths can solve.
Try it in two minutes
- Recall that equal pans mean equal values.
- Recall that LHS names the left side and RHS the right side.
- Link a stick pattern step to its rule.
- Ask what the letter stands for.
Try at home. Weigh fruit against coins and write the match in words with a letter.
Solving step by step on both sides
Part of: Seeing the unknown
Adding and taking away undo each other, and times and divide undo each other. To solve 4p plus 11 is 47, take 11 from both sides to get 4p is 36, then split by 4 to get p is 9. Putting 9 back gives 47, so it checks. Guessing values works but takes long; balanced steps are quicker.
Why it matters. It gives a sure path to the hidden number plus a way to confirm it.
Try it in two minutes
- Recall that adding and taking away undo each other.
- Recall that times and divide undo each other.
- Link checking to putting the value back.
- Ask why both sides need the same step.
Try at home. Solve x plus 6 is 15 by taking 6 off both sides.
Using equations to solve real problems
Part of: Using equations well
Many stories hide one number: plates at 30 each plus a 60 delivery charge. With 6 people the bill is 240. Given 540 with a 60 charge, snack money is 480, which buys 16 plates. Two savers, one starting at 3000 adding 450 a month and one at 3600 adding 300, meet after 4 months. A think-add-double trick undoes in reverse.
Why it matters. It shows equations paying off in shops, parties and savings.
Try it in two minutes
- Recall naming the unknown first.
- Recall fixed charge versus per-plate cost.
- Link undoing to the people count.
- Ask how to check the bill.
Try at home. Plan 8 plates at 30 with a 60 charge and find the total.
Catching mistakes and old Indian algebra
Part of: Using equations well
A common slip turns 4x plus 6 is 10 into 4x is 16 by adding 6 instead of taking it away. Brahmagupta, in 628 CE, gave a direct rule for Ax plus B is Cx plus D: x is D minus B split by A minus C. Old Indian writers called this study seed maths and wrote unknowns with signs like ya for as much as needed, while known amounts were called rupa.
Why it matters. It builds checking habits and pride in an old Indian science.
Try it in two minutes
- Recall that moved terms flip their sign.
- Recall that moved factors divide the other side.
- Link seed to hidden answer.
- Ask who wrote the first algebra book.
Try at home. Break one step on purpose and let the child find it.
What your child will practise
- Catching mistakes and old Indian algebra: Mission Control Quest (Collect the Answer)
- Solving step by step on both sides: Candy Quest (Flip and Match)
- Solving step by step on both sides: Number Quest (Match It Up)
- Turning balances and patterns into equations: Desert Quick Fire (Quick Fire)
- Using equations to solve real problems: Candy Puzzle (Clue Puzzle)
- Quiz: Catching mistakes and old Indian algebra (8 questions)
- Quiz: Solving step by step on both sides (8 questions)
- Quiz: Turning balances and patterns into equations (8 questions)
- Quiz: Using equations to solve real problems (8 questions)