Young Geniuses · Ages 13 to 14
Proof by Induction Word Problems
Structure a proof by induction and verify the base case. A Grade 8–9 reasoning worksheet with answer keys.
The learning journey
Every activity is one step. Here is where this one fits.
- PlayLearn the idea in a game
- Practise(you are here)Lock it in on paper
- ReviewCome back and keep it sharp
- MasterTake on a harder challenge
- AchieveEarn a certificate
About Proof by Induction Word Problems
Proof by Induction Word Problems introduces ambitious upper-secondary learners to one of the most elegant techniques in mathematics: proof by mathematical induction. Each problem states a result that holds for every positive whole number — such as a formula for the sum of the first n whole numbers, the first n odd numbers, or the first n square numbers — and asks the student to structure the proof and verify the base case by stating the value of each side when n equals one. Mathematical induction is an enrichment topic that appears in extension and early high-school courses across the US, UK, Canada and Australia, and it is a wonderful first encounter with rigorous proof: the idea that if a statement is true for a starting value, and its truth for one value guarantees its truth for the next, then it must hold for all of them. Beginning with the base case builds the disciplined, step-by-step habit that good proof requires, and grounds an abstract method in a concrete first step. The statements vary so the worksheet stays fresh, and the five levels introduce a wider range of results. Each page prints cleanly on a standard A4 sheet, and every level downloads with its own answer key. There is no advertising and no sign-up.
Common questions
- What is proof by induction?
- A method proving a statement for all positive integers by checking a base case and an inductive step.
- What grade is this for?
- Grade 8 to Grade 9 learners aged 13 to 14, as an enrichment topic.
- Is an answer key included?
- Yes, every level has its own answer key.
A hand for grown-ups
- Before you start
- These need thinking time, not speed. Set the expectation that a good puzzle is meant to take a while.
- While they work
- Resist jumping in. A long pause is a child thinking, not a child stuck — give it room before offering a nudge.
- Afterwards
- Ask "how did you work that out?" more than "is it right?". The reasoning is the skill; the answer is just the evidence.
- Watch out for
- Guessing to escape the discomfort of not knowing. Reassure them that being stuck for a bit is normal and fine.
- Away from the screen
- Play strategy games, do puzzles, ask "what comes next?" with patterns of objects. Reasoning is a muscle.
Where to go next
Chosen by the skills this activity practises.