This worksheet builds computational thinking, teaching students to trace and design algorithms — including search, sort and greedy route-finding — to solve spatial and optimisation problems. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- An algorithm is a precise, finite sequence of steps that solves a problem — every step must be unambiguous and the process must terminate.
- linear search checks each item in turn (worst case n comparisons for n items); binary search repeatedly halves a sorted list (worst case ⌈log₂n⌉ comparisons) — binary search is far more efficient for large n.
- bubble sort repeatedly compares and swaps adjacent out-of-order items, making repeated passes until no swaps are needed.
- A greedy algorithm makes the locally best choice at each step, without reconsidering earlier choices — this is often fast but does not always give the globally optimal (best overall) result.
- Algorithmic efficiency compares how the number of steps grows with the size of the input — this matters for choosing which algorithm to actually use in practice.
What your child will practise:
- Tracing a search algorithm (linear or binary) step by step on a given list, counting comparisons.
- Tracing a sort algorithm (bubble sort, insertion sort) step by step, tracking the list's state after each step.
- Applying a greedy algorithm (nearest-neighbour routing, coin change, first-fit bin packing) to a spatial or optimisation problem.
- Comparing the efficiency of two algorithms for the same task, using a specific input size.
- Determining whether a greedy algorithm's result is actually optimal, or find a counterexample where it isn't.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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