Technologies K–10 · Years 3–4
Higher or lower: finding a number from 1 to 100 in 7 guesses
Design and Production (NSW Science and Technology K–6, 2017) (algorithms); Digital Technologies: Processes and production skills, Generating and designing (ACARA v9)
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The idea
Comparing each guess with the secret number (higher or lower) and always guessing the middle of what is left halves the search each time, so any number from 1 to 100 is found in at most 7 guesses.
What you need
- 1 number line from 1 to 100 per pair, with 2 pegs to mark the lowest and highest numbers still possible
- Mini whiteboard and marker for the secret number
- Recording sheet: round, secret number, guesses in order, number of guesses
How to do it
- The chooser writes a secret whole number from 1 to 100 on the whiteboard and hides it.
- The guesser always guesses the middle number between the two pegs (start with 50). The chooser answers 'higher', 'lower' or 'correct'.
- Move one peg to just past the guess after each answer, so the pegs always show the numbers still possible.
- Record every guess and count them. Play 5 rounds, then swap roles.
- Play 2 rounds with a different method: guess 1, 2, 3 and so on in order. Count the guesses.
- Describe the halving method as numbered steps that another pair could follow.
What you should see
With the halving method the guesser never needs more than 7 guesses for 1 to 100, and needs 5.8 on average over all 100 possible secrets; the secret 30 is found by guessing 50, 25, 37, 31, 28, 29, 30. Guessing 1, 2, 3 in order needs up to 100 guesses and 50.5 on average. For 1 to 1000 the halving method needs at most 10 guesses. The learner knows it worked when no round with the halving method takes more than 7 guesses.
What changes
This activity lists no variables to change, measure and keep the same.
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- Guessing lucky numbers is as good as halving (halving guarantees at most 7 guesses; luck does not).
- A range ten times bigger needs ten times more guesses (1 to 1000 needs only 3 more guesses than 1 to 100).
- The halving method works on a jumbled list (it needs the numbers in order).
Safety card
Hazards
- None beyond normal classroom activity
Controls
- Not applicable
Note
No chemicals or heat.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Science and Technology K–6 Syllabus (2017), NESA. The syllabus taught in 2026; the 2024 syllabus replaces it from 2027. Code read from the official syllabus document (DOCX) on 2026-09-22.ST2-3DP-T
- Science and Technology K–6 Syllabus (2024), NESA. Implementation from 2027, so this code describes the future syllabus. Code read from the outcomes page on 2026-09-22.ST2-DDT-02
- Australian Curriculum v9AC9TDI4P02
Sources
The pages the author read to write this activity.