Activity guides / Learning / HD-L03
Count every triangle: a 10-minute discussion
Use a clear diagram and a six-item list to compare methods and check that no triangle is missed or counted twice.
By Handy Day Tools · Planning guide · Updated 8 October 2026
- Time
- 10 minutes
- Participants
- 1–12 learners; pairs or a small group
- Starting point
- Learners able to recognize a triangle and follow a labelled diagram
Print and prepare
Free, no signup. The 3-page guide includes the adult plan (pages 1–2) and a participant sheet (page 3). Print at actual size on the matching paper.
Download the matching thinking card
Check the preview before printing. Your entries stay in the tool's browser page. Resource use terms.
What this practises
Count systematically, explain what counts as different, and check a complete list. The steps below provide opportunities to practise; they do not promise measured developmental gains.
Before you start
Learners can recognize three straight sides and count small groups. The adult explains the A/B/C and 1/2 labels.
Materials
One participant sheet per learner and pencils. Page 3 includes the same diagram as thinking card HD-T-triangles-01. Keep pages 1-2 with the adult.
Run the activity
Think quietly · 2 minutes
Show the printed diagram. Count triangles made from drawn lines only. Overlaps count, and different positions count separately. Ask for a first answer without racing.
Compare two methods · 3 minutes
Invite a traced triangle and a reason for counting it. Explain that labels A, B and C name rays from the top; 1 and 2 name horizontal bases. Avoid judging a learner by a first guess.
List and check · 3 minutes
Start with base 1. List pairs AB, AC and BC. Repeat with base 2. Trace each of the six listed triangles and check for duplicates.
Change one condition · 2 minutes
Ask what one extra horizontal line would add. Sketch it between the bases, list its three ray pairs and explain the new total.
Questions to ask
- What makes this a triangle?
- How does your list show that nothing was counted twice?
- Why must each triangle use one horizontal base?
Offer more support
Trace one triangle at a time with a finger or removable overlay. Start with the AB pair and compare its two bases. Let a partner read labels aloud; do not use a speed challenge.
Extend the activity
Draw one more horizontal base and explain which three new triangles it creates. This changes a condition; it is not a new randomly generated puzzle.
Answers and checking
Base 1: AB1, AC1, BC1. Base 2: AB2, AC2, BC2. Total 6. All rays meet at the top, so any triangle uses two rays and one horizontal base. Two horizontal bases cannot meet to form a triangle. One extra base adds 3 triangles, for a new total of 9.
Limits and care
Different positions count even when shapes look alike. Labels are outside the diagram and are not sides. Our teaching adaptation has not been tested for learning gains and is not an IQ test.
After you try it
Note the actual group size, time used, a question that helped, and a change you would make. This is a proposed activity plan, not a report of a classroom or event trial. Share feedback with support; omit participants' names and personal details.
Further reading
These sources informed the choice of topic or teaching approach. The plan, timings and participant sheet are our own adaptation; they are not a trial or endorsement by those sources.