Pythagoras' theorem
Find a missing side of a right-angled triangle.
Planned. This module is part of the plan and is not written yet.
Why it matters
Builders check that a wall's corner is square with a triangle of string measuring 3, 4 and 5; Pythagoras' theorem is why that trick works.
Draft outline · in review- For
- Level 8–9 · JSS 2 to JSS 3 (BECE)
- Inside
- 5 lessons and a test · about 75 minutes
- Topic
- Pythagoras' theorem · core, 2 of 4
Inside the module.
5 lessons in order, about 75 minutes in all, then a short test. Learners go at their own pace; the minutes are a guide, not a timetable.
Draft outline · in review
Lesson 1: Squares on the sides
Draw squares on the sides of right-angled triangles and compare their areas.
Investigate15 min, from minute 0
Lesson 2: The longest side
Use a² + b² = c² to find the hypotenuse.
Worked example15 min, from minute 15
Lesson 3: A shorter side
Rearrange to find a shorter side: a² = c² − b².
Worked example15 min, from minute 30
Lesson 4: Real problems
Ladders, roofs, paths across fields and the builder's 3–4–5 check.
Practice20 min, from minute 45
Lesson 5: Review
Mixed questions, with feedback on each.
Review10 min, from minute 65
End-of-module test
Find the hypotenuse and the shorter sides of right-angled triangles, including in practical problems.
Mastered at 85% or more. Retake it until you pass; nothing is lost, and each try gives feedback.
Already know it? A Challenge Test (planned) clears the whole module: 90% overall, no objective below 75%.
Last stageafter about 75 min
Practicalities
Draft outline · in reviewBuilt to run offline
Planned to run on the Lantern's own computer, with no internet needed.
Languages
Planned first in English; every module aims to reach all of the Lantern's languages.
Try a question.
One question from the module, as a learner would meet it. Have a go, then open the worked solution a step at a time.
Draft outline · in review
A ladder 6.5 m long leans against a wall. Its foot is 2.5 m from the wall. How high up the wall does it reach?
Work it out on paper first, then show the answer and mark it yourself.
Particulars
Where it sits
What a learner can do after it
- Find the longest side of a right-angled triangle.
- Find a shorter side of a right-angled triangle.
Needs first
Level
Level 8–9 · JSS 2 to JSS 3 (BECE)
Level mappings are approximate. A qualified teacher or lecturer in each country must check them before they appear in the app.
Difficulty for its level
2 of 4 · Core
Time
About 75 minutes
Alignments
- Aligned to Common Corefull · in review8.G.B.7
Alignment in review until a qualified teacher or lecturer checks it. No exam body, university or vendor endorses us; learners still sit the real exam.
Challenge Test
Planned: a Challenge Test to prove you know it and skip it. Pass at 90% overall, with no objective below 75%.
University courses it previews
Architecture, Engineering, Surveying and Geoinformatics, Mathematics
The route here.
Everything this module builds on, drawn as a route from its foundations. Solid lanes must be mastered first, or cleared by a Challenge Test; dashed lanes are suggestions that never lock anything.
- MA-NUM-POW-01Squares, cubes and rootsMaths · Primary 6 to JSS 2 (Level 6–8) · Planned
- MA-GEO-PYT-01Pythagoras' theoremMaths · JSS 2 to JSS 3 (BECE) (Level 8–9) · Planned · the destination Needs Squares, cubes and roots (required).
Help light the room where this is learned.
Every route on this map starts in a classroom with 24 stations, a tutor that works offline and a facilitator upstairs. Four are planned and waiting for light.