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Centre for Research in Mathematics Education (CRME)
MARS: geometry: Pythagoras’ theorem
This collection features ten resources on the topic of properties of Pythagoras’ theorem.
The resources feature:
- Concept development lessons that focus on developing conceptual understanding of significant mathematical ideas.
- Problem solving lessons that focus on the application of previously learned mathematics to non-routine unstructured problems.
- Tasks that provide mathematically rich problems that come with work for students to peer assess.
The Mathematics Assessment Resource Service (MARS) is a collaboration between the University of California at Berkeley and the Shell Centre team at the University of Nottingham, with support from the Bill and Melinda Gates Foundation. The team is known around the world for its innovative work in maths education.
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Proving Pythagoras’ theorem
This lesson develops the concept of producing and evaluating geometrical proofs. In particular students work on:
- Interpreting diagrams
- Identifying mathematical knowledge relevant to an argument
- Linking visual and algebraic representations
- Producing and evaluating mathematical...
Sorting equations of circles 1
This lesson develops the concept of using Pythagoras’ theorem to derive the equation of a circle and translating between the geometric features of circles and their equations.
The initial activity involves looking at a circle with end points of the diameter at (6, 0) and (–6, 0). Questions relate to...
Square
This task is designed to assess how well students understand applying Pythagoras’ theorem to finding the gradient of a slope.
The task looks at points plotted on a set of axes. The points are joined to make a quadrilateral. The first task is to calculate the length and slope of each side. Students must then...
Proofs of the Pythagorean theorem
This task is designed to assess how well students understand geometrical proofs.
The task presents three attempts to prove Pythagoras’ theorem. Students must look carefully at each attempt and determine which is the best ‘proof’. They must explain their reasoning as fully as possible.
This task is...
Pages
| Subject(s) | Mathematics |
|---|---|
| Age | 11-14 |
| Published | 2010 to 2019 |
| Published by | 
Submitted by Anna Richardson on
|
| Collections | |
| Direct URL | https://www.stem.org.uk/cxfg88 |
