'Algebra: Euler’s dice' is a reimagining of classic V8 sequence 'Algebra: Prisms and Pyramids''
- On the 'In this sequence' tab you'll find all the lessons in this sequence, a suggested implementation plan and curriculum alignment.
- The 'Behind this sequence' tab shows how key mathematical ideas develop over the sequence.
- Have you taught this sequence? Use the Feedback button to let us know how it went!
Lessons in this sequence
Task 1 • What is a polyhedron?
Students build definitions of “polyhedra”, “prisms” and “pyramids” by sorting objects and testing their ideas against tricky examples. They then turn their definitions into a classification algorithm.
Task 2 • Patterns and pronumerals
Students count faces, edges, and vertices across a range of prisms and pyramids, record their findings in a shared class table, and use those findings to write algebraic rules. They then discover Euler's rule from their own data.
Task 3 • Design your die
Students respond to a brief from a game designer who needs dice with unusual numbers of faces (e.g. 7-faced or 13-faced dice). They choose a face count, use their algebraic rules to identify what polyhedron their die needs to be, verify it using Euler’s rule, and build it.
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Curriculum and syllabus alignment
Year 7
Students use algebraic expressions to represent situations, describe the relationships between variables from authentic data and substitute values into formulas to determine unknown values.
They solve linear equations with natural number solutions. Students create tables of values related to algebraic expressions and formulas, and describe the effect of variation.
Students classify polygons according to their features and create an algorithm designed to sort and classify shapes.
Algebra
Space
Design and create algorithms involving a sequence of steps and decisions that will sort and classify sets of shapes according to their attributes, and describe how the algorithms work
This sequence asks one question: what dice are mathematically possible to construct?
To answer it, students take on a brief from a game designer who is making a superstition-themed board game and needs a custom die for each of a set of numbers considered lucky or unlucky across different cultures (e.g. a 7-faced die or a 13-faced die).
In Task 1 students work out what makes something a polyhedron, a prism, or a pyramid. They test their definitions against tricky examples and build a classification flowchart.
In Task 2 students count faces, edges, and vertices for different prisms and pyramids and look for patterns. They write algebraic rules and discover Euler’s rule ($F + V - E = 2$) from their own data.
In Task 3 students pick a lucky or unlucky number, use their rules to find the right shape for a die with that number of faces, check the shape is valid, and build it.
'Algebra: Euler’s dice' is a reimagining of classic V8 sequence 'Algebra: Prisms and Pyramids''
- On the 'In this sequence' tab you'll find all the lessons in this sequence, a suggested implementation plan and curriculum alignment.
- The 'Behind this sequence' tab shows how key mathematical ideas develop over the sequence.
- Have you taught this sequence? Use the Feedback button to let us know how it went!