Year 7 Prisms and Pyramids

Australian curriculum number (ACMNA175)

Who is this Sequence for?

This stand-alone lesson is designed for students who are beginning to learn algebra. Students commencing this lesson will need to understand that pronumerals stand for numbers and know the most basic conventions of algebra. For the Euler’s formula task, students also need be able to collect like terms, e.g. they will need to be confident that 2b ≠ b+2 and be able to simplify expressions such as (b+2) – 2b. The lesson can involve solving very simple equations.

Summary of learning goals

This sequence provides an accessible context for students to use simple algebra. Students build their skills in algebra by developing algebraic rules for the numbers of faces, edges and vertices in prisms and pyramids. They make deductions about unknown prisms and pyramids from these rules (links to equation solving) and then use their algebraic expressions to show that Euler’s Formula works for all prisms and pyramids. Students also build their spatial skills through construction of pyramids and prisms.

Rationale for this sequence

A focus on properties of familiar 3D shapes has been selected as the vehicle for describing relationships with algebra. Students work with concrete objects, number patterns, verbal expressions and algebraic expressions of the relationships that they find. Together, all these representations provide meaning and purpose for the algebra. Application of their algebraic rules to Euler’s Formula could be a first opportunity for students to prove a result using algebra.

 

reSolve Mathematics is Purposeful

This lesson emphasises the links between algebra and the physical world, in this case 3D shapes. Students develop skills in reasoning and communication as they make and justify generalisations, verbally and algebraically. The geometric situation illustrates the meaning of the algebra, and the algebra can describe the geometry and make predictions about it. Students develop a sense of why algebra is useful.

 

reSolve Tasks are Challenging Yet Accessible

Using constructed prisms and pyramids as a vehicle for developing algebraic understanding provides students with an accessible entry point to generalisation. There is an opportunity to link formal equation solving processes with intuitive methods.

Students are challenged to manipulate algebraic variables to find unknowns, and to produce two short algebraic proofs.

 

reSolve Classrooms Have a Knowledge Building Culture

The lesson is a guided investigation in which students can work together to discover patterns and make deductions. Each task builds on the previous task to help students move toward a greater understanding of what algebra can do.