Year Nine Proportional Reasoning Mini-pack

This unit from the National Strategies is a sequel to the Year Eight multiplicative relationships unit. It provides an opportunity to revise, consolidate and extend ideas introduced in Year Eight and to make links to other mathematical strands, particularly shape and space. Making such links, especially with visual contexts, can help pupils to understand proportion. This unit has been structured into three phases for teaching and includes an outline of three teaching phases and supporting resources, such as supplementary notes consisting of prompts for oral and mental starters and main activities.

Phase 1 (about three lessons) • Phase 1 builds on the idea of scaling numbers, introduced in the Year Eight mini-pack, to consider successive scalings and their inverses. • It re-examines the use of tabular arrays to set out proportional relationships and find unknowns (followed through in phases 2 and 3).

Phase 2 (about three lessons) • Phase 2 links numerical work to geometry – the invariant properties of enlargement and the concept of similarity. • It considers relationships ‘within’ and ‘between’ similar shapes.

Phase 3 (about three lessons) • Phase 3 considers problems from a variety of contexts (numerical, graphical, spatial, statistical), to identify the underlying relationships of proportionality. • It revises and develops methods for solving proportion problems. • The phase places particular emphasis on problems involving percentage increases and decreases. The ITP Photographic enlargements offers an alternative way of presenting the activity, Photographic enlargements outlined on pages 23-24 of the Year Nine Proportional reasoning mini-pack. It is accompanied by comprehensive 'how to' notes.