# Complex Shapes and Scale Drawings

## Learning Objectives

Learning about the effectiveness of renewable energy – solar panels:

- Demonstrate how to take measurements from scale drawings.
- Solve a problem using measurements from a scale drawing.
- Calculate areas of complex shapes.
- Analyse your solution to understand its impact.

## Lesson Description

The lesson is aimed at the knowledge and skills requirements for KS3 and KS4 Mathematics.

This maths topic uses the real-life context of the British America’s Cup team INEOS TEAM UK. Students will explore the modelling and data analysis behind INEOS TEAM UK’s team’s solar panel array during the 35th America’s Cup. Over two lessons, they will use the blueprint of the base’s roof to design the array, calculate area and analyse real data to evaluate the energy produced.

Use the film to discuss the motivations behind the team’s decision to install solar panels, the impact it has and the ways they monitor its efficiency and effectiveness.

The class-facing presentations provide clear lessons with differentiated worksheets to reinforce the curriculum-linked learning objectives.

This resource can be used either in sequence or flexibly as an introduction to a topic, or for a quick activity.

## CURRICULUM LINKS

**ENGLAND**

**KS3 NC Maths:**

Ratio, proportion and rates of change.

Model situations mathematically.

Change freely between related standard units [for example time, length, area, volume/capacity, mass].

Use scale factors, scale diagrams and maps.

Draw, measure and interpret scale drawings.

Calculate areas of composite shapes.

Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction.

Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions.

Geometry and measures.

Calculate and solve problems involving: perimeters of 2-D shapes and composite shapes.

Working mathematically.

Solve problems: begin to model situations mathematically and express the results using a range of formal mathematical representations.

**KS4 NC Maths:**

Compare lengths, areas and volumes using ratio notation and/or scale factors; make links to similarity.

Calculate and solve problems involving areas of composite shapes.

Convert between related compound units.

Interpret and use fractional (and negative) scale factors for enlargements.

Interpret plans.

Calculate surface areas.

GCSE Mathematics.

**AQA:**

R1 Change freely between related standard units.

R2 Use scale factors, scale diagrams and maps.

**Edexcel:**

R1 Change freely between related standard units (e.g. time, length) and compound units (e.g. speed) in numerical and algebraic contexts.

R2 use scale factors, scale diagrams and maps.

G14 use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money, etc.).

**OCR:**

10.01c Use the scale of a map, and work with bearings. Construct and interpret scale drawings.

**WALES**

**KS3 Maths:**

Use ratio and proportion to calculate quantities, including cases where the ‘total’ is not given.

**SCOTLAND**

Third Level Maths – Curriculum for Excellence:

Scale drawings: word problems.

Use a formula to calculate the area of a shape.

**NORTHERN IRELAND**

**KS3 Maths:**

Recognise the need for scales and when to use them.

Identify suitable scales and scale ratios for plans and maps.

Use scales and scale ratios to read a map and calculate actual distances.

Understand terms such as plan, scale and ratio.