Year level: Year 10

Strand: Measurement

Lesson length: 60 mins

In this lesson, students build on their skills in finding volumes and surface areas of prisms and cylinders to design a multi-level celebration cake for a party. They use mathematical modelling to vary the size and shape of the component cakes and to calculate how much frosting is needed.

### Achievement standard

Students solve measurement problems involving surface area and volume of composite objects and use mathematical modelling to solve practical problems involving  proportion and scaling, evaluating and modifying models, and reporting assumptions, methods and findings.

### Content descriptions

Students solve problems involving the surface area and volume of composite objects using appropriate units. AC9M10M01

Students use mathematical modelling to solve practical problems involving proportion and scaling of objects; formulate problems and interpret solutions in terms of the situation; evaluate and modify models as necessary, and report assumptions, methods and findings. AC9M10M05

### General capabilities

Numeracy

• Understanding geometric properties (Level 7)
• Proportional thinking (Level 7)

Critical and Creative Thinking

• Interpret concepts and problems (Level 6)
• Draw conclusions and provide reasons (Level 6)
• Consider alternatives (Level 6)
• Evaluate actions and outcomes (Level 6)
• Identify, process and evaluate information (Level 6)

Digital Literacy

Select and operate tools (Level 6)

Opportunities for assessment are provided below and can be downloaded from the ‘What you need’ section.

• Review students’ worksheets and provide feedback.
• Distribute and collect the exit ticket. Note that there are two identical exit tickets per A4 page.

Prior to this lesson, it is assumed that students have knowledge of:

• volume and surface area of cylinders and prisms
• area of composite shapes
• some understanding of basic spreadsheet functionality including performing calculations using symbols such as = * / and ^.
• Some students may have trouble decomposing a composite solid – use physical and virtual manipulatives such as stacked cake tins or food boxes to demonstrate how composite solids can be decomposed into their constituent parts.
• Students may experience difficulties finding volumes – display key formulae (V = lwh, V = Ah and V = πr2h ) on the whiteboard, ask students to identify the meaning of each pronumeral and demonstrate on a diagram where they appear in each solid.
• Some students may make errors calculating surface area and miss or double-count faces, include ‘hidden’ faces or the bottom of the cake or forget to include the filling. They may wish to find the area of the top of each cake, which is partly covered by the smaller cake above. Encourage students to carefully mentally ‘walk around their cake’ marking off each face as they find its area and to think about how cakes can be mentally ‘moved’ to complete odd shapes and simplify calculations. Have students design a cake that matches the design in the samples in the Excel model so they can a correctly calculate surface area in the model, which they can then use to check their manual calculations.
• Students may have gaps in spreadsheet skills/knowledge – explicitly demonstrate and explain the key features and operation of spreadsheets. Use the provided Excel model and encourage students to interrogate formulae in cells to understand how the calculations have been derived. For students creating their own models, encourage use of online help videos.

## What you need:

• Lesson plan (Word)

• Teacher's slides (PowerPoint)

• Excel model (Excel)

• Exit ticket (Word)