YEAR 9 AUTUMN TERM PROJECT NETS and SURFACE AREA

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1 YEAR 9 AUTUMN TERM PROJECT NETS and SURFACE AREA Focus of the Project The aim of this is to develop students understanding of nets, surface area and volume. The tasks below allow students to explore these concepts whilst consolidating earlier work from Year 7 and Year 8. With their knowledge of shapes and area from earlier units, students should be able to access these tasks and begin investigating the properties of various solids. How to run this project Schools are free to run this project in whatever way fits their curriculum and allocation. For example, some schools have Maths days where some of the tasks could be used. Others may wish to use lesson time at the beginning or end of half terms to start some tasks and then let the students work through them as homeworks, either as individuals or in small groups. You might want to set aside a regular slot within other lessons to allow students to share their progress so far and discuss other options for continuing the project. How to mark this project As ever, we would never impose a system of schools, but this particular project would seem to lend itself very well to peer-assessment. In addition, students could be asked to work in pairs or groups to develop their own marking criteria. If the work is being done during lesson times, then progress can be checked and plenaries could be used to reinforce key findings; perhaps students could be asked to share something they have discovered during that lesson. Links to MM KS3 Programme of Study This project has direct links to: Year 7 Unit 4 multiplication inc. area Year 7 Unit 12 2D shapes Year 8 Unit 6 Length and area Year 8 Unit 11 3D shapes and nets Year 8 Unit 12 surface area and volume Links to National Curriculum KS3 Programme of Study This project meets the requirements of the develop fluency, reason mathematically and solve problems elements of the new KS3 Curriculum. Several other elements of the Curriculum are directly met when using these projects: calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders) use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D

2 Suggested tasks for this Project Making Nets As a very simple investigation, students could be asked to explore nets to develop their geometric reasoning and visualising skills. Students could be given a variety of 3D shape pictures and asked to construct accurate nets by considering the properties of the shapes and by experimenting and refining their ideas. Different students/pairs/groups could be given different solids to work on that would be accessible but suitably challenging. Making cubes Students could be asked to come up with all possible hexominoes (there are 35) and then asked to explore which would also be nets of cubes. Alternatively, a selection of hexominoes could be provided and students could be asked to determine which would make cubes when folded. A nice was of doing this is to have students just use visualisation to come up with an answer and then to check it by cutting and making the nets. An example of this is done here: The hexominoes are: And these make cubes:

3 Exploring cubes further As an extension to the previous task students could be asked to explore how nets and the position of faces are linked by trying to determine which nets would give a particular cube. Again, they should be encouraged to visualise before doing any cutting and making.

4 Chocolate Boxes Yummy Choccy Co. sells chocolates and truffles in cuboid boxes. The boxes need to have a volume of 1000cm 3. Can you come up with 4 different cuboids with this volume? For each one, find the surface area. In order to minimise costs, the company needs to use as little packaging as possible and so wants to minimise the surface area. Investigate different cuboids and their surface areas. This task lends itself well to manipulatives and multilink cubes could be used to make different cuboids of equal volume and to compare surface areas. Discussion can also be had about the practicalities of the difference shapes in the context of the question (e.g. 1000x1x1 would not be a sensible chocolate box!). Students could extend the investigation to consider other shaped solids, such as cones, prisms and pyramids. Cylinder Cans The Souper Soup Co. produces soups in cylindrical tins. Each tin needs to hold 400cm 3. Can you come up with three different tins that would have that volume when rounded appropriately? Find the surface area of each tin. Suppose the Souper Soup Co. wants to minimise costs and wants to use as little material as possible in making the tins. Investigate different cylinder sizes and their effect on the surface area. Can you advise the company about the best size tin to make? This can be a quite open-ended task or there could be constraints added to support students. For example, the height could be fixed meaning students only need to vary the radius. This task lends itself well to use of tables or spreadsheets for analysis and is a great opportunity to introduce students to calculator functions such as the table function. The answer is less important than the approach and exploration but the surface area is minimised if the height is the same as the diameter i.e. the cylinder is as tall as it is wide.

5 Making cuboids This task consolidates the work on ratios and sequences as well as surface area and volume. Different ratios and starting surface areas can be explored. This is also an excellent opportunity to discuss language and the use of terms such as depth, breadth, width, height etc. Task: The ratio of the length : height : width of a cuboid is 1:2:3. It has a total surface area of 4960cm 2. (This element of the task can be left out and students could simply be given the dimensions to begin with). Two cuboids are placed together. What is the exposed surface area? How many answers can you find? Three cuboids are placed together to make a larger cuboid. What is the exposed surface area? How many answers can you find? What s the minimum surface area? What s the maximum surface area? What about four cuboids? Are there more than three answers this time? The task can be constrained to consider only single layer cuboids like those above and students could explore the patterns in the change in surface area. OR, students could explore how many different cuboids can be made and to make links with factors. For example, with three cuboids the options are: 1x1x3, 1x3x1, 3x1x1 but for four cuboids the options are: 1x1x4, 1x4x1, 4x1x1, 2x2x1, 1x2x2, 2x1x2 Real life 3D shapes Students could be asked to find 3D shapes in real life. Perhaps they could bring them in or bring in photographs which could be used to create a classroom display. Time could also be spend exploring real life volumes and surface area by investigating questions such as What is the volume of the school hall? or What is the surface area of the science block.