Optimizing: Security CamerasProjector Resources Security Cameras A shop owner wants to prevent shoplifting. He decides to install a security camera on the ceiling of his shop. The camera can turn right round through 360°. The shop owner places the camera at point P, in the corner of the shop. The plan view shows where ten people are standing in the shop. P-1

Optimizing: Security CamerasProjector Resources Math Content Standards This task asks students to select and apply mathematical content from across the grades, including the content standards: H.M:Model with MathematicsH.M:Model with Mathematics 6.RP:Understand ratio concepts and use ratio reasoning to solve problems.6.RP:Understand ratio concepts and use ratio reasoning to solve problems. 6.G:Solve real-world and mathematical problems involving area, surface area, and volume.6.G:Solve real-world and mathematical problems involving area, surface area, and volume. P-1

Optimizing: Security CamerasProjector Resources Mathematical Practices This lesson involves a range of mathematical practices from the standards, with emphasis on: MP1:Make sense of problems and persevere in solving themMP1:Make sense of problems and persevere in solving them MP2:Reason abstractly and quantitatively MP3:Construct viable arguments and critique the reasoning of othersMP3:Construct viable arguments and critique the reasoning of others MP4:Model with mathematics P-2

Optimizing: Security CamerasProjector Resources Plan View P-2

Optimizing: Security CamerasProjector Resources Planning a Joint Solution P-3 1.Take turns to explain your work and how you think it could be improved. 2.Listen carefully to each other and ask questions if you don’t understand or agree. 3.Once everyone in the group has explained their method, plan a joint method that is better than each of your separate ideas. 4.Make sure that everyone in the group can explain the reasons for your chosen method. 5.Write a brief outline of your planned method on your large sheet of paper.

Optimizing: Security CamerasProjector Resources Security Cameras 1.Which people cannot be seen by the camera at P? Explain your answer, showing clearly on the diagram how you know. 2.The shop owner says, “15% of the shop is hidden from the camera.” Show clearly that he is correct. 3.The shop owner decides to move the camera so that it can see as much of the shop as possible. a.Show on the plan view the best place for the camera, so that it can see as much of the shop as possible. b.Explain how you know that this is the best place for the camera. P-4

Optimizing: Security CamerasProjector Resources Sample Response to Discuss P-5 1.Each choose a sample response to work through and write your answers on your mini-whiteboards. 2.Explain your answers to the rest of the group. 3.Listen carefully to explanations. Ask questions if you don’t understand. 4.Once everyone is satisfied with the explanations, write the answers to the questions below the sample response. 5.Try to ensure that the student who writes the answers is not the student who explained them.

Optimizing: Security CamerasProjector Resources Sample Responses to Discuss: Simon P-7

Optimizing: Security CamerasProjector Resources Sample Responses to Discuss: Ellie P-8

Optimizing: Security CamerasProjector Resources Sample Responses to Discuss: Rhianna P-9