Getting to know you…

1. Task: • Think of 3 questions that you could ask the other students in the class • Question one should give you Qualitative data • Question two should give you Discrete Quantitative data • Question three should give you Continuous Quantitative data • Design a data collection sheet for each question and gather the data. • Keep your data safe. You will need it for future lessons… • You might need: • Ruler or tape measure • Weighing scales Getting to know you… maths@kes

2. Task: • Use your data from the previous task to: • Calculate an ‘average’ for each set of data. … • Draw a range of graphs and charts to represent your findings. You should include: • Frequency table • Bar chart(s) • Pie Chart(s) • Histogram(s) • Cumulative Frequency graph(s) • Write a report explaining what your graphs and calculations tell you about the group. • Which averages are most useful/ possible/ easiest for each set of data? • Which graphs are most useful/ possible/ easiest for each set of data? • You might need: • Protractor or pie chart scale • Graph Paper Doing Data… maths@kes

3. Task: Calculate an estimate of your volume. • Show your calculations clearly • State any assumptions and simplifications you made • You might need: • Formula sheet • Ruler • String • Weighing scales How big are you? maths@kes

4. Task: The toilet roll has 200 sheets. • How big would a toilet roll with 320 sheets be? • Show your calculations clearly • State any assumptions and simplifications you made • Draw a clear diagram of your ‘large’ toilet roll. • How much paper would be required to ‘wrap’ your roll? • You will need: • A Toilet roll • You might need: • Formula sheet • String Resizing Roll maths@kes

5. Task: Calculate how much metal would be needed to create • each of the containers shown. • Show your calculations clearly • State any assumptions and simplifications you made • Extension: What volume would each hold? • What length of weld would be used to create each one? • You will need: • Picture sheet • You might need: • Formula sheet How much metal? maths@kes

6. How much metal?- picture sheet maths@kes

7. Imagine you have 24m of wire. • Warm up: What rectangles could you make? • What length and width would each have? What area would each have? • Which would have the largest area? • Task: • What ‘sectors of a circle’ could you make? • What radius, arc length and angle would each have? What area would each have? • Which would have the largest area? • Extension: Can you solve this using algebra? • Show your calculations clearly • State any assumptions and simplifications you made • You might need: • Formula sheet • String • Compasses • Protractor Maximum sectors maths@kes

8. Imagine you have 20m of wire. • Task: • What triangles could you make? • Are there any limitations to the lengths of each side? • What area would each have? • Which would have the largest area? • What angles will each one have? • Extension: Can you solve this using algebra? • Show your calculations clearly • State any assumptions and simplifications you made • You might need: • Formula sheet • Compasses • String Maximum triangles maths@kes

9. Task: • Draw a triangular ‘ash cloud’ of the map of the British isles. • What is the perimeter of your triangle? • What is the area of your triangle? • What are the angles of your triangle? (in degrees and radians) • What are the equations of the three sides of your triangle? • Extension: • Give your partner SOME of the information above. • Can they reproduce your ash cloud? • Show your calculations clearly • State any assumptions and simplifications you made • You will need: • map sheet • You might need: • Formula sheet Ash Cloud maths@kes

10. Ash Cloud- map sheet maths@kes

11. In Sheffield the time of sun rise can be modeled as T = 2Cos(D) + 6 • Task: • Use the model above to estimate the time of sunrise today. • Use the model to plot times of sunrise on the first day of each month of the year • In Edinburgh the time of sunrise can be modeled as T = 3Cos(D) + 6 • Plot a similar graph for this model • In Minsk the time of sun rise can be modeled as T=2Cos(D) + 4 • Plot a graph of sunset times in Minsk • Suggest sun set and sun rise models for other places • What assumptions and simplifications do you think have been made? • You will need: • Graph paper or graph sheet • You might need: • Map sheet Where T = Time of sunrise (am) in GMT D = Day of the year eg Jan 1st =1 Sun rise maths@kes

12. Sun rise- map sheet maths@kes

13. Sun rise- graph sheet maths@kes

14. Task: • Find the gradient of your function at various places on your graph. • Plot the ‘gradient function’ on the same graph (or a different piece of graph paper) • What do you think your ‘gradient function’ is? • What assumptions and simplifications have you made? • You will need: • Graph sheet(s) Graph Gradients maths@kes

15. Graph Gradients- sheet 1 y = sin x maths@kes

16. Graph Gradients- sheet 2 y = cos x maths@kes

17. Graph Gradients- sheet 3 y = x2 maths@kes

18. Graph Gradients- sheet 4 y = x3 maths@kes

19. Graph Gradients- sheet 5 y = ex maths@kes

20. Graph Gradients- sheet 6 y = x2+x3 maths@kes

21. Task: • For each shape on the picture sheet: • Write an expression for the volume of the tank • Write an expression for the area of each face and for the total surface area • You will need: • Picture sheet • You might need: • Formula sheet Algebra Assortment maths@kes

22. Algebra Assortment-picture sheet maths@kes

23. Task: Think of things that spin. A record A CD A hard disk drive A drill The earth A roundabout … How fast do they spin? Convert your angular speeds to a variety of measures You spin me right round maths@kes

24. Task: • Roll a pen down a slope and record how far it rolls off the end (D). • Change one of the ‘variables’ (, h, l) • Roll the pen again and record the distance. Repeat! • Plot a suitable graph and try to find a link between your variable and the distance traveled. • Think about how you could improve your accuracy • You will need: • Pen • Plank • Books • Ruler/ tape measure Projectile Pen maths@kes

25. Task: • For each rocket find out: • The displacement function • The displacement when the time is 5 seconds • The velocity function • The velocity when the time is 10 seconds • The acceleration function • The acceleration at time zero seconds • Which rocket would win a race over a distance of 100m? 1km? What about other distances? • You will need: • Data sheet • You might need: • Formula sheet Rocket Race maths@kes

26. Rock-It Displacement = t2 + t3 Rock-Star Displacement = e2t - 1 Rock-n-Roll Displacement = 100sin(0.5t) Rocket Race - Data sheet Rock-A-Billy Velocity = t5-1 Rock-Lobster Velocity = et Rock-in-Robin Velocity = 50sin(t) Rock-A-Round Acceleration = t Initial velocity = 20m/s Rock-Fort Acceleration = e0.5t Initial velocity = 5 m/s Rock-Rooster Acceleration = 50sin(t) Initial Velocity = 0m/s All rockets have an initial displacement of 0m Some have a ‘flying start’ (initial velocity  0 m/s) maths@kes

27. Heating Oil is used to heat remote locations and those that are not on the gas mains. Task: Design a tank to hold 980 litres of heating oil. The tank is to be free standing and made of plastic. Try to minimize the amount of plastic you will need to use Create a scale model of your tank in card You will need: Thin card Scissors or craft knife You might need: Protractor Compasses Formula sheet Winter Fuel maths@kes

28. Task: Find values for the missing lengths, widths, perimeters and areas for metal sheets with the areas shown on the picture sheet. Which are easy to solve? Which are harder to solve? Why? Do any of the sheets have more than one possible solution? Which ones? Could any of the sheets be squares? Which ones? You will need: Picture sheet Metal Sheets maths@kes

29. Area = x2 + 8x + 15 Area = 2x2 + 14x + 24 Metal Sheets- Pictures Area = 15x2 - 3x Area = 3x2 + 11x + 6 Area = 3x2 + 12x - 15 Area = x2 + 2x - 8 Area = 4x2 + 20x + 24 Area = x2 + 6x + 9 Area = 2x2 + 5x + 2 Area = x2 - 25 Area = 6x2 - 24 Area = 2x2 + x - 15 Area = 2x2 + 3x maths@kes

30. Task: Sort the cards into appropriate sets Can you suggest values for the constant ‘k’ in each case? Resources: You will need: Scissors Card sheet You might need: Glue or tape Getting Hot, Hot, Hot maths@kes

31. Getting Hot, Hot, Hot- Card sheet maths@kes

32. Task: Starting from a circle of thin card, create the curved surface of a cone. Calculate the capacity of your cone. What is the maximum volume you can create? What area of card have you used? You will need: Coning ‘circle sheet’ Scissors You might need: Tape or glue Formula sheet Coning maths@kes

33. Coning - Circle sheet maths@kes

34. Task: Shiner and Britee make projector bulbs. Each company claims that their bulbs have an average lifetime of 1000 hours. Look at the information on the data sheets decide which of the two types of projector bulb you are going to order. Explain your reasoning You will need: Data sheets for Shiner and Britee projector bulbs Strike a light maths@kes

35. One pallet of Britee bulbs was tested. • The number of faulty bulbs in each box was as follows: One pallet of Shiner bulbs was tested. The number of faulty bulbs in each box was as follows: Strike a light- Data sheet • The working bulbs from the first carton of Shiner bulbs were • tested and had the following distribution of lifetimes: • The working bulbs from the first carton of Britee bulbs were • tested and had the following distribution of lifetimes: maths@kes

36. Task: Investigate the length of belt needed to go round two pulley wheels when they are various distances apart. Change the sizes of the pulleys Make the pulleys different sizes You might need: Formula sheet String Circular objects Protractor On the Pulleys maths@kes

37. engineering_objectives.xls Gives a quick reference to which tasks cover which topics Teachers notes.doc A summary of each task Resources you will or might need Learning Objectives What prior knowledge can be expected Ideas for differentiating the activity by outcome or support or different ability students maths@kes