maths@kes getting to know you… task: think of 3 questions that you could ask the other students in...

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Getting to know you…Task: Think of 3 questions that you could ask the other students in the classQuestion one should give you Qualitative dataQuestion two should give you Discrete Quantitative dataQuestion 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



Doing Data…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



How big are you?

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



Resizing Roll

Task: The toilet roll has 200 sheets.How big would a toilet roll with 320 sheets be?



Draw a clear diagram of your ‘large’ toilet roll.How much paper would be required to ‘wrap’ your roll?

You will need:• A Toilet rollYou might need:• Formula sheet• String



How much metal?

Task: Calculate how much metal would be needed to create each of the containers shown.



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?- picture sheet



Maximum sectors

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 clearlyState any assumptions and simplifications you made

You might need:• Formula sheet• String• Compasses• Protractor



Maximum triangles

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?



You might need:• Formula sheet• Compasses• String



Ash Cloud

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?



You will need:• map sheetYou might need:• Formula sheet



Ash Cloud- map sheet

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Sun riseIn 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) + 6Plot a similar graph for this model

In Minsk the time of sun rise can be modeled as T=2Cos(D) + 4Plot 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 GMTD = Day of the year eg Jan 1st =1



Sun rise- map sheet





Sun rise- graph sheet





Graph GradientsTask: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)



y = sin xGraph Gradients- sheet 1



y = cos xGraph Gradients- sheet 2



y = x2Graph Gradients- sheet 3



y = x3Graph Gradients- sheet 4



y = exGraph Gradients- sheet 5



y = x2+x3Graph Gradients- sheet 6



Algebra AssortmentTask: 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-picture sheet



You spin me right roundTask: Think of things that spin.A recordA CDA hard disk driveA drillThe earthA roundabout…

How fast do they spin?

Convert your angular speeds to a variety of measures



Projectile PenTask: 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



Rocket RaceTask: For each rocket find out:The displacement functionThe displacement when the time is 5 seconds

The velocity functionThe velocity when the time is 10 seconds

The acceleration functionThe 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 - Data sheet

Rock-It

Displacement = t2 + t3

Rock-Lobster

Velocity = et

Rock-n-Roll

Displacement = 100sin(0.5t)

Rock-A-Billy

Velocity = t5-1

Rock-Star

Displacement = e2t - 1

Rock-in-Robin

Velocity = 50sin(t)

Rock-Fort

Acceleration = e0.5t

Initial velocity = 5 m/s

Rock-A-Round

Acceleration = tInitial velocity = 20m/s

Rock-Rooster

Acceleration = 50sin(t)Initial Velocity = 0m/s

All rockets have an initial displacement of 0mSome have a ‘flying start’ (initial velocity 0 m/s)



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 cardScissors or craft knife

You might need:ProtractorCompassesFormula sheet

Winter Fuel



Metal SheetsTask: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- Pictures

Area = x2 + 8x + 15

Area = 4x2 + 20x + 24

Area = 3x2 + 12x - 15

Area = 2x2 + 14x + 24

Are

a =

x2 -

25

Area = x2 + 2x - 8

Area = x2 + 6x + 9 Area = 2x2 + 5x + 2

Area = 2x2 + x - 15Area = 6x2 - 24

Area = 3x2 + 11x + 6

Area = 2x2 + 3x

Are

a =

15x

2 -

3x



Getting Hot, Hot, HotTask: Sort the cards into appropriate sets

Can you suggest values for the constant ‘k’ in each case?

Resources:You will need:ScissorsCard sheet

You might need:Glue or tape



Getting Hot, Hot, Hot- Card sheet

The value (in £1000) of a car at time, t, after being bought.

The temperature of a cup of tea at time, t, after being made.

The population (in billions) of the world at time, t, in years after year 1800

The number of students studying on an engineering diploma at time, t, after the course starts.

The number of bacteria in a colony at time, t, after being fed.

The temperature of a sauna at time, t, after being switched on

A = 30 + 10ekt

B = 11e -kt

C = 100 - 80e-kt

D = 100 + 20e-kt

E = 0.3ekt

F = 20 + 80e-kt



ConingTask: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 glueFormula sheet



Coning - Circle sheet



Strike a lightTask: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- Data sheetOne pallet of Shiner bulbs was tested. The number of faulty bulbs in each box was as follows:

2 0 3 4 0

2 1 4 0 0

0 1 0 0 1

3 3 3 1 3•The working bulbs from the first carton of Shiner bulbs were

tested and had the following distribution of lifetimes:

Time to failure Number of bulbs

900<t<950 2

950<t<980 4

980<t<990 8

990<t<1000 22

1000<t<1020 15

1020<t<1050 3

1050<t<1100 2

1100<t<1200 2

•One pallet of Britee bulbs was tested. •The number of faulty bulbs in each box was as follows:

1 2 2 0 2

3 3 0 3 0

1 2 2 3 3

3 4 1 2 3

•The working bulbs from the first carton of Britee bulbs were

tested and had the following distribution of lifetimes:Time to failure Number of bulbs

900<t<950 0

950<t<980 5

980<t<990 7

990<t<1000 20

1000<t<1020 18

1020<t<1050 5

1050<t<1100 4

1100<t<1200 0



On the PulleysTask:Investigate the length of belt needed to go round two pulley wheels when they are various distances apart.Change the sizes of the pulleysMake the pulleys different sizes

You might need:Formula sheetStringCircular objectsProtractor







engineering_objectives.xls

Gives a quick reference to which tasks cover which topics





Teachers notes.docA summary of each taskResources you will or might needLearning ObjectivesWhat prior knowledge can be expectedIdeas for differentiating the activity by outcome or support or different ability students

maths@kes getting to know you… task: think of 3 questions that you could ask the other students in...

Documents

data task

roll task

formula sheet slide

set of data

data collection sheet

formula sheet string

picture sheet slide

data safe