Equipment: Tennis Ball

keep your eye on the ball

Equipment: Tennis Ball 2 blocks of polystyrene Ruler String

Useful Formula: CircleC = 2pr 4 Sphere SA = 4pr 2 V = pr 3 3

Questions: 1. Using the equipment provided, determine the radius of the tennis ball.

1. There is more than one possible method here. 2. Describe the measurements you made. (e.g. to measure the diameter of the ball I…) 3. Draw a diagram to show what you did. 4. Show all calculations. (You must do at least one calculation, regardless of your method!)

2. What is the surface area of the tennis ball? Show all calculations. State units.

Bonus Question

How much fuzz is on the tennis ball if the fuzz is 2mm in length?  Decide what type of problem you are solving here. (i.e. is it area or volume?)  Draw a diagram of the ball and its fuzz.  Show all calculations.  Give two limitations of the model you have used to find your answer, or explain why a different model could have been used. Kryptic Kryptonite

Equipment: Pink Rock Scales

Useful Formula: Cuboid V = l ҙ w ҙ h mass (g) Density D = volume (cm 3 )

Questions:

Lois Lane has found an unusual rock she suspects might be kryptonite. If she can find out the density of the rock she will know.

She needs to calculate the volume and the mass.

1. Sketch a mathematical shape approximately the same shape as the rock. Clearly show the measurements necessary to find the volume.

2. Calculate the volume of the rock. Show all working. Include units.

3. Use the scales provided to determine the mass of the rock.

4. Work out the density of the rock.

5. Give one limitation of your mathematical model.

Bonus Question

Lex Luther wants to make a life size sculpture of Superman out of Kryptonite. How much Kryptonite will he need?

(Clearly state all your estimates / assumptions made)

How much will the statue weigh? Concrete blocks

Equipment: Concrete Block

Useful Formula:

1 a + b A = x 2 A = l ҙ w A = bh A = ҙ h 2 2

Questions:

Tim Taylor has a backyard full of concrete blocks like the one given.

He wants to know the area of the largest face so that he knows how much ground each of his smaller blocks will cover.

1. Calculate the area of the largest face.

2. The area Tim wants to pave is 4m by 6m. How many blocks will he need?

Bonus Question

Tim needs concrete to pave this area. He needs a base layer of 5cm, as well as a 2cm strip between each of the blocks.

What area will he be able to cover using the number of blocks you calculated in Question 2?

How much concrete will he need? Swing problem

Equipment: Stop Watch Pendulum Ruler and tape, to tape it to desk.

Questions:

1. Set the length of the string to 25 cm and record the time taken for the pendulum to do 20 cycles.

(One cycle is the time taken for the pendulum to do 1 swing away from a point and back.)

2. How long does one cycle take?

3. Set the length of the string to 50cm and record the time taken for the pendulum to do 20 cycles.

4. How long does one cycle now take?

5. What is the connection between string length and cycle time?

Bonus Question

Estimate how long it would take for a 3 metre pendulum to complete one cycle.

Bonus bonus Question

l Use the formula t  2 , where t = time taken in seconds, g and l = length of pendulum; to find a value for g, which is the gravitational constant on Earth. The knee bone’s connected to the…

Equipment: Height measuring set Ruler

Questions: Humerus radius 1. Measure your height to the nearest centimetre.

2. Measure the length of your tibia, humerus and radius bones to the nearest centimetre. 3. The following are some formulas that archaeologists use to work out the height a person was from bones they have discovered. Use each of the formulas to calculate your height.

Male Female tibia H = 81.788 + 2.4t H = 72.64 + 2.5t H = 73.66 + 3.0h H = 65.024 + 3.1h H = 80.518 + 3.7r H = 73.406 + 3.9r

4. Which formula gives the best estimate of your true height?

Bonus Question 1. In ancient times people used to believe that intelligence was related to the volume of your skull. Choose a suitable shape to model your own skull. Take appropriate measurements so that you can estimate your skull’s volume.

Bonus Bonus Question Choose an appropriate model to estimate the amount of skin covering your head (i.e. the surface area of your skull). Include a diagram, all measurements and calculations in your answer. Make sure you include an explanation of what you are calculating at each step. Crowd control

Use the picture below to answer the following questions:

1. Given that the swimming pool in this picture is 50m long, work out the scale of the drawing.

2. Use a suitable shape to model the park. Use your shape to estimate the area of the entire park.

3. How many people do you think can fit in a 1 by 1 metre area? Use your answer to estimate the number of people in the park.

4. Give two limitations of the model you have used to find your answer, or explain why a different model could have been used.

Bonus Question Estimate how long it would take to evacuate this park. Clearly explain all your estimations and / or assumptions.

The icing’s on the cake

Equipment: Ruler Cake Shapes

Useful Formula: a  b A  x 2 A  l  w A   h 2 2 CylinderV  r h Cuboid V  l  w  h PrismV  area of end  h

Questions:

Mark is trying to decide between 3 different shapes of birthday cake as shown below. (rectangular, circular, heart shaped)

A template of the base of each cake is in the box. All of the cakes will be 7cm high.

1. Calculate the volume of each cake - which is the largest?

2. Each of the cakes will be iced. The top and sides must be covered. Calculate the area you will have to ice for each cake. Which cake needs the most icing?

Bonus Question

Your task is to design a wedding cake. There will be 100 guests and each guest should receive a piece of cake. What would be an appropriate size (i.e. volume) for each guest?

Design a cake with at least two tiers so that there is sufficient cake for all of your guests. Clearly explain all your working. aotearoa area

Equipment: Ruler Map of New Zealand

Questions:

1. Trace a copy of the map of New Zealand on the right into your book.

2. Use the map to estimate the perimeter and area of New Zealand.

 Divide the map up into shapes you know how to calculate the area of.

 Use the scale to convert your answers into kilometres and square kilometres.

Bonus Question

Round your answer sensibly. What are the limits of accuracy of your answers?

The true area of New Zealand is 28670 km2. What are the limits of accuracy of this figure?

The true perimeter of New Zealand is 15134 km. What are the limits of accuracy of this figure?

Shapes, circles and golfing lakes

Equipment: Ruler Shape A Circular protractor

Useful Formula: 1 a  b A  x 2 A  l  w A  bh A   h A  r 2 2 2

Questions:

1. Find the area of shape A. 2. What are the limits of accuracy of your answer? 3. Trace the circular protractor. Model the shape of the protractor using simple shapes. Make appropriate measurements and calculate its area. 4. The map below is of a small lake on a golf course. The scale is 1cm = 5m. The map is marked out in 1 cm squares. Find the area of the lake. money, money, money

Equipment: Ruler Briefcase Bundle of Cash

Useful Formula: V = l ҙ w ҙ h

Questions:

As the ninth caller into the local radio station you have won one million dollars in cash. The catch is, you are required to turn up at the radio station with a briefcase and you are only allowed to take as much money as you can carry away.

1. How many ten dollar notes will fit in this briefcase? Hint: You will need to calculate the volume of the briefcase and the volume of the fifty ‘ten dollar notes’.

2. How many briefcases would you need to carry one million dollars? What denomination of notes would they need to be in order to fit one million dollars into this briefcase? 3. Give at least two limitations of your model.

Bonus question:

How much would one million dollars (in ten dollar bills) weigh? Clearly explain all of your reasoning and calculations.

What would be the greatest amount that an average person could carry by themselves? Clearly state all your assumptions.

Free throw

Useful Formula:

1 a + b A = x 2 A = l ҙ w A = bh A = ҙ h V = l ҙ w ҙ h 2 2

Questions:

The photo below shows Michael Jordan at the hoop.

Given that Michael Jordan is 198m tall. Estimate the following:

 His arm span  His finger span  His foot length  His bicep measurement  His head length  His leg length

Bonus Questions:

Estimate the following:

 How high he can jump  The height of the basket  The area of the backboard  The diameter and volume of the basketball  The amount of surface area of the ball his hand covers