Session 1

In this session ākonga discuss the attributes of an orange that could be measured.

1. Present the class with an orange.
   Ask: How can you measure an orange?
2. Focus the discussion on the attributes of an orange that could be measured. List the possibilities on the board. For example:
   • Amount of juice 
   • Amount of pith
   • Skin
   • Circumference (distance around the middle)
   • Weight (Mass)
   • Number of seeds
   • Volume
   • Temperature
   • Strength
   • Flexibility
3. Explain to ākonga that these options are all attributes or features/characteristics of an orange. 
4. Display a range of measurement tools (e.g. scale, ruler, tape measure, measuring cups). Ask ākonga to describe how they would measure each attribute of an orange (the method), and what equipment they would use. For example, How could we measure the amount of skin on an orange? What method would we use? What equipment would we use? 
5. Make a shared chart with instructions for each measuring approach. As ākonga mention the use of specific equipment (e.g. scales), model the correct way to use the tool and to read the scale.
6. Explain to ākonga that over the next four days they will be measuring different attributes of an orange in small groups. The results from these investigations will contribute to a written class report about The Orange.
    

Sessions 2-4

This session is focussed around small groups of ākonga attempting to measure the attributes of an orange. The small groups could be organised startegically to encourage tuakana-teina. The measurements identified will be compiled into a class report on The Orange.

1. Obtain a copy (online or hard copy) of the book Mr. Archimedes' Bath by Pamela Allen and read it to the class. This story, from a New Zealand author, is a description of the famous observation Mr Archimedes made about displacement of water (in his bath) to find the volume of an oddly shaped object (himself). Archimedes was a great mathematician and scientist from ancient Greece. The real story about Archimedes investigating the metal in a crown is worth investigating later, and could provide an opportunity for extension.
2. As a class, discuss what the story is about.
3. Explain that we are going to use Mr Archimedes' discovery to measure one thing about an orange, its volume.  Volume is how much 3-dimensional space something takes up.  
   We can measure the volume of our orange by measuring how much water it pushes out of a container.  Finding volume is one of the stations set up for you to investigate. The amount of water displaced (pushed out) is measured in millilitres. 1 millilitre is the same volume as 1 cubic centimetre (1cm³). That is the space of 1 Base Ten cube (show a cube).
   Demonstrate finding the volume of another object, such as a ball, using the Archimedes ‘dunking’ method.
4. Explain to ākonga that finding the volume of an orange is one of five Investigation stations they will visit in the next lessons.
   You are going to collaborate in small groups (mahi tahi) and work your way around the stations over the next three sessions. It is important that you record the results of your investigations about “The Orange” so we can discuss your results as a class. Note that station 2 asks students to find an average, and station 4 asks students to measure an angle - you may need to model these processes.
5. An important feature of the investigations is that Investigation Four and Five (Segments and Juice) follow each other and destroy the essential equipment (the orange). Investigation Three results in a peeled orange. No oranges are harmed in Investigations One, and Two. Having a few spare oranges is a good idea.

Below is a list of materials needed for each Investigation Station. Allocating ākongato different stations allows you to maximise the use of any equipment, particularly measurement scales and containers. Students should make sure that they record their results for each station. Instructions for each station are included in the Copymasters.

Ensure all ākonga abide by health and safety protocols while carrying out these investigations. This includes hand washing, equipment washing, having a safe and clean working environment, and the safe use of knives. Discuss this as a class before beginning the station investigations.

Station 1:  Volume of the orange

You will need:

• Copymaster 1
• One orange
• A plastic ice cream container or some other large pot or container.
• A bowl that fits in the ice cream container but can completely contain an orange.
• A measurement jug (with mLs marked on the scale)

Station 2:  Weight of an orange

You will need:

• Copymaster 2
• Several oranges
• Kitchen scales for weight or a set of balance scales with weights

Station 3:  Area of an orange peel

You will need:

• Copymaster 3
• An orange
• A plastic knife to get the peeling started
• 1cm square grid paper (Copymaster 6)

Station 4:  Segments of an orange

You will need:

• Copymaster 4
• An orange
• A knife to cut your orange in half
• Cutting board to protect the desk
• A protractor
• A protractor (cleaned)
  Extras: other citrus fruit to investigate

Station 5:  Juice of an orange

You will need:

• Copymaster 5
• An orange
• A juicer (lemon squeezer)
• A teaspoon
• Two cups to hold the juice as you measure it.

During, or at the end of each session, gather the class to address learning needs that arise. The needs might be skills, such as reading scales on a measurement container or set of scales, conceptual, such as the connection between capacity measures and volume measures, or about managing tasks. 

Session 5

In this session, ākonga complete the write up of their Orange investigations, which are then compiled into a class report on The Orange. Collation of data affords opportunities for graphing and interpreting displays.

For example, the class might collect and display the weights for all the oranges. Since the data is measurement data, ākonga might use a dot plot or a stem and leaf plot to represent these data. The average can be interpreted in context as a measure of the centre of the distribution of weights. This graph was created using CODAP which is a freely available online graphing tool. Other digital tools such as Microsoft Excel or Google Maps could also be used. One type of average, the mean, is shown with the line.

Ensure you demonstrate how to use the graphing software or template you provide ākonga with. Provide clear expectations around what ākonga should write about their data (e.g. what is the mean, median, mode, highest and lowest quantities). Take into consideration the knowledge of statistics your ākonga already possess. You may need to plan some explicit teaching around interpreting the data. 

Ākonga might select another attribute to investigate as a group over the last session. Students could compare these with existing world records. Examples might be:

• How far does an orange roll down a ramp?
• How much time does the roll take?
• How long is an orange peel?
• What fraction of an orange are the pips, the peel, the flesh?
• How hot is an orange? How can you tell if an orange is sick by taking its temperature?
• How flexible is an orange? (Find a way to measure how out of shape an orange can get without bursting)
• What ratio of red and yellow paint produces the colour of an orange?
• How far can an orange be thrown and caught safely?
• Is an orange a perfect sphere? How far out of shape is it?
• Do oranges float in water? Does it still float if you peel it? Why does that happen?
• What numbers of oranges can be stacked to form a pyramid shape?