In this unit students select appropriate units for measurement and carry out practical measuring tasks. The context is measuring various attributes of an orange.
- Recognise that objects have many measurable attributes.
- Identify and measure attributes of common objects.
- Use devices to measure length, area, volume, capacity, and weight of objects.
- Express measures using numbers and units.
Measurement is about expressing a quantity for the attribute being measured, using a number and the unit. An attribute is a feature of an object such as its length, temperature, or mass (weight).
The units used in New Zealand are metric units, which are found within the Standard International Units of measurement (SI units). An important feature of modern measurement systems is that the units have an accepted size, so measurements mean the same irrespective of location in the world.
Common metric units used in New Zealand are:
- Length: Metre, centimetre, millimetre, kilometre
- Area: Square centimetre (cm2), square metre (m2), and square kilometre (km2)
- Volume: Cubic centimetre (cm3), cubic metre (m3)
- Capacity: Litre (L or l), millilitre (mL or ml)
- Weight: Gram (g), kilogram (kg)
- Temperature: Degrees Celsius (⁰C)
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to differentiate include:
- Modelling measurement of objects for students, especially use of scales.
- Asking students to work in mixed ability pairs.
- Reducing the demands of tasks, particularly not requiring the later part of each investigation.
The context for this unit is oranges. Since oranges are food, the context may not be appropriate for students from some cultures. It is important that the oranges are not wasted and are ultimately used as food at the completion of the unit. Adaptations can be made to the tasks to ensure the main objectives of the unit are retained.
- Replace oranges with foods more relatable to your students, such as carrots or taro.
- Replace oranges with non-foods such as balls, or other toys.
- Oranges (at least one per student)
- “Mr Archimedes Bath” by Pamela Allen (Available online)
- Measuring equipment including rulers, tape measures, weighing scales, measuring containers, thermometers.
- Plastic knives or peering knives
- Copymasters of Investigation Stations One, Two, Three, Four, Five
- Copymaster Six (grid paper)
In this session students discuss the attributes of an orange that could be measured.
- Present the class with an orange.
Ask: How can you measure an orange?
- Focus the discussion on the attributes of an orange that could be measured. List the possibilities on the board. For example:
- Amount of juice
- Circumference (distance around the middle)
- Weight (Mass)
- Number of pips
- Note to students that these options are all attributes or features/characteristics of an orange. Not all attributes are interesting, such as colour!
- For each attribute, ask students to describe how they would measure that attribute. For example, How might we measure the amount of skin on an orange? Ask students to give an accurate description of the equipment required and the method used. Make a chart with instructions for each measuring approach.
- Explain to students that over the next four days they will be measuring different attributes in small groups and then writing up a report about The Orange.
In small groups students attempt to measure attributes of an orange. These measurements will be compiled into a class report on The Orange.
- If you can, obtain a copy, read Mr. Archimedes' Bath by Pamela Allen. You can find several readings of the book on YouTube. The story 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.
- Discuss what the story is about.
- Explain that we are going to use what Mr Archimedes found out to measure one thing about an orange, its volume. Volume is about 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. The other attribute we discussed last session can also be measured in different ways. 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 1cubic centimetre (1cm3). That is the space of 1 small Base Ten cube (Show a cube).
Demonstrate finding the volume of another object, such as a carrot, using the Archimedes ‘dunking’ method.
- Finding the volume of an orange is one of five Investigation Stations students need to visit in the next lessons (One investigation in Session Two and two stations for sessions three and four).
You are going to work in small groups and work your way around the stations over the next three sessions. It is important that you record the results of your investigations on a chart about “The Orange” so we can discuss your results as a class.
- 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 students to different stations allows you to maximise the use of any equipment, particularly measurement scales and containers. Instructions for each station are contained in the Copymasters.
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 (Look for mL)
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
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.
In this session students 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 students might use a dot plot or a stem and leaf plot to represent those 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. One type of average, the mean, is shown with the line.
Students might select another attribute to investigate as a group over the last session. 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? (set a World Record)
- 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?