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This is a CAD model of The Pantheon in Rome. It was built more than 1800 years ago and still stands today in its entirety! That's some pretty good engineering and architecture made possible by accurate mathematical modelling!
In this standard you will need to demonstrate these methods as listed in standard (with clarifications added where applicable):
I can work out
perimeters of 2D objects; circumferences of circles
areas of polygons (triangles to quadrilaterals); areas of circles
surface areas of common 3D objects
volumes of prisms; volumes of cylinders
volumes of pyramids; volumes of cones; volumes of spheres
unit conversions between length and area, between length and volume, and between volume and capacity in metric system
Work through the section below at your pace until you feel confident enough to tackle mixed problem.
What is mathematical modelling?
What is mathematical modelling?
Mathematical modelling is a process that helps mathematicians simplify a complex problem into its core parts to enable them to find a good solution. The usual steps are described below:
Determine what you want to know.
Determine what you already know.
Determine the physical principles (are there 1D, 2D or 3D limitations for example or compound units such as speed at play) that govern the model you want to create.
Identify the equations that you will need to use to find your answer.
Look at what others have done - don’t reinvent the wheel!
Create a diagram/plan for your model.
Create your model! (Once you have finished the planning phase, you should be able to create your model.)
Use your model.
Test your model.
Determine how the model could be improved.
Key skills suggested order of learning
Key skills suggested order of learning
You need to be confident working in 1 (perimeter or circumference), 2 (area) and 3 (volume) dimensions for this standard! The following sections tackle each of these ideas separatly.
You need to be confident working in 1 (perimeter or circumference), 2 (area) and 3 (volume) dimensions for this standard! The following sections tackle each of these ideas separatly.
Use the links below to see an introduction to managing these concepts :)
Use the links below to see an introduction to managing these concepts :)
1. Perimeter and Circumference
1. Perimeter and Circumference
How do we work out the perimeter of flat shapes?
How do we work out the perimeter of flat shapes?
Perimeter is a 1 dimensional measurement that describes how far it is around a shape.
What is PI? We need to understand where pi came from and what we use it for if we are going to be able to work out the circumference of a circle.
What is PI? We need to understand where pi came from and what we use it for if we are going to be able to work out the circumference of a circle.
Watch the first minute or so of this video to see how to calculate the distance around the outside of a circle (circumference)
(Area is after the 1minute mark)
Watch the first minute or so of this video to see how to calculate the distance around the outside of a circle (circumference)
(Area is after the 1minute mark)
2. Area of Triangles and Quadrilaterals
2. Area of Triangles and Quadrilaterals
Click on the title to watch this video to learn about how to calculate the area of some common 2D shapes. Area of Circles appears in the video above after the 1 minute mark :)
rectangles
triangles
parallelograms
trapeziums
circles
3. Metric units conversion: lengths, areas and volumes
3. Metric units conversion: lengths, areas and volumes
You need to be confident working with all kinds of metric units in this topic and converting between them :)
You need to be confident working with all kinds of metric units in this topic and converting between them :)
What is metric system?
What is metric system?
Key words:
base 10
prefix
suffix
How to convert lengths and areas in metric system?
How to convert lengths and areas in metric system?
How to convert volumes in metric system?
How to convert volumes in metric system?
6. Volumes of common 3D solids
6. Volumes of common 3D solids
Volumes of different solids
Volumes of different solids
Volumes of
prisms
pyramids
cylinders
cones
spheres
7. Right angled triangles: Pythagoras' Theorem
Use the website to get familiar with Pythagoras' Theorem c^2=a^2+b^2
How to apply Pythagoras' Theorem to find the surface area of a right-angled triangular prism.
Extension: Simple trigonometric ratios
This video recaps all the Year 10 SOH-CAH-TOA learning as well as Pythagoras.
You can use this link to get the overall idea of how we define trig ratios from a right-angled triangle.
Basic navigation spheros activity
Digital Tools for Mathematical Modelling
Digital Tools for Mathematical Modelling
How to use the SketchUp for schools for building basic shapes or advanced shapes.
How to use the SketchUp for schools for building basic shapes or advanced shapes.
Sketchup for schools for measurement.pdfSurface areas: Net diagrams
Surface areas: Net diagrams
You can use the pdf file to help you visualise 2D net diagrams from 3D solids.
Geometric-Nets-Printable-Pack.pdfPractice Tasks
Practice Tasks
Have a go at either of these task and check out the mark schedule below to see what level you are working at.
Have a go at either of these task and check out the mark schedule below to see what level you are working at.
Don't forget to let your teacher know when you think are ready to assess!
Don't forget to let your teacher know when you think are ready to assess!
Task sheets
Task sheets
Answers and feedback
Answers and feedback
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