Shape

Surface Area and Volume

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Your homework this week is to take a photo of a rectangular prism in your home and label it with the measurements that will enable students to calculate the surface area and the volume of the prism. Some examples include a refrigerator, a freezer, a blanket box or a chest of drawers. What is the surface area of the freezer above? Remember you need to use all three measurements of height, width and depth and double for back and front, both sides and top and bottom. Please send your homework to brittgow(at)gmail(dot)com and don’t forget your Mathsmate for Friday!

 

Learning Intentions for this unit

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1. Classify triangles according to their side and angle properties and describe quadrilaterals.

2. Establish the formulas for areas of triangles, rectangles and parallelograms and use these in problem solving.

3. Demonstrate that the angle sum of a triangle is 180 degrees and use this to find the angle sum of a quadrilateral.

Tripods, tricycles and triceratops!

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Learning Intention: To learn to work independently and improve student understanding of angles and triangles, specifically how they are classified.

Success criteria: You will complete all of the activities listed below before next Wednesday.

Sorry I am not at school today – you probably heard my voice failing due to a sore throat this week! While most of our class are at the MWC Winter Sports today (good luck footballers and netballers!) you have a few choices:

1. Page 236 from “Oxford Big Ideas 7” – Classifying triangles.

2. Mathsmate (Term 3, week 3) due tomorrow

3. Mathletics – I have set three new activities for each student about angles and triangles.

4. Go to the National Library of Virtual Manipulatives and choose “Congruent Triangles”. You need to use the sides and angles to create two triangles that look the same.

Measuring Angles, triangles by side length and angle size.

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Learning Intention: You will understand that angles are measured in degrees and be able to name and identify different types of angles and triangles. You will be able to use a protractor effectively and be able to estimate angle sizes.

Success Criteria: You will be able to estimate, draw, measure and identify angles measured in degrees. You will be able to identify, name and draw triangles by side length and by angle size.

This term we will start by measuring angles, using a “rotogram” and then a protractor. You will all need your geometry kit this semester – compass, sharp grey lead pencil, protractor and a good ruler.

What are acute, right, obtuse, straight and reflex angles?
What are equilateral, isosceles and scalene triangles?
What are acute, right and obtuse triangles?
Can you have an equilateral right angled triangle or an obtuse equilateral triangle?
Can you have an obtuse isosceles triangle or a right-angled isosceles triangle?

Task 1: Work in a group of three. Each person should draw and cut out six copies of an equilateral, isosceles or scalene triangle, using different coloured paper. Share your shapes so that each person in the group has two of each type of triangle. Now, tear off the corners of one of each type of triangle and match up the corners to demonstrate the sum of the angles in a triangle.

Task 2: Do the same for acute, obtuse and right angled triangles. Do you think the sum of the angles in a triangle will always be the same? Can you explain why? Do you think the same would be true for quadrilaterals, pentagons and hexagons etc?

The Maths Masters have written a very interesting article in The Age about the triangles in Federation Square.
Read more →

Angles in Polygons

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Building construction in Perth

Learning Intention: Students will understand the relationships between lines, shapes and their angles in triangles, quadrilaterals and other polygons.

Success Criteria: You will be able to calculate the missing angles in various two-dimensional shapes and parallel lines by knowing the sum of the angles of that shape and which angles are equal, complementary or supplementary.

You know that the sum of the angles in a triangle is 180 degrees and in a quadrilateral is 360 degrees, but do you know how to work out the sum of the angles in any polygon? What is an exterior angle? What are complementary and supplementary angles? What are opposite, corresponding, alternate and co-interior angles? These are the questions we will answer in the next unit of work.

Composite shapes

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composite shape

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Learning Intention:  Understand that the area of all composite shapes can be calculated by breaking the shape down into known areas.

Success Criteria: You will be able to summarize the formulae to calculate the area of the following 2 dimensional shapes and break down a composite shape by identifying each of the known shapes and correctly calculating their area.

  • squares and rectangles
  • triangles
  • parallelograms
  • trapeziums
  • circles and annuli

Some examples of these kinds of problems are in Exercise 8G (page 326) of MathsQuest8. Here are some other activities to learn about the area of composite shapes.

  • An L-shaped room has a perimeter of 20m. What might the area of the floor be?
  • The difference in areas of two rectangles is 32cm (squared). What might the widths and lengths of the two rectangles be?

Your homework (due Friday) is one of the following:

  • Use Google Maps or Google Earth to find an aerial view of an unusual shape, take a screen shot and calculate it’s area using the scale measurements. Copy your screen shot into “Paint”, add the measurements, calculate the area and email it to me. You may choose a large building, carpark or arena (the MCG or Etihad stadium for example) or perhaps your farm or property.
  • Use a stencil or simple font to write the initials of your name,  and calculate the area of the letters. Make sure you email me a copy of your calculations, or leave a comment below about your task.

Surface Area and Volume of Prisms

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prisms

Image Source – Hexagonal prisms at the Giant’s Causeway in Ireland.

Firstly, what is a prism? A prism is a 3D shape that has cross-sections parallel to the base faces the same. Prisms are named for their base, so a prism with a triangular base is called a triangular prism (like a Toblerone package) and one with a pentagonal base is called a pentagonal prism. To work out the surface area of a prism, you need to calculate the area of each face and add them together. To calculate the volume of a prism, you need to work out the area of the base and multiply by the height of the prism ( the distance between congruent faces).