Geometry

Euler’s Formula with jubes and toothpicks

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Learning Intention: To distinguish between prisms and other three-dimensional shapes and to work out the relationship between vertices, edges and faces (Euler’s Formula).

These two Year 7 students are making three-dimensional models with jubes and toothpicks (or satay sticks) to record vertices, edges and faces. Start with simple shapes, such as triangular pyramids, cubes and square pyramids, distinguishing between shapes that are prisms and those that are not. When students have made at least six or more shapes ask them to see if they can find a relationship between V (vertices); E (edges) and F (faces). I usually give a clue that they only need to use addition and subtraction (not multiplication or division).

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Year 8 – Measurement and Geometry

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National Curriculum Standards: Students convert between units of measurement for area and for volume. They find the perimeter and area of parallelograms, rhombuses and kites. Students name the features of circles, calculate circumference and area, and solve problems relating to the volume of prisms.

To calculate the volume of any prism, multiply the area of the base by the height (or in the case above, the trapezium by the length of the trailer). Make sure all the units are the same before starting your calculations.

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Year 7 – Measurement and Geometry

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National Curriculum Standard: “Students use formulas for the area and perimeter of rectangles.”

The perimeter of a rectangle is calculated by adding the four sides. The area of a rectangle is calculated by multiplying the length by the width.

Perimeter =2 x (L+W) = 2L + 2W

Area = Length x Width = LW  

Find at least three rectangles around the classroom and measure the length and width. Draw a sketch showing the object and the measurements, including the units (millimetres, centimetres or metres). Calculate the perimeter and the area of the object using the formulae above.

For example; your laptop, the table top, your maths book, a window pane, the door, the whiteboard, the front of the heater, the noticeboard etc.

The perimeter of the locker door will be:

(2 x 35) + (2 x 59) = 70 + 118 = 188 cm

The area of the locker door will be:

35 x 59 = 2065 cm^2 (square centimetres)

Great Victorian Coding Challenge

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Over the next few weeks we are working with Scratch to create projects that demonstrate maths concepts using simple drag-and-drop programming. Please make sure you have completed the following steps:

1. Join Scratch with your school Username (eg gow0054) and Password. Being a registered member allows you to save and share your work. Make sure Mrs Gow has recorded your Scratch username.

2. Join the Hawkesdale P12 College Studio and the Victorian Coding Challenge (1, 2 and 3) Studios on Scratch, so you can share your work and see what other students have created.

3. Challenge #1: Create a character that draws a shape and upload to the Hawkesdale P12 College page.

4. Draw your initials, like these students in 5/6 Clark/Smith. Can you translate and reflect your initials so they appear in all four quadrats?

5. Challenge #2: Create a project that explains a maths concept. For example:

  • Draw  your initials in block letters and calculate their perimeter and the area they cover. Use the Cartesian Co-ordinate grid as a background.
  • Explain how to calculate the perimeter of a polygon or circle.
  • Name the parts of a circle (radius, diameter, circumference, sector, arc)
  • Describe different triangles (equilateral, isoceles, scalene, right-angled, acute-angled or obtuse-angled)
  • Explain how the sum of angles in a triangle always equals 180 degrees.
  • Explain how the sum of angles in a quadrilateral always equals 360 degrees
  • Explain how to calculate the area of a polygon (triangle, rectangle, parallelogram, trapezium, kite) or circle
  • Describe right angles, straight angles and complementary (adds to 90 degrees), supplementary (adds to 180 degrees) and equal angles.
  • Describe ‘pi’ and how it can be used to calculate the circumference and area of circles.
  • Describe Euler’s Rule about the faces, vertices and edges of a polyhedron (Faces + Vertices – Edges = 2)

Make sure you add your project to the Hawkesdale P12 College Studio page.

6. Challenge #3: Create a simple game that uses maths concepts. It could be something like this Hungry Fish game. Someone even created a Scratch project for Co-ordinate Grid Battleships.

Welcome Back for Term 2!

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This term we will be studying Measurement and Geometry.

Year 7 Maths (JacPlus Chapter 9 – Measurement and Chapter 5 – Geometry) 

By the end of this term I hope you will be able to:

  • Use appropriate units of measurement
  • Calculate the perimeter of 2D shapes
  • Calculate the area of triangles, quadrilaterals and composite shapes.
  • Identify types of polygons (different triangles and quadrilaterals)
  • Estimate, measure and draw angles between 0 and 360 degrees.
  • Identify the properties of parallel and perpendicular lines and the angles that form between them.
  • Calculate the missing angles in polygons, knowing that the internal angles of a triangle add to 180 degrees.
  • Recognise various transformations (translations, reflections, rotations and dilations)

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Year 8 Maths (JacPlus Chapter 7 – Congruence and Chapter 10 – Measurement)

By the end of this term I hope you will be able to:

  • Use and convert units of measurement for perimeter, area and volume
  • Calculate the area of various quadrilaterals.
  • Calculate the area and perimeter of circles.
  • Calculate the volume of various prisms using formulae.
  • Identify congruent shapes
  • Transform various shapes (translate, dilate, rotate and reflect).
  • Solve geometric problems using congruence.
  • Work out problems around different time zones using the 24 hour clock.