Learning Intention: To understand why, in any triangle, the exterior angle is equal to the sum of the two interior angles not adjacent to it.
Success Criteria: To be able to calculate the missing angles in a triangle, given enough information.
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.
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.
Your homework (due Friday) is one of the following:
This week we have been learning how to calculate the perimeter and area of circles and annuli (donut shapes) using ‘pi’. Remember that ‘pi’ is the ratio between the diameter and the circumference of a circle and is approximately equal to 3.14 or 22/7. Try this interactive at Illuminations, the Circle Tool.
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).
Go to the Shape tool and draw, color, paste, slice, rotate, reflect, expand, and contract various shapes. Create a picture that has vertical or horizontal symmetry (eg. mountain reflected in a lake, a rocket ship, UFO, Christmas tree, an animal – use your imagination). Make sure you take a screen shot, convert it to a jpeg file in Irfanview and email as an attachment to me at my gmail address. This is an assessment task, so use at least five different shapes!
Ben P. and Elektra have both used octagons and squares to tessellate. What other shapes can you find that tessellate? Is there a rule to predict which shapes will or won’t fit together? Might it have something to do with angles?
Once you have completed your tessellation, using the Tessellation Creator, take a screenshot, paste it into Irfanview then crop and save the file as a JPEG image. Then send your work as an attachment to my gmail account. The most creative tessellations will win an icecream voucher from the canteen.
![Ben's_tessellation[1]](https://technomaths.edublogs.org/files/2010/11/Bens_tessellation1-281zqme.jpg "Ben's_tessellation[1]")
Last week you learnt about Transformations – Reflections, Rotations, Translations and Dilations. Try this 2D Geometry tutorial with Jermaine to check that you understand what each of these terms mean. This week we will use these to create Tessellations – repeated shapes that create patterns that fill a space, without leaving any gaps. Tessellated tile verandahs were popular in houses of the Victorian and Edwardian periods. Using the Tessellations Creator find out which of the regular polygons (equilateral triangles, squares, regualr pentagons, hexagons etc) will tessellate. Check your answers at Tessellation: The Mathematics and Multimedia. Explore the world of Tessellations at www.tessellations.org and CoolMath.com.
When you play battleships you are learning more than just how to blow up your partner’s ships. It is a great way to learn about cartesian co-ordinates and mapping. Here is a selection of videos about the cartesian plane or cartesian co-ordinate mapping system from Online-math-learning. This simple maze game from Shodor Interactives requires the player to use cartesian co-ordinates to map a route to the target, avoiding the mines. The Graph Mole has two versions of the game with an animated introduction to cartesian co-ordinates. You could also use a grid on the interactive whiteboard in Elluminate or GroupBoard to set up your own battleships game with a partner. This game at “Free Online games” would be a whole lot better if it used mapping co-ordinates instead of just ‘point and click’ to the target square. IXL maths has some activities, including “points on the cartesian plane” and “co-ordinate graphs as maps“.
This one, “Co-ordinate Battleships”, created by Colin from Flying Colours Maths in UK, is especially good because it has both positive and negative co-ordinates. Play against the computer by typing the co-ordinates into the box. if anyone finds a way to play with a partner using an online whiteboard or grid co-ordinates, please let me know by leaving a comment in the chat.
Screen capture from Tom Barrett’s blog edte.ch
Maths Maps is an innovative learning activity designed by Tom Barrett, using Google Maps. There are three maps to choose from: Measures in Madrid, Shapes in Paris and Data Handling in Nottingham. Each map has questions marked with six colour-coded levels of difficulty from kindergarten to Year 5. The idea is to zoom in on a marker and answer the associated question – What is the name of the shape? How many tables can you see? What do you call the type of 3D shape above the Louvre?
Anne Mirtschin’s Year 9/10 Information Technology had a go at creating their own “Maths Maps” , or virtual treasure hunts, using maps from their local area. The idea was that they produce a “maths map” for students in a younger year level, targeting their questions for specific levels. This was an engaging activity that improves student’s on-line navgational and thinking skills as well as practising measuring, spatial orientation and basic operations.
Before the end of term we will be looking at transformations in Maths – reflections, translations, dilations and rotations. Your assessment task will be to create a poster your name, with each of the letters transformed in a different way. Transformations are useful for security cameras (to make number plates photographed at an angle easier to read for example) and computer graphics that make realistic animated movies or computer games. Read more at the Maths by Email newsletter.
Transformations definitions and demonstrations at Maths if Fun!
An excellent interactive site to learn more about Transformations at MathsNet.
