‘Navigate your way around the world, and in the jungle, using rotations!’
Choose four places around the world that you really like or would love to visit. Add them to the world map. Write a brief guidebook entry for the “rotations” journey you want your partner to take and then leave them to work out where the centre of rotation needs to be.
Think you understand rotation and centres of rotation? Try the “Jungle Obstacle” course, recording each of your moves. Watch out for the obstacles! Pass your “moves” sheet to your partner for them to check if you made it through the Jungle safely or not! Overview of the two tasks below:
Around the World
Students will need computers. Geogebra will need to be installed on the computers, it can be downloaded for FREE: Geogebra download.
First you will need to design your own journey around the world (see video overview above) using this ActivInspire file. If your school uses other whiteboard software you can make the same file using this map image as a background. If you would rather not use technology, but get students using pencil and string for this first activity, print off one of these world maps (free from http://english.freemap.jp/), students can then print off from google (or draw) and cut and paste their favourite places onto the map.
- Use this worksheet to record your moves from the Jungle Obstacle course Geogebra file.
- If you are using Autograph download this Jungle Obstacle file.
- These activities raise many interesing discussion points concerning different strategies for finding a centre, and angle, of rotation: Rotation Navigation TN
- Students can use the ActivInspire ready made file in the “resources” section above, or the teacher can quickly create, using the “map” image above the same file in whatever presentation software the school uses. Alternatively, the activity can be done using pencils and string on the “printable maps” above. Students’ use their intuition to get an intuitive, conceptual grasp of the role and importance of the “centre of rotation” in a creative, game style activity.
- Students often come up with a wide range of correct solutions. It is important to take time, and examples, to discuss the number of centres of rotation and different angle solutions that students have used and that could be possible.
- Once the role of the centre of rotation has been understood, students then use the above geogebra embedded file, or autograph file, to complete and record their rotation moves around the Jungle obstacle course.
- Students pass the completed worksheet onto their partner who checks whether or not they allow a safe navigation through the Jungle i.e. does every move land on the red line and avoid the obstacles? This provides students with great experience of using coordinates to define the centre of rotation, and angles and direction (clockwise or anticlockwise) to complete the rotation.
For a detailed overview and help with performing rotations in Autograph and Geogegra see the video below. The Geogebra help runs until 2m10 into the video, the autograph help starts as of 2m10. Fast forward, rewind and pause as appropriate.
‘Discover Pythagoras’s theorem by investigating the areas of these Skewey Squares’
This is a fantastic investigation full of surprises that really help to understand how mathematical phenomena can be discovered by just playing with ideas. Using cm2 paper, can you draw a square with an area of 4cm2? What about 5cm2? In fact what whole number areas can be made with squares? This seems obvious at first, but a bit of lateral thought is required to answer this question fully!
There is a series of student worksheets to go with this activity that can be given out separately or all at once. Start with Skewey Squares and the the Hint Sheet. This can be followed by Skewey Squares to Pythagoras Theorem.
The following screen cast uses dynamic geometry just to quickly demonstrate how squares can be drawn at different angles to find areas other than square numbers.
Here follows an outline of what the task is.
- Try to draw squares with integer values from 1 to 30 and consider which are possible and which are not.
- Also with the numbers from 1 to 30, try to express as many as possible as the sum of two squares.
- Consider the common ground between the two previous investigations and what can be concluded from two sides of a right angled triangle.
- Work towards an expression of Pythagoras’s theorem and practise it in the context of this investigation.