Bite-size Workshops June 2012 Mitch Howard Wendy Gibbs Stephen McConnachie

Why Bite-size Workshops? Show and tell. – we are really keen for more volunteers to present – Could be as little as 10 mins Help develop a culture of sharing of resources and ideas within Canterbury. Bit of a social get together. Networking Professional development – For presenters as well as guests – Feedback on ideas.

Ideas for future sessions Working with Primary schools Maths software demonstrations Group-work ideas Games Speed Date sharing Term 3 Week 7 Please feel free to any other suggestions or volunteer to do some show and tell.

2.1 Coordinate Geometry Historical background Discovery of rules Teaching and Practice of skills (direct instruction) Problem solving and discovery within a geometric context.

Where does it come from? Rene Descartes (1596 – 1650) – French Mathematician and Philosopher. – Cartography – m/watch?v=BHihkRwisb E m/watch?v=BHihkRwisb E “I think, therefore I am” How could I describe the position of those flies?

Maps before Descartes

portolan maps

Portolan chart by Jorge de Aguiar (1492), the oldest known signed and dated chart of Portuguese origin

Mapa mundi The T-O map was common. In this map format, Jerusalem was depicted at the centre and east was oriented toward the map top. About 1290 a.d.

Cartesian number plane

3 Dimensions

Problem 1 Find the midpoint of a straight line segment between two points, for example (2,5) and (6,3). Do lots of examples choosing different pairs of starting points. Generalise for the mid-point between any two points P 1 and P 2. Check the generality holds when negative ordinates are used.

Problem 2 Find the distance between two points (without measuring), for example (2,5) and (6,3). Do lots of examples choosing different pairs of starting points. Generalise for the mid-point between any two points P 1 and P 2. Check the generality holds when negative ordinates are used. (x 1, y 1 ) and (x 2,y 2 )

Hints Start with easier ones first – Horizontal or vertical What shapes could help you?

Skills, Rules and Formulas Midpoint Distance between 2 points Gradient Equation of a line Parallel and perpendicular lines Simultaneous equations

Task 1 Sketch up a rough set of axes and plot where the following points would be: (-18, 6) (0, 12) (-12, -12) (6, -6) What are your suspicions about the relationship between them? How could we use our coordinate geometry skills to confirm or deny our suspicions. What else could we find out about them?

PointsgradientDistanceMidpointEquation A(-18,6) B(0,12)

2.1 assessment Grade ADemonstrate at least 3 of the skills MRelate parts of the skills to the context. E.g. showing two lines are perpendicular EProving suspicions about the relationships. Make and justify conclusions. Investigate further properties.

Skill Relationship Conclusion and justification

Skill Relationship Conclusion and justification

Hints Make a sketch Decide what needs to be found out. Are there any obvious relationships? Justify them Are there any potentially interesting relationships? Justify them

Task 2 Sketch up a rough set of axes and plot where the following points would be: (-9, 15) (9, 27) (-3, 3) (15, 15) What are your suspicions about the relationship between them? How could we use our coordinate geometry skills to confirm or deny our suspicions. What else could we find out about them?

Task 3 Sketch up a rough set of axes and plot where the following points would be: (0,0) (10,-25) (-15,-15) (-10,-5) What are your suspicions about the relationship between them? How could we use our coordinate geometry skills to confirm or deny our suspicions. What else could we find out about them?

Feedback on practice assessment Always sketch and label a diagram first – So you get the lettering correct Visualise the shape and potential properties Can check if you calculations make sense against the diagram. Make a plan Working – Write Equation Substitution Answer (-16) squared

Actual assessment

Back up task

What was good Students knew what to expect in terms of the structure of how they were to be assessed They were encouraged to discover things and investigate. Easy to differentiate instruction. Other mathematical concepts such as properties of shapes and terminology such as altitudes, perpendicular bisector etc. (these required little teaching) Communicating mathematically Logic and proof It was actually fun using Geogebra to make up questions. The students responded really well.

2.2 Graphs The lesson sequence will have to be done at another time But...