Robyn came in again on Tuesday, 15 April, this time to discuss Grade 11 functions. If I have to be honest, functions is probably my favourite section in Mathematics, so I really enjoyed these conversations. There was a funny moment where we both got confused about the effects of ‘a’ and ‘b’ on the exponential function. (I am sure that we are not the only ones who get confused at times.) | |

We managed to figure it out and correct the wrongs, and then we spoke a little about how the subject Maths can be used to teach learners about how to cope with failure. Robyn brought up Dr. Carol Dweck’s research on fixed and growth mindsets. I promised to post a link to some of her work, and here is a YouTube interview with her, giving a brief overview: https://www.youtube.com/watch?v=MTsF2TaEaJA

__Robyn shared a couple of links for this section:__

Quadratic functions:http://academics.utep.edu/Portals/1788/CALCULUS%20MATERIAL/2_1QUADRATIC%20FNS%20AND%20MODELS.pdf

Textbook chapter: https://everythingmaths.co.za/grade-11/05-functions

End of chapter exercises: https://everythingmaths.co.za/grade-11/05-functions/05-functions-10.cnxmlplus

I have a few extra links for this section:

The Quadratic Function

Summary of the properties of the parabola:http://mrpilarski.wordpress.com/2010/01/05/using-properties-of-parabolas-to-graph-a-parabola/

This is a good resource to use for examples on finding the equation of a graph : http://www.algebra.com/algebra/homework/quadratic/Quadratic_Equations.faq.question.1829.html

A YouTube video showing how to draw parabola, not a resource to be used with learners as the different American terminology may confuse them:http://www.youtube.com/watch?v=8HvZHo-LSvQ

How to draw a parabola using their basic knowledge:http://www.purplemath.com/modules/grphquad.htm

A good resource, as one can generate multiple questions on an applet for finding the equation of parabola graphs: http://analyzemath.com/parabola/FindEqParabola.html

The Hyperbolic Function

PDF notes on the parabola and hyperbola:http://www.mathsexcellence.co.za/papers/graphs/GR11_GRAPHS_1.pdf

The Exponential Function

A resource that explores the different shapes of the exponential graph by investigating the variables in the equation: http://www.purplemath.com/modules/expofcns.htm

A detailed look at the exponential function and examples in real world context. A nice resource for educators to use to improve their knowledge of this function:http://www.mathworks.com/moler/exm/chapters/exponential.pdf

A resource that is in a simple format that can be used with the learners for them to further understand the exponential function:http://www.mathsisfun.com/sets/function-exponential.html

A resource that provides a step by step tutorial on sketching the exponential graph. The properties such as domain, range, horizontal asymptotes and intercepts of the graphs of these functions are also examined in details: http://www.analyzemath.com/Graphing/GraphExponentialFunction.html

A resource to be used by teachers to brush up on their knowledge, a little complicated for learners: http://wcherry.math.unt.edu/math1650/exponential.pdf

Find the equation of exponential graphs:http://www.analyzemath.com/expfunction/find_exponential_function.html

Mixed Algebraic Functions

Various transformation are explored and investigated: http://www.purplemath.com/modules/fcntrans.htm

Free software that can be downloaded which draws graphs. Very easy to use: http://www.padowan.dk/

A colourful resource that shows clearly the transformation by colour coding:http://www.mathsisfun.com/sets/function-transformations.html

This resource provides ideas for teachers that can be used in the classroom: http://www.greatmathsteachingideas.com/wp-content/uploads/2012/03/A7.pdf

This resource can be used to revise the concept of gradient before moving onto gradient between two points: http://www.mathsisfun.com/gradient.html

__Robyn’s 3 pressure points:__

- The effects of “p” and “q” on the graphs. Especially “p”, as it is a new concept.
- Being aware of the sign changes when working with “p”
- The application of knowledge to more difficult questions such as finding points of intersection, lengths of segments, maximum and minimum values etc.

__Robyn’s 5 point teaching strategy:__

1. Firstly give the learners the parent function in each case, and then get the learners to plot the function, point-by-point.

This gives the learners a procedural understanding of how the graph/table behaves.

2. When the learners know what each parent function looks like, it will be good to go into the characteristics of each function by varying each characteristic. I would recommend starting with the “a” value. This would show characteristics of the shape and direction of the graph.

3. I would then recommend varying the “p” and “q” values in each function. This will enable learners to see the effect of these variables. This will allow the learner to see the vertical and horizontal shifts

4. Once the learner has a conception of the shape of the graph, and the effects of “a”, “p” and “q” on the graphs, they will be ready to work with different types of problems on functions. The teacher will also be able to remind learners about some things which have been learned previously, such as the substitution of a coordinate into the correct place in an equation.

5. The teacher can then go on to problems which require a more holistic conception of the graph, such as reflections about the x and y axes, calculation of lengths, and finding points of intersection.

__Mindset resources for this section:__

Remember that all of these are CAPS aligned!

https://www.youtube.com/watch?v=fQmpRGyEl68&list=PLOaNAKtW5HLSev0_5mAwrVPFlWkt2J3KC&index=7

https://www.youtube.com/watch?v=HioQMb1as4U&list=PLOaNAKtW5HLSev0_5mAwrVPFlWkt2J3KC&index=8

https://www.youtube.com/watch?v=04CaUOonMOc&list=PLOaNAKtW5HLSnwMEtKTDaZBq0zzIJIPHx&index=10

https://www.youtube.com/watch?v=X5mYRAxwLhA&list=PLOaNAKtW5HLSnwMEtKTDaZBq0zzIJIPHx

https://www.youtube.com/watch?v=SD4ltmn4QRM&list=PLOaNAKtW5HLSnwMEtKTDaZBq0zzIJIPHx

https://www.youtube.com/watch?v=Az8ZuCZZH6s&list=PLOaNAKtW5HLSnwMEtKTDaZBq0zzIJIPHx

https://www.youtube.com/watch?v=bRSrA3Wf8FI&list=PLOaNAKtW5HLSnwMEtKTDaZBq0zzIJIPHx

Robyn did have other links for the other grades, but most of them were to the Everything Maths textbook found at https://everythingmaths.co.za/

Next week’s show ill be on Grade 12 Differential Calculus and will be streamed at live.mindset.co.za on 22 April 15:00. I look forward to chatting with you then. Remember to tweet us with the hashtag #vtmaths.

Until next time, happy teaching!