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What Makes A Good Resource - Graph Transforms

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Created on 09 August 2010 by ncetm_administrator
Updated on 27 August 2010 by ncetm_administrator

Graph Transforms

Resource description:
This resource is for the Graphs and Transformations topic at A level. It is suitable as a summary of the topic in C1, or revision of the topic in preparation for extending the topic in C3. It can be used as a revision or consolidation exercise. I have made three separate card sorts, each one showing various transformations of a given function. For each function there is a student sheet (randomised so that the class can cut them out themselves) and the solution sheet. The three functions, each of which can be worked on separately are:

• $y=x^2$
• $y=sin(x)$
• $y=x^3+3x^2-1$

Teacher comment:

My students often find difficulty in recognising the effect of a transformation and how it is expressed in f(x) notation. In particular:

• Visualising the effect it has on the graph of the function
• Linking it to the conventional function notation e.g. $y=x^2+1$
• Describing the transformation in mathematical terms

so I wanted to find a resource that would enable them to make some of these connections for themselves.

What I did:

My Year 12 group have just finished the OCR C2 course. There are students of different abilities within the group so I wanted to consolidate their experiences before we started on C3.I gave the

$y=x^2$

card sort to the group with little explanation. Students worked in groups to and were able to make sense of the activity without much intervention from me, although they did seek some clarification from each other. In total it took the class 20 minutes to complete the card sort.

Reflection:

The students felt that it had enabled them to work effectively in groups and that through discussion they had clarified some of their ideas. The more able students matched the composite functions, even though this is not covered until the C3 course.

The A* students felt it was easy and that they could have completed a card sort involving a more complicated function. All of them agreed that the activity had enabled them to revise the topic in preparation for C3.

I did feel that the more able students could have coped with more challenge in the activity and this might have come from matching more complicated equations to their pictures, but the key idea of understanding the effects of transformations of graphs would not have gained from this added complication! I could differentiate in future by asking the class to draw their own sketches of the graphs rather than providing them with the pictures.

submitted by Barbara Crook, Bideford College and Ben Hall, Exmouth Community College, Devon

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