"Feel" the functions of nature's curves!
These two wire curves are different representations by students of the same function: Could they both be right? You can use your body to represent a function, now its time to sculpt some wire and "feel" the function: its highs, lows and turning points.
Just as a musician can hear a symphony when she/he sees a score of music, so a mathematician can see in algebraic functions the symphony of natures curves and lines, the blueprints of the universe!
Make a curve, then discuss the similarities and differences in each others wire curves, is there more than one way of representing the same function? Give reasons: try and use the graphs specific vocabularly you have learnt to describe your curves: x-intercept, amplitude, period, maximum etc.
Powerpoint of functions : construct these using your wire.
Different Graphs : print off these graphs and use them to construct, with wire, graphs to match the functions on the powerpoint. What are the key points that need to be fixed on the wire to get the curve right? Extension: Rewrite the degrees in radians?
- This activity is aimed at giving participants a real "feel" for graphs. Use your hands to sculpt the modelling wire (best material) or soldering wire to the right shape to fit the function.
- Look at the algebraic transformations of the function and try to transform your wire to match.
- Just as a musician hears a symphony when he looks at a sheet of music, so it is possible to write down the "algebraic score" that describes the wire pictures on the powerpoint. Is there more than one possibility? If so, give reasons.
- Time to get precise: Print off the "Different Graphs" PDF above and lay your wire on tp of a graph, bending the keypoints (maximums, minimums, x-intercepts, y-intercept) to their exact coordinates. With a mobile phone or school camera, take pictures to upload to a computer and paste into a homewok = a coordinate perfect(?), "wire image" of each function.