Tasks for using multiple representations to improve students’
mathematical understanding
1. Open the function Aplet. In the symbolic view (SYMB) enter an example of a
straight line y=mx+c such as F1(X)=2*X+3.
a. Enter a line with the same c but a different m, such as F2(X)=3*X+3.
View the graphs using PLOT.
How does c affect the line? Confirm this by viewing the table of values
NUM.
b. Edit F2 so that it has the same m but a different c, such as F2(X)=2*X+1.
By using PLOT and NUM describe how m affect the line. (You may find
ZOOM: INTEGER useful on the table of values).
c. For a given x-value what is the y-value (or vice-versa)?
d. What does m tell you about any two points on the line? How does this
relate to the table of values
e. Can the line ever be horizontal/vertical
f. Give me an example of a line
i. that passes through (2,5).
ii. that passes through the origin
iii. that passes through the x-axis at x = 3
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2. Open the Quad Explorer app. This features the graph of Y=a(X+h)²+v. +,- vary
a, vary h, vary v.
a. Explore the graphs by finding graphs with the following properties:
i. Has roots X1=1 and X2=3
ii. Has a repeated root at X=-3
iii. Has a vertex (minimum point) at (-1,2).
iv. Has one negative and one positive root.
v. Has a root at 0.
b. Write down examples of graphs with the following properties then use
the aplet to check your answers:
i. Has a repeated positive root.
ii. Has two distinct negative roots.
iii. Has a vertex in the first quadrant (x and y are positive).
iv. Has a root at 0 and positive root.
v. Has roots X1and X2 where X2 is twice as big as X2.
vi. Intersects the y-axis at a positive value and has one negative and
one positive root.
3. Open Function symbolic view (SYMB) and enter the equation of a function such
as F1(X)=X^2
a. On the PLOT screen trace a point on the curve. Measure the slope of
the curve at this point using MENU > FCN > Slope
b. Write down the x-value and the value of the slope for different values of
x.
c. Can you find a relationship between the x-value and the slope of the
curve.
d. Now try this for different values of x.
4. Open the sequence aplet.
a. Enter 2 sequences, e.g.:
U1(1)=2
U1(N)=U1(N-1)+3
U2(1)=1
U2(N)=U2(N-1)+4
Use the NUM and PLOT views to describe the sequences.
b. Can you define sequences U3(N) and U4(N) in terms of N so they are
the same sequences as as U1(N) and U2(N)
c. Can you find two sequences with the same 5th term?
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