Using Graphical Calculators in the Classroom

1
Using Graphical Calculators in the Classroom

• Richard Tarry
• Sept 2003

2
Setting up the calculator

• If necessary insert the 2 batteries supplied
• After you have inserted the batteries, pull out
  the protection strip
• All users reset the calculator by pressing a
  pen into the little hole above the battery
  compartment
• Press YES (F1) below the screen, then press MENU

3
Getting Started

• Press AC/ON to switch on
• The calculator uses a menu system
• Lets go into GRAPH
• Either press the menu number (4) or navigate with
  the cursor to the GRPH icon and push EXE
• Push MENU to get back to the home screen
• Press QUIT to return to an earlier screen

4
Useful Modes
5
Learning the keys

• Find out how to add, subtract, multiply, divide,
  square, square root, raise to a power (such as
  53)
• Find out the difference between the and (-)
  keys
• EXE is like , it gives the answer
• Find out what SHIFT and ALPHA do
• Find out how you can use the cursor to edit a
  calculation
• Find out how to use DELete INSert
• Clear the screen
• Switch OFF

6
Some easy calculations
Do the following calculations and write down your
answers

• 4.1 x 3.8
• 6.5 ? 0.175 then edit to 6.5 ? 0.185
• 2.32 1
• ?40 ?20 . then edit to ?4.4 ?2.1
• (2.35 1.82) ? 0.9
• 4.15 ? (-2.5)3

7
Variables Memories

• Results of calculations are stored automatically
  and manually
• Ans automatically stores the last answer
• X,T is an easy access storage and also acts as
  the variable x
• The ? stores a value into a memory
• A, B, C, D, . Z are all memories

8
Using variables and memories - Ans

• Calculate 2 x 1.4
• Then type 1 EXE and explain what has happened
• Now calculate 3 x 1.4 , followed by 5 Ans.
• Now type 2 x Ans.
• Describe in your notes how ANS can be used

9
Using variables and the X,T, ALPHA memories

• Clear the screen
• Type 2 ?X EXE, then 3x2 5x 12 EXE. Check the
  answer and explain what the calculator has done.
• Now type 15 ? ALPHA A EXE, and 5 ? ALPHA B EXE
• Type 2A EXE, then B ? 2 EXE
• Type 3A 4B EXE
• Describe how you can use ALPHA memories.

10

• Using RUN mode
• Reset the calculator by pressing a pen into the
  little hole above the battery compartment
• Press YES (F1) below the screen, then press MENU

11
SET UP for RUN

• Enter RUN
• Enter SET UP
• Use the cursor and the function keys to set Angle
  to Deg(rees)
• Use QUIT to return to a blank screen
• This is the most common setup change!

12
RUN Mode

• RUN mode features
• On-screen display algebraic order
• You should use brackets
• You can work with fractions
• You can edit (before and after AC)
• Ans stores the last answer
• You can store part answers in ALPHA memories

13
Now start the RUN tasks
14
In your groups, find and write down the following
formulas

• Gradient of a straight line
• Pythagoras
• Area of a circle
• Area of an sector using an angle fraction
• The cosine rule
• Volume of a cylinder
• The quadratic formula
• Distance between 2 points

15
Using the cosine rule whats that???

• Use the cosine rule to find the length of the
  missing sides of a triangle with sides a 4.1
  cm, c 6.3cm, when angle B 30o , 70o and 110o
• Type 4.126.322x4.1x6.3 cos70 EXE
• This gives b2 now type ?Ans EXE
• Use the edit function to change the angle
• You will need to use AC before the Replay find
  out how this works!
• You should get answers of b 3.42, 6.23 and 8.61

16
The quadratic formula..

• Use the quadratic formula to solve 3x2 5x -
  17 0. Save both answers.
• Remember to use brackets!
• Use the edit function to get the 2nd solution by
  changing a plus to a minus.
• You should get answers of -3.355 and 1.688
• You should have typed (-5?(52-4x3x-17))?(2x3)
  EXE but there are other methods using a memory
  rather than a single calculation

17
Generating a sequence

• Write down the first 4 terms of the sequence un1
  1.05Un 20with u0 1500
• First type 1500 EXE (This stores 1500 in Ans)
• Type 1.05Ans-20 EXE
• Press EXE again, and againDescribe a situation
  that this sequence could model.
• You should get answers 1555, 1612.75, 1673, 1737

18
Using formulas write down how you enter each
formula into the calculator

• Find the gradient of a line passing through
  (3.1, 1.8) and (1.7, -5.3)
• Find the area of a circle of diameter 10.5 m
• If a right angled triangle has two shorter sides
  of 120m and 150m, how long is the longest side?
• Solve 1.5x2 6.3x 1.8 0
• Find the volume of a cylindrical can measuring 6
  cm in diameter and 12 cm high.

19
Here are a couple more

• v2 u2 2as (Mechanics)
• What does this describe?
• And from the AS Using Maths paper
• Tw 33 (33 T)0.47 0.3?v 0.02v
• Tw is windchill temperature (oC)
• T is temperature out of the wind (oC)
• V is the wind speed (mph)

20
Harder problems

• Find the speed of a ball after 10m, which was hit
  at 12.8m/s, and which then decelerates at 3.5m/s2
• Find the distance between the 2 points in Q1 on
  the previous slide.
• Find the windchill temperature if the temperature
  out of the wind is 8oC when the wind is blowing
  at 5 mph,10 mph and 20 mph
• Find the area of a sector that comprises 80o of a
  circle of radius 5 cm giving your answer as a
  fraction. You can take p 22/7

21

• End of RUN mode exercises

22

• Using the Statistics mode
• Reset the calculator by pressing a pen into the
  little hole above the battery compartment
• Press YES (F1) below the screen, then press MENU

23
STAT mode

• Enter STAT
• Data can be stored in Lists 1 6
• You can navigate around the lists with the cursor
• You can simply overtype existing data or delete
  an entire list

24
Entering data

• Enter the following data into List 1
• 10, 9, 9, 12, 15, 8, 3, 17
• You need to push EXE after each number
• The top row of function keys are used in
  conjunction with the screen

25
Deleting and inserting data

• Use ?in the top row just below the screen to
  obtain DEL, DEL-A, INS
• Move the cursor onto the 2nd 9 in the list, press
  F1 (DEL) what happens?
• Now press F3 (INS) what happens?
• Overtype the 0 with 8.
• Move the cursor to any position in List 1. Then
  press F2 (DEL-A). What happens?

26
Working with some data

• Enter the following data into List 1
• 10, 8, 9, 12, 15, 8, 3, 17
• F1 controls graphing press it
• Now F2 might draw Graph 2 press it and see
• If there is an error message on screen you need
  to press AC
• Press QUIT to return to the previous screen

27
SET the calculator to produce some statistics

• The SET function assigns statistical variables to
  your data lists press SET (F4)
• Use the cursor to assign List1 to 1Var X and 1
  to 1Var F
• This tells the calculator that your data is in
  List 1 and that each data point has a frequency
  of 1
• Then press QUIT

28
Statistical Calculations

• Press CALC (F2 ), then 1 VAR (F1)
• Use the cursor to scroll down
• Check that n8 (this this a good way to check you
  havent missed any data)
• Write down the mean and standard deviation, and
  the median and quartiles (Q1 Q3).
• What is the range of the data?
• Press QUIT when you have finished

29
Statistical graphs

• Press GRPH (F1 )
• Use?to obtain SEL SET
• Press SET (F4 )
• Use the cursor to move down the settings list
• Notice how a new set of choices appears at the
  bottom of the screen for each setting

30
Set up some graphs

• Set up StatGraph1 with
• G-Type Pie
• Data List1
• Display Data
• Set up StatGraph2 with
• G-Type Box (you will need to use ?)
• XList List1
• Freq 1

31
Draw your statistical graphs and use Trace (F1)

• Press GRPH (F1), then GPH1
• QUIT and press GRPH then GPH2
• Now press SHIFT followed by Trace
• Use the horizontal cursor to locate points on the
  box chart
• Sketch the box chart labelling the Trace points
• Use G?T to return to the statistics screen and
  then QUIT
• Explain what the box plot shows.

32
Analysing grouped data

• Delete any previous data
• Enter data oppositeinto Lists 1 2
• Discuss in your group what this data means

33
Set up for stats

• Enter CALC press SET
• Set up List1 as 1Var X and List2 as 1Var F
• Discuss what this means why not 2Var?
• QUIT to return to the List screen
• Enter CALC, 1VAR and scroll down the results

34
Analysis of the data

• Write down the answers to all these questions
  and make sure you understand them check if
  possible.
• Find the number of students who were surveyed
• Find the mean age
• Find the median age the quartiles
• Make a boxplot copy it show the position of
  the mean on your sketch
• QUIT

35
Another problem this time with two variables

• The data is on the next slide
• Enter the data in List 1 (Age) List 2 (Height)
• Use CALC and SET to to set up 2Var X
  List12Var Y List22Var F 1
• QUIT, press CALC and 2VAR

36
Data showing the ages and heights of some children
37
Questions

• What is the mean age of the children?
• What is their mean height?
• Press REG, then F1 (X)
• Copy down the values for a, b, r and write down
  the equation.
• Substitute a b into the equation and discuss
  what it means.

38
Further analysis

• Press GRPH then?then SET
• Set up StatGraph1 to draw a scattergram with
  Xlist set to List1, Ylist set to List2, Freq as 1
• QUIT and use GRPH to draw the scattergram
• Press x what do you notice?
• Then press DRAW. Copy what you see and relate it
  to your equation.

39
Advanced analysis

• Heres some more data to add to your lists
• Draw a scattergram but this time choose x2
• Write down the equation
• Compare the x and x2 graphs and explain what
  this shows

40
Useful tips

• If you want to clear the screen, press SHIFT,
  Sketch, then Cls (F1 ) the last graph only will
  be redrawn
• After you have drawn a graph, press G?T to return
  to the screen showing data
• You can COPY the equation into the Graph
  Functions list for later use

41

• End of Statistics section

42

• Using the Graphs mode
• Reset the calculator by pressing a pen into the
  little hole above the battery compartment
• Press YES (F1) below the screen, then press MENU

43
Working with Graphs

• From the menu, enter the GRPH mode
• Type 2X3 (use the X,T key) next to Y1 then EXE
• Press EXE again (or DRAW)
• Use Zoom (F2) OUT to display both intercepts
• Use Trace (SHIFT F1) to find the coordinates of
  the intercepts
• Make a rough sketch of the graph labelling the
  intercepts

44
Adjusting the view

• Press G?T a few times and see what happens.
• Press SHIFT F3 to obtain the V(iew) Window.
• Use the cursor to move down the settings
  discuss what they all do.
• Reset to Xmin to (-)4, max to 4, Ymin to (-)2,
  max to 6. You need to use EXE to store each
  setting you change.
• Redraw the graph.

45
Investigating graphs

• Press G?T to return to the Graph Function screen
• At Y2 type in 5 X and draw the graphs
• Adjust the View to show all intercepts add the
  new graph to your sketch

46
Using the Trace to solve equations simultaneously

• Press Trace (SHIFT F1)
• Use the left-right cursor to move along a graph
• The up-down cursor enables you to jump to the
  other graph
• Find the coordinates of the intersection as
  accurately as you can
• Now use Zoom and Trace to improve your accuracy
  write down your answer to 3 dp.

47
Simultaneous equations

• Solve y 2x 3 and y 5 x algebraically
  in your groups.
• Compare your answers to what you got for the
  graphical solution.
• Now solve y 3x 5 and y 4 - ½ x by
  algebra. Check your answer by drawing appropriate
  graphs.

48
Moving on Quadratic transformations

• Delete all previous graph functions
• Draw Y1 X2 and set the View to INIT(ial)
• Draw Y2 (X3)2 and Y3 (X2)2
• Return to the Graph Functions - investigate how
  to select and deselect functions.
• Make a labelled sketch showing all 3 graphs,
  their equations and x-intercepts.

49
Whats the rule?

• Make a table like the one above
• What do you think the rule is? Make up another
  equation and predict the transformation.
• Verify your prediction using the calculator

50
More transformations

• Delete or deselect functions Y2 Y3
• Draw Y X2, Y X2 2 and Y X2 3
• Adjust the View to show all the y-intercepts and
  copy a sketch
• Make a new table showing the transformations
• Predict, verify and formulate the rule as before.
  
• Whats the difference between the rules?

51
Combining transformations

• On the next slide are some quadratic functions
• Each is a double transformation from Y X2
  describe both transformations fully.
• Predict what the graphs will look like and sketch
  them.
• Verify using the calculator.

52
Transformations.

• Here they are
• Y (x - 5)2 3
• Y (x 3)2 1
• Y (x 10)2 50
• Y (x 100)2 500
• Y (x 200)2 - 80

53
Drawing a simple trig graph

• Delete all previous functions
• Press SET UP (SHIFT MENU)
• Change Angle to Deg(rees)
• QUIT and enter Y1 sin X
• Set the View to TRIG draw the graph
• Make a rough labelled sketch
• Show the coordinates of all intercepts and the
  maximum minimum points

54
A simple trig equation (advanced task !!)

• Return to Graph Functions
• Enter another equation at Y2 so that you will be
  able to draw and solve sin x 0.5
• Use Trace (and Zoom) to find four solutions to
  this equation as accurately as you can.
• Sketch and label your graphs
• How are the solutions related to each other?

55

• End of GRAPHING sessions !!

56

• Advanced stuff for A2 !!

57
More advanced graphing- parametrics

• Enter RUN mode, then SET UP
• Change F-Type to Parametric
• QUIT and enter GRAPH mode
• DELete existing functions

58
Demonstrate projectile motion

• QUIT RUN mode and enter GRAPH
• Set up the V-Window to Xmin 0, max 280,
  scl20Ymin -20, max 70, scl 10Tmin 0, max
  8, ptch 0.1

59
Projectile motion task

• A projectile is fired at a speed of 50 m/s, and
  an angle of 200 to the horizontal.
• Write down the equations of motion which will
  give the horizontal and vertical position of the
  projectile at time t s after firing
• Enter these equations as Xt1 and Yt1 .

60
Projectile task

• You should have writtenXt1 50Tcos20 andYt1
  50Tsin20 4.9T2
• If you did NOT write this, show on paper that
  these are correct

61
Modelling projectile motion

• Press DRAW, and use Trace to find the maximum
  height and the range of the projectile
• By changing the angle, find the maximum range
  that could be achieved, and the height at this
  angle
• Write down the range height at each angle you
  choose

62

• THE END