Station A: Data Collection I
Water Draining
As a class, complete the table, comparing the height of water remaining and
the time elapsed.
1.
How long did it take for the tube to completely drain?2.
At what time was the largest drop in height?3.
At what time was the smallest drop in height?
4.
Use the TI-nspire to create a scatter plot. Sketch it here.5.
What type of relationship is being shown? (Lin/Quad/Exp) ___________________6.
Determine an appropriate equation for your data.Height = ________________________________________
7.
According to your equation, what was the height of the water at 22 seconds?Time
(s)
Height
(mm)
0
Station B: Data Collection II
Radioactive Half-Life
Radioactive material breaks down in a process known as radioactive decay. The time it takes for half of it to decay is known as its half life.
e.g. If the half life of a material is 9 hours, then an 8 kg sample will decay to 4 kg in 9 h.
You will model the decaying process of the radioactive chemical Pignatium. Pignatium decays about of its mass each day.
Data Collection and Presentation
The 100 dice will each represent 100 g of Pignatium.
Roll the dice to represent each day.
The grams (dice) that turn up “six” will have decayed (and must be removed)
Repeat the process until there are less than 6 grams remaining.
Record the data below. Graph the results. Label your graph properly. Day Mass (Dice)
Remaining
0 100 g
1 2 3 4 5 6 7 8 9 10 11 12 13
Conclusions: Answer on the back of this sheet
1. What is the y-intercept of this graph? Why does that make sense?
2. What type of relation (Linear/Quadratic/Exponential) appears to exist? Explain. 3. Based on your observations, what appears to be the half life of Pignatium? Justify. 4. Give an equation that represents the mass of Pignatium as a function of time.
Station C: Data Collection III
HANGING BAG
A bag has been suspended from the ceiling. Record the height (of the
top) in the table below. Now add one book at a time, recording the
height of the bag each time.
Modeling
a) Create a Scatter Plot of the data by hand.
b) What type of model will best fit the data?
c) Determine an equation to represent the data.
d) Show all calculations on the grid.
y = ______________________,
Analysis
e) What would have been (without
measuring) the height when 4 books
were in the bag? Show your solution.
f) Assuming the elastic cord could
withstand the load, how many books
would it take for the bag to stretch to
the floor? Show work.
g) What is the rate of change (Slope) for
this relationship? __________
h) What does the slope represent in the
context of the data?
Critical Thinking
i) How would the graph appear if a stronger elastic was used? (Add a dotted line to your
graph to illustrate this case.)
Number
of Books Height 0
1 2 3 5 6 7
Station D: Patterning I
Blocks
Use the sequences of squares below to answer the questions that follow.
a) Sketch the next term in the sequence.
b) Complete the table. The first three rows are done.
c) What model would be appropriate for each colour? White __________ Grey __________ Black ___________
d) Support each model choice from above.
e) Create a formula for the number of each colour. Use ‘n’ for the stage.
#W = ___________; #G = _______________; #B = ______________
f) How many of each colour would there be in the 100th stage?
g) A figure in the sequence has 56 grey tiles, what stage is it?
Stage #White #Grey #Black
0 4 0 0
1 4 4 1
2 4 8 4
3 4 5 6 7
Stage 0 Stage 1
Station E: Patterning II
Triangular Numbers
Data
The following pattern generates the triangular numbers. The triangular numbers are the total number of circles at each level. For example, Level 0 = 0, Level 1= 1, Level 2 = 3, Level 3 = 6….
Level 0 Level 1 Level 2 Level 3 Level 4
a) Sketch the next triangular number and add it to the table.
b) Determine the next three triangular numbers and complete the table. Analysis
c) Use the differences to determine a model for this relationship. ________________ d) Give a formula for the Triangle number (T), in terms of the level, (n).
T = ______________________________
e) Use your formula to determine the value of the 100th triangular number?
Beyond
f) Can you use your formula to figure out the sum of the numbers from 1 to 20?
g) Can you use your formula to figure out the sum of the numbers from 55 to 80?
h) The number 11026 is a triangular number. Which level is it at?
Level Number
0 0
1 1
2 3
Station F: Patterning III
Triangle Fractals
A Koch Snowflake is a pattern that starts with an equilateral triangle. Each subsequent diagram cuts each line segment into three pieces and replaces the middle segment with a smaller equilateral triangle (With only two exposed sides). See the diagrams.
Each line segment becomes
1. Complete the table that counts the number of sides. Do not try
to count the sides in Figures 3, 4, or 5. (…use a pattern)
2. Use the first and/or second differences (or ratios) to determine
the nature of the relationship. Circle the best choice.
Linear, Quadratic, Exponential
3. Give an equation that gives the number of sides
(N)
of each figure (
x)
.
N = ______________________________
Analysis
4.
How many sides would the 15th figure have? Explain.
5.
Which figure would have exactly 786432 sides?
6.
How would your equation change if you started with a pentagon (5 sides)?Figure Number
of Sides
0
3
1
2
3
4
5
0
Station G: Internet I
Working in the Trades
1.
Follow the instructions to locate a data set that will give
you data concerning the number of males enrolled in a
trades program in Canada for the last 20+ years. Then use
this data to predict the number of males that will be
registered next year.
Go to http://www.statcan.gc.ca/. Select English.``Browse by key Resource``>>Data Tables>>CANSIM
Enter “Table 477-0051” in the search line. Click SEARCH. A partial table will come up. Select “Add/Remove Data”.
Select 1. Geography>>Canada (only), 2. Major Trade Groups>>Total Major Trade Groups, (deselect the others) 3. Sex>>Male, 4.Time Frame>>1991 to 2007, 5. Screen output format>>Table, Time as rows. Then APPLY.
a) Complete the table. Some years have been left off to
reduce the work.
b) Enter the data into a TI-nspire. Switch Year to Time (The years 1991-2007 become the
Times 0 – 17), create a scatter plot. Sketch it here.
c) What type of relationship would model this data? ____________________
d) Give an equation that models this data.
Num = _______________________________
e) Use the equation
to predict
the number of males in a Major trade group in 2004.
Hint (Time = 14)
Number = ______________
f) In 2004, there were 267775. How does your prediction compare to the true value?
Year Time
# Males in
Trades
1991
0
1992
1
1993
2
1994
1995
1996
1997
1998
1999
2000
2001
Station H: Internet II
Cellular Phone Sales
1. Goto:
http://hypertextbook.com/facts/2002/BogusiaGrzywac.shtml.
There is a list of “Sales of Cellular Phones`` in the US from
1984-1993.
2. Complete the table.
a) Enter the data into a TI-nspire. Use Time instead of `Year`
(1984-1993 becomes 0-9). Count the phone sales in
thousands. (i.e. 7000 becomes 7, and 11 million becomes
11000). Create a scatter plot. Sketch it here.
b) What type of relationship would model this data? _____________________
c) Give an equation that models the data, include the ‘r’ value.
Num = ____________________
r = __________
d) Use the equation to predict the number of cell phones being sold in the US the year 1997.
Hint (Time = 13)
e) Could you use this equation to predict the number of cell phones in use today?
Year
Time
# Sales
(1000s)
1984
0
7
1985
1
1986
2
1987
1989
1990
1991
1992
Station I: Internet III
City Waste Production
Goto:
http://www.seattlecentral.edu/qelp/sets/038/038.html#Show.There is a list of “Tons of Solid Waste produced and the
Population of the municipality.
a) Select any 8 cities with a variety of populations. Do not
use Wasco. Complete the table.
b) Enter the data into a TI-nspire. (Ignore per capita.)
Create a scatter plot. Sketch it here.
c) What type of relationship would model this data? _____________________
d) Give an equation that models this data, include the ‘r’ value.
Num = __________________________
r = __________
e) Use your equation to predict the amount of waste (in tons) in Wasco (pop. 22600).
Predicted Value ________________
f) According to the table, Wasco produces 17997 tons of waste. How does that value
compare to your predicted value?
Station F: Pizza Slices
Consider cutting a pizza into the maximum number of pieces. We want to determine a formula for the maximum number of pieces (not necessarily equal) that can be created with ‘n’, a certain number of cuts.
0 cuts 1 cut 2 cuts 3 cuts 4 cuts
1 slice 2 slices 4 slices 7 slices A) Show that 4 cuts can produce 11 slices.
B) Complete the table. Use patterns to fill in the lower rows.
C) Calculate the first and second differences to determine an appropriate model. Model _________________________ Explain.
D) Determine a formula for the number of pieces, P in terms of the number of cuts, n. P = ________________________
E) How many pieces could 25 cuts produce?
F) If you have managed to cut a pizza into 121 pieces, how many (minimum) cuts were used? Cuts Pieces
0 1
1 2
2 4
3 7
