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Unit #1 - Data Management Outline (20 Hours)Topic Outcome Activities

VariablesDependent & Independent

C3 Gather data, plot the data using appropriate scales and demonstrate

Concept mapping Text activities p. 3, 4, 5, 6

Data Management Unit 2

an understanding of independent and dependent variables, and domain and range.

Pendulum LabDesign Your Own Lab F1

Design and conduct experiments using statistical methods and scientific inquiry.

Grandfather Clock Activity p. 3 Curriculum Doc.

Text activities p. 5

Design Lab & Report F1Design and conduct experiments using statistical methods and scientific inquiry.

Quiz on variable types Ski jump activity P. 3 Curriculum Doc. Chapter Project Intro p. 6

MeasurementAccuracy vs. precisionSignificant Figures

D7 Determine the accuracy and precision of a measurement.

Text. P. 8-9

Practicing Sig. Figures D1Determine and apply formulae for perimeter, area, surface area and volume.

Text. P. 10 Focus C In-class Assignment from p.5 Curriculum Doc.

Complete In-class assignment on Precision & Sig. Figures D1

Determine and apply formulae for perimeter, area, surface area and volume.

Text. P. 10 Focus C In-class Assignment from p.5 Curriculum Doc.

Describing Data:Finding the Average

The Mean, median and mode.F2

Demonstrate an understanding of the concepts and issues that pertain to the collection of data.

Quiz on Measurement & Sig. figs. Text. P. 15 Investigation 2 Test p. 16-18

Data lab – Pulse Rates F1Design and conduct experiments using statistical methods and scientific inquiry.

Quiz on mean, median and mode. Curriculum doc. P. 7

Distribution of Data Stem-&-leaf Plots Box-&-Whisker Plots F3 Construct various displays of data

Text p. 19-25 Curriculum doc. P. 9

Distribution of Data Box-&-Whisker Plots F3 Construct various displays of data


Distribution of Data Histograms A2

Analyze graphs or charts of situations to identify specific information


Chapter Project work F5

Analyse statistical summaries, draw, conclusions and communicate results about distributions of data.

Text p. 31

Using Data to Predict C9 Construct and analyze graphs and tables involving two variables.


Interpreting graphs using interpolation and extrapolation F10

Use interpolation, extrapolation, and equations to predict and solve problems.


Line of Best Fit F15 Approximate a line of best fit from a scatter plot.


Chapter Review Text p. 39-46 Curriculum doc. P. 9

Cause-and-effect Relationships & Mind Mapping

Experiments often search for a “Cause and Effect” Relationship. Mind maps can be used to represent cause-and-effect relationships.

Adding the correct amount of water can make plants grow taller

Exposing plants to more sunlight can make plants grow taller

Adequate rainfall increases growth


FOCUS QUESTION:

In Canada, Christmas tree farmers work hard to grow high quality trees that are harvested in Canada and sold locally and around the world. Each year, the farmers must ensure that there are enough trees of the appropriate size for use as Christmas trees. To do this, they must predict the factors that affect growth. Here are some of the factors that affect tree growth:

Wind speed; Number of pests that live in the trees; Amount of space that the trees have in which to grow; Number of people available to tend the tree farm.

1. On the following page, complete the mind map for this situation by adding the 4 variables above.2. Add at least 2 other factors you can think of that can affect tree growth.3. List the factors that the farmer can control. Explain how the farmer can control each factor in your

list.

Tree Farm Mind Map

Name: ____________________________________________ Date: ___________________

Mind Map

Using enough high quality soil can make plants grow taller

Adding a high quality plant food (fertilizer) can make plants grow taller


Factors the farmer can control How the farmer can control them:

VariablesIndependent variable: A factor that affects another factor in an experiment or a relationship.

Dependent Variable: The factor that is affected by the other factors in an experiment of a relationship. It can be thought of as the result or “what you measure”. This “depends” on what you did to it.


For example: How well you do on a test might depend on the number of classes you attended, how much you participated in the class activities, or how long you studied for the test.

In this example, what you measure (the result) is your test score. It is the DEPENDENT VARIABLE. What you did to achieve your test score (attending class, participating in class activities and length of time studying) are the INDEPENDENT VARIABLES.

In order to know exactly how one particular variable will affect another, you must hold all other possible variables constant. You must make sure that only one variable changes during an experiment and everything else is kept the same. All the other factors that might possibly affect the results of your experiment are known as “CONTROL VARIABLES”.

For example, if you want to know what affect light will have on the growth of tomato plants, you might grow 10 plants. Ideally, you should collect 10 identical pots, add exactly the same amount and type of soil to each pot, plant the same number and type of seeds in each pot, add the same type and amount of fertilizer to each pot and water the pots with the same amount of water. The ONLY thing that should be different is the amount of light you expose each of the plants to during the experiment. That way you will know that any difference between the plants is caused by the different light conditions and not some other variable.

Journal Entry

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Write a reflection on your understanding of variables. Describe at least one other the real-world cause-and-effect relationship. Identify the independent, dependent and control variables.


Check you Understanding #1

Name: __________________________________________ Date: ___________________

1) Identify the independent and dependent variables in each of the following

Situation Independent Variable Dependent Variable

AJim says that the amount of lumber that he can cut depends upon the time that he spends in the woods

BKarina says that the amount of time that you spend walking to school depends mainly on the distance of your home from the school.

C Kim earns more money in a 6 hour shift that she earns in a 4 hour shift.

DRob drives a transport truck. He is interested in the relationship between the amount of diesel fuel he uses and the size of the load in the trailer.

2) Complete the following table:

Description

Cause-and-Effect

Relationship (Yes or No)

Variables

Dependent Variable

Independent Variable

A The length of a candle and the amount of time it has been burning.

B The mark you get on a test and the time you spend studying.

C The speed of a car and the distance from the nearest gas station.

D The length of a movie and the admission price.

E The age of a car and its current value.

F The population of a community and its distance from the coast.

G The faster you drive and the number of speeding tickets you receive.

H The length of a beach and the size of the waves that crash on it.

IThe number of pages of the test paper and the time permitted to write the exam.


Check you Understanding #1 - Continued

Name: __________________________________________ Date: ___________________

3) Ski jumping is a popular event at the Winter Olympic Games. The following factors may affect the distance a skier jumps:a. Length of the ramp;b. Force with which the skier pushes to start;c. Wind speed;d. Wind direction;e. Model of the skis;f. Slope of the ramp.

Draw a mind map to illustrate the relationships between the dependent and the independent variables.

Factors the skier can control Factors the Jump Designer can control

Factors outside the control of anyone

Douglas Fir, 2.4m, $25$25



White pine, 2.0m, $20$25



Scotch Pine, 2.6m, $55$25




Check you Understanding #1 - Continued

Name: __________________________________________ Date: ___________________

4) Taylor wants to see how the prices of various types of trees depend upon the height.

Douglas Fir White Pine Scotch Pine

$55

$50

$45

$40

$35

$30

$25

$20

$15

$10

$5

$02.0m 2.2m 2.6m 2.0m 2.2m 2.6m 2.0m 2.2m 2.6m


a) Create a bar graph to show how the price of each type of tree depends upon the height.

Describe the relationship. ________________________________________________________

The Grandfather Clock Experiment - Pendulums

Name: __________________________________________ Date: ___________________

Cost ($)

Length (l) – is measured to the center of the bob.

Amplitude (a) – is the horizontal distance the bob moves to one side.

Mass of the bob

Amplitude of swing (height of release)


Journal Entry #2

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

A clockmaker is investigating the movement of the pendulum in a grandfather clock. The period of a pendulum is the time taken for the pendulum bob to make one complete swing (back and forth).

Three of the variables to consider when setting up a pendulum experiment are:

1. The mass of the bob (the weight on the end of the string);2. The length of the pendulum (the length of the string); and 3. The amplitude of the swing (the high the bob swings outward).

In this math lab, you will conduct experiments to find out which one affects the period of the pendulum.

You will carry out experiments to find out how each of the above variables affects the period of the pendulum (how long it takes to travel back and forth once).

Set up experiments and record your data in the tables below.

Eric made a long pendulum with a large bob and set it in motion with a large amplitude. He found that the long pendulum had a greater period than one with a short length, a small bob and small amplitude. He concluded that all three factors affect the period. What’s wrong with his conclusion?


______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Unit Project Bouncing Ball to Different Heights

Name: ________________________________________ Date: _______________________


As you already know, different balls bounce to different heights. During this unit you will investigate the relationship between the type of ball and the height to which the ball will bounce when dropped from a known height. You will be referring to the data, and examining the data in different ways, as you go through the chapter.

Stage 1

1) Identify the dependent variable: _____________________________________________

2) Identify the independent variables. Identify the variables that you can control.

3) Create a mind map to show how the variables interact.

Measurement


1) List as many things as possible that can be measured:

2) Look closely at the measuring devices below. Answer the questions on the following page.

Measuring cup Stopwatch Ruler Electronic balance

Clock Balance scale Thermometer Graduated cylinder

Bathroom scale Beaker Tape measure Wind speed meter

Speedometer Trundle wheel Radar gun Digital thermometer

Measuring Devices - continuedExploring the pictures on the previous page, answer the following questions:


a) What quantity can you measure with each tool? Write it in the space below the name of the device on the previous page.

b) Many of the devices measure the same quantity. Why are there different types of measuring tools for the same quantity?______________________________________________________________________________________________________________________________________________

c) What do you think the term measurement precision mean? ______________________ ______________________________________________________________________________________________________________________________________________

d) Which instruments provide the most precise measurements for each type of quantity? Why?

Distance Time Weight Temperature Speed

e) For each tool, what sorts of errors could the used make if he or she were not careful? Are they errors of precision or accuracy or both? Definitions are on the next page.

Measuring cupStop watchRulerElectronic balanceClockBalance ScaleThermometerGraduated cylinderBathroom scaleBeakerMeasuring tapeWind speed meterSpeedometerTrundle wheelRadar gunDigital Thermometer


Accuracy & Precision

Accuracy Accuracy is how close a measured value is to the actual (true) value. Accuracy is the difference between our own calculation and the accepted “real” value. Accuracy has a lot to do with your skill with using measuring tools and the care you take when reading the measure.

Precision Precision is how close the measured values are to each other. Precision has a lot to do with how finely spaced the divisions are or how specific the tool is able to measure. The smaller the unit you use to measure with, the more precise the measurement is.

Sometimes in real life we don't want to be precise.

For example, if someone driving by stops and asks you how far it is to the next town, you wouldn't reply 'It's about 3,270,132 centimetres'. Or if asked your age, you certainly wouldn't say '7776023 minutes'.

These answers are more precise than 'about 30 kilometres' and 'I'm fifteen'. But you use the less precise answers anyway ... probably because they're easier to remember.

In the top ruler measurement we can only see that the pencil is somewhere between 9 and 10 cm long.

∴ ~9.5 cm long The underlined digit is a guess

In the second measurement, you can see that the tip of the pencil falls just after the 5th division after the 9 cm marker.

∴ 9.51 cm long The underlined digit is a guess.

Therefore, we can state, with greater precision the length of the pencil using the 2nd ruler (with mm markings rather than just cm markers).


Examples of Precision and Accuracy:

Low AccuracyHigh Precision

High AccuracyLow Precision

High AccuracyHigh Precision

Significant Digits

The following are examples that show how to count the number of significant figures. Using the examples, try to develop 4 rules that cover all the examples. Digits that ARE NOT significant are crossed out.

Number # Significant Digits Number # Significant Digits

34.5 3 24703 53000 1 3000. 4

70600 3 0.00705 30.0250600 6 4503007000 7

475002 6 4750020 60.0003064006000 10 4050073.0 8

Create your rules:

Rule # 1: (What have you noticed about non-zero digits?). When are they significant?

______________________________________________________________________________

Rule #2: (What have you noticed about zeros in the middle of numbers?

______________________________________________________________________________

Rule #3: (What have you noticed about zeros that appear to the left of non-zero digits?)


______________________________________________________________________________

Rule #4: (What have you noticed about zeros that appear to the right of non-zero digits?)

____________________________________________________________________________________________________________________________________________________________


http://www.youtube.com/watch?v=5UjwJ9PIUvE

To recap:

1) ALL non-zero digits are significant. E.g. 4.5 (2 sig. figs.); 615.2384 (7 sig. figs.)2) Any zero sandwiched between non-zero digits ARE significant. E.g. 405 (3 sig. figs.)3) Any zero that comes to the right of non-zero digits are significant IF THERE IS A

DECIMAL POINT somewhere in the number. IF there are no decimals, non-sandwiched zeros to the right are NOT significant. E.g. 5,000.0 (5 sig. Figs) but 5,000 (only 1 sig. fig. because there is no decimal).

4) ANY zero to the left of a non-zero digit (when not sandwiched) are NOT significant. E.g. 0.00523 (only 3 sig. figs. – the 523),

Count the significant digits:

Number # of significant digits? Rules Applied

A 52.7

B 407 000

C 230700.0

D 0.005035

E 0.036400600

F 1050034.0900

G 24.000000

H 10.830600

I 0.00206

J 10300.00

K 5038.0050

L 0.0000002

M 2.0000002

N 2.000000200

O 605300200000

Investigation #1: Measuring Accuracy and Precision

http://www.youtube.com/watch?v=5UjwJ9PIUvE


Name: _________________________________________ Date: _________________________

Purpose: To explore the precision and accuracy when measuring.

Procedure:

A. Working with a partner, use a centimetre ruler to measure the dimensions of the figures below. Be as accurate and as precise as possible. Calculate the areas of each figure. Each partner should carryout their own measurements and their own calculations.

B. Compare your measurements and the calculated areas for each polygon (shape) with your partner’s measurements. How do they compare?

C. Repeat the above measurements, but this time use a millimetre ruler. Report each measurement in centimetres. For example, report a measurement such as 82.2 mm as 8.22 cm.

Figure Area Formula My measurement (cm)

My Calculated Area (cm2)

My partner’s measurements

(cm)

My partner’s calculated areas

(cm2)

Difference between my area calculations and

my partner’s ( cm2)

Rectangle A = lw l= ________w= _______

l= ________w= _______

Trapezoid A = ½h(a + b) a= _______b= _______h= _______

a= _______b= _______h= _______

Triangle A = ½ bhb= _______h= _______

b= _______h= _______

Parallelogram A = bhb= _______h= _______

b= _______h= _______

Figure Area Formula My measurement My Calculated My partner’s My partner’s Difference

RectangleTrapezoid

Parrallelogram

Triangle

Using a centimeter ruler

Using a millimeter ruler


(cm) Area (cm2) measurements (cm)

calculated areas (cm2)

between my area calculations and

my partner’s ( cm2)

Rectangle A = lw l= ________w= _______

l= ________w= _______

Trapezoid A = ½h(a + b) a= _______b= _______h= _______

a= _______b= _______h= _______

Triangle A = ½ bhb= _______h= _______

b= _______h= _______

Parallelogram A = bhb= _______h= _______

b= _______h= _______

D) Which measurements were more precise: the ones found using a centimetre ruler or the millimetre ruler? Explain.

______________________________________________________________________________________

______________________________________________________________________________________

______________________________________________________________________________________

______________________________________________________________________________________

E) What are some of the reasons for the differences in the values between you and your partner?

______________________________________________________________________________________

______________________________________________________________________________________

______________________________________________________________________________________

______________________________________________________________________________________

Journal Entry #3

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Describe how the fineness of the scale on your measuring instrument affects the precision of the measurements you need to make. What are some real-world situations where this information is necessary?

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