Advanced Mathematics I

Advanced Mathematics I

(secondary)

essential UNIT 9 (E09)

(Probability and Statistics)

(July 2013)

Unit Statement: Almost daily we are presented with some kind of statistical information. In this unit the student will explore fundamental ideas about statistics and statistical analysis of data.

Essential Outcomes: (must be assessed for mastery)

The Student Willuse the fundamental counting principle to find number of ways in whichconsecutive events can occur (11.1)

TSWdistinguish between permutations and combinations and use formulas to find nPr and nCr (11.1)

TSWdistinguish between theoretical and experimental probability and use a two sided coin or a fair dice to demonstrate the law of large numbers for equally likely events (11.2)

TSWfind probability of multiple events (11.3)

TSWdistinguish between mean, median and mode.

TSW use a graphical calculator to analyze a set of values with a Box and Whisker Plot (11.5)

TSWdefineand interpret the meaning of standard deviation, and manually find standard deviation for a given set of values.

TSW use a graphical calculator or other software (such as MS Excel) to find standard deviation for a given set of values. (11.6)

TSWapply unit facts and concepts to a Real-Life application

Introduced and Practiced Outcomes:

The StudentWillinterpret and find variance for a given dataset.

Key terms and concepts:

QSI ADV MATHEMATICS I E09

Fundamental counting principle

Event

Permutation

Combination

theoreticalvs experimental probability

dependent events

independent events

mutually exclusive events

mean

median

mode

central tendency

variability

box and whisker plot

interquartile range

standard deviation

variance.

QSI ADV MATHEMATICS I E09

Suggested Assessment Tools and Strategies:

Attached Rubric or teacher-generated rubric that assesses ALL Essential Outcomes (TSWs).

* Examples of possible hands-on activities for this unit:

Analyze a probability of wining in a game of roulette.

What is the probability that a randomly flying meteor will hit your school?

Suggested Resources:

Textbook:Prentice Hall, Algebra 2, Pearson, ISBN -13: 978-0-13-350043-1, the online version of the textbook can be accessed at

Solve it! – short exercises in the textbook/also listed in teacher resources online

Practice form G, Practice form K – in teacher resources online

Additional Problems - in teacher resources online

Enrichment activities – in teacher resources online

Technology Links:

Teacher and student resources available through the publisher at

Simulate the binomial distribution:

EVALUATION RUBRIC FOUND ON FOLLOWING PAGE……………………

QSI ADV MATHEMATICS I E09

Suggested Unit Evaluation Rubric - ADV MATH I – E09

To receive a ‘B’ in the unit a student must demonstrate mastery of all TSWs
To receive an ‘A’ in the unit a student must demonstrate ‘A’ level mastery on at least 3 of the 5 identified TSWs.

Student name:______Date:______

TSW / ‘A’ LEVEL / ‘B’ LEVEL / Notes
1 use the fundamental counting principle to find number of ways in which consecutive events can occur / Students will apply the fundamental counting principle to simple everyday situations i.e. choosing a set of clothes to wear for the day. / The idea of randomness may be introduced as well as the fact that based on objective and subjective factors not all outcomes are always equally likely.
2 distinguish between permutations and combinations and use formulas to find nPr and nCr / Student evaluates a given problem and correctly choses combinations or permutations. / Student explains the difference between permutations and combinations and applies the correct formula when told whether to use permutations or combinations.
3 distinguish between theoretical and experimental probability and use a two sided coin or a fair dice to demonstrate the law of large numbers for equally likely events / Student correctly applies principles of probability in multi step combinatorics problems i.e. problem 4 on page 683 / Student will distinguish between examples of theoretical and experimental probabilities and will calculate both.
Student will calculate theoretical probabilities for a coin and for a fair dice and compare them to experimental probabilities. Students will combine their results to demonstrate the law of large numbers. / It is fun to bring to class a coin or a dice that is “tweaked” and have students use it.
It is important to note the idea of randomness and outcomes being equally and not equally likely. For example, a baseball thrown by a professional pitcher will not be thrown at random, so calculating geometrical theoretical probabilities with the ball thrown at random is not the best representation of the actual situation.
4 find probability of multiple events / The student will classify pairs of events as independent, dependent and mutually exclusive and will take this into account when calculating AND and OR probabilities.
5 distinguish between mean, median and mode / Using appropriate examples, student explains why arithmetic mean may not be the best representation of the central tendency. / Student evaluates mean, media and mode for a given set of data.
6 use a graphical calculator to analyze a set of values with a Box and Whisker Plot / Student explains the meaning of the box and the whiskers. The explanation includes a discussion on four quartiles, how each quartile is found and uses the term interquartile range. / Student uses graphical calculator to find and interpret a Box and Whisker Plot of a given dataset.
7define and interpret the meaning of standard deviation, and manually find standard deviation for a given set of values. / Student will create sets of data with the same central tendency but different st. dev. / Student explains what st.dev. is and calculates st. dev. manually for a small dataset, n ≤ 5.
8 use a graphical calculator or other software (such as MS Excel) to find standard deviation for a given set of values. / Student uses a graphical utility to find st.dev. for larger datasets.
9apply unit facts and concepts to a Real-Life application / Reflects on the project and consistently justifies the mathematical concepts used and how they apply to the activity. / Activity clearly demonstrates mastery of key concepts of the unit as defined in this rubric. Student articulates and explains mathematical concepts used. / The criteria for demonstration of mastery and beyond mastery of this TSW is developed by the teacher based on the activity (see Suggested Assessment Tools for examples of possible activities)

QSI ADV MATHEMATICS I E09