PreCalculus

Contents Page

Standard Algebra

COURSE: PROBABILITY AND STATISTICS

TOPIC: Probability

STAGE 1: IDENTIFY DESIRED RESULTS
Content Standard(s) Generalizations about what students should know and be able to do
Established Goals: CT Frameworks: a) Use a variety of numerical representations in the base ten system to describe quantitative relationships. b) Understand and apply basic concepts of probability. NCTM Standards: a) Develop a deeper understanding of very large and very small numbers and of various representations of them. b) Understand the differences among various kinds of studies and which types of inferences can legitimately be drawn from each. c) Know the characteristics of well-designed studies, including the role of randomization in surveys and experiments.
Enduring Understandings Insights earned from exploring generalizations via the essential questions (Students will understand THAT…)	Essential Questions Inquiry used to explore generalizations
The more times an experiment is conducted the closer the empirical probability of an event occurring will be to its theoretical probability. When calculating probabilities scientific notation is necessary to represent small probabilities.	How many times should an experiment be conducted in order to make sure the conclusions are valid? Is the proper notation being used when representing small probabilities? What is the probability of winning a certain game?
Knowledge and Skills What students are expected to know and be able to do
Students will know… What an experiment is and how many times an experiment should be conducted. Scientific notation and how to represent large answers to counting problems and small answers to probability problems.	Students will be able to… Conduct an experiment several times in order to make a conclusion. Represent results in the proper notation Solve problems involving probability Create a game based on probability
STAGE 2: DETERMINE ACCEPTABLE EVIDENCE
Performance Task(s) Authentic application in new context to evaluate student achievement of desired results designed according to GRASPS (Goal, Role, Audience, Setting Performance, Standards)	Other Evidence Application that is functional in a classroom context only to evaluate student achievement of desired results
Students will conduct individual experiments and record their results. The class will then combine all of its data and determine whether the individual or class experiment brought the result closer to the theoretical probability. Students will create their own game (including game board, instruction pamphlet, and game pieces) based on the rules of probability and the study of current games on the market.	Classwork on experiments to emphasize the law of large numbers. Applications in class involving probability. Quizzes
STAGE 3: DEVELOP LEARNING PLAN
Learning Activities: Complete applications in Exploring Probability. Class experiments with spinners, dice, and coins to emphasize the law of large numbers. Play games and record relative frequencies of certain results.

COURSE: PROBABILITY AND STATISTICS

TOPIC: Statistics

STAGE 1: IDENTIFY DESIRED RESULTS
Content Standard(s) Generalizations about what students should know and be able to do
Established Goals: CT Frameworks: a) Collect, organize and display data using appropriate statistical and graphical methods. b) Analyze data sets to form hypotheses and make predictions. NCTM Standards: a) Understand the meaning of measurement data and categorical data, of univariate and bivariate data, and of the term variable. b) Understand histograms, parallel box plots, and scatter plots and use them to display data. c) For univariate measurement data, be able to display the distribution, describe its shape, and select and calculate summary statistics.
Enduring Understandings Insights earned from exploring generalizations via the essential questions (Students will understand THAT…)	Essential Questions Inquiry used to explore generalizations
There are several types of measures of central tendency and when is each type appropriate to use. Statistical graphs can be altered in a way to make a certain argument look favorable. Plots are necessary to interpolate and make predictions about future trends.	When is it appropriate to use mean instead of median or vice versa when making a claim using a measure of central tendency? Is a plot an appropriate representation of the data collected? What trends can be predicted by a chart representing the collection of certain data?
Knowledge and Skills What students are expected to know and be able to do
Students will know… What measure of central tendency is most appropriate for making a certain claim. When a plot is influencing the perception of a reader .	Students will be able to… Calculate mean and median by paper and pencil and with a TI-82 calculator. Construct number line plots, dot plots, stem and leaf plots, box plots, scatter plots, and time series plots with an appropriate scale. Make predictions based off of statistical plots.
STAGE 2: DETERMINE ACCEPTABLE EVIDENCE
Performance Task(s) Authentic application in new context to evaluate student achievement of desired results designed according to GRASPS (Goal, Role, Audience, Setting Performance, Standards)	Other Evidence Application that is functional in a classroom context only to evaluate student achievement of desired results
Given a set of data the students must determine which plot(s) are most appropriate to represent the data in a fashion as to determine a specific conclusion.	Applications in class involving statistics. Quizzes and tests.
STAGE 3: DEVELOP LEARNING PLAN
Learning Activities: Complete application problems in Exploring Data for classwork and homework. Conduct experiments and analyze the results using data collected from other class members. Play games and record relative frequencies of certain results. Use a TI-82 calculator to find mean, median, lower extreme, upper extreme, quartile 1, and quartile 3 for a large set of data.

COURSE: PROBABILITY AND STATISTICS

TOPIC: Permutations and Combinations

STAGE 1: IDENTIFY DESIRED RESULTS
Content Standard(s) Generalizations about what students should know and be able to do
Established Goals: CT Frameworks: a) Discrete mathematics is an effective problem solving tool. NCTM Standards: a) Develop an understanding of permutations and combinations as counting techniques.
Enduring Understandings Insights earned from exploring generalizations via the essential questions (Students will understand THAT…)	Essential Questions Inquiry used to explore generalizations
Permutations and combinations are necessary when counting a large number of outcomes. Permutations and combinations are used to solve different types of problems.	When is it appropriate to use a permutation or combination to solve a problem?
Knowledge and Skills What students are expected to know and be able to do
Students will know… The definitions and formulas for evaluating a permutation and combination. How to evaluate permutations and combinations on a TI-82 calculator.	Students will be able to… Solve counting and probability problems involving permutations and combinations.
STAGE 2: DETERMINE ACCEPTABLE EVIDENCE
Performance Task(s) Authentic application in new context to evaluate student achievement of desired results designed according to GRASPS (Goal, Role, Audience, Setting Performance, Standards)	Other Evidence Application that is functional in a classroom context only to evaluate student achievement of desired results
The students will be introduced to several different types of lottery games and must determine when order does and does not matter. Then they will calculate all the different possible outcomes that a lottery game possesses and why it is more likely to lose when playing.	Classwork examples. Quizzes and Tests. Conclusions about simulations conducted in class determining a game’s fairness.
STAGE 3: DEVELOP LEARNING PLAN
Learning Activities: Solving examples from Introduction to Statistics and Probability Ch. 3. Solving examples from games of chance to calculate probabilities and examine fairness. Analyzing examples to determine when a permutation or combination should be applied to solve the problem.