Organization of Data for Analysis
By the end of this course, students will:
– locate data to answer questions of significance or personal interest, by searching well-organized databases;
– use the Internet effectively as a source for databases;
– create database or spreadsheet templates that facilitate the manipulation and retrieval of data from large bodies of information
that have a variety of characteristics (e.g., a compact disc collection classified by artist, by date, by type of music).
Using Diagrams to Solve Problems
By the end of this course, students will:
– represent simple iterative processes (e.g., the water cycle, a person’s daily routine, the creation of a fractal design), using diagrams that involve branches and loops;
– represent complex tasks (e.g., searching a list by using algorithms; classifying organisms; calculating dependent or independent
outcomes in probability) or issues (e.g., the origin of global warming), using diagrams (e.g., tree diagrams, network diagrams,
cause-and-effect diagrams, time lines);
– solve network problems (e.g., scheduling problems, optimum-path problems, critical-path problems), using introductory graph
theory.
Using Matrices to Model and Solve Problems
By the end of this course, students will:
– represent numerical data, using matrices, and demonstrate an understanding of terminology and notation related to matrices;
– demonstrate proficiency in matrix operations, including addition, scalar multiplication, matrix multiplication, the calculation of
row sums, and the calculation of column sums, as necessary to solve problems, with and without the aid of technology;
– solve problems drawn from a variety of applications (e.g., inventory control, production costs, codes), using matrix methods.
Counting and Probability
Overall Expectations
By the end of this course, students will:
• solve counting problems and clearly communicate the results;
• determine and interpret theoretical probabilities, using combinatorial techniques;
• design and carry out simulations to estimate probabilities.
Specific Expectations
Solving Counting Problems
By the end of this course, students will:
– use Venn diagrams as a tool for organizing information in counting problems;
– solve introductory counting problems involving the additive and multiplicative counting principles;
– express the answers to permutation and combination problems, using standard
combinatorial symbols, [e.g.,
– evaluate expressions involving factorial notation, using appropriate methods (e.g., evaluating mentally, by hand, by using a
calculator);
– solve problems, using techniques for counting permutations where some objects may be alike;
– solve problems, using techniques for counting combinations;
– identify patterns in Pascal’s triangle and relate the terms of Pascal’s triangle
5 blocks west and 3 blocks south of her home. Assuming that she leaves home and walks only west or south, how many different routes can she take to school?);
– communicate clearly, coherently, and precisely the solutions to counting problems.
Determining and Interpreting Theoretical Probabilities
By the end of this course, students will:
– solve probability problems involving combinations of simple events, using counting
techniques [i.e.,
– construct a discrete probability distribution function by calculating the probabilities of a discrete random variable;
– calculate expected values and interpret them within applications (e.g., lottery prizes, tests of the fairness of games, estimates
of wildlife populations) as averages over a large number of trials;
– determine probabilities, using the binomial distribution manufacturer estimates that 0.5% of the bulbs manufactured are
defective. If a client places an order for 100 bulbs, what is the probability that at least one bulb is defective?);
– interpret probability statements, including statements about odds, from a variety of sources.
Statistics
Overall Expectations
By the end of this course, students will:
• demonstrate an understanding of standard techniques for collecting data;
• analyse data involving one variable, using a variety of techniques;
• solve problems involving the normal distribution;
• describe the relationship between two variables by interpreting the correlation coefficient;
• evaluate the validity of statistics drawn from a variety of sources.
Specific Expectations
Collecting Data
By the end of this course, students will:
– demonstrate an understanding of the purpose and the use of a variety of sampling techniques (e.g., a simple random sample, a
systematic sample, a stratified sample);
– describe different types of bias that may arise in surveys (e.g., response bias, measurement bias, non-response bias, sampling
bias);
– illustrate sampling bias and variability by comparing the characteristics of a known population with the characteristics of samples
taken repeatedly from that population, using different sampling techniques;
– organize and summarize data from secondary sources (e.g., the Internet, computer databases), using technology (e.g.,
spreadsheets, graphing calculators).
Analysing Data Involving One Variable
By the end of this course, students will:
– compute, using technology, measures of one-variable statistics (i.e., the mean, median, mode, range, interquartile range,
variance, and standard deviation), and demonstrate an understanding of the appropriate use of each measure;
– interpret one-variable statistics to describe characteristics of a data set;
– describe the position of individual observations within a data set, using percentiles
Solving Problems Involving the Normal Distribution
By the end of this course, students will:
– identify situations that give rise to common distributions (e.g., bimodal, U-shaped, exponential, skewed, normal);
– demonstrate an understanding of the properties of the normal distribution (e.g., the mean, median, and mode are
equal; the curve is symmetric about the mean; 68% of the population are within one standard deviation of the mean) and
use these properties to solve problems;
– make probability statements about normal distributions, on the basis of information drawn from a variety of applications.
Describing the Relationship Between Two Variables
By the end of this course, students will:
– define the correlation coefficient as a measure of the fit of a scatter graph to a linear model;
– calculate the correlation coefficient for a set of data, using graphing calculators or statistical software;
– demonstrate an understanding of the distinction between cause-effect relationships and the mathematical correlation between
– describe possible misuses of regression (e.g., use with too small a sample, use without considering the effect of outliers,
inappropriate extrapolation) and evaluating validity
By the end of this course, students will:
– explain examples of the use and misuse of statistics in the media;
– assess the validity of conclusions made on the basis of statistical studies, by analysing possible sources of bias in the studies
(e.g., sampling bias)
– identify examples of discrete random variables (e.g., the sums that are possible when two dice are rolled);
Integration of the Techniques of Data Management
Overall Expectations
By the end of this course, students will:
• carry out a culminating project on a topic or issue of significance that requires the integration
and application of the expectations of the course;
• present a project to an audience and critique the projects of others.
Specific Expectations
Carrying Out a Culminating Project
By the end of this course, students will:
– pose a significant problem whose solution would require the organization and analysis of a large amount of data;
– select and apply the tools of the course (e.g., methods for organizing data, methods for calculating and interpreting measures
of probability and statistics, methods for data collection) to design and carry out a study of the problem;
– compile a clear,well-organized, and fully justified report of the investigation and its findings.
Presenting and Critiquing Projects
By the end of this course, students will:
– create a summary of a project to present within a restricted length of time, using communications technology effectively;
– answer questions about a project, fully justifying mathematical reasoning;
– critique the mathematical work of others in a constructive fashion.
Overall Expectations
By the end of this course, students will:
• organize data to facilitate manipulation and retrieval;
• solve problems involving complex relationships, with the aid of diagrams;
• model situations and solve problems involving large amounts of information, using matrices.
Specific Expectations
Organizing Data
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