August 11, 2009

Section 5 is all about applications to area, especially probability.

- Mathematics > General
- Mathematics > Data Analysis & Probability
- Mathematics > Geometry
- Mathematics > Measurement
- Mathematics > Patterns
- Mathematics > Problem Solving

- Grade 6
- Grade 7
- Grade 8
- Grade 9
- Grade 10

Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

Reporting the number of observations.

Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.

Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.

Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event.

Design and use a simulation to generate frequencies for compound events.

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

determine experimental and theoretical probabilities related to simple and compound events using data and sample spaces.

construct a scatterplot and describe the observed data to address questions of association such as linear, non-linear, and no association between bivariate data;