All Lessons

(A) Describe the volume formula V = Bh of a cylinder in terms of its base area and its height

(B) Model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas

(A) Solve problems involving the volume of cylinders, cones, and spheres

(B) Use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders

(Y10A) Solve problems involving surface area and volume of right pyramids, right cones, spheres and related composite solids (ACMMG271)

(Y11-12) Use formulas to find the volume and capacity of regular objects such as cubes, rectangular and triangular prisms and cylinders (ACMEM103)

(Y11-12) Use formulas to find the volume of pyramids and spheres (ACMEM104)

HSG.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*

(C) Use models and diagrams to explain the Pythagorean theorem.

HSG.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*

(B) Apply the relationships in special right triangles 30°-60°-90° and 45°-45°-90° and the Pythagorean theorem, including Pythagorean triples, to solve problems.

(Y9) Investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles (ACMMG222)

HSG.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*

(A) Determine probabilities, including the use of a two-way table

(Y11-12) Interpret information presented in two-way tables (ACMEM038)

(Y11-12) Identify relative frequency as probability (ACMEM152)

HSS.CP.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.

(A) Determine the number of ways an event may occur using combinations, permutations, and the Fundamental Counting Principle

(Y9) List all outcomes for two-step chance experiments, both with and without replacement using tree diagrams or arrays. Assign probabilities to outcomes and determine probabilities for events (ACMSP225)

HSS.CP.9 (+) Use permutations and combinations to compute probabilities of compound events and solve problems.

(B) Determine the mean absolute deviation and use this quantity as a measure of the average distance data are from the mean using a data set of no more than 10 data points

(B) Analyze numerical data using measures of central tendency (mean, median, and mode) and variability (range, interquartile range or IQR, and standard deviation) in order to make inferences with normal distributions

(Y10A) Calculate and interpret the mean and standard deviation of data and use these to compare data sets (ACMSP278)

(Y11-12) Calculate and interpret statistical measures of spread, such as the range, interquartile range and standard deviation (ACMEM055)

HSS.IDA.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

(A) Represent numeric data graphically, including dot plots, stem-and-leaf plots, histograms, and box plots

(Y11-12) Display numerical data as frequency distributions, dot plots, stem and leaf plots, and histograms (ACMEM046)

HSS.IDA.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).

(D) Summarize categorical data with numerical and graphical summaries, including the mode, the percent of values in each category (relative frequency table), and the percent bar graph, and use these summaries to describe the data distribution.

(Y9) Calculate relative frequencies from given or collected data to estimate probabilities of events involving 'and' or 'or' (ACMSP226)

(Y11-12) Identify relative frequency as probability (ACMEM152)

HSS.IDA.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

(A) Compare two groups of numeric data using comparative dot plots or box plots by comparing their shapes, centers, and spreads

(Y9) Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread (ACMSP283)

(Y10) Construct and interpret box plots and use them to compare data sets (ACMSP249)

(Y10A) Calculate and interpret the mean and standard deviation of data and use these to compare data sets (ACMSP278)

(Y11-12) Compare back-to-back stem plots for different datasets (ACMEM057)

HSS.IDA.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

(B) Write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.

(E) Write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems.

(Y11-12) Find the line of best fit by eye (ACMEM141)

(Y11-12) Use the line of best fit to make predictions, both by interpolation and extrapolation (ACMEM145)

HSS.IDA.6.A Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.

(C) Compare different linear models for the same set of data to determine best fit, including discussions about error

(Y11-12) Find the line of best fit by eye (ACMEM141)

(Y11-12) Use technology to find the line of best fit (ACMEM142)

HSS.IDA.6.B Informally assess the fit of a function by plotting and analyzing residuals.

(A) Calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association

(Y11-12) Use technology to find the correlation coefficient (an indicator of the strength of linear association) (ACMEM144)

HSS.IDA.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.