All Lessons

(C) Determine the effect on the graph of f(x) = √x when f(x) is replaced by af(x), f(x) + d, f(bx), and f(x - c) for specific positive and negative values of a, b, c, and d

(A) Analyze the effect on the graphs of f(x) = x3 and f(x) = 3√x when f(x) is replaced by af(x), f(bx), f(x - c), and f(x) + d for specific positive and negative real values of a, b, c, and d

HSF.IF.7.B Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

HSG.C.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

HSG.CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.

HSG.CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

(A) Generalize the critical attributes of similarity, including ratios within and between similar shapes

HSG.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

HSG.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

HSG.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

(D) Solve problems involving the lateral and total surface area of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid by determining the area of the shape's net.

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

(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

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

6.G.1 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.

HSG.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments.

(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.*

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

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.

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.