All Lessons

(C) Graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems

HSF.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

(G) Graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d, in mathematical and real-world problems

(Y10A) Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations (ACMNA267)

HSF.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

(F) Graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions

(I) Determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing

(E) Determine or analyze an appropriate piecewise model for problem situations

(Y11-12) Interpret and use graphs in practical situations, including travel graphs and conversion graphs (ACMEM124)

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

(A) Solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula

HSF.IF.8.A Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

(A) Solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula

HSF.IF.8.A Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

(D) Write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms

(B) Represent arithmetic sequences and geometric sequences using recursive formulas

HSF.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.*

(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.

(A) Apply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to solve non-contextual problems

(Y10A) Prove and apply angle and chord properties of circles (ACMMG272)

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.

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

(Y9) Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar (ACMMG220)

HSG.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

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

(A) Identify points, lines, line segments, rays, angles, and perpendicular and parallel lines

(Y11-12) Use symbols and conventions for the representation of geometric information; for example, point, line, ray, angle, diagonal, edge, curve, face and vertex (ACMEM107)

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.

(B) Prove two triangles are congruent by applying the Side-Angle-Side, Angle-Side-Angle, Side-Side-Side, Angle-Angle-Side, and Hypotenuse-Leg congruence conditions

(Y8) Develop the conditions for congruence of triangles (ACMMG201)

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.

(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.