All Lessons

(A) Distinguish between undefined terms, definitions, postulates, conjectures, and theorems

(A) Investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools

(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.

(A) Describe and perform transformations of figures in a plane using coordinate notation

(Y8) Define congruence of plane shapes using transformations (ACMMG200)

HSG.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

(A) Describe and perform transformations of figures in a plane using coordinate notation

(Y8) Define congruence of plane shapes using transformations (ACMMG200)

HSG.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

(A) Describe and perform transformations of figures in a plane using coordinate notation

(Y8) Define congruence of plane shapes using transformations (ACMMG200)

HSG.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

(A) Describe and perform transformations of figures in a plane using coordinate notation

(Y8) Define congruence of plane shapes using transformations (ACMMG200)

HSG.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

(B) Determine the image or pre-image of a given two-dimensional figure under a composition of rigid transformations, a composition of non-rigid transformations, and a composition of both, including dilations where the center can be any point in the plane

(C) Apply the definition of congruence, in terms of rigid transformations, to identify congruent figures and their corresponding sides and angles

(Y8) Define congruence of plane shapes using transformations (ACMMG200)

8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

HSG.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

(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) Distinguish between categorical and quantitative data

(Y11-12) Identify examples of categorical data (ACMEM043)

(Y11-12) Identify examples of numerical data (ACMEM044)

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.

(F) Analyze categorical data, including determining marginal and conditional distributions, using two-way tables.

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

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.

(F) Analyze categorical data, including determining marginal and conditional distributions, using two-way tables.

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

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

(Y11-12) Describe the patterns and features of bivariate data (ACMEM138)

(Y11-12) Describe the association between two numerical variables in terms of direction (positive/negative), form (linear/non-linear) and strength (strong/moderate/weak) (ACMEM139)

HSS.IDA.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.