Jan 26, 2016 - In Topic D, students learn that radical expressions naturally arise in geometry, such as the height of an isosceles triangle or the lateral length of a cone. The Pythagorean Theorem is applied to...
Jan 26, 2016 - Topic C revisits the Pythagorean Theorem and its applications, now in a context that includes the use of square roots and irrational numbers. Students learn another proof of the Pythagorean Theorem...
Jan 26, 2016 - In Topic B, students learn that to get the decimal expansion of a number (8.NS.A.1), they must develop a deeper understanding of the long division algorithm learned in Grades 6 and 7 (6.NS.B.2, 7.NS....
Jan 26, 2016 - In Topic A, students learn the notation related to roots (8.EE.A.2). The definition for irrational numbers relies on students’ understanding of rational numbers, that is, students know that rational...
Jan 26, 2016 - In Topic D, students examine bivariate categorical data by using two-way tables to determine relative frequencies. They use the relative frequencies calculated from tables to informally assess...
Jan 26, 2016 - In Topic C, students use linear and nonlinear models to answer questions in context (8.SP.A.1, 8.SP.A.2). They interpret the rate of change and the initial value in context (8.SP.A.3). They use the...
Jan 26, 2016 - Topic B uses linear functions to model the relationship between two quantitative variables as students move to the domain of Statistics and Probability. Students make scatter plots based on data. ...
Jan 26, 2016 - Topic A begins to examine the relationship between two variables using linear functions (8.F.B.4). Linear functions are connected to a context, using the initial value and slope as a rate of change...
Jan 26, 2016 - In Topic B, students apply their knowledge of volume from previous grade levels (5.MD.C.3, 5.MD.C.5) to the learning of the volume formulas for cones, cylinders, and spheres (8.G.C.9). First,...
Jan 26, 2016 - In Topic A of Module 5, students learn the concept of a function and why functions are necessary for describing geometric concepts and occurrences in everyday life. The module begins by explaining...
Jan 26, 2016 - Optional Topic E is an application of systems of linear equations (8.EE.C.8b). Specifically, a system that generates Pythagorean triples. First, students learn that a Pythagorean triple can be...
Jan 26, 2016 - Simultaneous equations and their solutions are the focus of Topic D. Students begin by comparing the constant speed of two individuals to determine which has greater speed (8.EE.C.8c). Students...
Jan 26, 2016 - In Topic C, students know that the slope of a line describes the rate of change of a line. Students first encounter slope by interpreting the unit rate of a graph (8.EE.B.5). In general, students...
Jan 26, 2016 - In Topic B, students work with constant speed, a concept learned in Grade 6 (6.RP.A.3), but this time with proportional relationships related to average speed and constant speed. These relationships...
Jan 26, 2016 - In Topic A, students begin by transcribing written statements using symbolic notation. Then, students write linear and non-linear expressions leading to linear equations, which are solved using...
Jan 26, 2016 - It is recommended that students have some experience with the lessons in Topic D from Module 2 before beginning these lessons. In Lesson 13 of Topic C, students are presented with a general proof...
Jan 26, 2016 - Topic B begins with the definition of similarity and the properties of similarities. In Lesson 8, students learn that similarities map lines to lines, change the length of segments by factor r, and...
Jan 26, 2016 - Topic A begins by demonstrating the need for a precise definition of dilation instead of “same shape, different size” because dilation will be applied to geometric shapes that are not polygons. ...
Jan 26, 2016 - Optional Topic D begins the learning of Pythagorean Theorem. Students are shown the “square within a square” proof of the Pythagorean Theorem. The proof uses concepts learned in previous topics of...
Jan 26, 2016 - In Topic C, on the definition and properties of congruence, students learn that congruence is just a sequence of basic rigid motions. The fundamental properties shared by all the basic rigid motions...
Jan 26, 2016 - Topic B is a critical foundation to the understanding of congruence. All the lessons of Topic B demonstrate to students the ability to sequence various combinations of rigid motions while...
Jan 26, 2016 - Throughout Topic A, on the definitions and properties of the basic rigid motions, students verify experimentally their basic properties and, when feasible, deepen their understanding of these...
Jan 26, 2016 - In Topic B, students’ understanding of integer exponents is expanded to include the concept of magnitude as a measurement. Students learn to estimate how big or how small a number is using magnitude...
Jan 26, 2016 - In Topic A, students begin by learning the precise definition of exponential notation where the exponent is restricted to being a positive integer. In Lessons 2 and 3, students discern the structure...
