SimilarityStudents learn about dilation and similarity and apply that knowledge the AngleAngle criterion for similar triangles. The module begins with the definition of dilation, properties of dilations, and compositions of dilations. One overarching goal of this module is to replace the common idea of “same shape, different sizes” with a definition of similarity that can be applied to geometric shapes that are not polygons, such as ellipses and circles.
Students describe the effect of dilations on twodimensional figures in general and using coordinates. Building on prior knowledge of scale drawings, they demonstrate the effect dilation has on a figure when the scale factor is greater than zero but less than one (shrinking of figure), equal to one (congruence), and greater than one (magnification of figure). Once students understand how dilation transforms figures in the plane, they examine the effect that dilation has on points and figures in the coordinate plane. Beginning with points, students learn the multiplicative effect that dilation has on the coordinates of the ordered pair. Then students apply the knowledge about points to describe the effect dilation has on figures in the coordinate plane, in terms of their coordinates. Students demonstrate that a twodimensional figure is similar to another if the second can be obtained from a dilation followed by a congruence. Knowledge of basic rigid motions is reinforced throughout the module, specifically when students describe the sequence that exhibits a similarity between two given figures. Students apply their knowledge of proportional relationships and rates to determine if two figures are similar, and if so, by what scale factor one can be obtained from the other. By looking at the effect of a scale factor on the length of a segment of a given figure, students will write proportions to find missing lengths of similar figures. CongruenceStudents learn about translations, reflections, and rotations in the plane and, more importantly, how to use them to precisely define the concept of congruence. Up to this point, “congruence” has been taken to mean, intuitively, “same size and same shape.” Because this module begins a serious study of geometry, this intuitive definition must be replaced by a precise definition.
Translations, reflections, and rotations are examples of rigid motions, which are rules of moving points in the plane in such a way that preserves distance. For the sake of brevity, these three rigid motions will be referred to exclusively as the basic rigid motions. The exploration of these basic rigid motions is done with handson activities using an overhead projector transparency. What needs to be emphasized is the language and the precision of the elements (lines of reflection, angles and centers of rotation, and vectors of translation) of the transformations and that these motions define congruence. Operations with Rational NumbersThis module uses the Integer Game: a card game that creates a conceptual understanding of integer operations and serves as a powerful mental model that students can rely on during the module. Students build on their understanding of rational numbers to add, subtract, multiply, and divide signed numbers.
Students use a number line to model the addition and subtraction of integers and to demonstrate that an integer added to its opposite equals zero, representing the additive inverse. They recognize that subtracting a number is the same as adding its opposite. Reallife situations are represented by the sums and differences of signed numbers. Students extend integer rules to include the rational numbers and use properties of operations to perform rational number calculations without the use of a calculator. Students develop the rules for multiplying and dividing signed numbers. They use the properties of operations and their previous understanding of multiplication as repeated addition to represent the multiplication of a negative number as repeated subtraction. Students make analogies to the Integer Game to understand that the product of two negative numbers is a positive number. They recognize division as the inverse process of multiplication, so signed number rules for division are consistent with those for multiplication, provided a divisor is not zero. Students represent the division of two integers as a fraction, extending product and quotient rules to all rational numbers. They realize that any rational number in fractional form can be represented as a decimal that either terminates in s or repeats. Students recognize that the context of a situation often determines the most appropriate form of a rational number, and they use long division, place value, and equivalent fractions to fluently convert between these fraction and decimal forms. 
Class Notes and Homework Files

Past Due WorkWeek of October 28
Monday: * 20 skill minutes of Khanacademy due 11/04 * 8.3.5 Homework Set due 10/29 Tuesday: * 8.3.6 Homework Set due 10/30 Wednesday: * 8.3 Mid Module Review due 10/31 * 8.3 Mid Module Test on 10/31 Thursday: * none Friday: * 8.3.8 Homework Set due 11/04 Week October 21 Monday: * 20 skill minutes of Khanacademy due 10/28 * 8.3.3 Homework Set due 10/22 Tuesday: * 8.3.4 Homework Set due 10/23 Wednesday: * none Thursday: * none Friday: * none Week of October 14 Monday: * none Tuesday: * 20 skill minutes on Khanacademy due 10/21 * 8.2 End of Module Review due 10/16 * 8.2 Test on 10/16 * 8.2 Khanacademy Overview due 10/16 (80 minutes since 9/13) Wednesday: * none Thursday: * 8.3.1 Homework Set due 10/18 Friday: * 8.3.2 Homework Set due 10/21 Week of October 7 Monday: * none Tuesday: * 20 skill minutes on Khanacademy due 10/15 Wednesday: * none Thursday: * 8.2.13 Homework Set due 10/11 Friday: * 8.2.14 Homework Set due 10/15 * 8.2 End of Module Test on 10/16 * 8.2 Khanoverview due 10/16 (80 minutes since 09/13) Week of September 30 Monday: * 20 skill minutes on Khanacademy due 10/08 * 8.2.9 Homework Set due 10/01 Tuesday: * 8.2.10 Homework Set due 10/02 Wednesday: * 8.2.11 Homework Set due 10/03 Thursday: * 8.2 Mid Module Review due 10/04 * 8.2 Mid Module Test on 10/08 Friday: * 8.2.12 Homework Set due 10/09 Week of September 23 Monday: * 20 skill minutes on Khanacademy due 09/30 * 8.2.4 Homework Set due 09/24 Tuesday: * 8.2.5 Homework Set due 09/25 Wednesday: * 8.2.6 Homework Set due 09/26 Thursday: * 8.2.7 and 8 Homework Set due 09/27 Friday: * 2019 Math League Practice due 09/30 Week of September 16 Monday: * 20 skill minutes on Khanacademy due 09/23 Tuesday: * 7.1.5 Homework Set due 09/18 Wednesday: * 7.1.6 Homework Set due 09/19 Thursday: * 7.1.7 Homework Set due 09/23 Friday: * none Week of September 9 Monday: * 7.2.11 Homework Set due 09/10 Tuesday: * Job Application due 09/13 Wednesday: * 7.2.12 Homework Set due 09/12 Thursday: * 7.2.16 Homework Set due 09/13 Friday: * 7.2 End of Module Review due 09/16 * 7.2 Test on 09/17 Week of September 1 Monday: * none Tuesday: * none Wednesday: * none Thursday: * I caught myself..... due 09/06 Friday: * 7.2.7 and 9 Homework Set due 09/09 