## 8.1 Rigid Motions, Congruence, Dilations, & Similarity

Students experiment with rotations, translations, reflections, and dilations, and they describe these transformations both qualitatively and using coordinates.

Students experiment with rotations, translations, reflections, and dilations, and they describe these transformations both qualitatively and using coordinates.

Students connect proportional relationships, lines, and linear equations.

Students write systems of equations in two variables, relate them to pairs of lines on a graph, and make sense of what the interactions of the lines mean (e.g. where they intersect, conincide, or are parallel).

Students interpret, compare, and analyze functions and their representations and also use functions to model real-life situations and solve problems.

Students analyze measurement data qualitatively via scatterplots and, in cases where lines are implied, explore associations quantitatively by building linear models, translating from one representation to another, and interpreting given models in a variety of applications and contexts.

Students explore laws of exponents and use them to transform expressions; they also use scientific notation to describe and perform calculations on very-large and very-small quantities.

Students consider square roots as the inverse of squaring and explore square-to-root relationships in terms of the area and side length of a given square. This work encourages a closer look at the magnitude of numbers, their position on the numberline, decimal expansion, rational numbers, and subsequently at the idea of irrationality. Students explore the reasonsing of the Pythagorean Theorem and use it to solve real-world problems.

Students make sense of cubes and cube roots, using geometric contexts to resaon with power expressions; they also expand their work in three-dimensional geometry by analyzing the sizes of various solid figures and computing the surface areas and volumes of cones, cylinders, and spheres.