(offering 40 POINTS I HAVE A DBA IN ABOUT 45 MINUTES AND MY TEACH IS MRS. SOWERS IF THAT HELPS!!

Eureka Math Parent Guide

A GUIDE TO SUPPORT PARENTS AS THEY WORK WITH THEIR STUDENTS IN MATH.

GRADE 8

MODULE 3

GRADE FOCUS

Eighth grade mathematics is about (1) formulating

and reasoning about expressions and equations, with a

special focus on linear equations and systems of linear

equations; (2) grasping the concept of a function and

using functions to describe quantitative relationships; (3)

analyzing two- and three-dimensional space and figures

using distance, angle, similarity, and congruence, and

understanding and applying the Pythagorean Theorem.

• Module 1: Integer Exponents and Scientific Notation

• Module 2: The Concept of Congruence

» Module 3: Similarity

• Module 4: Linear Equations

• Module 5: Examples of Functions from Geometry

• Module 6: Linear Functions

• Module 7: Introduction to Irrational Numbers Using Geometry

LET’S CHECK IT OUT!

MODULE 3 FOCUS

In this 14-lesson module, students learn about dilation

and similarity and apply that knowledge to a proof of the

Pythagorean Theorem based on the Angle-Angle criterion

for similar triangles. Students learn the definition of a

dilation, its properties, and how to compose them. 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 shapes that are not

polygons, such as ellipses and circles.

MORE SPECIFICALLY, CHILDREN WILL LEARN HOW TO:

• Use physical models, transparencies or geometry

software to understand congruence and similarity.

• Describe the effect of dilations, translations, rotations,

and reflections on two-dimensional figures using

coordinates.

• Understand that a two-dimensional figure is similar to

another if the second can be obtained from the first by

a sequence of rotations, reflections, translations.

• Use informal arguments to establish facts about

the angle sum and exterior angle of triangles, about

the angles created when parallel lines are cut by a

transversal, and the angle-angle criterion for similarity

of triangles.

• Explain a proof of the Pythagorean Theorem and use

the Theorem to determine unknown side lengths

in right triangles in real-world and mathematical

problems in two and three dimensions.

TOPIC OVERVIEW

Topics are the lessons within a module that help children

master the skills above. Here are the lessons that will

guide your child through Module 3:

• Topic A: Dilation

• Topic B: Similar Figures

• Topic C: The Pythagorean Theorem

WORDS TO KNOW

• Dilation: Dilation is where the polygon grows or

shrinks but keeps the same overall shape. It’s a little

like zooming in or out on a camera.

• Similar: Two geometrical objects are called similar if they

both have the same shape, or one has the same shape

as the mirror image of the other. More precisely, one

can be obtained from the other by dilation (enlarging or

shrinking), possibly with additional translation, rotation

and reflection. This means that either object can be

rescaled, repositioned, and reflected, so as to coincide

precisely with the other object.

• Congruence: Two figures or objects are congruent if

they have the same shape and size, or if one has the

same shape and size as the mirror image of the other.

In the picture below, the two triangles on the left are

congruent, while the third is similar to them. The last

triangle is neither similar nor congruent to any of the

others because the angles are not the same. Note that

congruence permits alteration of some properties,

such as location and orientation, but leaves others

unchanged, like distance and angles.

Explanation:

either b) they were often feared and despised by other native cultures. or

c) their obsession allowed them to coexist with many other native cultures because of their peaceful nature.

1. darius the great     persia  

2. piankhi       nubia

3. ezana       aksum

4.     nebuchadnezzar     babylonia

5. shalmaneser iii     assyria