Geometry is one of the oldest branches of all mathematics. “GEO METRIA” actually means “to measure the earth”. We’re going to discover how to measure lengths, angles, and areas. Geometry helps us decide what materials to use when we build things, where to point our rocket to land on Mars, what design to make our bridge or skyscraper so it is strong in the direction we need it to be, how much paint and carpet we need to buy for our house, where we should point our telescopes to find the planets and stars, figuring out when the next meteor shower will be - it’s everywhere you look!

This course *requires* algebra. If you haven't completed Algebra 1, please go back and do this now. Students typically need 3-8 weeks per session in order to thoroughly work through each concept covered. We will have multiple opportunities for your student to connect with us live and get support as they work through the content.

Each session, in addition to attending classes with our teachers and working through the geometry workbooks, your kids will be working their way through a math obstacle course, designing and building several projects, and exploring how geometry is used in the science and engineering fields. Students will need materials in order to participate in all the hands-on fun for all levels, including both *Beginner* and *Intermediate *students. All students will be given challenges and projects with each session!

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## Geometry Session #1

### Shapes & Constructions

#### Uses Workbook #1

**Getting Started with Geometry **For the *Intermediate* and *Advanced* Levels of Geometry, students need to be comfortable performing all four operations (add, subtract, multiply and divide) for integers, fractions and decimals; be fluent in handling ratios, proportion, and percent; and be able simple solve linear equations in order to be ready for geometry.

We're going to discover the point, the line and the plane, and then use our geometry tools to construct shapes, inscribe objects, and explore how geometric figures are built.

During our Geometry study unit, we will have special building projects for each session. If you would like to do these special projects, you will need materials (shopping list here). These bonus projects are *optional*, you can choose to do the workbooks and regular assignments instead.

**Project #1: Eggstronaut Challenge**

Please make sure you have your regular geometry materials during class (notebook, pencil, ruler, compass, protractor) each day, regardless of whether you choose to do the bonus projects or not.

NOTE: Take your time with each session. If your student need several weeks to complete one session, please don't rush and take the time you need to thoroughly explore and enjoy the learning process.

Skills: geometry fundamental concepts (point, line, plane, intersections, parallel, perpendicular, angle, colinear, congruence); constructions (triangles, circles, arcs, hexagons, bisectors, copying angles); transformations (dilation, translation, rotation, reflection); types of triangles; multiplying segments; word problems; technical drawing techniques; solving problems through modeling and geometric constructions.

## Geometry Session #2

**All About Angles**

#### Uses Workbook #2

Welcome to our session in angles! We get angles when we have intersections of lines and planes, and knowing how to handle them is going to be important because they show up everywhere in geometry. Students will work through a new workbook in addition to having a new in-depth packet that explores angles in more detail, several games and activities, and a Lab Challenge project!

We're going to take two sessions to cover angles in-depth. For this session, we're focus just on the *Angles* part of the packet. Expect to see applying angles to geometric shapes, like *Triangles* in the next session.

New for Geometry is our special hands-on building projects that we have for each session. These bonus projects are in addition to the workbooks and regular assignments that we have available for our students.

**Project #2: Flashlight Laser Maze Challenge**

This is our second challenge project. We'll have a new project in each session. The purpose of these projects is to connect the math work we do in geometry with practical applications in science and engineering. You will need materials if you want to build these projects. These projects are designed to encourage kids to think about the challenge and come up with their on unique solutions!

NOTE: Take your time with each session. If your student need several weeks to complete one session, please don't rush and take the time you need to thoroughly explore and enjoy the learning process.

Skills: geometry fundamentals, constructing shapes and figures using a straight edge and ruler; angle relationships; complementary, supplementary, vertical and adjacent angles, writing and solving linear equations; using a protractor to measure angles; bisecting lines and angles; constructing perpendiculars; properties and working with circles; constructing squares, rectangles, and parallelograms; relationships with alternating interior angles.

## Geometry Session #3

### Plane Geometry: Triangles

#### Uses Workbook #2

Triangles are the name of the game in this session! We get triangles when we have a shape with three sides and three angles. We notice triangles in the roof on homes, when we stack things in a pyramid, for cars on a truss bridge, the shape of sails on boats, and when satellites triangulate our position using maps and location information.

Engineers use triangles to figure out force vectors in buildings and how fast rockets are accelerating. Knowing how to handle triangles are one of the most important skills we will learn in math, especially if you want to become an engineer.

Students will continue to work through the second workbook in addition to having a new in-depth packet that explores triangles in more detail, several games and activities, and a Lab Challenge project!

This session is a continuation from the work we did in the previous session on *Angles*. We are now going to apply angles to geometric shapes (*Triangles*) so we can really get good at handling these!

**Project #3: Truss Bridge Challenge**

This is our third challenge project. The purpose of these projects is to connect the math work we do in geometry with practical applications in science and engineering. You will need materials if you want to build these projects. These projects are designed to encourage kids to think about the challenge and come up with their on unique solutions!

NOTE: Take your time with each session. If your student need several weeks to complete one session, please don't rush and take the time you need to thoroughly explore and enjoy the learning process.

Skills: geometry fundamental concepts constructions (triangles, bisectors, angles); types of triangles; angle relationships; types of angles; applying triangle knowledge to real world problems; write and solve linear equations; angle relationships within a triangle; triangle inequality theorem; relating angles and sides of triangles; Pythagorean and trigonometric functions (sin, cos, tan) to define triangles; solving problems through modeling and geometric constructions.

## Geometry Session #4

### Plane Geometry: Circles

#### Uses Workbook #3

Circles are figures with no line segments and no vertices, which makes them pretty unique. We're explore radius, diameter, circumference and area and the relationship between each of these so it's easy for you to calculate the things you need accurately.

We use circles when we calculate surface area, volume, or take cross sections of objects, so before we dive into those areas, we have to really explore circles to get a good understanding of this unique figure.

Every time you drill a hole, bounce a ball, ride a roller coaster or drive down the freeway, circles are involved. Astronomers use circles and ellipses to describe the motion of planets, stars, and comets. Engineers use circles in their technical drawings for gears, tires, wheels and showing how holes line up when bolting plates together; circles are used to ensure they have large enough diameter pipe for the water flow; and so much more! Mechanical engineers use circles to calculate the different speed each car tire makes when taking a left turn.

Students will continue to work through their workbook in addition to their in-depth packet that explores geometry in more detail, several games and activities, and a Lab Challenge project!

**Project #4: Forest Ranger Lab Challenge**

This is our fourth challenge project. The purpose of these projects is to connect the math work we do in geometry with practical applications in science and engineering. You will need materials if you want to build these projects. These projects are designed to encourage kids to think about the challenge and come up with their on unique solutions!

Skills: calculate area and circumference of a circle and use them to solve word problems; understand the relationship between the circumference and area of a circle; metric and standard measurement systems.

## Geometry Session #5

### Plane Geometry: Rectangles, Parallelograms, Triangles, Trapezoids and Composite Figures

#### Uses Workbook #3

Plane Geometry is the study of two dimensional shapes and figures, and how they relate to each other. This is a large area of geometry, so we'll be spending extra time getting to know triangles and trapezoids, rectangles and parallelograms, circles and squares, and their infinite combinations!

Engineers use composite figures to do their analysis, which means that they break down complex shapes into more manageable pieces, like triangles and quadrilaterals. Knowing how to handle each of these shapes is one of the most important skills we will learn in math, especially if you want to become an engineer.

Students will continue to work through their workbook in addition to their in-depth packet that explores geometry in more detail, several games and activities, and a Lab Challenge project!

**Project #5: Spacecraft Challenge** This is our fifth challenge project, and since it is longer and more complex, we will be spending *two *sessions on this challenge project. The purpose of these projects is to connect the math work we do in geometry with practical applications in science and engineering. You will need materials if you want to build these projects. These projects are designed to encourage kids to think about the challenge and come up with their on unique solutions!

Skills: Calculate perimeter and area of different types of triangles, trapezoids, squares, rectangles, parallelograms and quadrilaterals; composing and decomposing shapes into other shapes; creating solving real-world problems with composite figures.

## Geometry Session #6

### Plane Geometry: Similarity

#### Uses Workbook #3

In Geometry, two figures are similar if they have the same shape, regardless of the position or orientation of either one. This means the image you see of yourself in the mirror is *similar. *The image in the mirror is smaller than the original, yet it has the same proportions as the original.

We use this idea of similarity in engineering and physics to help us measure things that are too large (like trees and mountains) by being able to compare them with objects closer in. Astronomers use similarity to estimate the distance to nearby stars by watching the slight shift stars make compared with background stars. We can find the diameter of the sun by comparing it with the diameter of the moon, even though we could never wrap a measuring tape around either!

Students will finish their workbook in addition to completing the in-depth packet that explores similarity in more detail, several games and activities, and a Lab Challenge project!

**Project #5: Spacecraft Challenge** *(continued from previous session)* This is our fifth challenge project, and since it is longer and more complex, we will be spending *two *sessions on this challenge project.

Skills: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale; calculate perimeter and area for geometric shapes and composite figures in real world applications; use models and formulas to connect perimeter, circumference and area; determine critical attributes of similarity; solve problems involving similar shapes and scale drawings.

## Geometry Session #7

### Surface Area

#### Uses Workbook #4

In Geometry, surface area is the total outside area from all surfaces of a shape. There are different ways of calculating it, depending on the type of shape. For a cube, we use the area of a square and multiply it by six to get the total surface area. For a cylinder, we take the surface area of a circle and multiply it by the height. Each shape has it's own unique surface area calculation and it's fun to figure out how!

Surface area is the area of all the faces that cover a 3D shape. For example, if we want to find out how much paint we need to cover a cube, we would add up the area of each face to find the total surface area, which is the surface that the paint will be applied to.

Students will continue to work through their workbook in addition to their in-depth packet that explores geometry in more detail, several games and activities, and a Lab Challenge project!

**Project #6: Solar Cookie Challenge** This is our sixth challenge project, and this time you get to enjoy the tasty results of your work! The purpose of these projects is to connect the math work we do in geometry with practical applications in science and engineering. You will need materials if you want to build these projects. These projects are designed to encourage kids to think about the challenge and come up with their on unique solutions!

Skills: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. solving real-world problems with surface area and lateral surface area.

## Geometry Session #8

### Volume

#### Uses Workbook #4

Volume is how much 3D space a shape takes up. We first calculate the area of one of the sides, and then extend this calculation to include the length of the object through multiplication. Volume is absolutely everywhere! Every time you fill a bowl, save leftovers from dinner into containers, put toys in a box or drink a glass of water, volume is involved!

Students will finish workbook #4 in addition to completing the in-depth packet that explores volume in more detail, enjoy several games and activities that help discover more about these ideas with volume, and complete a Geometry Lab Challenge project!

**Project #7: Geology Rock Hound & Earthquake Lab Challenge **This is our final challenge project, and there are *two* labs included! First, you get to be a geologist for the day and learn how to study rocks and perform field tests on samples, and then you'll visit a seismic station to triangulate the epicenters of four different earthquakes. The purpose of these projects is to connect the math work we do in geometry with practical applications in science and engineering. You will need materials if you want to build these projects. These projects are designed to encourage kids to think about the challenge and come up with their on unique solutions!

Skills: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Calculating density, measuring mass and volume using the metric system, triangulating positions using geometry, and so much more!

## Geometry Sessions #9 & #10

We've covered a lot so far! Lines, circles, arcs, constructions, perpendiculars, squares, rectangles, angles, triangles, perpendiculars, parallels, tangents, area, polygons, quadrilaterals, surface area and volume!

Students literally were crawling, hopping, skipping and thinking their way through a mathematical obstacle course as they work through activities, games, puzzles, challenges, projects and hands-on labs with every session.

**We've put together two bonus sessions: ****Advanced Geometry Sessions #9 and #10** which cover Right Angle Geometry. This is above and beyond what is normally expected between Algebra 1 and Algebra 2, but it's such a power tool in mathematics and used everywhere by scientists and engineers that I thought you'd really appreciate it!

Students began to use trigonometry as they created a bridge between geometry, algebra and physics during the in-depth Math Labs we've already introduced.

##### Looking for the Full In-Depth Review? Go here.

Students that complete both Algebra and Geometry will be more than ready to enter high school math classes in both *Algebra 2* and high school *Geometry*.

## Grades 7-8th Standardized Test

This is a end-of-year full comprehensive test you can give your student after they have completed all content from Units 4 & 5 *and* Statistics *and *Probability *and *all the review sessions included in each. This is an official standardized test so do your best!

## Do you have a calculator that will work for Geometry class?

Texas Instruments TI-30Xa Scientific Calculator.

- Easy for your child to READ THE DISPLAY
- Screen shows at least 10 digits
- Must-have buttons: inverse (labeled as 1/x or x
^{-1}), exponents (labeled as y^{x}or x^{y}or 'EXP') - Your calculator must have the ability to do square roots (if it doesn't have a square root button, you can use the exponent button).
- Intermediate and Advanced students must have the ability to do trig functions (SIN, COS, and TAN).