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Shapes & Constructions 

Welcome to our new unit on Geometry! In this session, 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.

Day 3 handout covers Transformations, and will serve as both the in-class handout and the workbook for this week which we will start during class. If you complete this entire handout, you can skip the Transformations Packet #1-6 in the Intermediate section below (they both cover the same thing, just a different format), but do take the Part #7: Quiz before doing the Transformations Escape Room! 

Beginner Level Math Class

We're going to explore different geometry skills in our workbooks. We'll continue to practice with concept and word problems and have fun learning!

Download your Geometry Workbook #1

To help you with your daily practice, I've  put together the a new workbook for you. All levels of students will work through Geometry Workbook #1: Constructions. Plan to complete 3-4 pages per day. After you complete the pages, you may check the answer key. 

Geometry Workbook:  Constructions

This is the first workbook in geometry. I've put together a set of videos that will walk you through selected problems in this workbook, Constructions. Plan to complete 3-4 pages per day. After you complete the pages, you may check the answer key.

Bonus: Geometry Wall Art Reference Guide

A geometry teacher allowed me to share this with you. You can print it out mini-sized, cut them out and tape them into your math journal, or you can print them out larger to decorate your wall as we work through these concepts in our course together. This bonus bundle is entirely optional, you do not need to print this out in order to complete the content in this session (it's over 200 pages). This is just something a little extra in case you'd like to have this as you work through our geometry course!

Math Obstacle Course Challenge #1: Jailbreak!

During the live class, near the end of the beginner session, we had a special challenge. The video below contains both the challenge and the solution. Be sure to work your way through the challenge first before looking at the solution! 

Intermediate Level Math Class

Are you ready to really practice your new math skills? Let's get really good at geometry by doing several different activities and games as we are figuring out solutions!

Transformations

Sometimes we need to flip, rotate, or move shapes in geometry. The three most important transformations are rotation, reflection, and translation.  The important thing to remember about transformations is that afterwards, the shape still has the same size, area, angles and line lengths.  When we do any of these three translations, we say that the before and after shapes are congruent.

Another important transformation is resizing, also called dilation, contraction, compression, enlargement or expansion.  This is where we make a shape bigger or smaller without changing any of the angles.  You'll also notice that the proportions still stay the same.

When we resize shapes, we say that the before and after shape are similar. It's simple to resize if you remember these three steps:

1. Draw a line from the central point to the corner
2. Increase or decrease the length of that line
3. Place a dot at the new point

The other important transformation is reflection. A reflection is a flip over a line. These are everywhere you look, especially if you're looking into a mirror or seeing your reflection in a window. These are special transformations because every point is the same distance from the center line and the reflection shape has the same size as the original. The central line (also called a mirror line) can be vertical, horizontal, or in any direction. It's common when you flip an object to keep the same label of all points with an added tick mark ( ' ) after it, like this: A --> A' so it's easy to keep track of which is which. 

Transformations Reference Guide

This is a craft project you can create to help keep track of what to do for each type of transformation.

Math Activity: Escape Room

This is a fun way to review what we've been learning this session with an escape room! Please make sure you work through the Transformations Packet and Quiz before you enter this escape room. After you've completed the escape room, enter in the lock codes into the form below. (Answer key at bottom of page in Session #2.)

Math Build Activity: Pantograph

The pantograph was developed in the 1600s as a way of making exact copies before there were copy machines. This model has the ability to scale an image that you trace by using a four-bar mechanism linked together in a parallelogram shape. 

Math Build Activity: Hexagon Box

Using only a compass, ruler, scissors and tape, you can construct and create a hexagonal box complete with a lid! Use thicker paper for a more sturdy box. No handout needed - just grab a sheet of paper and let's get started!

TIP: Size the lid 0.5 cm  larger than the circle you use for the box.

Math Challenge Project #1: Eggstronauts

This is our first 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!

Materials needed:

• Plastic eggs (recommended, especially during your trials)
• Real (raw) eggs (optional, only to test your final design)
• Coins, washers, sand or dirt to add mass to the plastic egg
• Cotton balls (to fill the empty space inside the plastic egg)
• Tape measure
• Stopwatch or timer
• Egg harness materials: rubber bands, string, tape, scissors, glue
• Kitchen scale (measuring in grams)
• Parachute material (plastic bags or tablecloths, wrapping paper, tissue paper, or plastic grocery or trash bags

Advanced Level Math Class

This week, we want all students (including Advanced) to work through the Constructions workbook. This workbook serves as a foundation for the labs we're planning for the next six sessions. This first session, the Advanced lab is in Mechanical Drawings. If you've worked through all of the Beginner and Intermediate level content (including the Challenge Project), then you are ready for the labs here in this section.

Math Challenge

Each session, I have a special Math Challenge for you to work on after you work through some of the content in this area of math. The goal for these special math challenges is for you to be able to communicate your great ideas with your family and friends, without them being in a math class or having any knowledge of a specific area of math. You should be able to convey your great ideas to most people that are interested in hearing what you have to share. Many families find this part of the math program exciting for them to participate in with their student!

Solution to Algebra Session #7 Math Challenge

Two dozen. If you increase both the number of hens and the amount of time available four-fold, the number of eggs increases 16 times. 16 x 1.5 = 24.