Math 8

Unit 4 Measuring Prisms and Cylinders

Lesson 841 Exploring Nets

Focus

The FOCUS section introduces the main concept that will be covered in the lesson.

TEXT Page 170

Read/Work through the  Focus  section at the top of page 170 in  your textbook.

Watch

This is a “thought experiment”,   not always easy to think about a three dimensional object based on a two-dimensional picture!
Do your best, then watch the video where I show the object that results from this net.

Video Tutorial

Investigate

Investigate an idea or problem, with a partner if possible.
The investigation provides the background for the ideas presented in the lesson.

TEXT Page 170

Read/Work through the  Investigate  section on Page 170 in your textbook.

You may not have a partner to work with.  
No worries!  
You can do this activity on your own.
Do your best to answer the questions, then watch the Video Tutorial for help or to check your answers.

This is certainly NOT an easy activity.
Here are a few suggestions for reasonably common items you could use that you can actually pull apart instead of tracing, cutting and taping.

A Toblerone chocolate bar.   You can buy one, do the Investigation, then eat it!   Bonus!

A cereal box,  or maybe a box from an Amazon delivery,  or a shoe box....  any “box”  would work here.

A BOX that is a “cube” or close to a cube.

However,  anything you have will work.   Actually DOING the activity is the important thing here.

Watch

Cube

Video Tutorial  Cube

In the video I talk about nets for a cube.   I got lucky and gave the right number,  ELEVEN.

The demonstration below shows all 11 DIFFERENT nets that fold up into a cube.
Notice that all the nets have 6 faces, 6 squares, as expected for a cube.
Not every arrangement of 6 squares in a net will actually fold up into a cube.
(as you saw illustrated in the video)
You can click and drag to “see” the object in simulated 3-D space.
You can also use the slider to fold and unfold to see how you go back and forth between the net (2-D) and the cube (3-D)

Box

A small variation on the cube,  pretty much the same idea here, except the faces are rectangles, instead of  squares.
(a square is just a special case of a rectangle)

Video Tutorial  "Box"

Toblerone

Video Tutorial  Toblerone Bar

More demonstrations

Optional,  but a few further demonstrations between nets and the resulting 3-D object that is formed.
Helpful background for this lesson and the rest of the unit.
Don’t worry about details,  just work with these for an overview of the process.

Polyhedra

These are covered in the Connect part of the lesson, but THIS VIDEO is a quick introduction.

Dodecahedron Stage

At the closing ceremony of the 2000 Olympic Games held in Sydney, the convertible stage was a dodecahedron.

Two congruent parts were unfolded to form a flat stage, folded up again, and then lifted on a central pole.

I was surprised there weren’t more images on the internet.  Maybe they are all protected by copyright?
But,   it did happen....

Link  (Getty Images)

Connect

Connect summarizes the math in the lesson.
A presentation of ideas connected to the lesson focus.

TEXT Page 171

Read/Work through the  Connect  section on Page 171 in your textbook.

Even if you KNOW you are going to watch the video, READING this section is still important.

Getting the same information in multiple ways can help with understanding.

There is a TON  of vocabulary here.

Having this shared vocabulary will be a huge help for this unit (and future math studies)

Watch/Interact

VIDEO  (Nets)
THIS WEBSITE lets you see various examples of possible nets for a cube.
You can guess if it will work or not, and then VIEW an animation that shows the result of folding the net.

Video Tutorial  POLYGONS
Interact  Open Math Reference site

Video Tutorial  POLYHEDRA

Video Tutorial  PRISM

Video Tutorial  PYRAMID

Video Tutorial  CYLINDER

Examples

Examples will give you TOOLS for solving problems, and also show you that there may be different ways to approach a question.

Example 1

TEXT Page 171

Work through Example 1 on Page 171 in your textbook.

Watch

Video Tutorial

Example 2

TEXT Pages 171-172

Work through Example 2 on Pages 171 - 172  in your textbook.

NOTE!    Your teacher will let you know if they expect you to do these constructions using just a ruler and a compass (classical construction) or if they will be more “relaxed”.   In this example I will be using my computer and illustration program to do the example, which might be a bit different from how your teacher expects you to do it.

Watch

Video Tutorial

Practice Problems

Doing Practice Problems

Practice problems reinforce the math presented in this lesson.

•	Work through the practice problems for this lesson.
	These problems are for practice, you don’t need to hand them in!
	(your teacher may assign specific questions for you to complete)

•	Use the answers in the back of the book to CHECK YOUR WORK!

•	If you make a mistake, TRY TO FIX IT!

•	If you need help or want more information, view the video solutions provided.

•	If you still need more help,  CONTACT YOUR TEACHER!

Types of Practice Problems

Discuss the Ideas invites you to talk about the math.
If possible share your thoughts/ideas/answers with another person.
If you can help them understand, then you likely have good understanding yourself.

Check questions require basic understanding of the ideas of the  lesson.

Apply questions will require you to dig deeper for a solution.

Take It Further questions offer enrichment and extension.

Notes

Question 1,    This was covered in the lesson.  It doesn’t matter where the circles are places, as long as there is a circle on EACH side of the rectangle.
(It won’t work if the circles are both on the same side)

Question 15,    not much more to say than what the textbook says.   Another possible difference is that with wrapping paper, it’s not a “perfect” net since we need a lot of overlap in order to cover a gift and tape it .   (the better you are at wrapping a gift, the less paper you waste)

Question 16,    a great question, but it would take a lot to explain and/or illustrate.   If lots of students ask about this, I can create models to show how they fold/unfold.  The answers in the textbook are accurate, you will need to make sure you understand how/why they would work.

Video Solution Links

Check your work for every problem you do!
If you make a mistake,  try to fix it!
Use the video solutions for more information.
If a problem still doesn’t make sense, ASK YOUR TEACHER FOR HELP!

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