In Jacobs Geometry Chapter 15 Lesson 1 problem 57, we are asked,
“In how many planes do the square faces of the cube faces of the unfolded hypercube lie?”
The Solutions Manual says 13 planes. Let’s see how they got that number.
Imagine the red, yellow, and blue lines drawn on the hypercube as planes.
Counting vertical planes from right to left: marked in red we have 5.
Counting vertical planes from front to back: marked in yellow we have 4.
Counting horizontal planes from bottom to top: marked in blue we have 4.
5 + 4 + 4 = 13 planes.
Need help with your homework problem? AskDrCallahan video instruction students can submit questions to email@example.com or through our website form on the student help page. Please always include the course, chapter, lesson, and problem number. Any description of your struggle is also very helpful so we get directly to your issue. We love to help.
Chapters 13 and 16 were originally omitted from our Geometry course
for time constraints. The concepts in those chapters are advanced, though not difficult. Students will not likely see them on the ACT/SAT or even in college, except for specialized fields. When needed in a college track, they will be covered anew. They are often skipped at the high school level.
Geometry Chapter 13 and Chapter 16
However, we now recommend Chapter 13 be covered. Chapter 14 briefly refers to concepts introduced there and some students need the information. Others will be okay just referring back. Most of our students still skip chapter 13. We still consider Chapter 16 optional for everyone.
We have lectures for both chapters now on our website for FREE.
Remember that our video instruction, online or DVD, can be used with any printing of the 3rd Edition of Jacobs Geometry.
For Chap 13, Lesson 6, #32, the basis for the answers is the figure for #6. If we look carefully at the grid, applying the Pythagorean Theorem gives XY^2 = 2^2 + 2^2 = 8, so XY = sqrt8 = 2sqrt2. YZ^2 = 1^2 + 1^2 = 2, so YZ =sqrt2. Therefore XY = 2YZ.
The 3rd edition of the Harold Jacobs Geometry textbook has gone through three different printings with 3 different covers and ISBNs. If you are picking a text and looking at used options, it can be confusing. So let me try to help.
First, all 3 versions are basically the same – as long as they say 3rd edition. They look like the photos below.
The Three Geometry Textbook Versions that Still Work
The original published by Freeman – ISBN: 978-0-7167-4361-3 and the corresponding Teachers Guide which contains the solutions to the problems. This book had a separate Test Bank for tests. The second printing published by My Father’s World – ISBN: 978-1-61999-109-5 and the corresponding Teachers Guide which contained the tests and the Answer Key.
The third printing published by Master Books – ISBN: 9787-1-68344-020-8. This is the latest and if you are buying new, this is what you are getting. The tests are in the Teacher’s Guide and the answers are in the Solutions Manual. You will need all 3 books for the course.
The Geometry Videos that Support the above Books
All 3 of the printings will work with the AskDrCallahan videos. The various printings have minor changes in page numbers, drawings, and some problems have changed – but the basic content remains the same. But, just to be more confusing, the videos come in 3 different packages. All are the same content but they might look different. All require the student to have one of the 3 textbooks, the tests, and a set of solutions.
1 – The online videos, offered by AskDrCallahan, contain the same instruction, and bypass the need for DVDs and a DVD player. They are the same content as on the DVD. The online videos come in two options.
- Monthly option – Pay for the course monthly and cancel anytime by logging into your AskDrCallahan account (or email us to cancel). This option is perfect if you think you will need just a few months.
- Lifetime access – If you need a full year, or have siblings who might use the course later, then this is your option. One price one time.
2 – The latest version of the DVDs is published by Master Books – UPC: 713438-110236-8
3 – The original DVDs published by us (AskDrCallahan) and no longer available new. -ISBN:978-0-615-27810-0
I am used to having parents tell me that they think their kid is behind, missed something in 3rd grade, or has a suspected learning disability. That dialogue is almost always the first thing parents say when they are outlining why they need help from a math tutor. For some students, however, they do not need to be held back or to see a doctor. What they need is to move ahead and go on to the next step.
Continue reading When your child is actually ahead, not behind.
When I find great resources, I like to share them on the blog for parents and educators who might be looking for just that tool. I do not have any professional affiliation with this product, I just like it, and I want to share with you things that will help make your education experience the best it can be, with hopefully the least amount of obstacles for you.
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Are you panicked about Calculus? Maybe it’s time to be more panicked about a world where no one builds bionic arms, solves environmental problems, or seeks a cure for cancer–because that’s the reality you’ll have if kids stop taking higher math in high school.
Continue reading Innovation in Life Starts with Higher Level Math in High School
When you plan a road trip, you use math literally every step of the way. What you may not know, however, is the right math term for what you’re calculating. So today, I’m going to walk you through a few steps of planning a road trip so you can see how Algebra helps you get from point A to point B successfully. Continue reading Real World Math | The Algebra of Planning a Road Trip
Around the world, education is not as often available as it is in more developed countries. Too many high school students that I work with here in the US take math education for granted. You see, a global perspective on mathematics and it’s place in the world is a problem we, as the adults, created–or at least allowed. Here’s what I think we can do to change that narrative and start a conversation that creates a better perspective on math and education in general.
Continue reading 3-step project idea to help you learn why learning math is important
Some of the links in this article are affiliate links. We don’t carry in our shop all the materials you would need to complete this activity, so we use links to share with you the products you would want to use so that you can do this activity at home. Some of those links are affiliates and we will make a small percentage commission, at no additional cost to you, if you use our links to purchase your supplies.
Have you ever wanted to build your own Lego Ferris Wheel or Train and be able to control it like a robot? Now you can!–and BONUS it counts as a math class activity. Keep reading to find out how to do it and at the bottom I’ll show you where in your Algebra II with Trig course this activity would fall so you can schedule it in your lessons.
Continue reading Raspberry Pi and A Robot Ferris Wheel you can build at home for less than $100