The McSquared Math Class Blog

Here are some general guidelines for simple programming, which will give you enough info to do that quadratic program yourself. What?!?!? You thought I’d just give you the actual program!?!?

Okay, okay, here’s a video about the quadratic formula….but no voice. So you might need to look at the slideshow first anyway. 🙂

Make a geogebra about the exponential function f(x) = a(c)^{b(x – h)} + k

Once again, you’ll be using epearl to document your progress and learning. Start by creating a new artifact called The Exponential Function, and fill in the task description AND the criteria, in your own words.

Your geogebra must include:

• as many sliders as this function needs in order to be able to vary the parameters and the base
• a text box with the fully loaded rule of the function currently set by the sliders
• a text box with the simplified version of the current rule ie f(x) = a(c)^x + k
• the graph of the function, including its asymptote, currently set by the sliders
• text boxes that appear/disappear as needed to give information about
  • whether the function increases/decreases
  • what the domain and range are
  • when the function has no zero
  • what the zero is if it has one
  • what the y intercept is
  • what the asymptote is
• all of the information displayed in an orderly way, ie not all over the screen at random places

Bonus points:

• The function’s colour depends on whether it increases or decreases.
• Your geogebra is uploaded to geogebratube and embedded in your blog.
• A checkbox that, when checked displays the rule and graph of the inverse of the current exponential function. I know we haven’t done it yet. That’s why it’s a bonus. 🙂

Due date: Wednesday Feb 12. 

There are two parts to this assignment – a post AND a comment:

The post:    

Pretend you’re explaining what logarithms are to someone who’s never heard of them. Make sure that after your explanation, they’d be able to:

• Figure out, without a calculator, these types of examples:
  1. log₅125
  2. log₂(1/16)
  3. log₄₉7
• Know when it’s absolutely necessary to use the log/ln buttons on their calculator, and how to use them.

Your post needs to have:

• at least one type of media inserted or embedded, such as an image, slides, a geogebra, a video, a voki, or a voicethread. I’ll help you with the tech part, but you have to do the math part!
• proper notation, eg actual subscript for the base. I do NOT want to see “log base 2 of 8”.
• your voice, your thought, evidence that you actually understand logarithms

Never heard of a voki? Here’s one:

The comments:

You must comment on 3 other peoples’ posts, the two people who are immediately above and below you in the blog list, and one other person of your choice. Your comments must:

• Follow the guidelines suggested here.

Due date: Friday, Feb 7

Happy New Year! Your first blog post assignment is to write a post about your holidays. What did you do? What did you get? Where did you go? Who did you see?

Once you’re done, read the posts of at least 3 other students in the blog roll on the right side of this page. Which 3 people? The people immediately above and below you in the list, plus one other person.

Leave a comment on each of those peoples’ posts.

Remember, no pictures of yourself, no full names, no addresses etc.

Instead of writing the entire test next week, you may instead write just the last section of it, which is the problem-solving section, as long as you’ve also done a geogebra about the rational function.

Here’s what the geogebra needs to have in it:

• Sliders to show the graph and equation of any rational function y = a/b(x – h)  + k for any values of a, b, h, and k.
• The corresponding asymptotes, their equations, the centre of the function, and its coordinates
• The coordinates of the zero (Z) of the function, if it exists (you must use a formula, not a button)
• The coordinates of the y-intercept (I) of the function, if it exists (you must use a formula, not a button)
• The coordinates of a point P on the function whose position is controlled by a slider with the name t.
• Text boxes that appear/disappear, and display the following info:
  • whether the function increases/decreases
  • what the domain and range are
  • when there is no zero
  • when there is no y-intercept
• Bonus: Display the solution to the inequation f(x) > 0.

Due Tuesday Dec 10. Of course, if you’d like to do the geogebra and the test, you are more than welcome to do so!

Once again, you’ll be using epearl to document your progress and learning. Create a new artifact called The Square Root Function, and fill in the task description AND the criteria, in your own words.

This time, whenever you make a new version of your ggb, you will also use the “New version” feature in epearl. Everything in the previous version is automatically copied into the new one, and all you have to do is add your new ggb into the doing section, and add to/edit the other fields as you need to.

You will be making the exact same type of geogebra for the square root function as you did for the linear one, with a few extras:

This one will also include, in addition to everything the linear one had (the bold section is what’s currently due):

• sliders for 4 parameters instead of 3. The extra one will be for the b parameter.
• a t-slider with a much bigger range than just [-5, 5].
• text boxes that appear/disappear to give information about
  • whether the function increases/decreases
  • what the vertex is
  • what the domain and range are
  • whether or not there is a zero
  • what the zero is
  • whether or not there is a y-intercept
  • what the y intercept is

This assignment is another geogebra one, but this time it will be documented using epearl. Why? Because I want to see the whole story of your geogebra/math learning adventure, not just what happened at the end!

First, here’s what to do in epearl:

Today:

• In epearl, create a new artifact called “The Linear Function”
• In “Planning” write a one- or two-sentence description of the task (see blue text below) as you understand it. DO NOT JUST COPY AND PASTE WHAT I WROTE! And don’t forget to save!

As you work on the assignment:

• I expect you’ll need to try this a few times before it all works perfectly, in which case, the first time you try it, whether or not it works, save that ggb file as The Linear Function 1. After that, every time you make a change to that file, you’ll need to save it with a different number tacked on at the end: eg The Linear Function 2, The Linear Function 3, etc. By the time you’re done, you’ll have 4 or 5 of these files saved, each different, and showing your progress.
• In “Doing“, attach all versions of the geogebra files as you save them.
• In “Reflecting“, document your learning as each version is attached. Eg. What’s working? What’s not? Have you come up with any strategies that work in ggb? Any problems with ggb? Is this hard, frustrating, fun, satisfying? Has it resulted in better math understanding, more motivation? Did you wake up in the morning and discover that your brain solved something while you were asleep? Did you start out thinking there’s no way I will ever be able to do this and then change your mind about that?

After you’re done, and you’re satisfied with your work:

• Name the final version The Linear Function Final.ggb, and put it in “Doing”.
• In “Reflecting”, tell me why you’re satisfied with this version. And anything else you want to say about this assignment.

AND HERE’S THE ASSIGNMENT: Create a geogebra file about the linear function that displays each of the following:

• The graph and equation of any linear function y = ax + k for any values of a and k.
• The coordinates of the zero (Z) of the function currently displayed (you must use a formula, not a button)
• The coordinates of the y-intercept (I) of the function currently displayed (you must use a formula, not a button)
• The coordinates of a point P whose position is controlled by a slider with the name t.

Here’s how I’ll assess your work:

• All of the blue and the green items have to be there. (blue = 10 marks, green = 10 marks)
• It has to be correct.
• There has to be more than just the final version of the file.
• The final version has to be on time. Due date is Sunday Oct 20, midnight Montreal time.
• MOST IMPORTANT OF ALL: Your descriptions and reflections have to belong to you. Don’t just parrot what someone else said, or embroider something pretty that you think I want to hear. (Teachers can spot that a kilometer away.) “It was fun” is okay, but “It was fun because I was so happy when I actually got it to work” is much better.
• Bonus points! There are bonus points!

Bonus points:

• The graph changes colour depending on whether the slope is positive, zero, or negative.
• Texts containing information about the function or the points pop up depending on the values of the parameters, such as “This function is increasing.”
• The point P leaves a trace as it moves along the line.
• For Science Math students only: Use your final version of The Linear Function to create and save another geogebra file, called The Absolute Value Function, that does all of the blue stuff for the absolute value function of the form y = a|x – h| + k. It might need a few extra sliders and, um, other stuff. 😉
• For Technical Science Math students only: Use your final version of The Linear Function to create and save another geogebra file, called The Quadratic Function, that does all of the blue stuff for the quadratic function of the form y = a(x – h)² + k. It might need a few extra sliders and, um, other stuff. 😉

Have at it!

Your answers to: How would you decide if two vectors are orthogonal?

Your answers to When would you use this way to find the dot product?