Real Applications Infused in Technology Math ACE Technology Math Real Applications Infused in Technology Math

Curriculum Re-do Boring Teaching for the purpose of testing Difficulty extending their knowledge Hard to get them excited

How? Time off for curriculum development Took about 6 weeks to make worthwhile activities. Looked at applications of all the topics A lot of research! Creating the application activities and a sample lesson plan Bringing it to their level (ex. GPS) The teacher (Jeff) created the Powerpoints to use throughout the classes and the tests and worksheet he wanted to use.

Functions and Relations Programming Functions in PHP

Functions in Computer Programming To start this unit, we will begin with a little video: Steve Jobs "Everybody should learn to program" We are going to learning in PHP, one of the many programming languages This is just a very basic introduction but connects very well with the mathematics we are learning Use an online simulator like onlinephpfunctions.com The "Your script:" part is where you code and once you press "execute code" the "Result" box is what would actually appear on the computer in front of the user. Copy the following text in the box and press “execute code” <?php echo "Hello World!"; ?>

Functions in Computer Programming Each section of code for php must start with <?php to tell the computer which language is being used The echo command tells the computer what to send to the screen for the user to see. Text in quotations is what the user will see Text without quotations are commands to be processed Every command must end with a ; (semicolon) Once your php section is done, you tell the computer by ending with ?> <?php echo "Hello World!"; ?>

Functions in Computer Programming Activity: With the code below, name and identify all the mistakes (there are 5), then fix it in order for it to work. < ?php eho Hello World!"

Functions in Computer Programming There are 5 errors: There is a space between ? and > on the first line Echo is spelt incorrectly The quotation is missing in front of Hello A semi-colon is missing at the end of World!" The code must be closed with ?>

Functions in Computer Programming Define a function in computer science: A function involves inputs and outputs. When you input something into a function, the function changes it and gives a new output. Each function has a name, just like you and me, so when you call it, the computer knows who you are talking to. In computer programming, you define a function at the beginning so that you can work with it later. Again, just like you and me, we must exist before anyone can interact with us.

Programming Functions in PHP Type the code below into the sandbox. We’re subbing 2 in for x in the equation: y = 2x + 4 <?php //Start PHP Code function f($x) { //Create function named f, accept values for x //$x is used as a variable instead of just x $answer_fx = 2*($x) + 4; //Calculate and store answer in $answer_fx echo "$answer_fx"; //Send answer to the screen } //Function is done f(2); //We now call / run the function and set $x = 2 ?> //End PHP Code

Programming Challenge Build a PHP function that uses: y = 3x – 5x + 1/4 The input to send to your function is: 0.25 The user should see the following output: Use variables whenever possible to generate your output. You’ll see why when we test it  Welcome to my PHP function: The equation is y = 3x - 5x + 1/4 The input is x = 0.25 The resulting y value is -0.25 The ordered pair is (0.25, -0.25) Thank you!

Extensions Function Practice Adding and subtracting Functions: Add the output of one function to the output of another E.g., A regular priced item is added to the price of a discounted item Composite Functions / Function within a function: Take the output from one function and send it as the input to another function E.g., Calculate a discount, then sales tax

Programming Functions in PHP - Activity <?php function f($x) { global $answer_fx; $answer_fx = 3*($x) + 5; echo "f($x) = $answer_fx\r\r"; return $answer_fx; } function g($r) { global $answer_gx; $answer_gx = 3*($r) - 2; echo "g($r) = $answer_gx\r\r"; return $answer_gx; f(2); g(2); $final_answer = $answer_fx + $answer_gx; echo "f(2) + g(2) = $final_answer"; ?>

Trigonometry GPS Trilateration

Trilateration Give the students a map of Lake Superior. They are lost. But they meet different people along the way who are able to tell them the following information: You are 200 km from Newberry You are 300 km from Hurkett You are 350 km from Thunderbay Where are they? They will need to use the map scale (3 cm = 100 km) to figure out the distance of the radius from each of these locations. Using a compass they will draw the 3 circles to see where they intersect.

Trilateration Tougher Challenge Give the students the following map and scenario. They will need to use Pythagorean Theorem to find the radius of the possible location from 3 different satellites. The 3 satellites will only meet in one place. Let’s use 2000 km as the distance satellites orbit around the Earth’s surface. (The real value is closer to 20,000 km) The speed of light is approximately 299,800,000 meters/second The first satellite is above Berlin and it took 0.0069 seconds for the signal to reach the satellite. The second satellite is above Madrid and it took 0.0089 seconds for the signal to reach the satellite The third satellite is above Bucharest and it takes 0.0073 seconds for the signal to reach the satellite Where is the cell phone?

Four Corners – Estimating Volume Intuitively 3D Geometry Four Corners – Estimating Volume Intuitively

Four Corners – 8.5” x 11” Paper Use your mathematical intuition to guess Which shape has the greatest volume? The short one. The tall one. They are the same. No Idea!

Four Corners Now make your Volume calculation using an 8.5in x 11 in piece of paper. Whoops, I don’t know the radius. What can I do? I do know the circumference right? Can I use the circumference and a bit of algebra to solve for the radius? YES!!! Now solve the volume of the letter size cylinder folding the paper both ways.

Four Corners Now that you know that they are different volumes, I want you to think about why… What can you say about the effects of changing the height? What can you say about the effects of changing the radius?

Thank you! We hope you have discovered some interesting applications to try with your ACE Technology Math classes! We are: Stephanie McKean smckean@georgebrown.ca and Jeffrey Peck jpeck@georgebrown.ca