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Lesson 3.2 General Patterns With 2 Variables

Two variables is nothing to freak out about.

Mark Watkins

on 17 October 2012

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Transcript of Lesson 3.2 General Patterns With 2 Variables

General Expressions with 2 Variables It's like general patterns with 1 variable, except there are 2 So what does this crazy two variable thing look like? What did we learn? Unit 3 Lesson 2 What is a general pattern? What is a variable? Well it's not so bad. General patterns with more than one variable aren't such a big deal. The same rules apply. Remember...a general pattern is a rule or pattern that uses variables because it is true with any variable substitution. x + 5 = 5 + x True no matter what x is. A variable is a symbol that represents a number. Can a variable change? Yes, until we a make a special case, and then the variable stops representing a number and actually becomes the number. Once we say N=5, N=5 every where else in the special case. N + 7 = 7 + N General Pattern 5 + 7 = 7 + 5 General Pattern 12 = 12 this is true The things that would stay the same for every special case are the same in the general pattern. The things that could change in a special case take on their variable form in the general pattern. Let me think of an example... I love to have company over for some grilling. Every gentleman that attends my backyard gathering will eat 1 hamburger Every lady that attends my get together eats THREE! I said 3 hamburgers. To find out how many burgers to cook I need to come up with a general pattern, or formula. The number of burgers each man and woman will eat is established and constant. What changes is how many show up. The things that change become variables. Let's have W represent the number of women and M represent the number of men. We will multiply separately and add the burgers once we have the number of women and men attending. (W 3) + (M 1) = how many burgers * * The RSVP list came back and there are going to be 10 women and 11 men. That one guy "had a date, but..." any way... (10 3) + (11 1) = * * special case The Computations (10 3) + (11 1) = * * 30 + 11 = 41 = I wish those women didn't eat so many hamburgers. Seriously, three hamburgers? OH NO!!! Everyone is bringing their kids. They each eat five hamburgers! Luckily I can assign them a variable, use my parentheses to establish order of operations, and put them in the general pattern. Then when I count them I will finish of the special case and run the numbers. I am going to represent the number of kids with the letter K, because I'm original. (W 3) + (M 1) + (K 5) = * * * Oh for goodness sakes. There are going to be 32 kids. So... (10 3) + (11 1) + (32 5) = * * * special case 30 + 11 + 160 = 201 general pattern In a general pattern, variables still represents unknown numbers that may change until the special case happens A 2 + B 2 = 2 (A + B) * * * 4 2 + 6 2 = 2 (4 + 6) * * * 8 + 12 = 2 10 * 20 = 20
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