graph the solutions for y = -3x + 4 (Jon’s age) = 2(Sally’s age) - 10 How old are Jon & Sally? Write down this problem on your COMMUNICATOR Be prepared to share your work with the class. Page 18 of your INB The point of this exercise is to get students thinking about the effects of 2 variables. Essentially, we have a “relationship” between the 2 variables, and one affects the other. There will be an infinite number of solutions. Ask a student how old Jon is? Or Sally? Students will say “it can’t be done – not enough information” I will say “really????” Ok, someone, pick a number. That’s how old we’ll say Sally is. If Sally is 11, how old is Jon? Make a table on the board and record the possible answers. Question: Is it easier to pick Sally’s age, and then find Jon’s age or vice versa?

Shade the area between %. This is where Mrs. Kalt would like you to be. If you’re not here, make a plan (write it down) to get there. Objective is to increase your test score each time you take a test until you are in “the zone”. Once you are in “the zone” your plan is to stay somewhere in the zone. Make your plan today to get where you want to be.

ITEMS of BUSINESS TEST REWORK counts as a homework assignment. It is DUE Tuesday Sept 23 th (A-day) & Wednesday Sept. 24 (B-day). I do not accept LATE rework for credit – even with a coupon. You can retake Ch 1 Test iff... - Practice Test is complete with work shown - Rework is complete with work shown - you have a 3x5 card made - Last day to Retake is Sept 29(A-day) & 30 th (B-day) - I will reserve 1 intervention for retakes (TBA). Or make an appointment before/after school. I know I spelled iff with 2 fs! It means if and only if – therefore iff.

Unit 2: Linear Functions This chapter will include some review from last year. Mostly, we will be solving equations – lots of equations! 2.1 Multiple Representations of Mathematical Relationships

Get into your 4-Square Groups graph the solutions for y = -3x + 4 Page of your INB Note: very few students will be able to even begin this problem. Common question: “how can you graph this when there isn’t a solution?”

11 = 2x +1 5 y = 2x + 1 (5,11) or (7,15) or (6,13) Infinite solutions! Trying to make a connectin here from last chapter (1-dimensional equations) to this chapter (2-dimensional equations).

It costs 8 less than the product of three and two times the number of people attending increased by 5. Oh, you mean C = 3(2n +5) -8 First talk about a mathematical relationship. What is a “relationship” in math? It’s when one variable has an effect on the other variable. They relate to each other somehow. Relationships are often difficult to describe. Here’s how Jake the dog describes a relationship between the cost and number of people attending… Now here’s how Finn the human describes the same relationship. Which do you prefer? Raise of hands. Why???

Use colored highlighters. Highlight the words and then write the corresponding operation.

1.The quotient of m and 9 is y 2.The difference of k and 10 is h 3. b is 5 less than 2a4.The sum of twice a number and 8 is y Answers: 1.m/9 – y (write division the big-boy way plz) 2.K-10 = h 3.b=2a – 5 (students will write b =5-2a) Ask: what is 5 less than 20? 20-5 compare 4. 2n+8 = y

Ask students how term number “relates” to the number of items in each group. Discuss with groups. Answers will likely be “+2”. No, no, no people! I asked how term number relates to items in group. You told me how number in each group relates to the number in the next group. Make a table with headings n & g. Fill out the table. Redirect students to find how numbers in column 1 relate to numbers in column 2. “I want an equation using n & g please.” Someone will come up with 2n-1 = g Next, ask how many dogs are in the 43 rd group? Answer: 2(43) – 1 = 85

Mrs. Kalt, but when would we ever really use a table?????? What are tables good/useful for? Students will say they are useful for organizing data. I will add that they are good for making comparisons between 2 sets of numbers... or for looking for “relationships” Why would I ask you this? Keep this at the back of your minds.

y = 2x + 1 solve Students, please write a solution for this on p. 16 of your notebooks. Go. Hurry. Just a solution. Start calling on students for possible solutions. Write them down as an ordered pair like (5,11) but put the x over the 5 and the y over the 11. Write them all over the page, kind of messy. Lots of possible solutions. Then say “gosh, this is a mess” I sure wish I had a way of organizing all these x and y’s. Perhaps a table???!!!

Students, follow along in your foldable. Remind me of some of the solutions that you all thought of. Write one in the table. Then have students plot that point (if possible). Write down another one. Plot it. After 2 points, have students guess what it’s gonna look like. They will guess a bunch of dots all over. Do a third point. Hmmm…they are in a line! Have them pick EASY values for x. Like 0,1,-1. Plot those points. Question: how many points do you think we could plot? Infinitely many. Then draw a ton of dots all in a straight line. Your graph should end up being a straight line. Make sure the line goes through the points. Make sure there are arrows on both ends. Question: Will it go on forever in both directions? Will there be any holes?

y = 3x-2

y = -x + 1

SHOW YOUR WORK Worksheet 2.1 Multiple Representations of Mathematical Relationships