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ALGEBRA 2 Chapter 1: Essential Questions How do variables help you model real-world situations? How can you use the properties of real numbers to simplify algebraic expressions? How do you solve an equation or inequality? Write your definitions. Remember you are responsible for knowing all these terms! They are key to your success in Math Vocabulary Word Variable Numerical Expression Algebraic Expression Constant Definition Examples 1-1 PATTERNS AND EXPRESSIONS Some patterns can be represented using diagrams, words, numbers or algebraic expressions. Variables can represent different quantities in real world situations and in patterns. This lesson communicates that searching for patterns is a proven problem solving technique and is a foundation for mathematical knowledge. PATTERNS AND EXPRESSIONS Please look at the arithmetic sequences below. 1. 1, 2, 4, 8, 16, 32, 64 … 2. 1, 4, 9,16 … Look at the patterns and draw what you think is the 9th number in the first sequence? What do you think the 6th number is in the second sequence? What is the pattern for the 1st and 2nd sequence? Can you write a rule for each sequence. PATTERNS AND EXPRESSIONS Please look at the arithmetic sequences below. 1. 2, 4, 8, 16, 32, 64 … 2. 1, 4, 9,16 … Look at the patterns and draw what you think is the 8th number in the first sequence? 256 What do you think the 6th number is in the second sequence? 36 In words, what is the pattern for the 1st and 2nd sequence? Doubling/Perfect squares PROBLEM 1 Look at the figures from left to right. What is the pattern? What should the next figure in the pattern look like? The pattern shows regular polygons with the number of sides increasing by one. The last figure shown above has six sides, so the next figure would have seven sides. GOT IT ? # 1 PAGE 4 Look at the patterns from left to right. What is the pattern? Draw the next figure in the pattern. Did you write your definitions? Remember you are responsible for knowing all these terms! They are key to your success in Math Vocabulary Word Definition Examples Variable A symbol, or letter that represents one or more numbers n r Numerical Expression A mathematical phrase that contains numbers and operation symbols (No equal sign: that is equation) 3+5 Algebraic Expression A mathmatical phrase containing one or more variables 6n + 8 3(2x - 3) + 7 Constant A quantity whose value does not change 3 x etc (5 – 2) + 8 2.5 1/2 PROBLEM 2 EXPRESSING A PATTERN WITH ALGEBRA. PAGE 5 Figure Number (Input) 1 2 3 : n 20 Process Column Number of Toothpicks 1(4) 2(4) 3(4) : ? ? Got it? # 2. How many tiles are in the 25th Figure in this pattern? Create a table like the one above. 4 8 12 : ? ? PROBLEM 3 USING A GRAPH, PAGE 6 PROBLEM 3, PAGE 6 Input(Fish Length) Process (Formula) Output (Capacity) 0 5 0+2 2 0+5 5 10 0 + 10 10 Output = Input + 2 = 17 + 2 = 19 So which tank will you buy?? GOT IT # 3, PAGE 6 GOT IT #3 PAGE 6 The graph shows the total cost of platys at the aquarium shop. Use a table to answer the questions. A. How much do 6 platys cost? B. How much to 10 platys cost? C. Why is the graph in Example 3, while the graph regarding platys is a set of points? LET’S LOOK AT SOME QUESTIONS LESSON 1-1 Text p 7, 1-7 working in pairs Practice workbook, p 3-4 all Finish for homework / Remember homework will not be accepted if ALL work is not shown. ******If you think it in your head or enter it in a calculator, you MUST write it down.**********