Geometric Patterns Lesson 1 MINDS ON! A LINEAR PATTERN can be identified by a COMMON DIFFERENCE between terms. For example 3,5,7,9… is a LINEAR PATTERN 3,5,8,12… is a NON-LINEAR pattern. 20 min MINDS ON! Is this a LINEAR PATTERN? How would you find the expression to represent it? How many shapes will be in the 5th shape? 20 min 20 min MINDS ON! Make a table of values! Term Number (x) 0 Pattern Rule: Term Value (y) First Difference 20 min MINDS ON! Let’s graph the relation! Why do you think this type of pattern is called Linear? EXPECTATION C1.1 identify and compare a variety of repeating, growing, and shrinking patterns, including patterns found in real-life contexts, and compare linear growing and shrinking patterns on the basis of their constant rates and initial values LEARNING GOAL Today we are learning to represent linear growing patterns. EXAMPLE 1,3,5,7,9,11 can be described as a pattern that starts with 1 and increases by 2 as it extends. ACTION! Make a table of values then define the pattern rule algebraically. Use the expression to find the perimeters of Frames 5, 10, and 100. ACTION! Make a table of values then define the pattern rule algebraically. Use the expression to find the perimeter of Frame 40. CONSOLIDATION CONSOLIDATION Complete all questions posted on Google Classroom. Number Patterns Lesson 2 MINDS ON MINDS ON! MINDS ON! Make a table of values! Term Number (x) 0 Pattern Rule: Term Value (y) First Difference 20 min MINDS ON! Let’s graph the relation! Why do you think this type of pattern is called Linear? EXPECTATION C1.1 identify and compare a variety of repeating, growing, and shrinking patterns, including patterns found in real-life contexts, and compare linear growing and shrinking patterns on the basis of their constant rates and initial values LEARNING GOAL Today we are learning to represent linear growing patterns. EXAMPLE 1,3,5,7,9,11 can be described as a pattern that starts with 1 and increases by 2 as it extends. ACTION! Make a table of values then define the pattern rule algebraically. CONSOLIDATION Complete all questions posted on Google Classroom. Tables, Graphs, and Equations Lesson 3 5 min MINDS ON Which of the following are LINEAR? 3, 7, 11, 14, 17 1 2 2 9 3 16 4 23 5 30 MINDS ON 8, 2, -4, -10, … Is this pattern linear? Is it growing or shrinking? Graph this pattern and describe it using an algebraic equation. EXPECTATION C1.2 create and translate repeating, growing, and shrinking patterns involving rational numbers using various representations, including algebraic expressions and equations for linear growing and shrinking patterns LEARNING GOAL We are learning to represent growing and shrinking patterns using tables of values and graphs EXAMPLE 4,6,8,10,12 can be represented as 2x + 2 Term Value 1 4 2 6 3 8 4 10 5 12 ACTION! 20 min Create a table of values, a graph, and an equation to represent this LINEAR PATTERN. 7, 0, -7, -14, -21 CONSOLIDATION Complete all questions posted on Google Classroom. Linear Patterns Lesson 4 MINDS ON Ms. Noxon needs to have a LOT of pencils for her students. Before the first day of school, she sets out 23 pencils, one for each student in the class. Every day after, she gives out an average of four pencils. Graph the pattern. Describe it algebraically. How many pencils will Ms. Noxon give out after 35 days, 75 days, and 200 days? Extension How many days will it take for Ms. Noxon to give out 500, 750, and 237 pencils? EXPECTATION C1.2 create and translate repeating, growing, and shrinking patterns involving rational numbers using various representations, including algebraic expressions and equations for linear growing and shrinking patterns LEARNING GOAL Today we are learning to use algebra to represent patterns. EXAMPLE the general term for the sequence 4, 5, 6, 7, ... can be written algebraically as n + 3, where n represents the term number ACTION 5 min Shira received a $250 award for her outstanding volunteer work in her community. She has decided to use the money to pay for a new bike which costs $470. If she saves $20/week, how long will it take her to save enough money for her new bike? CONSOLIDATION Ms. Noxon has to choose between two gym membership plans. Plan A: $50 monthly membership fee and $10 per visit. Plan B: $25 monthly membership fee and $15 per visit. Which plan is the better deal? Does this change at any point? 5 min CONSOLIDATION Complete all questions posted on Google Classroom. Graphs and Equations Lesson 5 5 min MINDS ON 1,4,7,10,13… How would you find the... 8th term? 15th term? 100th term? 500th term? MINDS ON! Create a table of values and an expression that correspond with the graph. 20 min EXPECTATION C1.3 determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in growing and shrinking patterns involving rational numbers, and use algebraic representations of the pattern rules to solve for unknown values in linear growing and shrinking patterns LEARNING GOAL Use a graph or equation to find an unknown value. EXAMPLE Given the graph that represents the pattern 1, 3, 5, 7, ..., find the 10th term. Given the algebraic equation that represents the pattern, t = 2n – 1, find the 100th term. EXTENSION! 5 min Kelly and Gary have part-time jobs. Kelly is paid $11/hr. How much will she earn for working 16 hours on the weekend? Gary also worked 16 hours on the weekend, but he earned $20 in tips. His total earnings were $180. How much does he earn per hour? ACTION! If you are given the following graph, how can you determine the 4th term? 20 min ACTION! If you are given the following equation, y = 3x - 2, how can you find the 9th term? ACTION! 20 min Create the corresponding patterns (first five values): a) 3x + 4 b) 2x + 3 c) x -1 d) 5x -3 CONSOLIDATION What is the 10th term? a) y = 3x - 3 b) 5 min PRACTICE You are going to be using the graphs and equations you created yesterday. 1. Using the equations you created, calculate the 10th, 15th, and 30th values for each pattern. 2. Create a new Cartesian plane and graph the lines including the new values. 3. Confirm your findings with the members of your group. 4. Given the following pattern, identify the COMMON DIFFERENCE, create an equation and a graph and identify the 10th, 15th, and 30th values. 2.5, 3.2, 3.9, 4.6, ... CHALLENGES! 1. Did any of your lines have a negative slope (e.g. -3x + 2)? If not, create a line with a negative slope and determine the 10th, 15th, and 30th values. Was this easier/harder than using patterns with a positive slope? What was the difference? 2. Can you find the missing term number? The equation for the line is y = 3x + 2 and the term value is 11. What is the term number? The equation for the line is y = -13x - 6 and the term value is -71. What is the term number? Create the corresponding pattern and graph to confirm your answers.