Unit 2 Representing Patterns PDF - Grade 8 Lesson Outlines

Unit 2 Grade 8 Representing Patterns in Multiple Ways Lesson Outline BIG PICTURE Students will: represent linear growing patterns (where the terms are whole numbers) using graphs, alge...

Unit 2 Grade 8 Representing Patterns in Multiple Ways Lesson Outline BIG PICTURE Students will: represent linear growing patterns (where the terms are whole numbers) using graphs, algebraic expressions, and equations; model linear relationships graphically. Day Lesson Title Math Learning Goals Expectations 1 What Do Patterns Tell Review patterning in real contexts, e.g., weather patterns, quilt 8m56 Us? patterns, patterns of behaviour, patterns in a number sequence or codes. CGE 2c, 3e Develop an understanding that all patterns follow some order or rule, and practice verbally expressing patterning rules. 2 Different Examine (linear) patterns involving whole numbers presented in a 8m56, 8m57, Representations of the variety of forms e.g., as a numerical sequence, a graph, a chart, a 8m60, 8m78 Same Patterns physical model, in order to develop strategies for identifying patterns. CGE 3b, 5a 3 Finding the nth Term Determine and represent algebraically, the general term of a linear 8m57, 8m58, pattern (nth term). 8m60, 8m62, Determine any term, given its term number, in a linear pattern 8m63, 8m78 represented graphically or algebraically. Check validity by substituting values. CGE 5b, 7j 4 Exploring Patterns Determine any term given its term number in a linear pattern 8m57, 8m58, represented algebraically. 8m60, 8m63, 8m73 Examine patterns involving whole numbers in a variety of forms. Explore and establish the difference between linear and non-linear CGE 3c, 4a patterns. 5 Space Race: Graphic Record linear sequences using tables of values and graphs. 8m58, 8m63, 8m78 Representations Draw conclusions about linear patterns. CGE 4f, 5a 6 When Can I Buy This Solve problems involving patterns. 8m56, 8m57, Bike? Use multiple representations of the same pattern to help solve 8m58, 8m73, problems. 8m60, 8m63, 8m78 Model linear relationships in a variety of ways to solve a problem. CGE 3c, 4f 7 Determining the Term Determine any term, given its term number, in a linear pattern 8m58, 8m61 Number represented graphically or algebraically. Determine the term number given several terms. CGE 3c, 4b, 4f TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 1 Unit 2: Day 1: What Do Patterns Tell Us? Grade 8 Math Learning Goals Materials Review patterning in real contexts, e.g., weather patterns, quilt patterns, patterns chart paper of behaviour, patterns in a number sequence or code. variety of everyday Develop an understanding that all patterns follow some order or rule and practice patterns variety of verbally expressing patterning rules. manipulatives BLM 2.1.1, 2.1.2 Assessment Opportunities Minds On… Small Groups  Graffiti Students should be in Based on class size, set up three stations with different patterning examples at heterogeneous each station, e.g., atlases/maps (landforms, weather), artwork, pine cones, groupings. nautilus shells, bird migration patterns. Student groups at each station record all A recorder can be the patterns they discover in 1–2 minutes. Students rotate through all three assigned in each group or all students stations. may be involved in Student groups summarize their findings and each group presents a brief recording. summary to the class. Encourage multiple representations of patterns. Action! Think/Pair/Share  Demonstration Using manipulatives, e.g., linking cubes, display the following patterns: 4, 8, 12, 16... and 1, 4, 7, 10.... Students determine a pattern and share with their partner. In a class discussion students express the pattern in more than one way, e.g., the first pattern increases by 4 each term, or the pattern is 4 times the term number, the pattern is multiples of 4; the second pattern increases by 3 each term, the pattern is 3 times the term number subtract 2. Individual  Practice Students complete BLM 2.1.1, extending the pattern and expressing it in words. Content Expectations/Observation/Journal/Mental Note: Circulate to assess for understanding of representing patterns. Consolidate Whole Class  Presentation Debrief Students represent the patterns visually and explain them. Home Activity or Further Classroom Consolidation Find a pattern that you like. Record the pattern in your math journal in pictures Provide examples of Exploration Reflection and words. patterns within the class. TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 2 2.1.1: Pattern Sleuthing Impact Math: Patterning and Algebra p. 16 TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 3 2.1.2: Pattern Sleuthing (Teacher) Possible student answers: 1. Number of sides increases on each polygon, with each term (next shape heptagon) 2. Shaded square location rotating counter-clockwise around square pattern (next diagram shaded in lower right area) 3. Increasing by odd numbers (3,5,7…) or square numbers (next term 25 dots) 4. Adding a row to the bottom of the diagram, with one more dot (next term row added with 5 dots) 5. Each term increasing by 7 (35, 42, 49) – extension answer: 7n 6. Each term increasing by 4 (19, 23, 27) – extension answer: 4n –1 7. Increasing by 3, by 4, by 5, etc. Related to question 3 – extension answer: 8. Increasing by consecutive odd numbers (25, 36, 59) – extension answer: n2 9. Increasing by consecutive odd numbers (35, 58, 73) – extension answer: n2 + 2n or n(n + 2) 10. Each number is doubled (32, 64, 128) – extension answer: 2n 11. Increasing by 2, by 4, by 8, by 16 (34, 66, 130) – extension answer: 2n + 2 12. Increasing by 4, by, 6, by 8 or by consecutive even numbers (30,42, 56) – extension answer: n2 + n or n(n + 1) Extension: This question is the Fibonacci sequence. The pattern is: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987. See the following websites: http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html http://www.fuzzygalore.biz/articles/fibonacci_seq.shtml http://en.wikipedia.org/wiki/Fibonacci_number TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 4 Unit 2: Day 2: Different Representations of the Same Pattern Grade 8 Math Learning Goals Materials Examine (linear) patterns involving whole numbers presented in a variety of forms, a visual pattern e.g., as a numerical sequence, a graph, a chart, a physical model, in order to develop BLM 2.2.1, strategies for identifying patterns. 2.2.2, 2.2.3 linking cubes rulers Assessment Opportunities Minds On… Pair/Share  Patterning Interesting visual Model how to share a visual pattern, e.g., art, nautilus shell, in both words and patterns can be pictures. Student A shares the pattern in words and pictures with Student B. Student found by doing an B shares the pattern in words and pictures with Student A. Regroup pairs to form online image groups of four. search. Student A in each pair will share Student B’s pattern with the group. Student B in each pair will share Student A’s pattern with the group. Action! Small Groups  Investigation In heterogeneous groups, students rotate through the stations (BLM 2.2.1) They record their work on BLM 2.2.2. (The empty circle area on this BLM is used on Day 3.) Whole Class  Connecting Students share their findings and record any corrections on their worksheet. They label the four rectangular sections as: Numerical Model, Graphical Model, Patterning Rule, Concrete Model (BLM 2.2.2). Lead students to the conclusion that all of these representations show the same pattern: What do you notice about the table of values and the concrete representation? What are the similarities? (i.e., they are all representations of the same pattern) Curriculum Expectations/Observation/Checklist: Circulate to assess understanding that the representations all show the same pattern. Consolidate Whole Class  Four Corners Debrief Post charts in the four corners of the room labelled as: Graphical Model, Patterning Rule, Concrete Model, Numerical Model. Below each label, draw a rough diagram to aid visual learners. Pose the question: For which model did you find it easiest to extend the pattern? Students travel to the corner that represents their answer and discuss why they think that they found that method easier. One person from each corner shares the group’s findings. Home Activity or Further Classroom Consolidation Complete the practice questions. Provide students Practice with appropriate practice questions showing multiple ways of representing linear patterns. TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 11/02/20105 2.2.1: Stations for Small Group Investigations TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 6 2.2.2: Small Group Investigation Record Sheet TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 7 2.2.3: Small Group Investigation (Answers) TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 8 Unit 2: Day 3: Finding the nth Term Grade 8 Math Learning Goals Materials Determine, and represent algebraically the general term of a linear pattern BLM 2.3.1, 2.3.2, (nth term). 2.3.3 linking cubes Determine any term, given its term number, in a linear pattern represented graphically or algebraically. Check validity by substituting values. Assessment Opportunities Minds On… Whole Class  Four Corners Give each student a card. Students travel to the corner that corresponds to the Cut BLM 2.3.1 into representation on their card, e.g., A student with a card that has a graph goes to the individual cards. graphical model representation corner. Students discuss “What is challenging about changing from one representation of a pattern to another?” Choose one person from Collect the cards each corner to share the group’s conclusions. from students to Pose the following scenario: Armando has a CD collection. He currently owns 2 use in a future CDs. Each week, he purchases a new CD for his collection. How could you activity. represent this in a model? Students in each corner describe the scenario, using the model represented in their corner. Action! Small Groups  Investigation With the class, model the results to the problem using two colours of linking cubes (2 red and 1 green for the first term, 2 red and 2 green for the second term, and so Word Wall on). Discuss why the first term has 3 CDs in it. Students use linking cubes to build term number term value the concrete model of the pattern up to the 6th term and complete BLM 2.3.2 in groups. Guide a class discussion about students’ findings (BLM 2.3.3). Representing/Oral Questions/Mental Note: Observe students as they work on the small-group activity. Consolidate Whole Class  Algebraic Representation Debrief Ask: How can we think about the algebraic expression in another way? Decide what the nth term represents (unknown term; a method to find any term; a “formula”). How might you find the 12th term of the pattern? Is it possible to find the 12th term without extending the table? Find the 12th term. Can you use the same method to find the 100th term? How can you determine if your nth term is correct? (Substitute the term numbers in for n and the resulting answers should be the term values.) Students record this algebraic representation of the pattern in the circle on the placemat from Day 2 (BLM 2.2.2). Home Activity or Further Classroom Consolidation Application Complete the practice questions. Provide students Exploration with appropriate Reflection practice questions. TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 9 2.3.1: Four Corners Cards Patterning Rule: Add one to the term number Pattern Rule: One plus three times a term number Pattern Rule: Subtract one from the term number Patterning Rule: Multiply the term number by three and subtract one Pattern Rule: Multiply the term number by two and add one TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 10 2.3.2: Patterns – Finding the nth Term Term Number of Red Cubes Number of Green Cubes Total Number of Number (n) ( ) ( ) Cubes (Term Value) 1 2 3 4 5 6 12 n 1. In your groups, complete the values for terms 1 through 6 on the chart using models. 2. Which colour has the same number of cubes all the way through the chart? This is called the constant because it does not change. Indicate this in the brackets under the appropriate heading. 3. Which colour has a different number of cubes in each model? This is called the variable because it varies or changes. Please indicate this in the brackets under the appropriate heading. 4. How is the variable related to the term number? 5. In words, describe the pattern. 6. If the term number is n, how could you figure out how many cubes are in that model? TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 11 2.3.3: Patterns – Finding the nth Term Answers (Teacher) Term Number of Red Cubes Number of Green Cubes Total Number of Cubes Number (Constant) (Variable) (Term Value) (n) 1 2 0 2 2 2 1 3 3 2 2 4 4 2 3 5 5 2 4 6 6 2 5 7 12 2 11 13 n 2 n–1 2 + n – 1 or n + 1 or 1 + n 1. In your groups, complete the values for terms 1 through 6 on the chart using your models. 2. Which colour has the same number of cubes all the way through the chart? This is called the constant because it does not change. Indicate this in the brackets under the appropriate heading. There is always the same number of red cubes. 3. Which colour has a different number of cubes in each model? This is called the variable because it varies or changes. Please indicate this in the brackets under the appropriate heading. The number of green cubes changes each term. 4. How is the variable related to the term number? The variable is 1 less than the term number. 5. In words, describe the pattern. The value is 2 more than 1 less than the term number. 6. If the term number is n, how could you figure out how many cubes are in that model? 2 + n – 1 or n + 1 or 1 + n TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 12 Unit 2: Day 4: Exploring Patterns Grade 8 Math Learning Goals Materials Determine any term given its term number in a linear pattern represented BLM, 2.4.1, algebraically. 2.4.2, 2.4.3 Examine patterns involving whole numbers in a variety of forms. Explore and establish the difference between linear and non-linear patterns. Assessment Opportunities Minds On… Whole Class  Summarizing Think Literacy: Review the terms constant and variable, using an example from Day 3. Mathematics, Grades 7–9, pp. 40–41 Make available the following materials at each station: linking cubes, Action! Small Groups  Exploration geoboards, toothpicks and/or Students rotate through stations (BLM 2.4.2). other appropriate materials. Word Wall variable constant Consolidate Whole Class  Summarizing Debrief Discuss the patterns students found during their station work. Pose questions: If time permits, Which patterns did you find more logical to extend and represent another way? demonstrate what linear and non- Why do you think some were more logical than others? linear patterns look like graphically Create class Frayer models for constant and variable. Formulate a working ® using GSP 4, definition for each term. See BLM 2.4.1. Fathom , or TM Define that linear patterns form a straight line that can be shown using a ruler but spreadsheet non-linear patterns do not form a line. software to give meaning to the In small groups, students sort the different patterns into two groups: linear and terms linear and non-linear. Groups justify their sorting to the class. non-linear. Use discrete examples Curriculum Expectations/Communicating/Observation: Listen as students so it is consistent discuss their choices and justify their reasoning as they sort. with their work. Home Activity or Further Classroom Consolidation In your journal, compare linear patterns to non-linear patterns, use as many Make available the Differentiated Reflection representations as possible. ® GSP 4 take-home How are they similar? version for students who may wish to How are they different? produce their sketches using software. TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 13 2.4.1: The Frayer Model (Teacher) Definition Facts/Characteristics numerical value that stays the same (is fixed fixed) does not change for different terms example: x + 1 ( the number 1 is the constant) a quantity that does not change constant Examples Non-examples constant pain always the same 5x + 3 (the number 3 is the constant) speed of light variable can represent more than one number n = 1,2,3,4 5x (the value of the term 5x changes for different values of x) Definition Facts/Characteristics value changes as term number changes place holder for the unknown value represents a range of values example 3x + 1 (x represents the variable) any letter of the alphabet could be used to a quantity capable of assuming a set of represent the variable values variable Examples Non-examples Constant equations: 3 + x = 7, (x is a variable) Constant formulas: A = lw (l and w can change) spreadsheets: cells B = A + 1 expressions 3x + 1 (x is the variable) stock prices interest rates TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 14 2.4.2: Exploring Patterns Station 1 Graph this pattern on the Cartesian plane. Name the constant. Name the variable. Station 2 Create a table of values. Write an expression for the nth term. Name the constant. Name the variable. TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 15 2.4.2: Exploring Patterns (continued) Station 3 Build the next two terms in Create the table of values the pattern using toothpicks. using the number of Note the toothpick pattern Draw them here: toothpicks. below. Write an expression for the nth term. Name the constant. Name the variable. Station 4 Create a table of values. Write an expression for the nth term. Name the constant. Name the variable. TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 16 2.4.2: Exploring Patterns (continued) Station 5 Create a table of values. Plot the points from your table of values. What do you notice? Name the constant. Name the variable. TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 17 2.4.2: Exploring Patterns (continued) Station 6 Write an expression for the nth term. Name the constant. Name the variable. Graph this pattern on the Cartesian plane. TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 18 2.4.3: Answers to Student Centres Station 1 Graph this pattern on the Cartesian plane. Variable: n Constant: –2 Station 2 Create a table of values. Write an expression for the nth term. 1 1 nth term = n2 2 4 3 9 Variable: n Constant: 0 Station 3 Build the next two terms in Create the table of values the pattern using toothpicks. using the number of Note the toothpick pattern Draw them here: toothpicks. below. Write an expression for the nth term. nth term = 4n Variable: n Constant: 0 TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 19 2.4.3: Answers to Student Centres (continued) Station 4 Create a table of values. Write an expression for the nth term. nth term = n + 1 Variable: n Constant: 1 Station 5 Create a table of values. Plot the points from your table of values. What do you notice? Variable: n Constant: 0 Station 6 Write an expression for the Graph this pattern on the nth term. Cartesian plane. nth term Variable: n Constant: TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 20 Unit 2: Day 5: Space Race: Graphic Representations Grade 8 Math Learning Goals Materials Record linear sequences using a table of values and graphs. BLM 2.5.1, 2.5.2 Draw conclusions about linear patterns. Assessment Opportunities Minds On… Whole Class  Connecting to Prior Learning Create a Venn diagram using the comparison from the Home Activity, Day 4 (BLM 2.5.1). Action! Whole Class  Simulation Using Graphs Using their prior knowledge of linear and non-linear patterns, groups create physical representations of the two types of patterns. Pose the problem: Using all the people in your group demonstrate what a linear graph would look like. Observe and comment on how students demonstrate different representations. Pose a second problem: Using all the people in your group demonstrate what a non-linear graph could look like. Note how students demonstrate different representations. Students share their feedback or observations. Consolidate Individual  Interpreting Graphs Debrief Students complete BLM 2.5.2. Curriculum Expectations/Procedural Knowledge: Students submit BLM 2.5.2 for feedback. Home Activity or Further Classroom Consolidation Complete the practice questions. Provide students Practice with appropriate practice questions. TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 21 2.5.1: Possible Venn Diagram Answers TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 22 2.5.2: Interpreting Graphs Name: For each graph below create a table of values and determine the nth term. 1. 2. 3. 4. TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 23 2.5.2: Interpreting Graphs (continued) 5. 6. 7. 8. TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 24 Unit 2: Day 6: When Can I Buy This Bike? Grade 8 Math Learning Goals Materials Solve problems involving patterns. BLM 2.6.1 Use multiple representations of the same pattern to help solve problems and prove that the solution is correct. Model linear relationships in a variety of ways to solve a problem. Assessment Opportunities Minds On… Whole Class  Review Hand each student a card (Day 3, BLM 2.3.1). Students find the other members of their group by matching all representations of the same pattern (patterning rule, numerical, graphical, and pictorial). In their groups, students develop an algebraic expression for their pattern. One student from each group shares the response. (If a group finishes before the others, challenge them to find a story that fits the pattern.) Possible Assumptions: Action! Small Groups  Discussion bike stays the Explain the task (BLM 2.6.1) and discuss assumptions students must make: What same price babysitting money assumptions are you making in order to consider solving this problem? stays the same Students highlight or underline key words in the problem, e.g., costs $350, she doesn’t spend received $300, $12, per week. any of the money she saves Students use the problem-solving model (understand the problem, make a plan, carry out the plan, look back at the solution) to complete the task and submit their work. Think Literacy: Individual  Performance Task Cross Curricular Approaches, Students complete this activity using BLM 2.6.1. Grades 7–12, pp. 76–80, Mind Maps. Problem Solving/Observation/Checkbric: Circulate to ask probing questions during the performance task. Mind maps can be done by hand or with software such as Smart Ideas (Ministry Licensed). Consolidate Whole Class  Discussion Provide a variety of manipulatives and Debrief Students reflect on the problem-solving model: What strategies did you use for technology. each part of the model? Students share many different strategies and representations. Home Activity or Further Classroom Consolidation Complete a mind map/web to summarize what you learned in this unit. Use the This activity can be Reflection appropriate vocabulary. used as a review or as an assessment tool. TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 25 2.6.1: A Problem-Solving Model: When Can I Buy This Bike? Name: Mackenzie has found the bicycle that she always wanted. It costs $350.00. She received $300 dollars as a gift from her family. How long would it take her to save enough money to purchase the bike if she earns $12 a week babysitting? Using the problem-solving method (Understand the Problem, Make a Plan, Carry out the Plan, Look Back at the Solution) solve the problem above. Explain your thinking using pictures, numbers, and words. You may use manipulatives and a variety of tools to help you determine the solution. If you need more space to show your solution use the back of the page. Understand the Problem Read and re-read the problem. Using a highlighter, identify the information given and what needs to be determined. Write a sentence about what you need to find. Make a Plan Consider possible strategies. Select a strategy or a combination of strategies. Discuss ideas to clarify which strategy or strategies will work best. Carry Out the Plan Carry out the strategy, showing words, symbols, diagrams, and calculations. Revise your plan or use a different strategy, if necessary. Look Back at the Solution Does your answer make sense? Is there a better way to approach the problem? Describe how you reached the solution and explain it. TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 26 Unit`2: Day 7: Determining the Term Number Grade 8 Math Learning Goals Materials Students will determine any term, given its term number, in a linear pattern BLM 2.7.1 represented graphically or algebraically BLM 2.7.2 Students will determine the term number given several terms Whole Class  Game Minds On… Play the ‘What’s the Rule?’ Game from BLM 2.7.1. Differentiation of One student acts as the equation machine. He/she is given one of the algebraic content or process (calculator) based expression cards from BLM 2.7.1. One at a time, classmates call out possible term on readiness in numbers between -5 and +5. Using mental math or a calculator, the equation machine order to save time: student responds with the term value resulting from plugging in the class suggested Students create term number into the expression on the card. Another student records the data in a table their own pattern of values on the board. After two sets of values are recorded, students may volunteer to rule game cards for the game. guess the pattern rule. Play for that card continues until the pattern rule has been named. Alternatively, go to http://www.shodor.org/interactivate/activities/fm/index.html and play the Function Machine game on-line. Small Groups  Discussion/Highlight Word Wall Vocabulary Action! Compare the mind maps that were created in the Reflection Activity from Day 6. Highlight key vocabulary that should be included that will be relevant to today’s Minimum Wage Rates performance task: linear, term number, term value, nth Problem Solving/ value, expression, etc. Observation /Checkbric: Circulate to ask Individual  Performance Task probing questions during the Students will complete the activity from BLM 2.7.2. performance task. Whole Class  Discussion Consolidate Pose the following questions to the class: Debrief What assumptions have we made regarding Minimum Wage Rate trends? (i.e.: Is it reasonable to assume that this data has always been or will always remain linear?) What economic influences would impact changes in wage rates? Why is it necessary for governments to enforce a minimum wage? Exploration Home Activity or Further Classroom Consolidation Students share Minimum Wage Rate data with family members to determine what wage rates were when parents were younger. Opportunity for real-world cross-curricular connections with: 1. Economic Systems in Gr. 8 Geography Explicitly 2. Science by having students design and experiment to see what relationships exist identify opportunity between two variables: for differentiation and extension of Relationship between the number of drops of water and the diameter of the spot on content or product a paper towel based on interest Relationship between the number of students and their arm spans or learning preference in order Relationship of the distance a toy car will travel relative to the height of the ramp to give students Relationship of the height of a bean plant compared to the number of days since choice sprouting Relationship of the height of a liquid relative to the volume in different sized containers TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 27 2.7.1: What’s the Rule? Equation Cards Grade 8 n+2 n+1 n-2 Subtract 2 from any Add 2 to any number given Add 1 to any number given number given n-1 Subtract 1 from any number 2n 2n+1 Double any number given, Double any number given given then add 1 2n+2 2n -1 2n - 2 Double any number given, Double any number given, Double any number given, then add 2 then subtract 1 then subtract 2 ½n Halve any number 3n Triple any number 5n Multiply any number by 5 TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 28  2.7.2: Minimum Wage Rates Grade 8 Minimum Wage Rate March 31, 2007 March 31, 2008 March 31, 2009 March 31, 2010 General Minimum Wage $8.00 $8.75 $9.50 $10.25 per hour per hour per hour per hour Students under 18 and $7.50 $8.20 $8.90 $9.60 working not more than per hour per hour per hour per hour 28 hours per week during the school year or working during a school holiday These are the minimum wage rates from the Ontario Ministry of Labour. 1. Explain why both the General Minimum Wage rate and the ‘Student’ rate are linear patterns. 2. Given this pattern of rate increase, what was the date when the General Minimum wage was $5.00? Show your work. 3. If a student worked the maximum of 28 hours in a week in 2007, what was his/her weekly wage? Show your work. 4. Who would earn more… A 15 year old working 8 hours in 2012 or a 20 year old working 11 hours in 2007? Explain. 5. Select either the General Minimum wage or the ‘Student’ wage. Write an expression for the nth term. 6. If the wage increase continues in this same pattern, what will the General Minimum Wage be when you turn 18? Show your work. TIPS4RM: Grade 8: Unit 2 – Representing Patterns in Multiple Ways 29