Functions four representations edmodo 2013 2014
- 1. What are the next three numbers in the list? • 1, 2, 3, 4, 5, … 6, 7, 8 • 7, 9, 11, 13, 15, … 17, 19, 21 • 2, 4, 7, 11, 16, … 22, 29, 37 • 0, 1, 4, 9, 16, 25, … 36, 49, 64 • 10, 7, 4, 1, -2, … -5, -8, -11
- 2. Some Special patterns • Arithmetic 1, 2, 3, 4, 5, … 7, 9, 11, 13, 15, … • Geometric 1, 3, 9, 27, 81, … • Fibonacci 1, 1, 2, 3, 5, 8, … 32, 16, 8, 4, 2, …
- 3. Toothpick Patterns 1st 2nd 3rd 4th Number of boxes (x, input, independent variable) 1 2 3 4 20 50 Number of toothpicks (y, output, dependent variable) 4 7 10 13 61 151 301 Unit rate of change (pattern): +3 Function: y = 3x + 1 100
- 4. Toothpick Patterns 1st 2nd 3rd 4th Number of boxes (x, input, independent variable) 1 2 3 4 20 50 Number of toothpicks (y, output, dependent variable) 3 5 7 9 41 101 201 Unit rate of change (pattern): +2 Function: y = 2x + 1 100
- 5. POD 5 Dec • Does the table below represent a function? • What is the independent variable? # of boxes 1 2 • What is the dependent variable? 3 • Can you write a rule for the table? 4 5 # of toothpicks 4 7 10 13 16
- 6. Mathematize Input (x) Output (y) 1 2 3 4 5 4 10 16 22 28 Unit rate of change (pattern): +6 Function: y = 6x – 2
- 7. Mathematize input 1 output 7 2 3 4 5 9 11 13 15 Unit rate of change (pattern): +2 Function: y = 2x + 5
- 8. Mathematize input 1 output 10 2 3 4 5 7 4 1 -2 Unit rate of change (pattern): -3 Function: y = -3x + 13
- 9. Linear Functions Your smart phone plan costs 35 dollars a month, plus 10 dollars per GB of data used. Fill out a table, create a graph, and write an equation to model the money you will spend each month on your phone. Table Graph GBs of Data 0 1 45 2 55 3 65 4 75 5 85 6 95 7 Unit rate of change: +10 Total Cost 35 105 Total Cost Equation: y = 10x + 35 GBs of Data
- 10. Linear Functions You want to ship math textbooks from Singapore. They cost 45 dollars each, plus 25 dollars total for shipping. Fill out a table, create a graph, and write an equation to model the cost of the textbooks. Graph Table Books Cost 1 70 2 115 3 160 4 205 5 250 6 295 7 340 8 385 Unit Rate of Change: +45 Total Cost Equation: y = 45x + 25 Books
- 11. Linear Functions A taxi service charges an initial three dollar fee, plus two dollars per mile driven. Fill out a table, create a graph, and write an equation to model the cost of the taxi service. Graph Table Miles Cost 0 3 1 5 2 7 3 9 4 11 5 13 6 15 7 17 Unit Rate of Change: +2 Total Cost Equation: y = 2x + 3 Miles
Editor's Notes
- #2: Discuss patterns; students will identify the next three numbers quickly, but they may have trouble describing the pattern. Some sequences have more than one pattern.
- #3: Ask students to identify the pattern.
- #4: Review Toothpick activity.
- #5: Review toothpick activity.
- #10: Spend some time discussing dependent and independent variables, and labeling the graph. Also a good time to review discrete and continuous data.