Writing linear functions edmodo
- 1. Functions Unit 4 Part 2 MCC8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1, 1), (2, 4), (3, 9), which are not on a straight line.
- 2. 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
- 3. Some Special patterns • Arithmetic 1, 2, 3, 4, 5, … 7, 9, 11, 13, 15, … • Geometric 1, 3, 9, 27, 81, … 32, 16, 8, 4, 2, … • Fibonacci 1, 1, 2, 3, 5, 8, …
- 4. Toothpick Patterns • Discovery activity
- 5. Toothpick Patterns 1st 2nd 3rd 4th Number of boxes 1 2 3 4 20 50 100 Number of toothpicks
- 6. Toothpick Patterns 1st 2nd 3rd 4th Number of boxes 1 2 3 4 20 50 100 Number of toothpicks
- 7. POD 3 Dec • Does the table below represent a function? # of # of • What is the independent variable? boxes toothpicks 1 4 • What is the dependent variable? 2 7 3 10 • Can you write a rule for the table? 4 13 5 16
- 8. Mathematize input 1 2 3 4 5 output 4 10 16 22 28 Common Difference(d) = ?
- 9. Mathematize input 1 2 3 4 5 output 7 9 11 13 15 Common Difference(d) = ?
- 10. Mathematize input 1 2 3 4 5 output 10 7 4 1 -2 Common Difference(d) = ?
- 11. Write a rule to find a term input 1 2 3 4 5 6 10 output 4 10 16 22 28 ? ?
- 12. Write a rule to find a term input 1 2 3 4 5 7 10 output 10 7 4 1 -2 ? ?
- 13. Write a rule to find a term input 1 2 3 4 5 8 20 output 2.0 3.5 5.0 6.5 8.0 … ?
- 14. Graph an arithmetic sequence. 1 2 3 4 5 1 2 3 4 5 Is this a function? What equation would model this data? y=x
- 15. Graph this sequence. 1 2 3 4 5 7 9 11 13 15 Is this a function? What equation would model this data? y = 2x+5
- 16. Functions Unit 4 Part 3 CC8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. *Comparing properties of two functions each represented in a different way will be addressed in Unit 5. In this unit we will focus on representing the same function different ways (algebraically, graphically, numerically in tables, or by verbal descriptions), and identifying the unit rate of change.
- 17. Relations and Functions • We will look at functions in four different ways 1. Numerically; tables and ordered pairs 2. Graphically 3. Verbally 4. Algebraically
- 18. Linear Functions Your cell phone plan costs 15 dollars a month, plus 10 cents per minute. Fill out a table, create a graph, and write an equation to model the money you will spend each month on your cell phone. Table Graph y Minutes Cost 0 15 50 Change in y = 2.5 25 17.5 Change in x = 25 50 20 75 22.5 100 25 Cost 125 27.5 25 150 30 175 32.5 Equation 5 x 25 100 200 300 Minutes
- 19. Linear Functions You want to ship math textbooks from Singapore. They cost 80 dollars each, plus 30 dollars total for shipping. Fill out a table, create a graph, and write an equation to model the cost of the textbooks. Table Graph Unit Rate of Books Cost Change Equation
- 20. Linear Functions A taxi service charges an initial five dollar fee, plus one dollar per mile driven. Fill out a table, create a graph, and write an equation to model the cost of the taxi service. Table Graph Miles Cost Equation
Editor's Notes
- #2: In Unit 4 we will only give examples
- #3: 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.
- #4: Ask students to identify the pattern.
- #5: Students work in pairs to complete toothpick activity.
- #6: Review Toothpick activity.
- #7: Review toothpick activity.
- #12: Students will tend to identify the recursive formula first by identifying the pattern off add 6. challenge them with higher terms that are inefficient to keep adding.6x -2 for any termor y + 6 for next term only
- #13: -3x + 13
- #14: 3/2x + ½ or 1.5x + .5
- #19: Spend some time discussing dependent and independent variables, and labeling the graph. Also a good time to review discrete and continuous data.