Complete Week 6 Package

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1 Complete Week 6 Package HighSchoolMathTeachers@2018

2 Table of Contents Unit 2 Pacing Chart Day 26 Bellringer Day 26 Activity Day 26 Exit Slip Day 27 Bellringer Day 27 Activity Day 27 Practice Day 27 Exit Slip Day 28 Bellringer Day 28 Activity Day 28 Exit Slip Day 29 Bellringer Day 29 Activity Day 29 Exit Slip Day 30 Bellringer Weekly Assessment

3 CCSS Algebra 1 Pacing Chart Unit 2 Unit Week Day CCSS Standards Mathematical Practices Objective I Can Statements 2 Linear Equations 6 Linear Functions and their Inverses 26 CCSS.MATH.CONTENT.HSF.IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* CCSS.MATH.PRACTICE.MP7 Look for and make use of structure. The student will be able to graph lines expressed in slopeintercept form or standard form, by hand. I can graph lines expressed in slope-intercept form or standard form, by hand. 2 Linear Equations 6 Linear Functions and their Inverses 27 CCSS.MATH.CONTENT.HSF.BF.B.4.A Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x-1) for x 1. CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them. The student will be able to find the inverse of a given linear function. I can find the inverse of a linear function. 2 Linear Equations 2 Linear Equations 2 Linear Equations 6 Linear Functions and their Inverses 6 Linear Functions and their Inverses 6 Linear Functions and their Inverses CCSS.MATH.CONTENT.HSF.LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). CCSS.MATH.CONTENT.HSA.REI.A.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning. CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. The student will be able to construct linear functions including arithmetic sequences from a table, graph or situation. The student will be able to understand, apply, and explain the results of using inverse operations. I can construct linear functions including arithmetic sequences from a table, graph or situation. I can understand, apply, and explain the results of using inverse operations. 30 Assessment Assessment Assessment Assessment HighSchoolMathTeachers@2018 Page 1

4 Day 26 Bellringer Day Solve for y : 6x + 2y = Solve for y x 3y = Solve for y 3x 5y = Solve for y: 5x y = 12 HighSchoolMathTeachers@2018 Page 2

5 Day 26 Bellringer Answer key Day y=-3x+6 2. y=-17/ 3 + 1/3 x 3. y=-12/5 + 3/5x 4. y=-12-5x HighSchoolMathTeachers@2018 Page 3

6 Day 26 Cricket Activity Cricket Chirps Vs. Temperature y = x + 40 y = temperature in degrees Fahrenheit x = cricket chirps per minute in degrees Celsius Fill in the table of values below and then draw the equation of the line on the graph. x y = x + 40 (x, y) Use the graph to answer these questions: 1. What would the temperature be if there are 20 chirps per minute? 2. If the temperature was 80 ⁰F, how many chirps per minute would there be? 3. Describe the relationship between temperature and chirps per minute. HighSchoolMathTeachers@2018 Page 4

7 Day 26 Cricket Activity Temperature Conversion Graph You can use this formula to convert from degrees Celsius to degrees Fahrenheit: y = 1.8x + 32 y = temperature in degrees Fahrneheit x = temperature in degrees Celsius Fill in the table of values below and then draw the equation of the line on the graph. x y = 1.8x + 32 (x, y) Use the graph to answer these questions: 1. What is zero degrees Celsius in Fahrenheit? 2. What is zero degrees Fahrenheit in degrees Celsius? 3. What temperature in degrees Celsius is the same in degrees Fahrenheit? HighSchoolMathTeachers@2018 Page 5

8 Day 26 Cricket Activity Answer Key Cricket Chirps Vs. Temperature y = x + 40 y = temperature in degrees Fahrenheit x = cricket chirps per minute Fill in the table of values below and then draw the equation of the line on the graph. x y = x (x, y) (0, 40) (10, 30) (20, 60) (30, 70) Use the graph to answer these questions: 4. What would the temperature be if there are 20 chirps per minute? 60 degrees F 5. If the temperature was 80 ⁰F, how many chirps per minute would there be? 40 chirps 6. Describe the relationship between temperature and chirps per minute. Temperature is 40 more than the number of chirps. HighSchoolMathTeachers@2018 Page 6

9 Day 26 Cricket Activity Temperature Conversion Graph You can use this formula to convert from degrees Celsius to degrees Fahrenheit: y = 1.8x + 32 y = temperature in degrees Fahrenheit x = temperature in degrees Celsius Fill in the table of values below and then draw the equation of the line on the graph. x y = 1.8x (x, y) (0, 32) (10, 50) (20, 68) (30, 86) Use the graph to answer these questions: 4. What is zero degrees Celsius in Fahrenheit? What is zero degrees Fahrenheit in degrees Celsius? What temperature in degrees Celsius is the same in degrees Fahrenheit? - 40 degrees HighSchoolMathTeachers@2018 Page 7

10 Day 26 Exit Slip Day 26 Create a table and graph the data given in the following function. f(x) = 3.5x HighSchoolMathTeachers@2018 Page 8

11 Day 26 Exit Slip Answer Key Day 26 x f(x) HighSchoolMathTeachers@2018 Page 9

12 Day 27 Bellringer Day Write a linear function to describe the set of data. Current (ampere), x Volt (ohms), y Write a linear function to describe the set of data. Mass (grams), x Force (newton), y Write a linear function to describe the set of data. Speed (m/s), x Distance (meters), y Write a linear function to describe the set of data. Time (sec), x Acceleration (m/s2), y HighSchoolMathTeachers@2018 Page 10

13 Day 27 Bellringer Answer Key Day y = 2x y = 5x y = 3 2 x y = 4x + 12 HighSchoolMathTeachers@2018 Page 11

14 Day 27 Activity FLOWCHART 1. Design a flowchart explaining how to find the inverse of a function. 2. Design a flowchart explaining how to find the function if you know its inverse. Be sure to include the following details: Answer the question, Do all functions have an inverse? Include at least three examples within your flowchart. Use appropriate notation and use it correctly. Use appropriate terminology effectively. You may find it useful to use Microsoft Word or Glogster. Both of these programs (along with many others) have flowchart clipart built in to their software. HighSchoolMathTeachers@2018 Page 12

15 Day 27 Activity Answer Key Stick a "y" in for the "f x " guy: Solve for Y: Switch the X and Y (because every (x, y) has (y, x) partner. Stick in the inverse notation, f 1 x HighSchoolMathTeachers@2018 Page 13

16 Day 27 Practice 1. Suppose you are given the following directions: From home, go north on Rt 23 for 5 miles Turn east (right) onto Orchard Street Go to the 3rd traffic light and turn north (left) onto Avon Drive Tracy s house is the 5th house on the right. If you start from Tracy s house, write down the directions to get home. How did you come up with the directions to get home from Tracy s? 2. Suppose you are given the following algorithm: Starting with a number, add 5 to it Divide the result by 3 The final result is 10. Working backwards knowing this result, find the original number. Show your work. Write a function f(x), which when given a number x (the original number) will model the operations given above. f(x) = HighSchoolMathTeachers@2018 Page 14

17 Day 27 Practice Write a function g(x), which when given a number x (the final result), will model the backward algorithm that you came up with above. g(x) = Using the functions you discovered above, fill in the table. x y = f(x) z = g(y) f(z) What patterns have you noticed in the columns (outputs)? In this scenario, f(x) and g(x) are inverses of each other because g(x) will undo the actions of f(x). Thus, we could write g(x) as f 1 (y) described as f inverse. HighSchoolMathTeachers@2018 Page 15

18 Day 27 Practice Answer Key 1. Suppose you are given the following directions: From home, go north on Rt 23 for 5 miles Turn east (right) onto Orchard Street Go to the 3rd traffic light and turn north (left) onto Avon Drive Tracy s house is the 5th house on the right. If you start from Tracy s house, write down the directions to get home From Tracy s house, go south for 5 houses on Avon Drive. Turn west (right) onto Orchard Street. Go for three traffic lights and turn south onto RT 23. Go for 5 miles and you will be at home. How did you come up with the directions to get home from Tracy s? Just follow the inverse directions. Or draw the directions and go back from Tracy s house to home. 2. Suppose you are given the following algorithm: Starting with a number, add 5 to it Divide the result by 3 The final result is 10. Working backwards knowing this result, find the original number. Show your work. Multiply the final result by = 30 Subtract 5 from it = 25 The original number is 25. Write a function f(x), which when given a number x (the original number) will model the operations given above. f(x) = x+5 3 Write a function g(x), which when given a number x (the final result), will model the backward algorithm that you came up with above. g(x) = 3x 5 Using the functions you discovered above, fill in the table. x y = f(x) z = g(y) f(z) What patterns have you noticed in the columns (outputs)? The first and the third columns are equivalent. And the second and the fourth columns are also the same. In this scenario, f(x) and g(x) are inverses of each other because g(x) will undo the actions of f(x). Thus, we could write g(x) as f 1 (y) described as f inverse. HighSchoolMathTeachers@2018 Page 16

19 Day 27 Exit Slip Day 27 Find the inverse of the following functions. Show your work. 1. y = 2x x f(x) HighSchoolMathTeachers@2018 Page 17

20 Day 27 Exit Slip Answer Key Day f 1 (x) = x x f(x) HighSchoolMathTeachers@2018 Page 18

21 Day 28 Bellringer Day Find the inverse of the function f(x) = 2x 5 2. Find the inverse of the function f(x) = 25 1 x 3. Find the inverse of the function f(x) = 3x Find the inverse of the function f(x) = 2x + 1 HighSchoolMathTeachers@2018 Page 19

22 Day 28 Bellringer Answer Key Day f(x) = 1 (x + 5) 2 2. f(x) = 1 (25 x) 3. f(x) = 1 3 (x 4) 4. f(x) = 1 2 (1 x) HighSchoolMathTeachers@2018 Page 20

23 Day 28 Activity Find the next two terms of each sequence. Then describe the pattern. The equations will be completed later. 1, 3, 5, 7, 9,, Description: Equation: 2, 7, 12, 17, 22,, Description: Equation: -416, -323, -230, -137,, Description: Equation: -2, -5, -8, -11,, Description: Equation: All of the patterns above are called arithmetic sequences. Hopefully you noticed something about their pattern that makes them similar. Complete the sentence below by writing a description of the pattern you noticed above. (If you need help, look in the textbook in section 11.1). Arithmetic sequences are sequences of numbers where. Let s look more closely at the first pattern 1, 3, 5, 7, 9 Suppose the domain is the position of a term (1, 2, 3, 4, etc.) and the range is the term (1, 3, 5, 7, 9, etc.). Make a graph of the points that are made (position, term) with the pattern. What quadrant(s) are these points in? Why? What kind of graph do you have? Write an equation for the graph. HighSchoolMathTeachers@2018 Page 21

24 Day 28 Activity How does this equation relate to the graph? How does this equation relate to the pattern? Do you think the graphs of other arithmetic sequences would look similar? Why or why not? Checkpoint 1: Stop at this point for class comparison. If you are done before others, make equations for the other three patterns listed at the top. Now, everyone should have the same equation for the pattern 1, 3, 5, 7, 9 However, we have a problem. This equation makes us use a number that is not on our pattern (-1). Let s say we want to use 1 as a starting point instead of -1 (since 1 is our first term in our sequence). So, suppose our equation is now y = 2x + 1. See if this works for the pattern. Try x = 1 (for the first term). Try x = 2 (for the second term). Try x = 3 (for the third term). What do you notice? HighSchoolMathTeachers@2018 Page 22

25 Day 28 Activity Our new equation y = 2x + 1 makes our pattern shift over one term (one x value). This means we are adding d one too many times! Let s alter the equation slightly to y = 2(x 1) + 1. This will shift all the x values (just like we ve done before) and we won t be adding the extra value of d. See if this works for the pattern. Try x = 1 (for the first term). Try x = 2 (for the second term). Try x = 3 (for the third term). What do you notice? Now, we have an equation y = 2 (x 1) + 1 that uses the first term and the common difference (slope). This can be used to make any equation for any arithmetic sequence. Let s use d = common difference, a 1 = first term, and a n = nth term. So, the nth term of any arithmetic sequence can be found by a n = a 1 + (n 1) d HighSchoolMathTeachers@2018 Page 23

26 Day 28 Activity Checkpoint 2: Find the rule/equation for the 2 nd pattern using the formula above. Now that you know arithmetic sequences need a common difference (number added or subtracted to the pattern) and you know how to find the nth term (or equation) for any arithmetic sequence, let s try some problems. Example 1: Is the sequence arithmetic? If so, what s the common difference? If not, why not? A) 2, -3, -8, -13, B) 1, 5/4, 3/2, 7/4, C) a n = n 2 D) a n = 4n + 3 Example 2: Write the first 5 terms if a 1 = 2 and d = 7. Checkpoint 3: Let s make sure we are on the right track with examples 1 and 2. Example 3: Write the rule/equation for the given information. A) a 1 = 2, d = 3 B) a 1 = 2, a 2 = 9 HighSchoolMathTeachers@2018 Page 24

27 Day 28 Activity Example 4: Find the indicated term of each arithmetic sequence. First find the equation, then plug in your n. A) a 1 = -4, d = 6, n = 9 B) a 20 for a 1 = 15, d = -8 Checkpoint 4: Let s make sure we got the answers to examples 3 and 4. Example 5: Write the equation for the nth term of each arithmetic sequence. A) 31, 17, 3,. Now, the next two are slightly different. I will give you a term and the d but the term isn t the first one. You need to work backwards to find the first term. B) a 7 = 21, d = 5 We know that a n = a 1 + (n 1) d So, using the given information, we have 21 = a 1 + (7 1) 5 Simplify and solve for a 1. HighSchoolMathTeachers@2018 Page 25

28 Day 28 Activity Now, find the equation. C) Follow the steps with this information: a 6 =12, d = 8. Checkpoint 5: Did we follow that? Example 6: Find the missing terms in each sequence. A) 6,,,, 42 B) 24,,,,, -1 Challenge: Let s do this one together. Use the given information to write an equation that represents the nth term in each arithmetic sequence. The 19 th term of the sequence is 131. The 61 st term is 509. HighSchoolMathTeachers@2018 Page 26

29 Day 28 Activity Answer Key Find the next two terms of each sequence. Then describe the pattern. The equations will be completed later. 1, 3, 5, 7, 9, 11, 13 Description: Add 2 to the previous term 2, 7, 12, 17, 22, 27, 32 Description: Add 5 to the previous term -416, -323, -230, -137, -44, 49, Description: Add 93 to the previous term -2, -5, -8, -11, -14, -17, Description: Add -3 to the previous term All of the patterns above are called arithmetic sequences. Hopefully you noticed something about their pattern that makes them similar. Complete the sentence below by writing a description of the pattern you noticed above. Arithmetic sequences are sequences of numbers where the difference between one term and the next is a constant. Let s look more closely at the first pattern 1, 3, 5, 7, 9 Suppose the domain is the position of a term (1, 2, 3, 4, etc.) and the range is the term (1, 3, 5, 7, 9, etc.). Make a graph of the points that are made (position, term) with the pattern. What quadrant(s) are these points in? Why? We see all points are in the first quadrant. That s because all domain and range values are positive numbers. What kind of graph do you have? We have a linear graph here. Write an equation for the graph y = 2x 1 How does this equation relate to the graph? How does this equation relate to the pattern? This equation represents the line on the graph and the pattern of the sequence. Do you think the graphs of other arithmetic sequences would look similar? Why or why not? Yes, the graphs of other arithmetic sequences would look similar, because all graphs of arithmetic sequences are linear graphs. HighSchoolMathTeachers@2018 Page 27

30 Day 28 Activity Now, everyone should have the same equation y = 2x 1 for the pattern 1, 3, 5, 7, 9 However, we have a problem. This equation makes us use a number that is not on our pattern (-1). Let s say we want to use 1 as a starting point instead of -1 (since 1 is our first term in our sequence). So, suppose our equation is now y = 2x + 1. See if this works for the pattern. Try x = 1 (for the first term). Try x = 2 (for the second term). Try x = 3 (for the third term). What do you notice? Our new equation y = 2x + 1 makes our pattern shift over one term (one x value). This means we are adding d one too many times! Let s alter the equation slightly to y = 2(x 1) + 1. This will shift all the x values (just like we ve done before) and we won t be adding the extra value of d. See if this works for the pattern. Try x = 1 (for the first term). Try x = 2 (for the second term). Try x = 3 (for the third term). What do you notice? We notice it works now Now, we have an equation y = 2(x 1) + 1 that uses the first term and the common difference (slope). This can be used to make any equation for any arithmetic sequence. Let s use d = common difference, a1= first term, and an= nth term. So, the nth term of any arithmetic sequence can be found by a n = a 1 + (n 1)d Checkpoint 2: Find the rule/equation for the 2nd pattern using the formula above. a n = 2 + 5(n 1) Now that you know arithmetic sequences need a common difference (number added or subtracted to the pattern) and you know how to find the nth term (or equation) for any arithmetic sequence, let s try some problems. Example 1: Is the sequence arithmetic? If so, what s the common difference? If not, why not? A) 2, -3, -8, -13 This sequence is arithmetic. Its common difference is 5. B) 1, 5/4, 3/2, 7/4 The sequence is arithmetic. The common difference is ¼. C) a n = n 2 The sequence is not arithmetic, because the common the difference between one term and the next is not a constant. D) a n = 4n + 3 The sequence is arithmetic. The common difference is 4. Example 2: Write the first 5 terms if a 1 = 2 and d = 7 a 1 = 2 a 2 = 5 a 3 = 12 a 4 = 19 a 5 = 26 HighSchoolMathTeachers@2018 Page 28

31 Day 28 Activity Checkpoint 3: Let s make sure we are on the right track with examples 1 and 2. Example 3: Write the rule/equation for the given information. A) a 1 = 2, d = 3 a n = 2 + 3(n 1) B) a 1 = 2, a 2 = 9 a n = 2 + 7(n 1) Example 4: Find the indicated term of each arithmetic sequence. First find the equation, then plug in your n. A) a 1 = 4, d = 6, n = 9 a n = 4 + 6(n 1) a 9 = 4 + 6(9 1) = 44 B) a 20 for a 1 = 15, d = 8 a n = 15 8(n 1) a 20 = 15 8(20 1) = 137 Checkpoint 4: Let s make sure we got the answers to examples 3 and 4. Example 5: Write the equation for the nth term of each arithmetic sequence. A) 31, 17, 3 a n = 31 14(n 1) Now, the next two are slightly different. I will give you a term and the d but the term isn t the first one. You need to work backwards to find the first term. B) a 7 = 21, d = 5 We know that a n = a 1 + (n 1)d So, using the given information, we have 21 = a 1 + (7 1)5 Simplify and solve for a 1. a 1 = 9 Now, find the equation. a n = 9 + 5(n 1) C) Follow the steps with this information: a 6 = 12, d = 8 12 = a 1 + (6 1)87 a 1 = 28 a n = (n 1) Checkpoint 5: Did we follow that? Yes, we did! Example 6: Find the missing terms in each sequence. A) 6, 15, 24, 33, 42 B) 24, 19, 14, 9, 4, -1 Challenge: Let s do this one together. Use the given information to write an equation that represents the nth term in each arithmetic sequence. The 19 th term of the sequence is 131. The term is th 61 st 509. a n = 31 + (n 1)9 HighSchoolMathTeachers@2018 Page 29

32 Day 28 Exit Slip Day 28 Given the explicit formula for an arithmetic sequence find the first five terms and the term named in the problem. 1. a n = n Find a a n = n Find a 27 HighSchoolMathTeachers@2018 Page 30

33 Day 28 Exit Slip Answer Key Day , 3, 10, 17, 24: a 34 = , -11.3, -13.4, -15.5, -17.6: a 27 =-63.8 HighSchoolMathTeachers@2018 Page 31

34 Day 29 Bellringer Day 29 Find the x and y intercepts of the equations. 1. 3x + 4y = x + 6y = x + 4y = y + 5x = 30 HighSchoolMathTeachers@2018 Page 32

35 Day 29 Bellringer Answer Key Day x intercept= (4,0), y intercept = (0,3) 2. x intercept = 4, y intercept = 2 2/3 3. x intercept = 6, y intercept = 3 4. x intercept = 6, y intercept = -10 HighSchoolMathTeachers@2018 Page 33

36 Day 29 Activity 1. Complete the table of values and x graph the line f ( x) 3 2 x y 0 2. Interchange (switch) the x and y coordinates from table 1 and graph the line on the same graph. x 0 y Find the slope & y-intercept of the line graphed in step 2. Write the equation (y = mx + b) y = Rewrite the equation in function form (replace y with g(x)) g(x) = 4. What do you notice about the two lines on the graph? 5. Fold the graph along the dotted line y = x. ( Fold so the graph shows on the outside) Take the point of your pencil and poke a hole through the points showing on one side of the fold. Open your paper and write a sentence describing your observations. 6. How can you describe the graphs of f(x) and g(x) with respect to the line y = x? 7. Find f(g(x)) (show the steps) HighSchoolMathTeachers@2018 Page 34

37 Day 29 Activity 8. Find g(fx)) (show the steps) 9. What do f(g(x)) and g(f(x)) have in common? Page 35

38 Day 29 Activity Answer Key Day 29 Activity 1. Complete the table of values and x graph the line f ( x) 3 2 x y Interchange (switch) the x and y coordinates from table 1 and graph the line on the same graph. x y Find the slope & y-intercept of the line graphed in step 2. m = 2 ; b = 3 Write the equation (y = mx + b) y = 2x + 3 Rewrite the equation in function form (replace y with g(x)) g(x) = 2x What do you notice about the two lines on the graph? They seem to be mirror images of one another across the dotted line. They intersect at (-3, -3). 5. Fold the graph along the dotted line y = x. ( Fold so the graph shows on the outside) Take the point of your pencil and poke a hole through the points showing on one side of the fold. Open your paper and write a sentence describing your observations. The holes poked through the first graph lined up with points on the second graph. 6. How can you describe the graphs of f(x) and g(x) with respect to the line y = x? f(x) and g(x) are reflections of one another across the line y = x. 7. Find f(g(x)) (show the steps) f(x) = x 3 / f(g(x)) = g(x) Find g(fx)) (show the steps) / f(g(x)) = (2x+3) 3 / f(g(x)) = 2x 2 2 / f(g(x)) = x g(x) = 2x + 3 / g(f(x)) = 2(f(x)) + 3 / g(f(x)) = 2 ( x 3 ) + 3 / g(f(x)) = (x 3) + 3 / 2 g(f(x)) = x 9. What do f(g(x)) and g(f(x)) have in common? They both simplify to x. HighSchoolMathTeachers@2018 Page 36

39 Day 29 Exit Slip Day 29 Find a formula for the sequence 1. 4, 7, 10, 13, 2. 1, -1, -3, -5, HighSchoolMathTeachers@2018 Page 37

40 Day 29 Exit Slip Answer Key Day a n = 4 + (n 1)(3) or a n = 3n a n = 1 + (n 1)( 2) or a n = 2n + 3 HighSchoolMathTeachers@2018 Page 38

41 Day 30 Bellringer Day Find expressions for the 20 th term of the following sequences: 2, 4, 6, 8, Find expressions for the 7 th term of the following sequences: 7, 14, 21, 28, Find expressions for the 15 th term of the following sequences: 5, 10, 15, 20, Find expressions for the 11 th term of the following sequences: 6, 12, 18, 24,... HighSchoolMathTeachers@2018 Page 39

42 Day 30 Bellringer Answer Key Day Page 40

43 HighSchoolMathTeachers Weekly Assessment Package Unit 2 Created by: Jeanette Stein 2018 HighSchoolMathTeachers 41

44 Algebra 1 Common Core Semester 1 Skills Number Unit CCSS Skill 1 1 A.REI.3 Solve two step equations (including proportions) 2 1 Order of Operations 3 1 Create a table from a situation 4 1 A.REI.10 Create a graph from a situation 5 1 F.BF.1 Create an equation from a situation 6 1 F.IF.1 Identify a function 7 1 F.IF.2 Evaluate a function 8 1 A.REI.6 Basic Systems with a table and graph 9 1 F.LE.1 Identify linear, exponential, quadratic, and absolute value functions 10 2 F.BF.3 Translate a graph in function notation 11 2 F.IF.6 Calculate Slope 12 2 S.ID.7 Interpret meaning of the slope and intercepts 13 2 F.BF.2 Construct an arithmetic sequence 14 2 F.BF.4 Find the inverse of a function 42

45 Number Unit CCSS Skill 15 3 S.ID.6 Find the line of best fit 16 3 S.ID.6 Predict future events given data 17 3 S.ID.8 Calculate Correlation Coefficient with technology 18 3 S.ID.9 Understand the difference between Causation and Correlation 19 4 S.ID.1 Create box plots 20 4 S.ID.2 Calculate and compare measures of central tendencies 21 4 S.ID.3 Understand the effects of outliers 22 4 S.ID.5 Use two way frequency tables to make predictions 23 4 N.QA.1 Convert Units 24 4 N.QA.3 Understand Accuracy 25 5 A.REI.3 Solve advanced linear equations 26 5 A.REI.1 A.CED.4 Solve literal equations and justify the steps 27 5 A.REI.3 Solve inequalities 28 5 A.REI.12 Graph inequalities 29 6 A.REI.6 Solve a system of equations by graphing 30 6 A.REI.6 Solve a system of equations by substitution 31 6 A.REI.5 Solve a system of equations by elimination 43

46 Unit 2 Weekly Assessments 44

47 Week #6 1. Emma understands that the function, f(x) = 3.5x + 10 gives her the cost for the band s t-shirts given the $10 set up fee and the price of $3.50 per shirt. She also knows that there are 88 band members. 2. Lauren keeps records of the distances she travels in a taxi and what she pays: Distance, d (in miles) Fare, F (in dollars) a. If you graph the ordered pairs (d, F) from the table, they lie on a line. How can you tell this without graphing them? What is the total cost for the shirts? b. Show that the linear function in part (a) has equation F = 2.25d c. What do the 2.25 and the 1.5 in the equation represent in terms of taxi rides? 3. Solve the following equations for x and justify the steps. 1 5x 3 a. (4x + 1) = 9 b. 10 =

48 Week #6 Continued 4. If you have $10, you can buy 4 cookies and no brownies or you can buy 5 brownies and no cookies. There are several other options as well. Graph the situation. 5. Let F assign to each student in your math class his/her locker number. Explain why F is a function. If you have $10 and you buy 1 cookie a day you will run out of money after 5 days. Graph the situation. Describe conditions on the class that would have to be true in order for F to have an inverse. Which situation has the cheaper cookie? (Circle one) 1 st 2 nd Not enough information 6. Candy bars cost $1.50 each. What is the total bill? What is the domain? What is the range? 46

49 Unit 2 - KEYS Weekly Assessments 47

50 Week #6 - KEY 1. Emma understands that the function, f(x) = 3.5x + 10 gives her the cost for the band s t-shirts given the $10 set up fee and the price of $3.50 per shirt. 2. Lauren keeps records of the distances she travels in a taxi and what she pays: Distance, d (in miles) Fare, F (in dollars) She also knows that there are 88 band members What is the total cost for the shirts? f(88) = 318 a. If you graph the ordered pairs (d, F) from $318 the table, they lie on a line. How can you tell this without graphing them? Yes, finding the slopes tells us that they are the same for both intervals. b. Show that the linear function in part (a) has equation F = 2.25d There is only one possible line in part (a) since two points determine a line. The graph of F = 2. 25d is a line, so if we show that each ordered pair satisfies it then we will know that it is the same line as in part (a). (3, 8.25)(5, 12.75)(11, 26.25) 2.25(3) = (5) = (11) = c. What do the 2.25 and the 1.5 in the equation represent in terms of taxi rides? The 2.25 represents the cost per mile for the ride. The 1.5 represents a fixed cost for every ride; it does not depend on the distance traveled Solve the following equations for x and justify the steps. a. 1 5x 3 (4x + 1) = 9 b. 10 = 3 4 4x + 1 = 27 (Mult prop of equality) 4x = 26 (Add prop of equality) X = 6.5 (Div prop of equality) 40 = 5x 3 (Mult prop of equality) 43 = 5x (Add prop of equality) 8.6 = x (Division prop of equality) 48

51 Week #6 Continued 4. If you have $10, you can buy 4 cookies and no brownies or you can buy 5 brownies and no cookies. There are several other options as well. Graph the situation. 5. a. Let F assign to each student in your math class his/her locker number. Explain why F is a function. F is a function because it assigns to each student in the class exactly one element, his/her locker number. cookies If you have $10 and you buy 1 cookie a day you will run out of money after 5 days. Graph the situation. b. Describe conditions on the class that would have to be true in order for F to have an inverse. Students would not share lockers. $ cookies Which situation has the cheaper cookie? (Circle one) 1 st 2 nd Not enough information 6. Candy bars cost $1.50 each. What is the total bill? What is the domain? Number of Candy Bars What is the range? Cost 49

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