2016 SFUSD Math Validation Test

Transcription

1 2016 SFUSD Math Validation Test The SFUSD course sequence for math provides a focused, coherent, and rigorous learning experience that balances mathematical content knowledge with mathematical practices. In this course sequence, students take CCSS Algebra 1 in 9th grade and CCSS Geometry in 10th grade. In 11th grade, students choose to take either CCSS Algebra 2 or a compression course, CCSS Algebra 2 + Precalculus, that will prepare them for AP Calculus in 12th grade. For more information about the course sequence, please visit: course sequence.html In keeping with California Senate Bill 359, the SFUSD Board of Education passed Board Policy (Math Placement Policy) which describes the process by which students will be placed in their 9th grade math class. (The entire policy can found at: Math Policy 2016.) There are two primary course alternatives: 1. Incoming 9th graders who have completed the Common Core State Standards (CCSS) Math course shall be placed in CCSS Algebra Incoming 9th graders who completed coursework at their middle school covering the subject matter taught in CCSS Math and CCSS Algebra 1, and received a grade of C or higher in their th grade math course, were eligible to take CCSS Geometry in 9th grade if they were able to pass the SFUSD Math Validation Test (MVT). (The coursework included in those classes can be found at: Math Policy 2016 ). For the school year only, students who completed a UC approved CCSS Algebra 1 course at an accredited high school or college (face to face or online), and who provided a transcript from the school where the course was taken showing completion (with a grade of C or better) of the entire year s coursework, were able to enroll in CCSS Geometry without having to pass the MVT. For the school year and subsequent school years, all students who have taken and passed a UC approved CCSS Algebra 1 course must pass the MVT in order to be eligible to enroll in CCSS Geometry as a 9th grader. The exams were scored by scorers who participated in extensive training on how to score the items based upon the rubrics. This training was facilitated by a Ph.D. mathematician. Each item was scored twice; if there was a discrepancy between those scores, it was settled by a third scorer. Additionally, 5% of the exams were randomly sampled and scored by experts from the Silicon Valley Math Initiative (SVMI), Lawrence Hall of Science, and UCOP to validate the scoring.

2 Item # SFUSD Math Validation Test July 2016: Task Alignment Mathematics of the Task CCSSM Grade Level CCSSM Content Standards Total Pts Item 1 Functions Modeling Item 2 Geometry Transformations, Pythagorean Theorem Functions.F Use functions to model relationships between quantities. Geometry.G Understand congruence and similarity using physical models, transparencies, or geometry software. Understand and apply the Pythagorean Theorem. Item 3 Functions Linear Functions HS High School Domains: Algebra and Functions Interpreting Functions F IF Analyze functions using different representations. Reasoning with Equations and Inequalities A REI Solve systems of equations. Item 4 Statistics Bivariate Data Statistics and Probability.SP Investigate patterns of association in bivariate data. Functions.F Use functions to model relationships between quantities. Item 5 Algebra System of Inequalities HS High School Domain: Algebra Creating Equations A CED Create equations that describe numbers or relationships. Reasoning with Equations and Inequalities A REI Solve systems of equations. Represent and solve equations and inequalities graphically. 9 Item 6 Functions Building Functions HS High School Domain: Functions Interpreting Functions F IF Understand the concept of a function and use function notation. Building Functions F BF Build a function that models a relationship between two quantities. Item 7 Functions Quadratic Functions HS High School Domains: Algebra and Functions Seeing Structure in Expressions A SSE Interpret the structure of expressions. Interpreting Functions F IF Understand the concept of a function and use function notation. Interpret functions that arise in applications in terms of the context. Analyze functions using different representations. 7

3 Flying Birds at the Beach Cherie loves the beach. She loves to watch all the birds flying over the ocean. Cherie spots a sea gull. Below is a graph of the flight of the bird on a distance - time graph. The vertical axis is meters traveled and the horizontal axis is time elapsed in seconds. 1. The sea gull took off and increased its height and speed. How long before the bird began to decrease its speed? seconds Explain how you know. 2. How far had the bird traveled before it came to rest? Explain how you know. meters _ MAC Test Flying Birds at the Beach Page 1

4 Cherie watched a pelican start on a cliff 12 meters high. The pelican dove straight down to the ocean at a constant rate. The pelican hit the ocean four seconds after takeoff, covering 6 meters and caught a fish. Two seconds later, the pelican flew up to the cliff at a constant rate traveling 56 meters in six seconds. The pelican came to rest and ate its prey. 3. Draw the story of the pelican s flights on the axes below. 140 Flying Pelican 120 Distance Traveled in Meters Time Elapsed in Seconds 4. What was the average speed of the pelican s entire trip to the ocean and back? meters per second MAC Test Flying Birds at the Beach Page 2

5 Transforming Triangles Antoinette is playing with a triangle ( ABC) on this grid below. A B C 1. What are the coordinates of Antoinette s triangle ( ABC)? 2. What is the length of line segment AC? Show how you figured it out. units MAC Test Transforming Triangles Page 9

6 Antoinette reflected triangle ABC over the line x = Draw the reflected image on the same coordinate plane. Label the new triangle DEF, where A maps to D, B maps to E and C maps to F. Write the coordinates of the points D, E and F. Antoinette translated triangle ABC 3 units to the right horizontally and 1 unit up vertically. 4. Draw the translated image on the same coordinate plane. Label the new triangle GHI, where A maps to G, B maps to H and C maps to I. Antoinette rotated triangle ABC 10º around the point (3,3). 5. Draw the rotated image on the same coordinate plane. Label the new triangle XYZ, where A maps to X, B maps to Y and C maps to Z. Explain why reflecting triangle ABC over the line AC does NOT map onto triangle XYZ. MAC Test Transforming Triangles Page 10

7 Where is Waldo? April and her good friend, Janice, are playing a game using the coordinate plane. They call the game, Where is Waldo? One player gives the clues to where Waldo is and the other player guesses the exact location using a coordinate pair April s first clue is that the coordinates of both x and y are even numbers. Determine one point on the graph above where Waldo might be located. Write the coordinate pair. Plot that point on the coordinate grid above. MAC Test Algebra Where is Waldo? Page 5

8 April s second clue is that Waldo is located at a point on the equation: y = -2x Graph the equation above on the coordinate plane. Explain whether or not Janice has enough information to determine the exact location of Waldo. 3. April states her third clue, A second line that goes through Waldo s point is perpendicular to the line of the first equation I gave you. What is the slope of this second line? 4. What are two possible Waldo points that Janice could guess correctly using the three clues given by April? 5. State a final clue about the second equation of the line that would provide enough information for Janice to know Waldo s exact point location. After applying your final clue, explain how you know there can only be one possible point. MAC Test Algebra Where is Waldo? Page 6

9 Uber Driver Sebastian is a new Uber driver. On his first day on the job, he picked up 11 different riders. Uber supplied him a log of each trip he drove that day, including the time it took to drive and the distance traveled for each trip. The table below is that data. Time (minutes) Distance (miles) On the axes below, create a scatterplot using the data from the Uber table above. Uber Trips 7 6 Distance in Miles Time in Minutes MAC Test Uber Driver Page 5

10 Given the data from the Uber trips, use the scatterplot to help solve the following questions: 2. On the scatterplot, draw a line that best fits the data of the Uber trips. Using this line, what is the relationship between the time and the distance of the trips? 3. Estimate the average speed of all the trips. miles per minute Explain how you estimated the average speed. 4. Write an equation of the line that best fits your data. 5. If a customer called Sebastian and asked him how long it would take for a trip that travels 3 miles, what should Sebastian tell the customer? minutes 6. On future days, Sebastian wants to make about $35 per hour from Uber fares. How much should he charge customers per mile? Show how you figured it out. MAC Test Uber Driver Page 6

11 Cookies for Cash You and your friends decide to have a cookie sale for your class. Since your friends favorite cookies are Peanut Butter and Chocolate Chip, you settle on selling those two types of cookies. You research on-line to determine the cost to make the two types of cookies and a price you can sell them. The table below is the information collected. Type of Cookie Cost to Make Price to Sell Chocolate Chip $0.30 $1.20 Peanut Butter $0.20 $1.60 You sold x number of Chocolate Chip cookies and y number of Peanut Butter cookies. 1. Write an expression to represent the cost of making all the Chocolate Chip and the Peanut Butter cookies. 2. You and your friends had a budget that would not exceed $12 to make all the Chocolate Chip and Peanut Butter cookies. Write an inequality to represent the amount spent on making the cookies and not exceeding the budget On the axes provided, sketch a graph of the inequality that represents the amount spent on making the cookies and not exceeding the budget of $12. MAC Test Algebra Cookies for Cash Page 1

12 Your class may earn at most $60 more than what it cost to make the two cookies. 4. Write an inequality representing the total income of selling the two cookies at that price. 5. On the same axes, sketch a graph of the inequality that represents the total income of selling the two cookies at the price that earn at most $60 more than what it cost to make the two cookies. 6. What is the point of intersection of the two inequalities? Show how you figured it out. 7. Explain the significance of the point of intersection in this situation. 9 MAC Test Algebra Cookies for Cash Page 2

13 Linda s Tiles Linda has taken up ceramics. She has created tile patterns with light and dark tiles. The first tile pattern she made is shown below: Linda s First Tile Pattern 1. How many light and dark tiles wide is the pattern? tile(s) Linda makes the next bigger pattern below: Linda s Second Tile Pattern 2. How many total light and dark tiles appear in Linda s second pattern? tile(s) Linda decided she wants to make a tile pattern, using the same structure as the first two she built, but smaller than her first tile pattern. She labels this pattern Zero Tile Pattern. 3. How many tiles would be in Zero Tile Pattern? Explain how you figured it out. tile(s) MAC Test Algebra Linda s Tiles Page 3

14 Linda continues to build a third, fourth and fifth tile pattern. 4. How many total light and dark tiles are in the fifth pattern? tile(s) Show how you figured it out. 5. Linda continues to build larger tile patterns with the same structure. Write a function f(x), to determine the total number of light and dark tiles in the xth pattern. Explain how you know your function is correct. MAC Test Algebra Linda s Tiles Page 4

15 Golden Gate Parabola The Golden Gate Bridge that spans the opening into the San Francisco Bay was considered an engineering marvel when it was built in The long cables stretched over two towers support the roadway of the bridge. The cables between the two towers are the shape of a parabola. The height of each tower is 230 meters from the surface of the ocean to the top. The horizontal distance between the two towers is 1,20 meters. 1. The roadway is 7 meters above the ocean surface. What is the height of the tower between the roadway and the top? meters All parabolas can be represented with an equation in the form of y = ax 2 + bx + c. 2. In the equation of the parabola that models the cables between the two towers, is the value of a positive or negative? Explain how you know. MAC Test Algebra Golden Gate Parabola Page 9

16 The cables are tangent to the roadway at the vertex point of the parabola. 3. On the coordinate plane below, sketch a graph of the parabola that models the cables between the two towers. Use a vertex point as (0,0) for your graph Determine the coordinates of tips of the two towers. 5. Explain how you know that the absolute value of a in the parabola equation is less than one. MAC Test Algebra Golden Gate Parabola Page 10 7