2016 SFUSD Math Validation Test

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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

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 8 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 8 and CCSS Algebra 1, and received a grade of C or higher in their 8th 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 August 2016: Task Alignment Mathematics of the Task CCSSM Grade Level CCSSM Content Standards Total Pts Item 1 Statistics Bivariate Data 8 Statistics and Probability 8.SP Investigate patterns of association in bivariate data. 6 Item 2 Geometry Transformations 8 Geometry 8.G Understand congruence and similarity using physical models, transparencies, or geometry software. 8 Item 3 Algebra Equations and Systems of Equations 8 Expressions and Equations 8.EE Analyze and solve linear equations and pairs of simultaneous linear equations. 8 Item 4 Algebra Equations and Systems of Equations HS High School Domain: Algebra Creating Equations A CED Create equations that describe numbers or relationships. Reasoning with Equations and Inequalities A REI Solve equations and inequalities in one variable. 7 Item 5 Algebra Functions, Systems of Equations 8 Functions 8.F Define, evaluate, and compare functions. Expressions and Equations 8.EE Understand the connections between proportional relationships, lines, and linear equations. Analyze and solve linear equations and pairs of simultaneous linear equations. 9 Item 6 Functions Building Functions HS High School Domain: Functions Building Functions F BF Build a function that models a relationship between two quantities. 10 Item 7 Functions Quadratic Functions HS High School Domain: Algebra Reasoning with Equations and Inequalities A REI Represent and solve equations and inequalities graphically. 8

3 Scatter Plot MAC Assessment Task Below is a statistical graph called a scatterplot. Number of People Number of Hours 1. What are the two variables of the data in the scatter plot graph? and 2. Write a situation that would involve the two variables and might produce a data set like this. MAC Test 8 Scatter Plot P 3

4 Here is another set of data that involves two variables. 3. Think of a situation that involves two variables and matches the data set. Label the axes to complete the graph. 4. Write a situation that would involve the two variables and produce the data set in the graph. 5. Draw in a line that best fits the data in the graph on this page. 6. How would the line that best fits the data be useful in making sense of the situation you described? 6 MAC Test 8 Scatter Plot P 4

5 Rigid Motion MAC Assessment Task Kyra enjoys making puzzles using rigid motion transformations. She drew right triangles on the coordinates axes below and labeled the triangles A through G. E D F G C B A Kyra writes the following clues: 1. Triangle A is reflected over the x- axis. Name the resulting triangle. MAC Test 10 Rigid Motion P 5

6 2. Write a single transformation that maps triangle A onto triangle D. 3. Triangle A maps onto triangle C through a rotation about the origin. What is the angle of rotation? What other angle of rotation can be used? 4. Find a two- step transformation that maps triangle A onto triangle E. 5. Kyra draws the right triangle H with vertices (- 4,1), (- 1,1), (- 1,4). Explain why triangle A cannot be mapped to triangle H using a rigid motion transformation. 8 MAC Test 10 Rigid Motion P 6

Environmental Club MAC Assessment Task The Environmental Club at school attends an annual community recycle event. They have recycling games.

7 Environmental Club MAC Assessment Task The Environmental Club at school attends an annual community recycle event. They have recycling games. A team is assigned an area of land that is scattered with litter. The goal is for a pair of participants to clean up the area in the fastest time possible. Tammy, working alone, could clean one-half the area in one hour. 1. How long would it take Tammy, working alone, to clean the entire area? hours Show how you figured it out. Her partner Melissa, working alone, could clean one-third of the area in one hour. 2. How much of the area could she clean in half an hour? Show how you figured it out. MAC Test 8 Environmental Club P 1 Silicon Valley Mathematics Initiative To reproduce this document, permission must be granted by the

8 3. If the partners worked together for 45 minutes, how much of the area would be clean? Show how you figured it out. 4. During the contest when they work together, how long will it take them to clean the entire area? Explain how you found your solution. 8 MAC Test 8 Environmental Club P 2 Silicon Valley Mathematics Initiative To reproduce this document, permission must be granted by the

The Basketball Game MAC Assessment Task Curry had a great basketball game last night. He scored 56 points. He made 7 free throws. Each free throw is worth 1 point.

9 The Basketball Game MAC Assessment Task Curry had a great basketball game last night. He scored 56 points. He made 7 free throws. Each free throw is worth 1 point. The rest of the points he scored were field goals, either 2-point or 3-point shots. 1. How many points did he score from shooting field goals? He made a total of 26 shots including free throws and field goals. Let x be the number of 2-point shots Curry made and let y be the number of 3-point shots he also made. 2. Write an equation to represent the 26 shots, including the number of free throws, 2-point shots and 3-point shots made. 3. Write another equation to represent the total number of points scored using the number of free throws, 2-point shots and 3-point shots made. MAC Test 9 The Basketball Game P 3

10 4. Use the two equations from question #2 and question #3 to determine the number of 2-point and 3-point shots Curry made. 2-point shots and 3-point shots made Show how you figured it out. 7 MAC Test 9 The Basketball Game P 4

11 Parallel and Perpendicular MAC Assessment Task You are helping your friend graph lines on the coordinate plane. 1. Draw a line on the coordinate axes through the points (-3, 4) and (-1, -2). Label the line J. 2. What is the slope of line J? MAC Test 8 Parallel and Perpendicular P 9

12 3. Write the equation for the line J. 4. Draw a line K on the graph parallel to J that passes through point (3, 1). Explain how you drew it to ensure that it was parallel. 5. Determine the equation of line L perpendicular to J that passes through point (-3, 4). Show how you figured it out. 6. Explain how the slopes of lines K and L are related. Where do these two lines intersect? Show how you figured it out. 9 MAC Test 8 Parallel and Perpendicular P 10

13 Toothpick Stairs This problem gives you the chance to: extend and check a given pattern use values in a table to derive a formula Jake makes staircases with toothpicks arranged in squares. He counts the number of toothpicks he uses and makes a table to show his findings. 1. Complete Jake's table. staircase number number of toothpicks on the perimeter of each staircase number of toothpicks inside each staircase How many toothpicks are there on the perimeter of staircase number 7? Explain how you figured it out. 3. How many toothpicks are there inside staircase number 8? Explain your reasoning. MARS 2001 Page 1 Toothpick Stairs: Grade 9

14 4. Represent the perimeter, P, as a function of the staircase number, S. 5. Represent the number of toothpicks inside the staircase, I, as a function of the staircase number, S. Explain how you figured it out. [15] 10 MARS 2002 Page 2 Toothpick Stairs: Grade 9

15 Perrin s Parabola MAC Assessment Task Perrin is experimenting with the parabola y=x 2. He draws the graph shown below: Perrin finds -3 on the x-axis. 1. What are the coordinates of the point on the parabola when x = -3? Label it point A on the graph above. 2. Perrin wants to determine the points of the parabola when y = 16. What are the points of the parabola? Label the point in the first quadrant B. MAC Test 11 Perrin s Parabola P 1

16 3. Write the equation of the line AB. Show how you figured it out. Perrin said, Pick any two points on the parabola. The absolute value of the product of the x-coordinates of the two points is equal to the y-intercept of the line through the two points. 4. Show that this statement is true for this case. 5. Prove that it is true for any two pairs of points on the parabola that lie on opposite sides of the axis of symmetry. 8 MAC Test 11 Perrin s Parabola P 2

LHS Algebra Pre-Test

Your Name Teacher Block Grade (please circle): 9 10 11 12 Course level (please circle): Honors Level 1 Instructions LHS Algebra Pre-Test The purpose of this test is to see whether you know Algebra 1 well