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: http://www.sfusdmath.org/secondary­course­sequence.html In keeping with California Senate Bill 359, the SFUSD Board of Education passed Board Policy 6146.1 (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: http://tinyurl.com/SFUSD­Math­Policy­2016 .) 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 1. 2. 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: http://tinyurl.com/SFUSD­Math­Policy­2016 ). For the 2016­2017 school year only, students who completed a UC approved CCSS Algebra 1 course at an accredited high school or college (face­to­face 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 2017–2018 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. SFUSD Math Validation Test July 2016: Task Alignment Mathematics of the Task Item # CCSSM Grade Level CCSSM Content Standards Total Pts Item 1 Functions – Modeling 8 Functions 8.F Use functions to model relationships between quantities. 8 Item 2 Geometry – Transformations, Pythagorean Theorem 8 Geometry 8.G Understand congruence and similarity using physical models, transparencies, or geometry software. Understand and apply the Pythagorean Theorem. 8 Item 3 Functions – Linear Functions HS High School Domains: Algebra and Functions Interpreting Functions F­IF Analyze functions using different representations. Reasoning with Equations and Inequalities A­REI Solve systems of equations. 8 Item 4 Statistics – Bivariate Data 8 Statistics and Probability 8.SP Investigate patterns of association in bivariate data. Functions 8.F Use functions to model relationships between quantities. 8 Item 5 Algebra – System of Inequalities HS High School Domain: Algebra Creating Equations A­CED Create equations that describe numbers or relationships. Reasoning with Equations and Inequalities A­REI Solve systems of equations. Represent and solve equations and inequalities graphically. 9 Item 6 Functions – Building Functions HS High School Domain: Functions Interpreting Functions F­IF Understand the concept of a function and use function notation. Building Functions F­BF Build a function that models a relationship between two quantities. 8 Item 7 Functions – Quadratic Functions HS High School Domains: Algebra and Functions Seeing Structure in Expressions A­SSE Interpret the structure of expressions. Interpreting Functions F­IF 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 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?
__________________ meters
Explain how you know.
__________________________________________________________________
MAC Test 8
Flying Birds at the Beach
Page 1
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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 68 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.
FlyingPelican
140
DistanceTraveledinMeters
120
100
80
60
40
20
0
0
2
4
6
8
10
12
14
TimeElapsedinSeconds
4.
What was the average speed of the pelican’s entire trip to the ocean and back?
____________________________________ meters per second
8
MAC Test 8
Flying Birds at the Beach
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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. WhatisthelengthoflinesegmentAC?
______________________units
Showhowyoufigureditout.
MAC Test 8
Transforming Triangles
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Antoinettereflectedtriangle∆ABCoverthelinex=4.
3. 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.
_________________________________________________________________
Antoinettetranslatedtriangle∆ABC3unitstotherighthorizontallyand1unitup
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.
Antoinetterotatedtriangle∆ABC180ºaroundthepoint(3,3).
5. Drawtherotatedimageonthesamecoordinateplane.Labelthenewtriangle
∆XYZ,whereAmapstoX,BmapstoYandCmapstoZ.
Explainwhyreflectingtriangle∆ABCoverthelineACdoesNOTmaponto
triangle∆XYZ.
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
8
MAC Test 8
Transforming Triangles
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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.
12
11
10
9
8
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
10
11
12
1. 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?
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April’s second clue is that Waldo is located at a point on the equation:
y = -2x + 10
2. 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.
_________________________________________________________________
_________________________________________________________________
8
MAC Test Algebra
Where is Waldo?
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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)
4
5
6
8
8
10
13
16
20
20
23
Distance(miles)
1.5
1
2
1.5
2.5
4
4
5
5
5.5
6.5
1. On the axes below, create a scatterplot using the data from the Uber table above.
UberTrips
8
7
DistanceinMiles
6
5
4
3
2
1
0
0
5
10
15
20
25
30
TimeinMinutes
MAC Test 8
Uber Driver
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Initiative [email protected]
Given the data from the Uber trips, use the scatterplot to help solve the following
questions:
2. Onthescatterplot,drawalinethatbestfitsthedataoftheUbertrips.Using
thisline,whatistherelationshipbetweenthetimeandthedistanceofthe
trips?
_________________________________________________________________
3. Estimatetheaveragespeedofallthetrips.
____________________milesperminute
Explainhowyouestimatedtheaveragespeed.
_________________________________________________________________
_________________________________________________________________
4. Writeanequationofthelinethatbestfitsyourdata.
_________________________________________________________________
5. IfacustomercalledSebastianandaskedhimhowlongitwouldtakeforatrip
thattravels3miles,whatshouldSebastiantellthecustomer?
_____________________ minutes
6. Onfuturedays,Sebastianwantstomakeabout$35perhourfromUberfares.
Howmuchshouldhechargecustomerspermile?
______________________________
Showhowyoufigureditout.
8
MAC Test 8
Uber Driver
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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
Chocolate Chip
Peanut Butter
Cost to Make
$0.30
$0.20
Price to Sell
$1.20
$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.
________________________________________________
70
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
3. 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
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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
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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?
___________________________tile(s)
Explain how you figured it out.
___________________________________________________________________
___________________________________________________________________
MAC Test Algebra
Linda’s Tiles
Page 3
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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.
________________________________________________________________
_________________________________________________________________
_________________________________________________________________
8
MAC Test Algebra
Linda’s Tiles
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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 1936. 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 1,280 meters.
1. The roadway is 78 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 = ax2 + 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
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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.
450
400
350
300
250
200
150
100
50
0
-800
-600
-400
-200
-50
0
200
400
600
800
-100
4. 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.
_________________________________________________________________
_________________________________________________________________
7
MAC Test Algebra
Golden Gate Parabola
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