PARCC Claims Structure: Mathematics the purposes of the PARCC Mathematics assessments, the Major...
Transcript of PARCC Claims Structure: Mathematics the purposes of the PARCC Mathematics assessments, the Major...
Master Claim: On-Track for college and career readiness. The degree to which a student is college and career ready (or
“on-track” to being ready) in mathematics. The student solves grade-level /course-level problems in mathematics as set forth in the Standards for Mathematical Content with connections to the Standards for Mathematical Practice.
Sub-Claim A: Major Content1
with Connections to Practices
The student solves problems
involving the Major Content1 for her
grade/course with connections to the Standards for Mathematical
Practice.
Sub-Claim B: Additional & Supporting
Content2 with Connections to
Practices
The student solves problems involving the Additional and Supporting
Content2 for her grade/course with
connections to the Standards for Mathematical Practice.
Sub-Claim E: Fluency in applicable grades (3-6)
The student demonstrates fluency as set forth in the Standards for Mathematical
Content in her grade.
PARCC Claims Structure: Mathematics
Sub-Claim C: Highlighted Practices
MP.3,6 with Connections to Content3
(expressing mathematical reasoning)
The student expresses grade/course-level appropriate mathematical reasoning by constructing viable
arguments, critiquing the reasoning of others, and/or attending to precision
when making mathematical statements.
Sub-Claim D: Highlighted Practice MP.4 with Connections to Content (modeling/application)
The student solves real-world problems with a degree of difficulty appropriate to the grade/course by applying knowledge and skills articulated in the standards for the
current grade/course (or for more complex problems, knowledge and skills articulated in the standards for previous grades/courses), engaging particularly in the Modeling
practice, and where helpful making sense of problems and persevering to solve them (MP. 1),reasoning abstractly and quantitatively (MP. 2), using appropriate tools
strategically (MP.5), looking for and making use of structure (MP.7), and/or looking for and expressing regularity in repeated reasoning (MP.8).
1
For the purposes of the PARCC Mathematics assessments, the Major Content in a grade/course is determined by that grade level’s Major Clusters as identified in the PARCC Model Content Frameworks v.3.0 for Mathematics. Note that tasks on PARCC assessments providing evidence for this claim will sometimes require the student to apply the knowledge, skills, and understandings from across several Major Clusters.
2
The Additional and Supporting Content in a grade/course is determined by that grade level’s Additional and Supporting Clusters as identified in the PARCC Model Content Frameworks v.3.0 for Mathematics. 3
For 3 – 8, Sub-Claim C includes only Major Content. For High School, Sub-Claim C includes Major, Additional and Supporting Content.
PARCC Mathematics Task Types
Selected Evidence Statement Keys, Texts, and Clarifications: Grade 3
Evidence
Statement Key Evidence Statement Text Clarifications MP
3.OA.1 Interpret products of whole numbers, e.g., interpret 5 7
as the total number of objects in 5 groups of 7 objects
each. For example, describe a context in which a total
number of objects can be expressed as .
i) Tasks involve interpreting products in terms of equal groups,
arrays, area, and/or measurement quantities. For more information
see CCSS Table 2, p. 89.
ii) Tasks do not require students to interpret products in terms of
repeated addition, skip-counting, or jumps on the number line.
iii) The italicized example refers to describing a context. But
describing a context is not the only way to meet the standard. For
example, another way to meet the standard would be to identify
contexts in which a total can be expressed as a specified product.
4, 2
3.OA.3-1 Use multiplication within 100 (both factors less than or
equal to 10) to solve word problems in situations involving
equal groups, arrays, or area, e.g., by using drawings and
equations with a symbol for the unknown number to
represent the problem.
i) All products come from the harder three quadrants of the times
table ( where and/or ).
ii) 50% of tasks involve multiplying to find the total number (equal
groups, arrays); 50% involve multiplying to find the area.
iii) For more information see Table 2, p. 89 of the CCSS and
Table 3, p. 23 of Progression for Operations and Algebraic
Thinking.
1, 4
3.NF.3a-1 Explain equivalence of fractions in special cases and
compare fractions by reasoning about their size.
a. Understand two fractions as equivalent (equal) if they
are the same size.
i) Tasks do not involve the number line.
ii) Tasks are limited to fractions with denominators 2, 3, 4, 6 and 8.
(See footnote CCSS, p. 24)
iii) The explanation aspect of 3.NF.3 is not assessed here.
5
3.C.3-1 Base arithmetic explanations/reasoning on concrete
referents such as diagrams (whether provided in the
prompt or constructed by the student in her response),
connecting the diagrams to a written (symbolic) method.
Content Scope: Knowledge and skills articulated in
3.NF.3b and 3.NF.3d.
i) Tasks may present realistic or quasi-realistic images of a
contextual situation (e.g., a drawing of a partially filled graduated
cylinder). However, tasks do not provide the sort of abstract
drawings that help the student to represent the situation
mathematically (e.g., a number line diagram or other visual fraction
model).
ii) Grade 3 expectations in this domain are limited to fractions with
denominators 2, 3, 4, 6, and 8. (See footnote CCSS, p. 24)
iii) For fractions equal to a whole number, values are limited to 0,
1, 2, 3, 4, and 5.
3, 5, 6
3.D.2 Solve multi-step contextual problems with degree of
difficulty appropriate to Grade 3, requiring application of
knowledge and skills articulated in 2.OA.A, 2.OA.B,
2.NBT.A, B, and/or 2.MD.B.
Tasks may have scaffolding if necessary in order to yield a degree
of difficulty appropriate to Grade 3.
4
5 7
a b 5a 5b
Selected Evidence Statement Keys, Texts, and Clarifications: Grade 3
Per the PARCC Calculator Policy, PARCC mathematics assessments for Grades 3 – 5 will not allow for calculator usage.
Evidence
Statement Key Evidence Statement Text Clarifications MP
3.NF.A.Int.1 In a contextual situation involving a whole number and
two fractions not equal to a whole number, represent all
three numbers on a number line diagram then choose the
fraction closest in value to the whole number.
i) Whole numbers are limited to 0, 1, 2, 3, 4, 5. Fraction
denominators are limited to 2, 3, 4.
2, 4, 5
3.Int.2 Solve two-step word problems using the four operations
requiring a substantial addition, subtraction, or
multiplication step, drawing on knowledge and skills
articulated in 3.NBT.
See 3.OA.8, 3.NBT.2, and 3.NBT.3
i. Addition, subtraction, multiplication and division situations in
these problems may involve any of the basic situation types with
unknowns in various positions (see CCSS Table 1, p. 88 and Table
2, p. 89 and the Progression document for Operations and
Algebraic Thinking.
1, 4
Selected Evidence Statement Keys, Texts, and Clarifications: Grade 7
Evidence
Statement Key Evidence Statement Text Clarifications MP Calculator
7.NS.1d Apply and extend previous understandings of addition and
subtraction to add and subtract rational numbers; represent
addition and subtraction on a horizontal or vertical number
line.
d. Apply properties of operations as strategies to add and
subtract rational numbers.
i) Tasks do not have a context.
ii) Tasks are not limited to integers.
iii) Tasks may involve sums and differences of 2 or 3
rational numbers.
iv) Tasks require students to represent addition and
subtraction on a horizontal or vertical number line or
compute a sum or difference, or demonstrate
conceptual understanding for example by producing or
recognizing an expression equivalent to a given sum or
difference. For example, given the sum 8.1 7.4, the
student might be asked to recognize or produce the
equivalent expression (8.1 7.4).
7, 5 No
7.NS.2a-1
Apply and extend previous understandings of
multiplication and division and of fractions to multiply and
divide rational numbers.
a. Understand that multiplication is extended from
fractions to rational numbers by requiring that operations
continue to satisfy the properties of operations, particularly
the distributive property, leading to products such as
1 1 1 and the rules for multiplying signed
numbers.
i) Tasks do not have a context.
ii) Tasks are not computation tasks but rather require
students to demonstrate conceptual understanding, for
example by providing students with a numerical
expression and requiring students to produce or
recognize an equivalent expression using properties of
operations, particularly the distributive property. For
example, given the expression 3 6 4 3 , the
student might be asked to recognize that the given
expression is equivalent to 3 6 4 3 3 .
7 No
7.NS.3 Solve real-world and mathematical problems involving the
four operations with rational numbers.
i) Tasks are one-step word problems.
ii) Tasks sample equally between addition/subtraction
and multiplication/division.
iii) Tasks involve at least one negative number.
iv) Tasks are not limited to integers.
1, 4 No
Selected Evidence Statement Keys, Texts, and Clarifications: Grade 7
Evidence
Statement Key Evidence Statement Text Clarifications MP Calculator
7.C.4 Base explanations/reasoning on a coordinate plane
diagram (whether provided in the prompt or constructed
by the student in her response).
Content Scope: Knowledge and skills articulated in
7.RP.A.
None 2, 3,
5, 6
Yes
7.D.1 Solve multi-step contextual word problems with degree of
difficulty appropriate to grade 7, requiring application of
knowledge and skills articulated in 7.RP.1, 2; 7.NS.1, 2, 3;
and 7.EE.1, 3, 4.
Tasks may have scaffolding if necessary in order to
yield a degree of difficulty appropriate to grade 7.
4, 1,
2, 5,
7
Yes
Selected Evidence Statement Keys, Texts, and Clarifications: Algebra 1
Evidence
Statement Key Evidence Statement Text Clarifications MP Calculator
F-IF.2 Use function notation, evaluate functions for inputs in
their domains, and interpret statements that use function
notation in terms of a context.
See illustrations for F-IF.2 at
http://illustrativemathematics.org
6, 7 Item
Specific
A-SSE.2-4 Use the structure of a numerical expression or polynomial
expression in one variable to rewrite it, in a case where
two or more rewriting steps are required.
i) Example: Factor completely 2 21 ( 1)x x . (A first
iteration might give 2( 1)( 1) ( 1)x x x , which could
be rewritten as ( 1)( 1 1)x x x on the way to
factoring completely as 2 ( 1)x x . Or the student might
first expand as 2 21 2 1x x x , rewriting as
22 2x x then factoring as 2 ( 1)x x .
ii) Tasks do not have a context.
7, 1 Neutral
A-REI.4b-1 Solve quadratic equations in one variable.
b) Solve quadratic equations with rational number
coefficients by inspection (e.g., for 2
49x ), taking
square roots, completing the square, the quadratic formula
and factoring, as appropriate to the initial form of the
equation.
i) Tasks should exhibit variety in initial forms. Examples of
quadratic equations with real solutions: 249t , 2
3 4a ,
27 x , 2
0r , 21 1
2 5y , 2
8 15 0y y , 22 16 30 0x x ,
22 1p p , 2
4t t , 27 5 3 0x x ,
3( 1)
4c c c ,
2(3 2) 6 4x x
ii) Methods are not explicitly assessed; strategy is assessed
indirectly by presenting students with a variety of initial
forms.
iii) For rational solutions, exact values are required. For
irrational solutions, exact or decimal approximations may be
required.
iv) Prompts integrate mathematical practices by not
indicating that the equation is quadratic. (E.g., “Find all real
solutions of the equation 2
4t t ”…not, “Solve the quadratic
equation 2
4t t .”)
7, 5 Item
Specific
Selected Evidence Statement Keys, Texts, and Clarifications: Algebra 1
Evidence
Statement Key Evidence Statement Text Clarifications MP Calculator
A.Int.1 Solve equations that require seeing structure in
expressions.
i) Tasks do not have a context.
ii) Equations simplify considerably after appropriate
algebraic manipulations are performed. For example, if 2 2
24 10 ( 5)x x p x , then find the value of p;
solve 2(3 2) 6 4x x .
7, 1 No
HS-Int.2 Solve multi-step mathematical problems with degree of
difficulty appropriate to the course that require analyzing
quadratic functions and/or writing and solving quadratic
equations.
i) Tasks do not have a context.
ii) Exact answers may be required or decimal
approximations may be given. Students might choose
to take advantage of the graphing utility to find
approximate answers or clarify the situation at hand.
iii) Some examples:
Given the function 2( )f x x x , find all values of k
such that (3 ) (3)f k f . (Exact answers are
required.)
Find a value of c so that the equation 22 1 0x cx
has a double root. Give an answer accurate to the tenths
place.
1, 5,
6
Yes
Selected Evidence Statement Keys, Texts, and Clarifications: Algebra 1
Evidence
Statement Key Evidence Statement Text Clarifications MP Calculator
HS.C.12.1 Construct, autonomously, chains of reasoning that will
justify or refute propositions or conjectures about
functions.
Content scope: F-IF.8a
i) Tasks involve using algebra to prove properties of
given functions. For example, prove algebraically that
the function ( ) ( 1)h t t t has minimum value 1/4;
prove algebraically that the graph of 2 1
( )4
g x x x
is symmetric about the line 1
2x ; prove that 2
1x is
never less than 2x .
ii) Scaffolding is provided to ensure tasks have
appropriate level of difficulty. (For example, the
prompt could show the graphs of 21x and 2x on
the same set of axes, and say, “From the graph, it looks
as if 21x is never less than 2x . In this task you
will use algebra to prove it.” And so on, perhaps with
additional hints or scaffolding.
3 Yes
HS.D.2-9 Solve multi-step contextual word problems with degree of
difficulty appropriate to the course, requiring application
of course-level knowledge and skills articulated in the
following standards but limited to linear and quadratic
functions: F-BF.1a, F-BF.3, A-CED.1, A-SSE.3, F-IF.4-6,
and F-IF.7/
i) F-BF.1a is the primary content; other listed content
elements may be involved in tasks as well.
4, 2 Yes
Evidence Statement Topic Tally: Grade 3
Tally the number of evidence statements for each of the following topics (some evidence
statements may apply to multiple topics).
Note: the number of evidence statements is not equal to the number of questions on each exam.
Topic PBA EOY
Add/subtract whole numbers
Multiply whole numbers
Divide whole numbers
Fractions
Word problems
Area
Other
Tally the number of evidence statements for each of the following domains (some evidence
statements may apply to multiple topics):
Note: the number of evidence statements is not equal to the number of questions on each exam.
Domain PBA EOY
Operations and Algebraic Thinking (OA)
Number and Operations in Base Ten (NBT)
Numbers and Operations – Fractions (NF)
Measurement and Data (MD)
Geometry (G)
Grade 2
PARCC Prototype Tasks: Grade 3
Task #1: Fluency:
Click on all the equations that are true.
CCSS(s): __________________________________
Claim(s) supported: _________ Type: _________
EOY Evidence Statement Key(s): __________________________________
Task #2: Fractions on a Number Line
CCSS(s): __________________________________
Claim(s) supported: _________ Type: _________
EOY Evidence Statement Key(s): __________________________________
PARCC Prototype Tasks: Grade 3
Task #3: The Field
CCSS(s): __________________________________
Part a:
Claim(s) supported: _________ Type: _________
PBA/EOY Evidence Statement Key(s): __________
Part b-question 1:
Claim(s) supported: _____Type: _________
PBA/EOY Evidence Statement Key(s):
__________
Part b-question 2:
Claim(s) supported: _____Type: _____
PBA Evidence Statement Key(s): _______
PARCC Prototype Tasks: Grade 3
Task #4: Flower Gardens
Part a-question 1:
CCSS(s): __________________________
Claim(s) supported: _____Type: ________
PBA/EOY Evidence Statement Key(s):
__________
Part a-question 2:
CCSS(s): ___________________________
Claim(s) supported: _____Type: _________
EOY Evidence Statement Key(s):
__________
Part a
PARCC Prototype Tasks: Grade 3
Parts b and c:
CCSS(s): __________________________________
Claim(s) supported: _________ Type: _________
PBA/EOY Evidence Statement Key(s): __________
Part b
Part c
PARCC Prototype Tasks: Grade 3
Part a
Task #5: Fractions on the Number Line
Part a:
CCSS(s): ____________
Claim(s) supported: _______ Type: _______EOY Evidence Statement Key(s):___________
Parts b and c:
CCSS(s): ____________
Claim(s) supported: _______ Type: _______
PBA Evidence Statement Key(s):___________EOY Evidence Statement Key(s):___________
Part b
Part c
PARCC Prototype Tasks: Grade 3
Part d-question 1:
CCSS(s): ____________
Claim(s) supported: _______ Type: _______
PBA Evidence Statement Key(s):___________
EOY Evidence Statement Key(s):___________
Part d-question 2 and part e:
CCSS(s): ____________
Claim(s) supported: _______ Type: _______
PBA Evidence Statement Key(s):___________
Part d
Part e
Part d-question 2
PARCC Prototype Tasks: Grade 3
Task #6: Mariana’s Fractions
Part a:
CCSS(s): ____________
Claim(s) supported: _______ Type: _______ EOY Evidence Statement Key(s):___________
Parts b and c:
CCSS(s): ____________
Claim(s) supported: _______ Type: _______ EOY Evidence Statement Key(s):___________
Part a
Part b
Part c
PARCC Prototype Tasks: Grade 3
Part d:
CCSS(s): ____________
Claim(s) supported: _______ Type: _______ PBA Evidence Statement Key(s):___________
Part e-question a:
CCSS(s): ____________
Claim(s) supported: _______ Type: _______ EOY Evidence Statement Key(s):___________
Part e-part b-part 1:
CCSS(s): ____________
Claim(s) supported: ____Type: _______
PBA/EOY Evidence Statement Key(s):
_________
Part e-part b-part 2:
CCSS(s): ____________
Claim(s) supported: ____Type: _______
EOY Evidence Statement Key(s):
_________
_
Part d
Part e-question a
Part e-question b
PARCC Prototype Tasks: Grade 3
Task #7: School Mural
Part a:
CCSS(s): ________________________________
Claim(s) supported: _________ Type: _______
PBA/EOY Evidence Statement Key(s): ________
EOY Evidence Statement Key(s): ____________
Part a
PARCC Prototype Tasks: Grade 3
Task #7: School Mural (continued)
Part b:
CCSS(s): ________________________________
Claim(s) supported: _________ Type: _______
PBA Evidence Statement Key(s): _____________
_________________________________________
Part b
Evidence Statement Topic Tally: Grade 7
Tally the number of evidence statements for each of the following (some evidence statements
may apply to multiple topics):
Note: the number of evidence statements is not equal to the number of questions on each exam.
Topic PBA EOY
Proportional relationships
Add/subtract rational numbers
Multiply/divide rational numbers
Expressions/equations with variables
Geometry
Statistics
Tally the number of evidence statements for each of the following domains (some evidence
statements may apply to multiple topics):
Note: the number of evidence statements is not equal to the number of questions on each exam.
Domain PBA EOY
Ratios and Proportional Relationships (RP)
The Number System (NS)
Expressions and Equations (EE)
Geometry (G)
Statistics and Probability (SP)
Grade 6
PARCC Prototype Tasks: Grade 7
Task #1: Speed
CCSS(s): _________________
Claim(s) supported: _________ Type: _________
PBA/EOY Evidence Statement Key(s): __________
PARCC Prototype Tasks: Grade 7
Task #2: School Supplies
CCSS(s): _________________
Claim(s) supported: _________ Type: _________
PBA/EOY Evidence Statement Key(s): __________
Part b
Part a
PARCC Prototype Tasks: Grade 7
Task #3: Anne’s Family Trip
CCSS(s): __________________________________
Claim(s) supported: _________ Type: _________
PBA/EOY Evidence Statement Key(s): __________________________________
(continued on next page)
Part a
PARCC Prototype Tasks: Grade 7
Part b
Part c
PARCC Prototype Tasks: Grade 7
Part b
Part a
Task #4: TV Sales
CCSS(s): __________________
Claim(s) supported: _________ Type: _________
EOY Evidence Statement Key(s): _______________
CCSS(s): __________________
Claim(s) supported: _________ Type: _________
PBA Evidence Statement Key(s): _______________
PARCC Prototype Tasks: Grade 7
Task #5: Spicy Vegetables
CCSS(s): __________________
Claim(s) supported: _________ Type: _________
PBA/EOY Evidence Statement Key(s): _______________
Part a
Part b
Evidence Statement Topic Tally: Algebra 1
Tally the number of evidence statements for each of the following topics (some evidence
statements may apply to multiple topics).
Note: the number of evidence statements is not equal to the number of questions on each exam.
Topic PBA EOY
Linear equations/functions
Quadratic equations/functions
Exponential functions
Other functions:
Square root, cube root, piecewise, absolute value,
rational, cubic with linear and quadratic roots
Polynomial expressions/equations
Inequalities
Other
Tally the number of evidence statements for each of the following domains (some evidence
statements may apply to multiple topics):
Note: the number of evidence statements is not equal to the number of questions on each exam.
Domain PBA EOY
Real Number System (N-RN)
Quantities (N-Q)
Seeing Structure in Expressions (A-SSE)
Arithmetic w/Polynomials and Rational Expression (A-APR)
Creating Equations (A-CED)
Reasoning w/Equations and Inequalities (A-REI)
Interpreting Functions (F-IF)
Building Functions (F-BF)
Linear, Quadratic, and Exponential Models (F-LE)
Interpreting Categorical and Quantitative Data (S-ID)
7th
/8th
grade
PARCC Prototype Tasks: Algebra 1
Task #1: Functions
CCSS(s): __________________________________
Claim(s) supported: _________ Type: _________
EOY Evidence Statement Key(s): ______________
PARCC Prototype Tasks: Algebra 1
Task #2: Seeing Structure in an Equation
CCSS(s): __________________________________
Claim(s) supported: _________ Type: _________
PBA/EOY Evidence Statement Key(s): __________
Task #3: Seeing Structure in a Quadratic Equation
CCSS(s): __________________________________
Claim(s) supported: _________ Type: _________
PBA/EOY Evidence Statement Key(
s): __________
PARCC Prototype Tasks: Algebra 1
Task #4: Quadratic Transformation
Part a
CCSS(s): ______________
Claim(s) supported: _____ Type: ________
EOY Evidence Statement Key(s): ________
Part a
PARCC Prototype Tasks: Algebra 1
Task #4: Quadratic Transformation (continued)
Part b-questions a and b
CCSS(s): ______________
Claim(s) supported: _____ Type: ________
EOY Evidence Statement Key(s): ________
Part b-question c
Claim(s) supported: _____ Type: ________
PBA Evidence Statement Key(s): ________
Part b
PARCC Prototype Tasks: Algebra 1
Task #5: Rabbit Populations
Part a:
CCSS(s): __________________________________
Claim(s) supported: _________ Type: _________
EOY Evidence Statement Key(s): _______________
Part a
PARCC Prototype Tasks: Algebra 1
Task #5: Rabbit Populations (continued)
Part b:
CCSS(s): __________________________________
Claim(s) supported: _________ Type: _________
PBA Evidence Statement Key(s): _______________
Part b
PARCC Prototype Tasks: Algebra 1
Task #5: Rabbit Populations (continued)
Part c:
CCSS(s): __________________________________
Claim(s) supported: _________ Type: _________
EOY Evidence Statement Key(s): _______________
Part c
PARCC Prototype Tasks: Algebra 1
Task #6: Isabella’s Credit Card
CCSS(s): __________________
Claim(s) supported: _________ Type: _________
PBA Evidence Statement Key(s): _______________
(continued on next page)
Part a
PARCC Prototype Tasks: Algebra 1
Task #6: Isabella’s Credit Card (continued)
Part b
Part c
PARCC Prototype Tasks: Algebra 1
Task #7: Golf Balls in Water
CCSS(s): _____________________________________
Claim(s) supported: _________ Type: _________
PBA Evidence Statement Key(s): _________________
Part a
PARCC Prototype Tasks: Algebra 1
Part b
PARCC Prototype Tasks: Algebra 1
Part c
PARCC Prototyping Project “Golf Balls in Water – High School”
Tom is doing an experiment adding golf balls to a glass jar containing water. The picture and the
table show what happens to the height of the water as Tom adds golf balls.
Part a:
Use the following options to complete the sentences and the equation below based on the results
of Tom’s experiment.
golf balls change glass jars water height 1.16
1.2 1.3 9.0 12.0 13.8
The height of the water changes at an average rate of about _______________centimeters per
golf ball. If these data were graphed with the number of golf balls as their independent variable,
the y-intercept for the graph would be about _______________centimeters. This means that for
zero _______________, the _______________is 9 centimeters. Tom’s table and graph can be
represented by the trend line with the equation y = _______________x+______________.
Part b:
There are several ways that Tom could modify the conditions of his experiment. What
modifications would increase the rate of change in the height of the water level with respect to
the number of golf balls? Select all that apply.
Use larger golf balls Add 5 cm of water to the glass jar
Decrease the diameter of the glass jar Drop the golf balls into the glass jar
two at a time
Drop the golf balls into the glass jar at a
faster rate
Number of golf balls, x Height of water in centimeters, y
0 9.0
1 10.2
2 11.5
3 12.7
4 13.8
PARCC Prototyping Project “Golf Balls in Water – High School”
Tom repeats his experiment with a different glass jar. The new glass jar, B, has a smaller
radius than the original glass jar, A.
Data from Experiment with Glass Jar A
Number of golf balls, x Height of water in centimeters, y
0 9.0
1 10.2
2 11.5
3 12.7
4 13.8
Tom forgot to write down the initial height of the water in glass jar B, but he measured the
water height at 9 centimeters after adding two golf balls.
Question a: When Tom creates graphs of the data from both experiments, how will the
y-intercepts of the graphs be different for glass jar A versus glass jar B? Explain how you
know.
Question b: How will the rate of change in the experiment using glass jar B be different than
the rate of change in the experiment using glass jar A? Explain how you know.
Question c: Suppose glass jar B has a water height of 5 centimeters with no golf balls, and
the water height increases at a rate of 2 centimeters per golf ball added. Tom continues to add
golf balls to each glass jar. He discovers that there is a number of golf balls at which the
height of the water in each glass jar is the same. How many golf balls will be in each jar
when the water in each reaches the same height?