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Curriculum Scaffolding for 9-12 Mathematics
9-12 Mathematics Reporting Standards
Reporting Standard 1- Linear Function Algebraically solve, graph, interpret & create models of linear relations.
Reporting Standard 2 - Quadratic Functions: Graphs, solves, interprets & creates models of quadratic functions.
Reporting Standard 3 - Advanced Functions: Analyze and apply polynomial, rational, and radical functions.
Reporting Standard 4 - Exponential and Logarithmic Functions: Analyze and apply exponential and logarithmic
functions.
Reporting Standard 5 - Trigonometric Relationships: Apply the trig relations to solve & simplify identities,
functions & models
Reporting Standard 6 - Geometric Structure: Apply attributes & relationships of geometric objects in diverse
contexts
Reporting Standard 7 - Congruence: Use theorems to prove and apply congruence
Reporting Standard 8 - Similarity: Use theorems to prove and apply similarity
Reporting Standard 9 - Measurements: Use geometric tools, theorems & algebra to find measurements.
Reporting Standard 10 - Statistics and Probability: Analyze variability in data to make informed decisions.
Reporting Standard 11 - Literacy: Construct viable arguments and critique reasoning.
Reporting Standards, Sub-Standards & Sample Problems by Course
Reporting Standard 1: Algebraically solve, graph, interpret & create models of linear relations.
Reporting Standard 2 - Quadratic Functions: Graphs, solves, interprets & creates models of quadratic functions.
Reporting Standard 3 - Advanced Functions: Analyze and apply polynomial, rational, and radical functions.
Reporting Standard 4 - Exponential and Logarithmic Functions: Analyze and apply exponential and logarithmic
functions.
Reporting Standard 5 - Trigonometric Relationships: Apply the trig relations to solve & simplify identities,
functions & models
Reporting Standard 7 - Congruence: Use theorems to prove and apply congruence
Reporting Standard 8 - Similarity: Use theorems to prove and apply similarity
Reporting Standard 9 - Measurements: Use geometric tools, theorems & algebra to find measurements.
Reporting Standard 10 - Statistics and Probability: Analyze variability in data to make informed decisions.
Reporting Standard 11 - Literacy: Construct viable arguments and critique reasoning.
1. Sub-Standard: Applies the order of operations and properties of real numbers to
solve multi-step problems.
Advanced
Proficient
Developing
Beginning
Describes multiple forms of
applications of operations and
properties of real numbers.
Simplifies and
evaluates problems
that involve exponents.
Simplifies and evaluates
problems that involve
distribution.
Simplifies or evaluates problems
that involve addition, subtraction,
multiplication, and division.
Algebra I Sample Problems
Advanced
Proficient
Developing Beginning
33-5-22+22+33
-32 (-3)2 + 4
-2(4 - 9) 3
52 + 4 - 8
Algebra II Sample Problems
Advanced
Proficient
Developing Beginning
(13)-245(2-14)2+(1-32)-1
30 - 5 -6(4 - 9)-2
2(-5 - 59 - 9)
4 - 9 36 - 7
Computer Science Problems
Advanced
Proficient
Developing
Beginning
var=(math.pow((x/3),2)*(4/5))/(math.pow((2(y/4),2)+math.pow(((x-(3/2)),-1);
var=math.pow(3,0)-x*6*math.pow((4-9),-z);
var=2*(-5-x)/(y8);
var=x+6;
Reporting Standard 2 - Quadratic Functions: Graphs, solves, interprets & creates models of quadratic functions.
Reporting Standard 3 - Advanced Functions: Analyze and apply polynomial, rational, and radical functions.
Reporting Standard 11 - Literacy: Construct viable arguments and critique reasoning.
2. Sub-Standard: Performs arithmetic operations with complex numbers.
Advanced
Proficient
Developing
Beginning
Justifies the number of complex
solutions for any polynomial and
solves for them.
Solves and explains
expressions with complex
answers.
Solves and rewrites
expressions with complex
numbers.
Uses operations to
simplify complex
numbers.
Algebra II Sample Problems
Advanced
Proficient
Developing Beginning
Determine the number of solutions, types of
solutions, and possible turning points for the
polynomial: 2x - 4x + 7
Solve 2x3 + 4x2+
8x = -16
Solve x +4 =
0
2
(3 + 2i)(5 - 4i)
=
2
Pre-Calc Sample Problems
Advanced
Proficient
Developing
Beginning
Find all the zeros of the
function.
f(x)=2x6+7x5-4x4+91x3330x2+220x-900
Find all zeros of the
function
f(x) = x -4x +9x-36
Find all zeros of the
function
f(x) = x2 - 2x + 5
multiply 6- 4i by its
conjugate pair
3
2
Reporting Standard 1: Algebraically solve, graph, interpret & create models of linear relations.
Reporting Standard 2 - Quadratic Functions: Graphs, solves, interprets & creates models of quadratic functions.
Reporting Standard 3 - Advanced Functions: Analyze and apply polynomial, rational, and radical functions.
Reporting Standard 4 - Exponential and Logarithmic Functions: Analyze and apply exponential and logarithmic
functions.
Reporting Standard 5 - Trigonometric Relationships: Apply the trig relations to solve & simplify identities,
functions & models
Reporting Standard 7 - Congruence: Use theorems to prove and apply congruence
Reporting Standard 8 - Similarity: Use theorems to prove and apply similarity
Reporting Standard 9 - Measurements: Use geometric tools, theorems & algebra to find measurements.
Reporting Standard 10 - Statistics and Probability: Analyze variability in data to make informed decisions.
Reporting Standard 11 - Literacy: Construct viable arguments and critique reasoning.
3. Sub-Standard: Interprets and writes equations and expressions in equivalent
forms to solve problems.
Advanced
Proficient
Developing
Beginning
Compares and contrasts
equivalent forms of
expressions or equations
to interpret the values.
Writes an expression or
equation in multiple
equivalent forms and
interprets the resulting values
in the expression.
Writes an expression
or equation in multiple
equivalent forms.
Writes an
expression or
equation in an
equivalent form.
Algebra I Sample Problems
Advanced
Proficient
Developing
Beginning
Write the equations for the
lines that pass through
(½, 7) & (¾,9) and (-⅗
,⅕) & ( -25 ,14). Describe
their relationship.
Write the equation for
the line that passes
through (1,3) and (-4,7)
in three forms and
graph the equation.
Write the equation for the
line that passes through (3, 4) and (5, 1) in slopeintercept form and pointslope form.
Write 5x - 2y =
10 in slope
intercept form.
Geometry Sample Problems
Advanced
Proficient
Developing
Beginning
Prove lines a
and b are parallel.
Lines a and b
are parallel. Solve for
x and y.
Write an equation and
solve to find each missing
angle measurement.
Write an equation and
solve to find each angle
measurement.
Algebra II Sample Problems
Advanced
Proficient
Given that the vertex of a
parabola is (2, - 4) and
passes through the origin
write the equation for the
quadratic.
Write f(x) = x + 5x + 7
in vertex form and use
the equation to graph
the parabola.
2
Developing
Beginning
Write f(x) = x +
5x + 7 in vertex
form.
Write the equation for the
line that passes through (-3,
4) and (5, 1) in slopeintercept form and pointslope form.
2
Pre-Calc Sample Problems
Advance
d
Proficien Developing
t
Beginning
Simplify the expression.
Verify that the equation is an
identity.
Calc Sample Problems
Advanced
Proficient
Developing
Beginning
Evaluate the
following
integral
A water tank has the shape of
an inverted circular cone with
the base radius 3 m and height
4 m. If water is being pumped
into the tank at a rate of 2
m3/min., find the rate at which
the water level is rising when
the water is 2 m deep.
Find the volume of the
solid that is created by
revolving the graph
y=3+6xabout the xaxis on the interval [0,
3].
Find the value of
dydx.
y=cos(3x4+12).
3x2exdx
4. Sub-Standard: Performs multiple operations with polynomials and monomials.
Reporting Standard 2 - Quadratic Functions: Graphs, solves, interprets & creates models of quadratic functions.
Reporting Standard 3 - Advanced Functions: Analyze and apply polynomial, rational, and radical functions.
Reporting Standard 11 - Literacy: Construct viable arguments and critique reasoning.
Advanced
Proficient
Developing
Beginning
Factors and simplifies
polynomials and monomials in
multiple forms and interprets the
results.
Factors and simplifies
polynomials and
monomials in multiple
forms.
Factors polynomials
using two or three
steps.
Reproduces
single step
factors.
Algebra I Sample Problems
Advanced
Proficient
Developing
Beginning
Solve 2x + 13x + 21 and explain what your
answers mean.
Factor 2x - 10x
+12
Factor x + 5x +
6
Factor x +
5x
2
2
2
2
Algebra II Sample Problems
Advanced
Solve 2x + 6x -8x -24 and draw
a sketch of your graph.
3
2
Proficient
Developing
Beginning
Solve 2x + 13x + 21 and explain
what your answers mean.
Factor 2x - 10x
+12
Factor 2x
+8x
2
2
2
Reporting Standard 3 - Advanced Functions: Analyze and apply polynomial, rational, and radical functions.
Reporting Standard 11 - Literacy: Construct viable arguments and critique reasoning.
5. Sub-Standard: Solves rational expressions using zeros and identities of
polynomials.
Advanced
Proficient
Developing
Beginning
Distinguishes the most efficient method to
solving zeros and explains the the meaning
of the zeros in the context of the polynomial
and deduces the type of polynomial using
multiple identities.
Explains the meaning of
zeros in the context of the
polynomials and
determines the type of
polynomial.
Explains the meaning
of zeros and classify
the polynomial.
Finds the zeros
and identify the
polynomial.
Algebra II Sample Problems
Advanced Proficient Developing Beginning
Pre-Calc Sample Problems
Advanced Proficient Developing Beginning
6. Sub-Standard: Creates and solves equations, inequalities, and systems.
Advanced
Proficient
Developing
Beginning
Creates and successfully solves
equations, inequalities, and
systems from word problems and
real world problems using multiple
methods.
Chooses and justifies the
most efficient method to
solve equations,
inequalities, and systems.
Explains the method used
for successfully solving
equations, inequalities,
and systems
Solves equations,
inequalities, and
systems using the
prescribed method.
Algebra I Sample Problems
Advanced Proficient Developing Beginning
Geometry Sample Problems
Advanced Proficient Developing Beginning
Algebra II Sample Problems
Advanced Proficient Developing Beginning
Pre-Calc Sample Problems
Advanced Proficient Developing Beginning
Calculus Sample Problems
Advanced Proficient Developing Beginning
7. Sub-Standard: Constructs and compares linear and exponential functions.
Advanced
Proficient
Developing
Beginning
Describes characteristics of
linear and exponential
functions.
Produces and contrasts
linear and exponential
functions.
Explains the properties of
linear and exponential
functions.
Identifies the properties of
linear and exponential
functions.
Algebra I Sample Problems
Advanced Proficient Developing Beginning
Algebra II Sample Problems
Advanced Proficient Developing Beginning
Pre-calc Problems
Advanced Proficient Developing Beginning
8. Sub-Standard: Applies the properties of trigonometric functions.
Advanced
Proficient
Developing
Beginning
Uses trigonometric
properties to solve real
world and word
problems.
Applies the properties of
trigonometric functions to
solve multiple functions.
Uses the sine, cosine, tangent
and the inverse trigonometric
functions to find missing
values.
Uses the sine, cosine, and
tangent trigonometric
functions to find missing
values.
Geometry Sample Problems
Advanced Proficient Developing Beginning
Pre-calc Sample Problems
Advanced Proficient Developing Beginning
9. Sub-Standard: Proves congruence.
Advanced
Proficient
Basic
Minimal
Proves and justifies congruence
using the most efficient method.
Proves and justifies
congruence using any
method.
Proves congruence
using any method.
Proves congruence using
the prescribed method.
Geometry Sample Problems
Advanced Proficient Developing Beginning
10. Sub-Standard: Proves similarity.
Advanced
Proficient
Basic
Minimal
Proves and justifies similarity using
the most efficient method.
Proves and justifies
similarity using any method.
Proves similarity
using any method.
Proves similarity using the
prescribed method.
Geometry Sample Problems
Advanced Proficient Developing Beginning
11. Sub-Standard: Applies the properties of two and three dimensional figures.
Advanced
Proficient
Developing
Beginning
Illustrates the properties of two
and three dimensional figures
Compares and contrasts the
properties of two and three
Interprets the properties of
two and three dimensional
Identifies the properties
of two and three
in real world situations.
dimensional figures.
figures.
dimensional figures.
Geometry Sample Problems
Advanced Proficient Developing Beginning
12. Sub-Standard: Applies the theorems of circles to find lengths and areas.
Advanced
Proficient
Developing
Beginning
Illustrates multiple methods to solve
for lengths and areas of circles in
real world and word problems.
Explains how to solve for
lengths and areas of circles
using any theorem.
Solves lengths and
areas of circles.
Solves lengths and areas
of circles using the
prescribed method.
Geometry Sample Problems
Advanced Proficient Developing Beginning
13. Sub-Standard: Summarizes and interprets data using multiple representations.
Advanced
Proficient
Basic
Minimal
Creates multiple representations
to summarize and interpret real
world data in order to reach viable
conclusions.
Interprets and reaches a
viable conclusion using
multiple representations of
the data.
Interprets and reaches a
conclusion using a
representation of the
data.
Uses prescribed
method to create a
representation of data.
Prob & Stats Sample Problems
Advanced Proficient Developing Beginning
Algebra I Sample Problems
Advanced Proficient Developing Beginning
Geometry Sample Problems
Advanced Proficient Developing Beginning
Algebra 2 Sample Problems
Advanced Proficient Developing Beginning
Pre-Calculus Sample Problems
Advanced Proficient Developing Beginning
Calculus Sample Problems
Advanced Proficient Developing Beginning
14. Sub-Standard: Evaluates statistical experiments.
Advanced
Proficient
Basic
Minimal
Assesses the validity of the
conclusions developed through
the analysis of statistical
experiments.
Predicts future values
through the analysis of
statistical experiments.
Explains the meaning of
numerical answers from
statistical experiments.
Finds numerical
answers from
statistical experiments.
Prob & Stats Sample Problems
Advanced Proficient Developing Beginning
Algebra 1 Sample Problems
Advanced Proficient Developing Beginning
15. Sub-Standard: Applies rules of probability to interpret data.
Advanced
Proficient
Basic
Minimal
Assesses the validity of the
conclusions developed through the
analysis of the probability of data.
Predicts future values
through the analysis of the
probability of data.
Selects the appropriate
rule of probability to
interpret data.
Uses the
prescribed rule to
interpret data.
Probability and Statistics Sample Problems
Advanced Proficient Developing Beginning
Algebra 1 Sample Problems
Advanced Proficient Developing Beginning