Download Standard 5: Statistics and Probability

CORE Mathematics 035 Blueprint
Page 1 of 16
How do I use this document?
This document contains the blueprint e.g. guidelines for the types of problems that will be on the Mathematics 035 test
in the Indiana CORE teacher licensure exam.


The blueprint is broken down into 5 domains.
Each domain has 1 or more standards and each standard has multiple parts.
o Domain I – Number Systems and Operations
 0001 Number and Quantity (Standard 1)
o Domain II – Algebra, Functions, and Calculus
 0002 Algebra (Standard 2)
 0003 Functions (Standard 3)
 0004 Calculus (Standard 6)
o Domain III – Measurement and Geometry
 0005 Measurement and Geometry (Standard 4)
o Domain IV – Statistics, Probability, and Discrete Mathematics
 0006 Statistics and Probability (Standard 5)
 0007 Discrete Mathematics (Standard 7)
o Domain V – Instruction and Assessment
 0008 Mathematics Instruction and Assessment (Standard 8)
There is a table for each domain that details the standard and its parts. The second column unpacks each of the
standards and provides additional resources online to learn, review, and/or practice a concept and/or problem solving
methodology.
To get the most out of this document, review each of the standards and ask yourself,
? Do I understand what this is saying?
? Can I solve a problem pertaining to this standard?
If the answer is no to either question, review the information underneath “Unpacking the Standards” next to the
standard. If additional help is needed, be sure to consult a tutor in the CRC.
There are math specific websites that can be used to review material, read up on material, and practice problems. Two
such websites are included below:
Title
URL
Math Courses Covered
Cliff Notes
http://www.cliffsnotes.com/math
Algebra



Algebra I
Algebra II
Linear Algebra
Basic Math
 Basic Math & Pre-Algebra
 Math Word Problems
Calculus
 Calculus
 Precalculus
Differential Equations
Geometry
Statistics
Trigonometry
CORE Mathematics 035 Blueprint
Page 2 of 16
Title
URL
Math Courses Covered
Spark Notes
http://www.sparknotes.com/math/
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









Pre-algebra
Geometry I
Geometry II
Geometry III
Algebra I
Algebra II
Trigonometry
Precalculus
Calculus AB
Calculus BC I
Calculus BC II
CORE Mathematics 035 Blueprint
Page 3 of 16
Introducing the Mathematics 035 CORE Exam
For the Mathematics 035 CORE Exam, the following domains and standards are covered:
Domain I – Numbers and Algebra
0001
Number and Quantity (Standard 1)
Standard 1: Number and Quantity
Standards
Unpacking the Standards
Standard 1: Number and Quantity
Mathematics teachers have a broad and comprehensive understanding of number systems, number
representations, number operations, and number theory, including:
1.1 Properties of
What are real numbers?
real and
Instagrok
What are real numbers
complex
search:
numbers and
their subsets
What are the properties of real numbers?
Dogpile
Properties of real numbers
search:
What are complex numbers?
Mamma 1
What are complex numbers
What are the properties of complex numbers?
Webcrawler Properties of complex numbers
1.2
Ordering and
What are different representations of numbers?
equivalence of
Search.com
Representations of numbers
different
search
representations
of numbers
How can you order different representations of numbers?
Ecosia
Practice ordering different representations of numbers
search
How can you determine if two numbers (in different representations) are equivalent?
Equivalent
Khan Academy
Fractions
Practice
Massachusetts Grade 10 Mathematics Test
Problems
Review
Massachusetts Comprehensive Assessment System Grade 10
Material
Mathematics 2nd Edition
1
Why I love mamma? Mamma simultaneously searches the major search engines, analyzes the results, set the terms in the correct
syntax and format and last but never least, and organizes the results in a uniform retrieval set based on relevancy and score.
CORE Mathematics 035 Blueprint
Standards
1.3
1.4
1.5
Page 4 of 16
Unpacking the Standards
Attending to
What is accuracy and precision?
accuracy and
Google
Mathematics precision and accuracy
precision with
search
different
representations
of numbers
Number sense
How can I develop number sense?
and place
Google
Develop number sense
value, including
Book
bases other
Search
than base 10
What is place value?
Ecosia
What is place value
search
Application and
use of factors
What is the best method for transitioning from base 10 to another base system?
Ecosia
Mathematics number base system tutorial
Mamma Best method change from base 10 to another base
What is a factor?
Bing
Mathematics what is a factor
search
How do I find the least common denominator?
Using prime
Explanation: Using prime factorization
factorization
Video: Using prime factorization
Spark Notes: Additional information
What is a multiple?
“Math is
fun”
website
http://www.mathsisfun.com/definitions/multiple.html
CORE Mathematics 035 Blueprint
Standards
Unpacking the Standards
1.6
What are vector spaces?
mamma
What are vector spaces
search
Properties of
vector spaces
and matrices
and their
applications
Page 5 of 16
What are the properties of vector spaces?
mamma
Properties of vector spaces
search
What are matrices?
mamma
search
What are matrices
What are the properties of matrices?
mamma
Properties of matrices
search
1.7
1.8
Where can I find practice problems for vector spaces and matrices?
mamma
Practice problems on vector spaces and matrices
search
What are traditional and alternative computational algorithms?
iSEEK
Traditional and alternative “computational algorithms”
Traditional and
alternative
computational
algorithms
Problem
Where can I find practice problems with different representations of numbers?
solving with
Dogpile
Problem solving with different representations of numbers
different
search
representations
of numbers
(fractions,
decimals,
percents,
scientific
notation
CORE Mathematics 035 Blueprint
Page 6 of 16
Standard 2: Algebra
Standards
Unpacking the Standards
Standard 2: Algebra
Mathematics teachers have a broad and comprehensive understanding of the structure of mathematical
expression, the application of algebraic techniques, and the use of equations and inequalities to model and solve
problems, including:
2.1 Algebraic
notation,
Duck-DuckMathematics algebraic notation example
language, and
Go Search
expressions
Duck-DuckMathematics algebraic language example
Go Search
Duck-DuckMathematics algebraic expressions example
Go Search
2.2 Simplification
What are different types of polynomials?
and
Duck-DuckDifferent types of polynomials
manipulation
Go Search
of polynomials
and rational
What are different methods for simplifying polynomials?
expressions
Duck-DuckHow to simplify a polynomial
Go Search
What are rational expressions?
Dogpile
What is a rational expression
search
2.3
2.4
Creating and
solving
equations and
inequalities
Modeling and
solving systems
of equations
and
inequalities,
including the
use of matrix
techniques
What are different methods for simplifying rational expressions?
Duck-DuckHow to simplify a rational expression
Go Search
Where can I find practice problems for solving equations?
Google
Creating equations from word problems
search
Where can I find practice problems for solving inequalities?
Google
Creating inequalities from word problems
search
What are the different ways to solve a system of two equations?
 Graphing
 Elimination
 Substitution, etc.
QWANT
What are different ways to solve a system of linear equations
What are different ways to solve systems of inequalities?
QWANT
What are different ways to solve a system of inequalities
search
How would you solve systems of equations using matrices?
Google
Using matrices to solve systems of equations
search
CORE Mathematics 035 Blueprint
Standards
Page 7 of 16
Unpacking the Standards
Standard 2: Algebra
Mathematics teachers have a broad and comprehensive understanding of the structure of mathematical
expression, the application of algebraic techniques, and the use of equations and inequalities to model and solve
problems, including:
2.5 Algebraic
What is algebraic reasoning?
reasoning and
Yandex
Problem solving with different representations of numbers
the proof and
search
justification of
algebraic
What are the proof and justification of algebraic techniques?
techniques
Yandex
Proof justification algebraic techniques
search
2.6 Graphical
What are different types of graphs and their equations?
representations
Google
Graphs and their equations
of equations
search
and inequalities
Given an equation, how would I graph it?
Google
Given an equation how would I graph it
search
2.7
Concepts of
linear and
abstract
algebra,
including
vector spaces
and matrices
involving both
real and
complex
numbers
Given an inequality, how would I graph it?
Dogpile
Given an inequality how would I graph it
search
What are linear algebra concepts?
Yippy
“linear algebra” + concepts
search
What are linear algebra concepts?
Info.com
Abstract algebra concepts
search
What are vector spaces?
Info.com
Vector spaces
search
How do matrices work in linear algebra?
Info.com
Linear algebra matrices
search
How do real and complex numbers work in linear algebra?
Info.com
Linear algebra real and complex numbers
search
Standard 3: Functions
Standards
Unpacking the Standards
Standard 3: Measurement and Geometry Indiana educators demonstrate knowledge of principles and procedures
of measurement, basic properties of two- and three-dimensional figures, and reasoning in geometry, including:
3.1
Properties of
What are the properties and patterns in mathematics?
patterns, ratios,
Mamma
Properties of patterns mathematics
CORE Mathematics 035 Blueprint
Standards
proportions,
relations, and
functions
Unpacking the Standards
search
What are the properties of ratios?
Google
What are the properties of ratios
search
What are the properties of proportions?
Ecosia
What are the properties of proportions
search
What are the properties of relations?
Duck Duck
What are the properties of relations
Go
search
3.2
Properties of
linear functions,
inequalities,
systems, and
their
representations
What are the properties of functions?
Webcrawler What are the properties of functions
search
What are the properties of linear functions?
Google
What are the properties of linear functions
search
What are the properties of inequalities?
Google
What are the properties of inequalities
search
What are the properties of systems of equations?
Ecosia
What are the properties of systems of equations
search
3.3
Modeling
problems with
linear functions,
inequalities,
systems, and
their
representations
What are the properties of systems of inequalities?
Duck Duck
What are the properties of systems of inequalities
Go
search
Modeling problems with linear functions
Yandex
Modeling problems with linear functions
search
Modeling problems with inequalities
QWANT
Modeling problems with inequalities
search
Modeling problems with systems of equations
Info.com
Modeling problems with systems of equations
search
Modeling problems with systems of inequalities
IxQuick
Modeling problems with systems of inequalities
Page 8 of 16
CORE Mathematics 035 Blueprint
Standards
3.4
3.5
Behaviors of
nonlinear
functions and
relationships
between their
various
representations
Manipulation of
functions,
including
transformation,
translation,
composition,
and other
manipulations
Page 9 of 16
Unpacking the Standards
search
Enter the phrase “Modeling problems with systems of inequalities”
What are nonlinear functions?
Google
What are nonlinear functions
search
What are different types of nonlinear functions?
Google
Different types of nonlinear functions
search
What is the transformation of a function?
Dogpile
Transformation of a function
search
What is a vertical shift?
Dogpile
What is the vertical shift of a graph
search
What is a horizontal shift?
Dogpile
What is a horizontal shift of a graph
search
What is a translation?
Dogpile
What is a translation mathematics
search
What is a reflection of a graph?
Dogpile
What is reflection mathematics
search
What changes would be made to function to have the graph shrink and/or stretch?
Dogpile
Shrink stretch graph
search
What is function composition? What notation is used to represent composition? How is
function composition calculated?
Dogpile
Composition of a function
search
3.6
Modeling
problems with
nonlinear
functions and
their
representations
What is the inverse of a function? How is the inverse of a function calculated?
Dogpile
Inverse of a function
search
Modeling problems with nonlinear functions
Google
Modeling problems with nonlinear functions
search
CORE Mathematics 035 Blueprint
Standards
Unpacking the Standards
3.7
What are the trigonometric functions?
Google
What are trigonometric functions
search
Trigonometric
functions and
the unit circle
Page 10 of 16
What is the unit circle?
Dogpile
What is the unit circle
search
3.8
3.9
3.10
Properties of
trigonometric
functions
Modeling
periodic
phenomena
with
trigonometric
functions
Polar
coordinates and
parametric
equations
How can you use the unit circle to solve geometric equations and/or word problems?
Mamma
Use the unit circle to solve trigonometric problems
search
What are the properties of trigonometric functions?
Webcrawler Properties of trigonometric functions
search
How do I model periodic phenomena with trigonometric functions?
Webcrawler Modeling periodic phenomena with trigonometric functions
search
What are polar coordinates?
Info.com
What are polar coordinates?
search
What are parametric equations?
Instagrok
Parametric equation
search
How do I covert from a polar equation to a parametric equation?
Google
Converting polar to parametric equations
search
Standard 4: Measurement and Geometry
An excellent reference that you want to use to study from as well as may utilize as a teacher is available on the School
Improvement in Maryland website at http://mdk12.org/instruction/clg/geometry/goal2.html
This particular standard covers numerous areas. As a result, in certain sub-standards (e.g. 4.1, 4.4, etc.), there is a list of
objectives that identify what you will need to know and/or be able to solve/calculate.
Standards
Unpacking the Standards
Standard 4: Mathematics teachers have a broad and comprehensive understanding of the principles and
procedures of measurement, Euclidean plane geometry and its applications, Euclidean coordinate geometry and its
applications, and the role of reasoning and proof in geometry, including:
4.1
Principles,
What is the English measurement system?
procedures, and
Mamma
English measurement system
applications of
search
CORE Mathematics 035 Blueprint
Standards
measurement
and geometry
Page 11 of 16
Unpacking the Standards
What is the metric measurement system
Search.com
Metric measurement system
search
How do I convert from English to metric and vice versa?
iSeek
Convert from English to metric
search
How do I solve word problems involving measurements?
Google
Word problems geometry measurement
search

4.2
Derivation and
application of
length,
perimeter, area,
and volume
formulas of
basic geometric
figures
Analyze the use of various units and unit conversions within the customary
(English) and metric systems.
 Calculate or estimate measures of lengths, areas and volumes.
 Apply the concepts of similarity, scale factors, and proportional reasoning to solve
indirect measurement problems.
How is length calculated?
Duck-DuckMathematics how is length calculated
Go
How is the perimeter of a shape calculated?
QWANT
Calculate the perimeter of a shape
How is area calculated?
PolyMeta
Mathematics calculate the area of a shape
How is surface area calculated?
Qrobe.it2
How do I calculate surface area
How would I calculate the volume?
Search.com
Calculate the volume of a 2d figure
4.3
4.4
2
Techniques of
indirect
measurement,
including
estimation and
proportional
reasoning
Properties and
construction of
figures and
How would I calculate the volume?
Search.com
Calculate the volume of a 2d figure
What are different techniques of indirect measurement?
Search.com
Indirect measurement
Resource:
http://www.eworkshop.on.ca/edu/resources/guides/Guide_Geometry_Spatial_Sense_456.
pdf
qrobe.it will proffer different search terms as you type.
CORE Mathematics 035 Blueprint
Standards
Page 12 of 16
Unpacking the Standards
shapes in two
and three
dimensions
Mamma
search
Reference properties construction figures shapes two three
dimensions


4.5
The use of
translations,
rotations,
reflections,
dilations, and
contractions in
relation to
similarity,
congruence, and
symmetries
Analyze properties of points, lines, planes and angles.
Use the properties of triangles, quadrilaterals, and other polygons and circles to
solve problems.
 Apply principles of similarity and congruence.
 Apply the Pythagorean Theorem and its converse.
 Use nets, cross sections, and projections to analyze three-dimensional figures.
 Analyze geometric arguments using
What is the concept of similarity?
infospace
What is the concept of similarity geometry
What is the concept of congruence?
infospace
What is the concept of congruence geometry
Where are practice problems involving similarity and congruence?
infospace
Practice problems similarity and congruence geometry
References
Yandex
Search
Virtual Nerd
Online math
learning
4.6
Coordinate and
transformation
geometry
Mamma
search
translation rotation reflection dilation contraction similarity
congruence symmetries
http://www.virtualnerd.com/common-core/grade-8/8_Ggeometry/A/3
http://www.onlinemathlearning.com/transformationcoordinates-8g3.html
Coordinate and transformation geometry


4.7
4.8
Conic sections
and their
applications
Modeling and
solving
problems using
geometric
concepts
Analyze two- and three-dimensional figures using coordinate systems.
Connect algebra and geometry by applying concepts of distance, midpoint, and
slope to classify figures and solve problems in the coordinate plane.
 Analyze transformations of figures in the coordinate plane.
 Analyze figures in terms of symmetry, and tessellations of the plane.
What is a conic section?
Google
Conic sections and their applications
How do I solve word problems involving conic sections?
Mamma
Word problems conic sections
search
Where are sample problems involving modeling and solving using geometric concepts?
Dogpile
Sample problems using geometric concepts
CORE Mathematics 035 Blueprint
Standards
Unpacking the Standards
4.9
What is an axiomatic structure of Euclidean geometry?
Google
Axiomatic structure of Euclidean geometry
4.10
Axiomatic
structures of
Euclidean and
non-Euclidean
geometries
Logical
reasoning,
justification and
proof in relation
to the axiomatic
structure of
geometry
Page 13 of 16
What is an axiomatic structure of non-Euclidean geometry?
Google
Axiomatic structure of non-Euclidean geometry
Google
search
Logical reasoning axiomatic structure geometry
Google
search
Logical reasoning axiomatic structure geometry
Standard 5: Statistics and Probability
When looking at the results of any Duck Duck Go searches, keep in mind that you can view relevant images and videos
by clicking on the Images and Video link at the top of the page as highlighted below:
Standards
Unpacking the Standards
Standard 5: Mathematics teachers have a broad and comprehensive understanding of the collection, presentation,
and interpretation and misinterpretations of data, and of the fundamental principles of probability, including:
5.1 Summarizing,
How do I read and interpret data?
representing, and
Khan Academy Reading and interpreting data
interpreting data
search
for one or two
variables
How do I represent data with two variables?
Google
Represent data two variables statistics
search
How do I summarize data with two variables?
Google
Summarize data two variables statistics
search
CORE Mathematics 035 Blueprint
Standards
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
Page 14 of 16
Unpacking the Standards
Making inferences
and evaluating
claims based on
data
Variability and
randomization in
data
How do I make inferences and evaluate claims?
Dogpile
Inferences evaluating claims statistics
search
Duck Duck Go
search


Variability in statistics
Randomization in statistics
Lines of best fit
Sampling, bias, and
misrepresentations
in data
Probabilities of
simple and
compound events
Calculation and
application of
expected values
Estimation of
probabilities by
observation and
use of simulations
Representations of
probabilities
5.10 Modeling and
solving problems
with normal,
uniform, and
binomial
probability
distributions
Duck Duck Go
Search
Lines of best fit
Duck Duck Go
Search
Sampling Bias Misrepresentation
Duck Duck Go
search
Probability simple and compound events
Duck Duck Go
Search
Calculation and application of expected value in statistics


Duck Duck Go
Search
Estimation of probability by observation
Estimation of probability by simulation
Duck Duck Go
Search
Representation of probabilities
Duck Duck Go
Search



Modeling and solving normal distribution
Modeling and solving uniform distribution
Modeling and solving binomial probability distribution
Standard 6: Calculus
Standards
Unpacking the Standards
Standard 6: Mathematics teachers have a broad and comprehensive understanding of the principles, techniques,
and applications of differential and integral calculus, including:
6.1
Limits,
What are limits in calculus?
continuity, and
Yandex
Calculus limits
the graphs of
search
functions
What is continuity in calculus?
Mamma
Calculus continuity
search
CORE Mathematics 035 Blueprint
Standards
6.2
Concept and
definition of the
derivative and
the second
derivative
Page 15 of 16
Unpacking the Standards
How would you graph limits and/or continuity on a graph?
Webcrawler Graph limits continuity calculus
search
What is a derivative?
Instagrok
Derivative
search
What is the first derivative used to calculate?
Mamma
Calculus first derivative
search
What is the second derivative used to calculate?
Dogpile
Calculus second derivative
search
What is the third derivative used to calculate?
Search.com
Problem solving with different representations of numbers
search
6.3
6.4
6.5
Techniques and
applications of
differentiation
Interpretation
and properties
of the definite
integral
Fundamental
theorem of
calculus
6.6
Techniques and
applications of
differentiation
6.7
Numerical
approximations
of definite
integrals
6.8
Infinite
sequences and
series
Google
search
Techniques and applications of differentiation
Google
search
Interpretations and properties of definite integrals
What is the fundamental theorem of calculus?
Instagrok
Fundamental theorem of calculus
search
How is the fundamental theorem of calculus used to solve problems?
Google
How is the fundamental theorem of calculus used to solve
search
problems
What are different techniques that can be used with/for differentiation?
How is differentiation used to solve problems?
Google
Techniques and applications of differentiation
search
What are definite integrals?
Instagrok
Definite integrals
search
How would you make a numerical approximations of definite integrals?
Search.com
Numerical approximations of definite integrals
search
What are infinite sequences and series?
Dogpile
Infinite sequences and series
search
CORE Mathematics 035 Blueprint
Standards
Unpacking the Standards
6.9
What are the properties of vector functions?
QWANT
Properties of vector functions
search
Properties of
vector functions
Page 16 of 16