scope and sequence grades 6–12 - pearson...
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Scope and Sequence Grades 6–12
Scope and Sequencefor Prentice Hall Mathematics
Prentice Hall MathematicsProven Results. Accessible Approach.
Our scope and sequence across Grades 6–12 is carefully developed to guarantee full coverage of important concepts and skills with no gaps to impede understanding.
The curriculum outlined here reflects a sound instructional design based on scientific mathematicsresearch and years of leadership in publishing mathematics materials.
Pre-K–8 Version Also Available
See PHSchool.com/math to obtain the Pre-K–8 Scope and Sequence.
Course 1
Chapter 1
Whole Numbers and Decimals
Chapter 2
Data and Graphs
Chapter 3
Patterns and Variables
Chapter 4
Number Theory and Fractions
Chapter 5
Adding and SubtractingFractions
Chapter 6
Multiplying and DividingFractions
Chapter 7
Ratios, Proportions, andPercents
Chapter 8
Tools of Geometry
Chapter 9
Geometry and Measurement
Chapter 10
Exploring Probability
Chapter 11
Integers
Chapter 12
Equations and Inequalities
Course 2
Chapter 1
Decimals and Integers
Chapter 2
Exponents, Factors, and Fractions
Chapter 3
Operations With Fractions
Chapter 4
Equations and Inequalities
Chapter 5
Ratios, Rates, and Proportions
Chapter 6
Percents
Chapter 7
Geometry
Chapter 8
Measurement
Chapter 9
Algebra: Patterns and Rules
Chapter 10
Graphing in the CoordinatePlane
Chapter 11
Displaying and Analyzing Data
Chapter 12
Using Probability
Course 3
Chapter 1
Integers and AlgebraicExpressions
Chapter 2
Rational Numbers
Chapter 3
Real Numbers and the Coordinate Plane
Chapter 4
Applications of Proportions
Chapter 5
Applications of Percent
Chapter 6
Equations and Inequalities
Chapter 7
Geometry
Chapter 8
Measurement
Chapter 9
Using Graphs to Analyze Data
Chapter 10
Probability
Chapter 11
Algebra: Functions
Chapter 12
Polynomials and Properties of Exponents
Pre-Algebra
Chapter 1Algebraic Expressions andIntegers
Chapter 2Solving One-Step Equationsand Inequalities
Chapter 3Decimals and Equations
Chapter 4Factors, Fractions, andExponents
Chapter 5Operations With Fractions
Chapter 6Ratios, Proportions, andPercents
Chapter 7Solving Equations andInequalities
Chapter 8Linear Functions and Graphing
Chapter 9Spatial Thinking
Chapter 10Area and Volume
Chapter 11Right Triangles in Algebra
Chapter 12Data Analysis and Probability
Chapter 13
Nonlinear Functions andPolynomials
Prentice Hall Mathematics Chapter Contents, Grades 6–12
2
Algebra 1
Chapter 1Variables, Function Patterns, and Graphs
Chapter 2Rational Numbers
Chapter 3Solving Equations
Chapter 4Solving Inequalities
Chapter 5Graphs and Functions
Chapter 6Linear Equations and Their Graphs
Chapter 7Systems of Equations and Inequalities
Chapter 8Exponents and Exponential Functions
Chapter 9Polynomials and Factoring
Chapter 10Quadratic Equations and Functions
Chapter 11Radical Expressions and Equations
Chapter 12Rational Expressions and Functions
Geometry
Chapter 1
Tools of Geometry
Chapter 2
Reasoning and Proof
Chapter 3
Parallel and Perpendicular Lines
Chapter 4
Congruent Triangles
Chapter 5
Relationships Within Triangles
Chapter 6
Quadrilaterals
Chapter 7
Similarity
Chapter 8
Right Triangles and Trigonometry
Chapter 9
Transformations
Chapter 10
Area
Chapter 11
Surface Area and Volume
Chapter 12
Circles
Algebra 2
Chapter 1
Tools of Algebra
Chapter 2
Functions, Equations, and Graphs
Chapter 3
Linear Systems
Chapter 4
Matrices
Chapter 5
Quadratic Equations and Functions
Chapter 6
Polynomials and Polynomial Functions
Chapter 7
Radical Functions and Rational Exponents
Chapter 8
Exponential and Logarithmic Functions
Chapter 9
Rational Functions
Chapter 10
Quadratic Relations
Chapter 11
Sequences and Series
Chapter 12
Probability and Statistics
Chapter 12
Periodic Functions and Trigonometry
Chapter 13
Trigonometric Identities and Equations
3
Prentice Hall Mathematics Curriculum Paths, Grades 6–12
4
Course 3 versus Pre-AlgebraIn choosing which text to use, refer to theTable of Contents on the previous page.Note that Prentice Hall Pre-Algebra featuresan increased focus on the algebra strandand provides a slower pace as studentswalk through the underlying skills needed
for success in algebra. Prentice HallMathematics: Course 3 also provides extensive coverage of the algebra strand but also balances this with more coverage of other strands such as measurement,geometry, and data analysis.
OPTIONS Grade 6 Grade 7 Grade 8
Option 1:
Basic
Prentice Hall Math Prentice Hall Math Prentice Hall MathCourse 1 Course 2 Course 3
Option 1:
Average
Prentice Hall Math Prentice Hall Math Prentice Hall MathCourse 1 Course 2 Course 3 or Pre-Algebra
Option 3:
Advanced
Prentice Hall Math Prentice Hall Math Prentice Hall MathCourse 1 Course 3 or Pre-Algebra Algebra 1
Algebra Over 2 Years Prentice Hall Algebra 1 canbe used for an Algebra 1 course taught over two years.Because the daily lessons are organized into parts withaccompanying assignments, teachers can easily slowthe pace to accommodate students who need moretime to acquire the Algebra 1 skills they need to contin-ue their study of mathematics. The Teacher’s Editionand Algebra 1A and 1B Lesson Plans feature a detailed pacing guide and other planning tools.
Basic Algebra The Basic Algebra Lesson Plans and Assessmentswhich accompanies Prentice Hall Algebra 1 allows teachers to use theregular text in classes that need special help and pacing with alternativecoverage of content. It also contains two alternative forms of assessmentfor each chapter.
Informal Geometry The Informal Geometry Lesson Plans andAssessments which accompanies Prentice Hall Geometry allows teach-ers to use the regular text in classes that are following a less rigorouscourse of study. Alternative pacing options and special help make thetext accessible to special needs students. It also contains two alternativeforms of assessment for each chapter.
5
Grade 9 Grade 10 Grade 11 Grade 12
Prentice Hall Math Prentice Hall Math Prentice Hall Math Prentice Hall Math Pre-Algebra Algebra 1 Geometry Algebra 2
Prentice Hall Math Prentice Hall Math Prentice Hall Math PrecalculusAlgebra 1 Geometry Algebra 2 Graphical, Numerical,
Algebraic
Prentice Hall Math Prentice Hall Math Precalculus: CalculusGeometry Algebra 2 Graphical, Numerical, Graphical, Numerical,
Algebraic Algebraic
Scope and Sequence
6
Level
● Introduce ● Develop ● Maintain and Apply
Number Properties and Operations
Number Sense CSE CSE CSE PRE- ALG GEO ALG1 2 3 ALG 1 2
Use place value to model numbers
whole numbers ● ● ● ●
decimals ● ● ● ●
Model rational numbers or numerical relationships
number line models ● ● ● ● ●
other models ● ● ● ● ●
Write or rename real numbers
read and write decimals ● ● ● ●
read and write integers ● ● ● ● ●
read and write rational numbers ● ● ● ● ●
irrational numbers ● ● ● ● ●
real numbers ● ● ● ● ●
Express multiple representations of rational numbers and translate between them
equivalent decimals ● ● ● ●
equivalent fractions ● ● ● ●
simplest form ● ● ● ●
mixed numbers and improper fractions ● ● ● ●
convert between fractions and decimals ● ● ● ●
Use scientific notation
scientific notation ● ● ● ● ● ● ●
Interpret calculator or computer displays in scientific notation ● ● ● ●
Find or model absolute value
absolute value ● ● ● ● ● ●
Compare and order numbers
whole numbers ● ● ● ●
decimals ● ● ● ●
fractions ● ● ● ● ●
integers ● ● ● ●●◗
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Level
Number Sense (cont’d)CSE CSE CSE PRE- ALG GEO ALG1 2 3 ALG 1 2
percents ● ● ● ● ● ●
rational numbers ● ● ●
irrational numbers ● ● ● ● ●
real numbers ● ● ● ●
Estimation
Establish Benchmarks
rational numbers ● ● ● ●
real numbers ● ● ● ●
Make appropriate estimates
rounding ● ● ● ●
clustering ● ● ● ●
compatible numbers ● ● ●
front-end ● ● ●
Determine reasonableness of results
determine reasonableness of answers ● ● ● ● ● ● ●
verify solutions ● ● ● ● ● ● ●
Estimate square and cube roots
square and square roots ● ● ● ● ● ●
cube roots ● ●
Number operations
Perform computation with rational or real numbers
add, subtract, multiply, and divide whole numbers ● ● ● ●
add and subtract decimals ● ● ● ●
multiply and divide decimals ● ● ● ●
add and subtract fractions, like denominators ● ● ● ● ●
add and subtract fractions, unlike denominators ● ● ● ● ●
add and subtract mixed numbers ● ● ● ● ●
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7
8
Level
Number operations (cont’d)CSE CSE CSE PRE- ALG GEO ALG1 2 3 ALG 1 2
multiply and divide fractions ● ● ● ● ●
multiply and divide mixed numbers ● ● ● ● ●
add and subtract integers ● ● ● ● ●
multiply and divide integers ● ● ● ● ●
use mental math ● ● ● ● ● ● ●
choose a computation method ● ● ● ● ● ● ●
Describe the effect of operations
check for reasonableness ● ● ● ● ● ● ●
Interpret rational number operations
add and subtract ● ● ● ●
multiply and divide ● ● ● ●
Solve application problems
solve problems using rational numbers ● ● ● ● ● ● ●
solve problems using real numbers ● ● ● ● ● ●
Ratios and proportional reasoning
Use ratios to describe problem situations
represent, read, and write ● ● ● ● ● ● ●
equal ratios ● ● ● ●
Use fractions to represent ratios and proportions
equivalent forms of ratios ● ● ● ●
trigonometric ratios ● ● ● ●
slope of a line ● ● ● ● ● ●
Use proportional reasoning
solve proportions ● ● ● ● ● ● ●
estimate solutions to proportions ● ● ● ● ● ●
reasoning with proportions ● ● ● ● ● ●
unit rate ● ● ● ● ●
unit price ● ● ● ●
distance, rate, time problems ● ● ● ● ● ●
scale drawings ● ● ● ● ● ● ●
similarity ● ● ● ● ● ●
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● Introduce ● Develop ● Maintain and Apply
9
Level
Ratios and proportional reasoning (cont’d)CSE CSE CSE PRE- ALG GEO ALG1 2 3 ALG 1 2
Solve problems involving percent
use percent models ● ● ● ● ●
write as ratio and decimal ● ● ● ● ●
greater than 100% ● ● ● ●
less than 1% ● ● ● ●
estimate ● ● ● ● ●
find using a proportion ● ● ● ●
find using an equation ● ● ● ●
find percent of a number ● ● ● ● ●
find percent one number is of another ● ● ●
find number when percent is known ● ● ●
percent change ● ● ●
application problems involving percent ● ● ● ● ● ●
Properties of number and operations
Describe odd and even integers
integers ● ● ● ● ●
Use factors, multiples, or prime factorization
factors ● ● ● ●
prime factorization ● ● ● ●
greatest common factor ● ● ● ●
multiples ● ● ● ●
least common multiple ● ● ● ●
factorials ● ● ● ● ●
Use prime and composite numbers
prime and composite numbers ● ● ● ● ●
Use divisibility or remainders
divisibility rules ● ● ● ●
remainders ● ● ● ●
Apply basic properties of operations
order of operations ● ● ● ● ● ● ●
positive exponents ● ● ● ● ● ● ●
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10
Level
● Introduce ● Develop ● Maintain and Apply
Properties of number and operations (cont’d)CSE CSE CSE PRE- ALG GEO ALG1 2 3 ALG 1 2
negative exponents ● ● ● ● ●
matrix operations ● ● ●
complex number operations
Explain a mathematical concept or relationship
verbalize and define concepts ● ● ● ● ● ● ●
Provide a mathematical argument
inductive reasoning ● ● ● ● ● ● ●
deductive reasoning ● ● ● ● ● ● ●
Measurement
Measuring physical attributes
Compare objects by attribute (length, area, volume, angle, weight, mass)
use customary units of length, area, volume, weight, capacity ● ● ● ●
use metric units of length, area, volume, mass, capacity ● ● ● ●
Estimate or compare size by attribute (area, perimeter, volume, or surface area)
estimate or compare lengths ● ● ● ●
estimate or compare areas ● ● ● ● ●
estimate surface areas and volumes ● ● ● ● ● ●
Solve problems involving the coordinate plane
distance formula ● ● ● ● ●
midpoints ● ● ● ● ●
slope ● ● ● ● ● ●
Solve problems of angle measure
angle relationships ● ● ● ● ● ● ●
radian measure
Use appropriate measurement instruments
compasses ● ● ● ● ●
protractors ● ● ● ● ●
rulers (metric and customary) ● ● ● ● ●
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11
Level
Measuring physical attributes (cont’d)CSE CSE CSE PRE- ALG GEO ALG1 2 3 ALG 1 2
Solve measurement problems
area of squares and rectangles ● ● ● ● ● ●
area of parallelograms ● ● ● ● ● ●
area of triangles ● ● ● ● ● ●
area of trapezoids ● ● ● ● ● ●
area of circles ● ● ● ● ● ●
area of composite figures ● ● ● ● ●
surface area of prisms ● ● ● ● ●
surface area of cylinders ● ● ● ● ● ●
volume of prisms ● ● ● ● ● ● ●
volume of cylinders ● ● ● ● ● ● ●
volume of cones and pyramids ● ● ● ●
volume of spheres ● ● ● ●
using indirect measurement ● ● ● ● ● ●
using trigonometric ratios ● ● ● ●
using rates ● ● ● ● ● ● ●
Use trigonometric relations in right triangles to solve problems
trigonometric ratios and right triangles ● ● ● ●
angle of elevation and depression ● ● ● ●
Systems of measurement
Select appropriate type of unit for a particular attribute
use length, area, volume, time, angle measure ● ● ● ● ● ●
Use conversion to solve problems
convert within customary system ● ● ● ● ● ●
convert within metric system ● ● ● ● ● ●
convert units of time ● ● ● ●
use dimensional analysis ● ● ● ● ●
Estimate measurement from one system to another
use conversion factors ● ● ● ●●◗
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12
Level
● Introduce ● Develop ● Maintain and Apply
Systems of Measurement (cont’d)CSE CSE CSE PRE- ALG GEO ALG1 2 3 ALG 1 2
Determine appropriate size of measurement units
choose appropriate units ● ● ● ●
Determine accuracy of measurement
precision ● ● ● ●
significant digits ● ● ● ●
Solve problems using scale drawings
scale drawings ● ● ● ● ● ●
Compare lengths, areas, or volumes of similar figures using proportions
similar polygons ● ● ● ● ●
similar space figures ● ● ●
fractals ●
Geometry
Dimension and shape
Describe/draw
line ● ● ● ●
line segment ● ● ● ●
points on a line ● ● ● ●
Identify geometric objects by description of its properties
identify polygons ● ● ● ● ●
classify quadrilaterals ● ● ● ● ●
classify triangles ● ● ● ● ●
classify angles ● ● ● ● ●
circles ● ● ● ● ●
solids ● ● ● ● ●
Identify, describe, or define geometric objects in a plane or space
visual representations ● ●
constructions ● ● ●
definitions ● ● ● ● ● ● ●
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13
Level
Dimension and Shape (cont’d)CSE CSE CSE PRE- ALG GEO ALG1 2 3 ALG 1 2
Draw figures from written description
polygons ● ● ● ● ●
circles, semicircles ● ● ● ● ●
similar triangles ● ● ● ●
space figures ● ● ● ●
Use two-dimensional representations of three-dimensional objects
nets for space figures ● ● ● ● ●
isometric drawings ● ● ● ●
perspective drawings ●
three-dimensional coordinate system
Describe or analyze properties of sphere and hemispheres
spheres and hemispheres ● ● ●
Demonstrate understanding of 2- and 3-dimension shapes in the real world
different viewpoints ● ● ● ● ● ●
Transformation of shapes and preservation of properties
Identify and classify types of symmetry
line (reflectional) symmetry ● ● ● ● ● ● ●
point (rotational) symmetry ● ● ● ● ●
Classify transformations as congruences or similarities
isometries (congruencies) ● ● ● ●
dilations ● ● ●
Recognize, perform, or describe the effect of transformations on 2- or 3-dimensional shapes
reflections across lines of symmetry ● ● ● ● ● ●
rotations ● ● ● ● ●
translations ● ● ● ● ● ●
dilations ● ●
Describe results of combining, subdividing, and changing shapes
plane figures ● ● ● ● ●
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14
Level
● Introduce ● Develop ● Maintain and Apply
Transformation of shapes and preservation CSE CSE CSE PRE- ALG GEO ALGof properties (cont’d) 1 2 3 ALG 1 2
Describe the outcome of successive transformations
transformations with coordinates ● ● ● ● ● ● ●
tessellations ● ● ● ● ●
composition of transformations ●
Justify and apply relationships of congruence and similarity
congruence ● ● ● ●
congruent polygons ● ● ● ●
similarity ● ● ● ● ●
similar polygons ● ● ● ● ●
Use relationships of proportionality and conservation of angle
congruent angles in similar figures ● ● ● ● ● ●
proportion in similar figures ● ● ● ● ●
Relationships between geometric figures
Use geometric properties and relationships to solve problems
draw a diagram ● ● ● ● ● ● ●
use a proportion ● ● ● ● ● ● ●
congruent angles ● ● ● ● ● ● ●
similar triangles ● ● ● ● ● ● ●
polygons ● ● ● ● ● ● ●
circles ● ● ● ● ● ● ●
space figures ● ● ● ● ● ●
Use geometric models to solve problems
use a model ● ● ● ● ● ● ●
Use the Pythagorean Theorem to solve problems
Pythagorean Theorem ● ● ● ● ● ● ●
Describe and analyze properties of circles
radius, diameter, center ● ● ● ● ●
arcs and angles ● ● ● ●
chords, tangents, secants ●●◗
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15
Level
Relationships between geometric figures (cont’d)CSE CSE CSE PRE- ALG GEO ALG1 2 3 ALG 1 2
Describe and analyze properties and relationships of polygonal plane figures
triangles ● ● ● ●
quadrilaterals ● ● ● ●
other polygons ● ● ● ●
Describe properties and relationships of lines
parallel lines ● ● ● ● ●
perpendicular lines ● ● ● ● ●
intersecting lines ● ● ● ● ● ●
lines with transversals ● ●
Position and direction
Describe relative positions of points and lines
midpoints ● ● ● ● ●
parallel and perpendicular ● ● ● ● ● ●
coordinate geometry ● ● ● ● ● ● ●
Describe intersections of figures in a plane or space
intersections of lines and planes ● ● ● ● ●
secants and tangents ●
coordinates in space
Describe or identify conic sections and other cross sections of solids
cross sections ● ●
conic sections
Represent figures in the coordinate plane or using equations
figures in the plane ● ● ● ● ● ●
equations for lines and planes ● ● ● ● ● ●
equations for quadratic curves ● ● ● ● ●
Use vectors to represent velocity and direction
use vectors
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16
Level
● Introduce ● Develop ● Maintain and Apply
Mathematical reasoning CSE CSE CSE PRE- ALG GEO ALG1 2 3 ALG 1 2
Make, test, and validate geometric conjectures
make and test conjectures ● ● ● ● ● ● ●
inductive reasoning ● ● ● ● ● ● ●
deductive reasoning ● ● ● ● ● ● ●
counterexamples ● ● ● ● ● ● ●
formal methods of proof ● ● ●
Data Analysis and Probability
Data representation
Read and interpret data
analyze and interpret data ● ● ● ● ● ● ●
Represent data set graphically and then solve a problem
decide how to present data ● ● ● ● ● ●
tables and charts ● ● ● ● ● ● ●
frequency tables ● ● ● ● ●
line plots ● ● ● ● ●
histograms ● ● ● ● ● ●
bar graphs ● ● ● ● ● ● ●
line graphs ● ● ● ● ● ● ●
circle graphs ● ● ● ● ● ● ●
stem-and-leaf plots ● ● ● ● ●
box-and-whisker plots ● ● ● ● ● ● ●
scatter plots ● ● ● ●
Use estimation and computation to solve problems from data sets
interpolation and extrapolation ● ● ● ● ● ●
Determine trends from data ● ● ● ●
Determine appropriateness and effectiveness of data representations
choose an appropriate graph or statistic ● ● ● ● ● ● ●
Compare and contrast different representations of same data
draw and compare different representations ● ● ● ● ● ● ●
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17
Level
Characteristics of data sets CSE CSE CSE PRE- ALG GEO ALG1 2 3 ALG 1 2
Calculate, use, or interpret mean, median, mode, range, interquartile and standard deviation
mean, median, and mode ● ● ● ● ● ● ●
range, interquartile range ● ● ● ● ● ●
standard deviation
analyze data ● ● ● ● ● ●
Identify outliers and determine their effect on particular statistics
outliers ● ● ● ● ● ●
Compare two or more data sets using appropriate statistical measures
identify misleading graphs and statistics ● ● ● ●
choose an appropriate graph or statistic ● ● ● ● ● ●
Select “best fit” line given a scatterplot and make predictions
trend lines ● ● ● ●
lines of best fit ● ●
Given a scatterplot, estimate the correlation coefficient
positive and negative correlation ● ● ● ●
correlation coefficient ● ●
Use or interpret a normal distribution
normal distributions
Experiments and samples
Identify sources of bias in sampling
analyze bias in surveys and data collection ● ● ● ●
Distinguish between random and non-random samples
analyze sampling techniques ● ● ● ● ●
Make inferences from sampling results
predict with sample proportions ● ● ● ● ● ●
margin of error
Evaluate design of a good survey or well designed experiment
plan and analyze a survey ● ● ● ● ● ●
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18
Level
● Introduce ● Develop ● Maintain and Apply
Probability CSE CSE CSE PRE- ALG GEO ALG1 2 3 ALG 1 2
Probability
independent events ● ● ● ● ●
dependent events ● ● ● ●
probability of complements ● ● ●
odds ● ● ● ● ●
Determine theoretical probability of simple and compound events
outcomes and events ● ● ● ● ● ● ●
sample space ● ● ● ●
Estimate probability of simple and compound events
estimate probability ● ● ● ● ● ● ●
simulations ● ● ● ● ●
Distinguish between experimental and theoretical probability
experimental probability ● ● ● ● ● ●
theoretical probability ● ● ● ● ● ● ●
Determine sample space or number of ways an event can occur for a given situation
tree diagram ● ● ● ● ●
counting principle ● ● ● ●
permutations ● ● ● ● ●
combinations ● ● ●
Use sample space to determine probability of possible outcomes
simple probability ● ● ● ● ●
compound probability ● ● ● ● ●
Represent probability using fractions, decimals, percents
use fractions, decimals, and percents ● ● ● ● ● ● ●
Determine probability of dependent and independent events
independent events ● ● ● ● ● ●
dependent events ● ● ● ● ●
Determine conditional probability using two-way tables
tree diagrams ● ● ● ● ●
two-way tables ●◗
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19
Level
Probability (cont’d)CSE CSE CSE PRE- ALG GEO ALG1 2 3 ALG 1 2
Interpret probability within a given context
conduct experiments and simulations ● ● ● ● ●
Algebra
Patterns, relations, and functions
Use, describe, extend numerical and geometric patterns and progressions
numerical patterns ● ● ● ● ● ●
geometric patterns ● ● ● ●
arithmetic sequences ● ● ● ●
geometric sequences ● ● ● ●
Express functions in general terms
function notation ● ● ● ●
tables ● ● ● ● ●
rules and equations ● ● ● ● ● ●
dependent and independent variables ● ● ● ● ●
Generalize pattern in a number sequence, table, or graph
look for and describe a pattern ● ● ● ● ● ●
words and graphs ● ● ● ● ● ●
Analyze or create patterns, sequences, or functions from a rule
input-output tables ● ● ● ● ● ●
graphs ● ● ● ●
Pascal’s triangle ● ●
Identify or analyze properties of functions
linear ● ● ● ● ● ● ●
quadratic ● ● ●
polynomial ● ●
radical ● ●
exponential ● ●
logarithmic
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20
Level
● Introduce ● Develop ● Maintain and Apply
Patterns, relations and functions (cont’d)CSE CSE CSE PRE- ALG GEO ALG1 2 3 ALG 1 2
rational ● ●
trigonometric
piecewise ●
Interpret meaning of slope or intercepts in linear functions
using slope ● ● ● ● ●
graphing and using intercepts ● ● ●
rate of change ● ● ● ●
Determine the domain and range of functions
domain and range ● ●
restrictions ●
Recognize and analyze the general forms of functions
families of functions ● ● ● ●
role of m and b in linear functions ● ● ● ● ●
role of coefficients in quadratic functions ● ●
role of constants in other functions ●
direct, inverse, joint variation ● ● ● ●
Express functions in recursive and explicit form
recursive formulas ● ● ● ● ●
explicit forms ●
Algebraic representations
Translate between different algebraic expressions
evaluate ● ● ● ● ● ● ●
graph ● ● ● ● ● ● ●
make a table ● ● ● ● ● ● ●
write an equation ● ● ● ● ● ● ●
describe ● ● ●
Analyze or interpret relationships
use linear relationships ● ● ● ● ● ● ●
use quadratic relationships ● ● ● ● ●
use other relationships ● ● ● ●
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21
Level
Algebraic representations (cont’d)CSE CSE CSE PRE- ALG GEO ALG1 2 3 ALG 1 2
Graph or interpret points represented by ordered pairs
ordered pairs ● ● ● ● ● ● ●
Solve problems in the coordinate system
graphing equations ● ● ● ● ● ● ●
graphing inequalities ● ● ●
Perform or interpret transformations of functions
linear functions ● ● ● ● ● ● ●
quadratic functions and relations ● ● ●
other functions ●
Make conclusions, generalizations, or valid arguments about relationships
linear relationships ● ● ● ● ● ● ●
other relationships ● ● ● ●
Use an algebraic model to make inferences or predictions
trend lines ● ● ● ●
lines or curves of best fit ●
Represent functional relationships in real-world contexts
proportional relationships (variation) ● ● ● ● ● ● ●
linear functions ● ● ● ● ● ● ●
quadratic functions ● ● ● ●
other functions ● ● ● ●
choosing among linear, quadratic,inverse, and exponential models ● ● ●
Solve problems involving growth and decay
exponential growth ● ● ●
exponential decay ● ● ●
Variables, expressions, and operations
Write algebraic expressions, equations, inequalities
write from word phrases ● ● ● ● ●
write from word sentences ● ● ● ● ●
write inequalities ● ● ● ● ●●◗
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22
Level
● Introduce ● Develop ● Maintain and Apply
Variables, expressions and operations (cont’d)CSE CSE CSE PRE- ALG GEO ALG1 2 3 ALG 1 2
Perform basic operations on algebraic expressions
evaluate ● ● ● ● ● ● ●
simplify ● ● ● ● ● ● ●
order of operations ● ● ● ● ● ●
factor ● ●
powers and roots ● ● ● ● ● ● ●
polynomial operations ● ● ●
rational expression operations
Write equivalent forms of algebraic expressions, equations, or inequalities
apply properties to expressions ● ● ● ● ● ● ●
apply properties to equations and inequalities ● ● ● ● ● ●
Equations and inequalities
Solve linear, rational, or quadratic equations or inequalities
solve one-step equations ● ● ● ●
solve two-step equations ● ● ● ● ● ● ●
solve systems of linear equations ● ● ●
solve one-step inequalities ● ● ● ● ● ●
solve two-step inequalities ● ● ●
solve absolute value equations ●
solve absolute value inequalities
solve rational equations ● ● ●
solve quadratic equations ●
solve logarithmic and trigonometric equations
Understand the concept of equivalence
properties of equations ● ● ● ● ● ●
properties of inequalities ● ● ● ● ● ●
Solve problems using linear or quadratic equations and inequalities
write from word sentences ● ● ● ● ● ●
use linear equations ● ● ● ● ● ●
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23
Level
Equations and inequalities (cont’d)CSE CSE CSE PRE- ALG GEO ALG1 2 3 ALG 1 2
use linear inequalities ● ● ● ● ●
use quadratic equations ●
Relate linear expressions and graphs of lines using slope, intercept
write and graph equations ● ● ● ● ●
Recognize the relationship between the solution of a system and its graph
linear systems ● ●
Use and evaluate formulas
geometric formulas ● ● ● ● ● ● ●
rate formulas ● ● ● ● ● ●
interest formulas ● ● ● ● ●
solve formulas for a given variable ● ● ● ● ● ●
Solve or interpret systems of equations or inequalities
systems of two linear equations ● ●
systems of three linear equations
Mathematical processes
Problem solving
Problem-solving skills
use a problem-solving plan ● ● ● ● ● ● ●
too much or too little information ● ● ● ● ● ● ●
use a proportion ● ● ● ● ● ● ●
use a calculator ● ● ● ● ● ● ●
use a computer ● ● ● ● ● ● ●
use estimation ● ● ● ● ● ● ●
use formulas ● ● ● ● ● ● ●
use graphs ● ● ● ● ● ● ●
Problem-solving strategies
choosing a strategy ● ● ● ● ● ● ●
draw a diagram ● ● ● ● ● ● ●
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24
Level
● Introduce ● Develop ● Maintain and Apply
Problem solving (cont’d)CSE CSE CSE PRE- ALG GEO ALG1 2 3 ALG 1 2
look for a pattern ● ● ● ● ● ● ●
make a graph ● ● ● ● ● ● ●
make an organized list ● ● ● ● ● ● ●
make a table ● ● ● ● ● ● ●
simulate a problem ● ● ● ● ● ● ●
solve a simpler problem ● ● ● ● ● ● ●
try, check, and revise ● ● ● ● ● ● ●
use logical reasoning ● ● ● ● ● ● ●
use multiple strategies ● ● ● ● ● ● ●
work backward ● ● ● ● ● ● ●
write an equation ● ● ● ● ● ● ●
Reasoning and proof
justify answers ● ● ● ● ● ● ●
make and test conjectures ● ● ● ● ● ● ●
make generalizations ● ● ● ● ● ● ●
reason from graphs ● ● ● ● ● ● ●
reason with proportions ● ● ● ● ● ● ●
recognize patterns ● ● ● ● ● ● ●
evaluate mathematical arguments ● ● ● ● ● ● ●
use or construct Venn diagrams ● ● ● ●
use deductive reasoning ● ● ● ● ● ● ●
paragraph proof
flow proof
two-column proof
indirect proof
Communication
interpret mathematical ideas through discussing, writing, reading ● ● ● ● ● ● ●
make convincing arguments using mathematical ideas ● ● ● ● ● ● ●
relate mathematical language to everyday language ● ● ● ● ● ● ●
analyze and evaluate mathematical thinking of others ● ● ● ● ● ● ●
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25
Level
Connections CSE CSE CSE PRE- ALG GEO ALG1 2 3 ALG 1 2
use connections among mathematical ideas ● ● ● ● ● ● ●
apply mathematics in contexts outside of mathematics ● ● ● ● ● ● ●
use technology ● ● ● ● ● ● ●
Representation
use representations to develop mathematical ideas ● ● ● ● ● ● ●
solve problems using pictures/diagrams ● ● ● ● ● ● ●
algebra tiles ● ● ● ●
decimal models ● ● ●
fraction models ● ● ● ●
number line models ● ● ● ● ●
two-color chips ●
factoring models ● ● ●
multiple representations of functions ● ● ● ●◗
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0-13-350164-7.3M.1106.AV.RF.RG
Grade 6 Grade 7 Grade 8
Pre-Algebra Algebra 1 Geometry Algebra 2