scope and sequence grades 6–12 - pearson...

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


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


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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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


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


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


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


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


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


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


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


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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