## 6th Grade Math

*Denotes new skill being taught for the first time.

A. Numeration (Meaning-Values-Relationships)

1. ________ * Identify and write scientific notation

2. ________ Know first 10 prime numbers

3. ________ Identify and describe the arithmetic characteristics of even and odd whole

numbers

4. ________ Compare and order whole numbers, fractions (with like and unlike

denominators), and decimals through millionths

5. ________ Read, write, and name whole numbers through trillions in:

· _____standard form

· _____expanded form

· _____numerical form

· _____word form

· *____exponential form

6. ________ Read, write, and identify the place values of decimals through billionths

7. ________ Understand the structure of Roman Numerals and their applications

8. ________ Round whole numbers expressed through trillions and decimals through

millionths

9. ________ Understand prime and composite numbers

10. _______ * Write numbers in scientific notation and write numbers expressed in

scientific notation in standard form

11. _______ * Identify ratios, write equivalent ratios, and compare two sets of data using

ratios

12. _______ * Express a fraction as a ratio of two numbers

13. _______ * Identify the terms of a proportion

14. _______ * Express proportions in terms of equivalent fractions

15. _______ Identify reciprocals/multiplicative inverses and understand their uses

16. _______ * Express whole numbers, decimals, and fractions as percentages

17. _______ * Introduce bases and exponents

18. _______ * Recognize the square of the first ten natural numbers

19. _______ Identify representations of percents and understand the relationships to their

decimal equivalents

20. _______ * Locate integers, their opposites, and their absolute value on a number line

21. _______ * Identify, compare, and order rational numbers

B. Computation (Operating with Numbers) Use of manipulatives is imperative.

1. ________ Divide whole numbers by 2- and 3-digit divisors to 4-digit quotients, with

and without remainders

2. ________ * Add three or more decimals through the ten thousandths place

3. ________ Multiply decimals to hundred thousandths and money amounts by decimals

and whole numbers

4. ________ Divide decimals to millionths and money amounts by whole numbers,

tenths, hundredths, and thousandths

5. ________ Calculate mentally in multiples of tens, hundreds, and thousands

6. ________ *Apply the concept of prime and composite to find the prime factorization

of a number

7. ________ *Add, subtract, multiply, and divide integers

8. ________ Apply order of operations to integer computation

9. ________ Compute and use the LCD, LCM, and GCF

10. _______* Rename fractions and mixed numbers as decimals and decimals as

fractions and mixed numbers

11. _______ Add, subtract, multiply, and divide fractions and mixed numbers, with like

and unlike denominators, by whole numbers, decimals, fractions, and

mixed numbers

12. _______ Multiply and divide money amounts by fractions

13. _______ * Write and use equivalent ratios and rates

14. _______ * Compute unit rate or unit price

15. _______ Use proportions to solve problems and a formula to solve proportions

16. _______ * Find the percentage, base, and rate of a number

17. _______ * Compute discount, sales price, sales tax, commission, and “Better Buy”

18. _______ * Use a number line to compare fractions, decimals, and percents

C. Communication

1. ________ Read, interpret, and create graphs, tables, charts, and maps

2. ________ Use appropriate mathematical vocabulary

3. ________ Explain verbally and in writing the strategy, process, and solution

4. ________ Use word processing software to:

· formulate original word problems

· enter journal responses to mathematical inquiries

· create geometric drawings

· type math symbols

· create data tables

5. ________ Use spreadsheet software to:

· calculate

· create graphs

· use formulas

6. ________ Use presentation software to:

· prepare reports

· illustrate concepts

· create practice reviews and assessments

D. Estimation

1. ________ Apply clustering, use compatible numbers, and reference benchmarks as

aids in estimating

2. ________ Round whole numbers, decimals, and fractions to any place value

3. ________ Estimate:

· _____whole numbers

· _____decimals

· _____fractions

· _____measurements

· _____percentage

· _____perimeter

· _____area

· _____circumference

· _____volume

E. Measurement

1. ________ Review and apply customary, metric, and nonstandard units

2. ________ Convert between and among customary, metric, and nonstandard units

3. ________ Calculate lapsed time

F. Geometry

1. ________ Identify parallel and perpendicular lines

2. ________ Apply the concept of proportion in creating scale drawings

3. ________ * Recognize and create tessellations

4. ________ Identify, classify, measure, and draw:

· _____segments/lines

· _____angles

· _____triangles

· _____quadrilaterals

· _____rhombus

· _____trapezoid

· _____circles

· *____solid figures

5. ________ Compute a missing dimension using a formula

6. ________ *Understand the relationship of sides to the size of the angles in a polygon

7. ________ Find the circumference, area, perimeter, volume, and surface area of

geometric figures

8. ________ Distinguish between congruent and similar, regular and irregular figures

9. ________ Recognize and apply formulas for geometric figures in appropriate situation

situations

G. Algebra

1. ________ * Identify, order, graph, add, subtract, multiply, and compare integers

2. ________ * Use inverse operations to solve equations

3. ________ * Understand the concept of and use variables

4. ________ Recognize and use properties of addition and multiplication (associative,

commutative, identity, zero, and distributive)

5. ________ Apply the correct order of operations

6. ________ Transform simple formulas

7. ________ Translate English phrases and sentences into mathematical expressions and

equations and evaluate / solve

8. ________ Simplify algebraic expressions

9. ________ Use the coordinate plane to graph ordered pairs in four quadrants

H. Patterns

1. ________ Identify, create, and use number sequences found by patterns

2. ________ Form patterns:

· _____ algebraic

· _____ with decimals

· _____ percent

· _____ with fractions

· _____ geometric (tessalations)

· *____ with integers

3. ________ Identify patterns in real world

I. Reasoning / Logic (Justification of answers and process)

1. ________ Justify solutions and explain verbally

2. ________ Predict outcomes, evaluate evidence, and verify solutions

J. Probability / Statistics / Data Analysis

1. ________ Collect, organize, construct, and interpret data represented on:

· surveys

· frequency tables

· line plots

· box-and-whisker plots

· stem-and-leaf plots

· line and double line graphs

· double bar graphs

· histograms

· circle graphs

· scatter diagrams

· tree diagram

2. ________ *Analyze graphs and statistics to determine misleading information

3. ________ Determine and interpret measures of central tendency (mean, median, and

mode) and the range of a set of data

4. ________ *Calculate the probability of an event and find the possible outcomes

5. ________ *Distinguish between independent and dependent events

6. ________ *Find permutations or combinations using the Counting Principle

7. ________ *Use theoretical and experimental probability

Math Pre Algebra

B. Computation (Operating with Numbers) Use of manipulatives is imperative.

1. ________ * Use matrices to organize and evaluate data

2. ________ Use proportions/equations to represent and solve percentage problems

3. ________ Compute using scientific notation

4. ________ Compute with whole numbers, integers, decimals, and simple and complex

fractions

5. ________ Apply order of operations to simplify expressions with and without

exponents

6. ________ *Compute using perfect square and cubic numbers and roots

7. ________ Convert between and among fractions, decimals, and percents

8. ________ Apply the Laws of Exponents

9. ________ Convert repeating decimals into fractions and percents

C. Communication

1. ________ Read, interpret, construct, and present graphs, tables, charts, and maps from

data in all subjects

2. ________ Use appropriate mathematical vocabulary

3. ________ Explain verbally, pictorially, in writing, and graphically the strategy,

process, and solution of mathematical ideas

4. ________ Use word processing software to:

· formulate original word problems

· enter journal responses to mathematical inquiries

· create geometric drawings

· type math symbols

· create data tables

5. ________ Use spreadsheet software to:

· calculate

· create graphs

· use formulas

6. ________ Use presentation software to:

· prepare reports

· illustrate concepts

· create practice reviews and assessments

D. Estimation

1. ________ Round whole numbers, decimals, fractions, and percents to any place value

2. ________ Estimate conversions between and among standard and metric units

3. ________ * Round irrational numbers

E. Measurement

1. ________ Use standard and metric systems of measurement to determine:

· _____ weight/mass

· _____ liquid volume/capacity

· _____ length

2008 Mathematics Curriculum Pre-Algebra

Diocese of Richmond

· _____ area

· _____ temperature

2. ________ Solve measurement problems requiring standard and metric system

conversions and select units of appropriate size and type (memorization of

conversion factors not required) Ex: feet to miles, milliliters to liters, yards

to meters, Fahrenheit to Celsius

F. Geometry

1. ________ Develop and apply perimeter, area, circumference, surface-area, and volume

formulas for polygons, spheres, pyramids, and other three-dimensional

figures

2. ________ Use proportions to solve problems, including scale drawings, with decimals,

fractions, and radicals

3. ________ Investigate rotations, reflections, translations, and dilations of two and threedimensional

figures

4. ________ Identify, compare, contrast, describe, and classify angles and polygons

5. ________ Develop solid figure constructions

6. ________ Use proportions to represent and evaluate relationships between similar

geometric figures

7. ________ *Apply the Pythagorean Theorem to right triangles with a missing dimension

8. ________ Define, recognize, and use similarity and congruence

9. ________*Describe and apply relationships created by two parallel lines cut by a

transversal

10. _______ Recognize and apply formulas for geometric figures in appropriate

situations

G. Algebra

1. ________ Identify, order, graph, add, subtract, multiply, and compare integers

2. ________ Use inverse operations to solve equations

3. ________ Solve multi-step linear equations and inequalities

4. ________ Recognize and use number properties (associative, commutative, identity,

zero, distributive, and closure)

5. ________ Solve proportional ratios with missing variables

6. ________ Transform and use formulas

7. ________ Translate English sentences into multi-step equations and inequalities and

solve; graph (when appropriate)

8. ________ Simplify algebraic expressions applying the correct order of operations and

given replacement values

9. ________ Use the coordinate plane to graph ordered pairs in four quadrants

10. _______ Understand the standard (general) and y-intercept form of a linear equation

11. _______ Recognize and utilize the slope and y-intercepts of a linear equation

12. _______ Use the slope and y-intercept to determine the graph of a line represented by

the equation

13. _______ Solve and graph linear inequalities on a coordinate plane

14. _______ Identify, calculate and graph ordered pairs of functions in a coordinate plane

2008 Mathematics Curriculum Pre-Algebra

Diocese of Richmond

15. _______ Model and solve linear equations; then graph on a coordinate plane

16. _______ Solve problems of various complexities which involve all types of rational

and real-life data

H. Patterns

1. ________ Create, describe, extend, and analyze numerical and geometric patterns

2. ________ Use patterns to represent and solve problems

3. ________ Use words and variables to generalize patterns

4. ________ Use calculators to investigate and develop exponential patterns (zero,

positive, and negative)

I. Reasoning / Logic (Justification of answers and process)

1. ________ Verify a solution is reasonable and explain its relationship to the original

problem

2. ________ Draw conclusions from concrete information/situations and justify

mathematical arguments through the use of mathematics

J. Probability / Statistics / Data Analysis

1. ________ Use information collected and displayed in the following to make

comparisons, predictions, and inferences:

· _____ lists

· _____charts

· _____ picture graphs

· _____ tree diagrams

· _____ frequency distributions

· _____ line bar

· _____ stem-and-leaf plots

· _____ box-and-whisker plots

· _____ scattergrams

· _____ histogram

· _____ circle graph

2. ________ Analyze graphs and statistics to determine misleading information

3. ________ Create and solve problems involving measures of central tendency (mean,

median, and mode) and the range of a set of data

4. ________ Calculate the probability of an event and explain the possible outcomes

5. ________ Recognize and apply probabilities in everyday situations

6. ________ Calculate the probability of an event and express outcome as a ratio,

decimal, and/or percent as appropriate to the situation

7. ________ Identify and describe permutations or combinations using the Counting

Principle or a tree diagram

8.________ Use theoretical and experimental probability representing everyday

situations and analyze grading scales, games of chance, and other real life

experiences

A. Numeration (Meaning-Values-Relationships)

1. ________ * Identify and write scientific notation

2. ________ Know first 10 prime numbers

3. ________ Identify and describe the arithmetic characteristics of even and odd whole

numbers

4. ________ Compare and order whole numbers, fractions (with like and unlike

denominators), and decimals through millionths

5. ________ Read, write, and name whole numbers through trillions in:

· _____standard form

· _____expanded form

· _____numerical form

· _____word form

· *____exponential form

6. ________ Read, write, and identify the place values of decimals through billionths

7. ________ Understand the structure of Roman Numerals and their applications

8. ________ Round whole numbers expressed through trillions and decimals through

millionths

9. ________ Understand prime and composite numbers

10. _______ * Write numbers in scientific notation and write numbers expressed in

scientific notation in standard form

11. _______ * Identify ratios, write equivalent ratios, and compare two sets of data using

ratios

12. _______ * Express a fraction as a ratio of two numbers

13. _______ * Identify the terms of a proportion

14. _______ * Express proportions in terms of equivalent fractions

15. _______ Identify reciprocals/multiplicative inverses and understand their uses

16. _______ * Express whole numbers, decimals, and fractions as percentages

17. _______ * Introduce bases and exponents

18. _______ * Recognize the square of the first ten natural numbers

19. _______ Identify representations of percents and understand the relationships to their

decimal equivalents

20. _______ * Locate integers, their opposites, and their absolute value on a number line

21. _______ * Identify, compare, and order rational numbers

B. Computation (Operating with Numbers) Use of manipulatives is imperative.

1. ________ Divide whole numbers by 2- and 3-digit divisors to 4-digit quotients, with

and without remainders

2. ________ * Add three or more decimals through the ten thousandths place

3. ________ Multiply decimals to hundred thousandths and money amounts by decimals

and whole numbers

4. ________ Divide decimals to millionths and money amounts by whole numbers,

tenths, hundredths, and thousandths

5. ________ Calculate mentally in multiples of tens, hundreds, and thousands

6. ________ *Apply the concept of prime and composite to find the prime factorization

of a number

7. ________ *Add, subtract, multiply, and divide integers

8. ________ Apply order of operations to integer computation

9. ________ Compute and use the LCD, LCM, and GCF

10. _______* Rename fractions and mixed numbers as decimals and decimals as

fractions and mixed numbers

11. _______ Add, subtract, multiply, and divide fractions and mixed numbers, with like

and unlike denominators, by whole numbers, decimals, fractions, and

mixed numbers

12. _______ Multiply and divide money amounts by fractions

13. _______ * Write and use equivalent ratios and rates

14. _______ * Compute unit rate or unit price

15. _______ Use proportions to solve problems and a formula to solve proportions

16. _______ * Find the percentage, base, and rate of a number

17. _______ * Compute discount, sales price, sales tax, commission, and “Better Buy”

18. _______ * Use a number line to compare fractions, decimals, and percents

C. Communication

1. ________ Read, interpret, and create graphs, tables, charts, and maps

2. ________ Use appropriate mathematical vocabulary

3. ________ Explain verbally and in writing the strategy, process, and solution

4. ________ Use word processing software to:

· formulate original word problems

· enter journal responses to mathematical inquiries

· create geometric drawings

· type math symbols

· create data tables

5. ________ Use spreadsheet software to:

· calculate

· create graphs

· use formulas

6. ________ Use presentation software to:

· prepare reports

· illustrate concepts

· create practice reviews and assessments

D. Estimation

1. ________ Apply clustering, use compatible numbers, and reference benchmarks as

aids in estimating

2. ________ Round whole numbers, decimals, and fractions to any place value

3. ________ Estimate:

· _____whole numbers

· _____decimals

· _____fractions

· _____measurements

· _____percentage

· _____perimeter

· _____area

· _____circumference

· _____volume

E. Measurement

1. ________ Review and apply customary, metric, and nonstandard units

2. ________ Convert between and among customary, metric, and nonstandard units

3. ________ Calculate lapsed time

F. Geometry

1. ________ Identify parallel and perpendicular lines

2. ________ Apply the concept of proportion in creating scale drawings

3. ________ * Recognize and create tessellations

4. ________ Identify, classify, measure, and draw:

· _____segments/lines

· _____angles

· _____triangles

· _____quadrilaterals

· _____rhombus

· _____trapezoid

· _____circles

· *____solid figures

5. ________ Compute a missing dimension using a formula

6. ________ *Understand the relationship of sides to the size of the angles in a polygon

7. ________ Find the circumference, area, perimeter, volume, and surface area of

geometric figures

8. ________ Distinguish between congruent and similar, regular and irregular figures

9. ________ Recognize and apply formulas for geometric figures in appropriate situation

situations

G. Algebra

1. ________ * Identify, order, graph, add, subtract, multiply, and compare integers

2. ________ * Use inverse operations to solve equations

3. ________ * Understand the concept of and use variables

4. ________ Recognize and use properties of addition and multiplication (associative,

commutative, identity, zero, and distributive)

5. ________ Apply the correct order of operations

6. ________ Transform simple formulas

7. ________ Translate English phrases and sentences into mathematical expressions and

equations and evaluate / solve

8. ________ Simplify algebraic expressions

9. ________ Use the coordinate plane to graph ordered pairs in four quadrants

H. Patterns

1. ________ Identify, create, and use number sequences found by patterns

2. ________ Form patterns:

· _____ algebraic

· _____ with decimals

· _____ percent

· _____ with fractions

· _____ geometric (tessalations)

· *____ with integers

3. ________ Identify patterns in real world

I. Reasoning / Logic (Justification of answers and process)

1. ________ Justify solutions and explain verbally

2. ________ Predict outcomes, evaluate evidence, and verify solutions

J. Probability / Statistics / Data Analysis

1. ________ Collect, organize, construct, and interpret data represented on:

· surveys

· frequency tables

· line plots

· box-and-whisker plots

· stem-and-leaf plots

· line and double line graphs

· double bar graphs

· histograms

· circle graphs

· scatter diagrams

· tree diagram

2. ________ *Analyze graphs and statistics to determine misleading information

3. ________ Determine and interpret measures of central tendency (mean, median, and

mode) and the range of a set of data

4. ________ *Calculate the probability of an event and find the possible outcomes

5. ________ *Distinguish between independent and dependent events

6. ________ *Find permutations or combinations using the Counting Principle

7. ________ *Use theoretical and experimental probability

Math Pre Algebra

B. Computation (Operating with Numbers) Use of manipulatives is imperative.

1. ________ * Use matrices to organize and evaluate data

2. ________ Use proportions/equations to represent and solve percentage problems

3. ________ Compute using scientific notation

4. ________ Compute with whole numbers, integers, decimals, and simple and complex

fractions

5. ________ Apply order of operations to simplify expressions with and without

exponents

6. ________ *Compute using perfect square and cubic numbers and roots

7. ________ Convert between and among fractions, decimals, and percents

8. ________ Apply the Laws of Exponents

9. ________ Convert repeating decimals into fractions and percents

C. Communication

1. ________ Read, interpret, construct, and present graphs, tables, charts, and maps from

data in all subjects

2. ________ Use appropriate mathematical vocabulary

3. ________ Explain verbally, pictorially, in writing, and graphically the strategy,

process, and solution of mathematical ideas

4. ________ Use word processing software to:

· formulate original word problems

· enter journal responses to mathematical inquiries

· create geometric drawings

· type math symbols

· create data tables

5. ________ Use spreadsheet software to:

· calculate

· create graphs

· use formulas

6. ________ Use presentation software to:

· prepare reports

· illustrate concepts

· create practice reviews and assessments

D. Estimation

1. ________ Round whole numbers, decimals, fractions, and percents to any place value

2. ________ Estimate conversions between and among standard and metric units

3. ________ * Round irrational numbers

E. Measurement

1. ________ Use standard and metric systems of measurement to determine:

· _____ weight/mass

· _____ liquid volume/capacity

· _____ length

2008 Mathematics Curriculum Pre-Algebra

Diocese of Richmond

· _____ area

· _____ temperature

2. ________ Solve measurement problems requiring standard and metric system

conversions and select units of appropriate size and type (memorization of

conversion factors not required) Ex: feet to miles, milliliters to liters, yards

to meters, Fahrenheit to Celsius

F. Geometry

1. ________ Develop and apply perimeter, area, circumference, surface-area, and volume

formulas for polygons, spheres, pyramids, and other three-dimensional

figures

2. ________ Use proportions to solve problems, including scale drawings, with decimals,

fractions, and radicals

3. ________ Investigate rotations, reflections, translations, and dilations of two and threedimensional

figures

4. ________ Identify, compare, contrast, describe, and classify angles and polygons

5. ________ Develop solid figure constructions

6. ________ Use proportions to represent and evaluate relationships between similar

geometric figures

7. ________ *Apply the Pythagorean Theorem to right triangles with a missing dimension

8. ________ Define, recognize, and use similarity and congruence

9. ________*Describe and apply relationships created by two parallel lines cut by a

transversal

10. _______ Recognize and apply formulas for geometric figures in appropriate

situations

G. Algebra

1. ________ Identify, order, graph, add, subtract, multiply, and compare integers

2. ________ Use inverse operations to solve equations

3. ________ Solve multi-step linear equations and inequalities

4. ________ Recognize and use number properties (associative, commutative, identity,

zero, distributive, and closure)

5. ________ Solve proportional ratios with missing variables

6. ________ Transform and use formulas

7. ________ Translate English sentences into multi-step equations and inequalities and

solve; graph (when appropriate)

8. ________ Simplify algebraic expressions applying the correct order of operations and

given replacement values

9. ________ Use the coordinate plane to graph ordered pairs in four quadrants

10. _______ Understand the standard (general) and y-intercept form of a linear equation

11. _______ Recognize and utilize the slope and y-intercepts of a linear equation

12. _______ Use the slope and y-intercept to determine the graph of a line represented by

the equation

13. _______ Solve and graph linear inequalities on a coordinate plane

14. _______ Identify, calculate and graph ordered pairs of functions in a coordinate plane

2008 Mathematics Curriculum Pre-Algebra

Diocese of Richmond

15. _______ Model and solve linear equations; then graph on a coordinate plane

16. _______ Solve problems of various complexities which involve all types of rational

and real-life data

H. Patterns

1. ________ Create, describe, extend, and analyze numerical and geometric patterns

2. ________ Use patterns to represent and solve problems

3. ________ Use words and variables to generalize patterns

4. ________ Use calculators to investigate and develop exponential patterns (zero,

positive, and negative)

I. Reasoning / Logic (Justification of answers and process)

1. ________ Verify a solution is reasonable and explain its relationship to the original

problem

2. ________ Draw conclusions from concrete information/situations and justify

mathematical arguments through the use of mathematics

J. Probability / Statistics / Data Analysis

1. ________ Use information collected and displayed in the following to make

comparisons, predictions, and inferences:

· _____ lists

· _____charts

· _____ picture graphs

· _____ tree diagrams

· _____ frequency distributions

· _____ line bar

· _____ stem-and-leaf plots

· _____ box-and-whisker plots

· _____ scattergrams

· _____ histogram

· _____ circle graph

2. ________ Analyze graphs and statistics to determine misleading information

3. ________ Create and solve problems involving measures of central tendency (mean,

median, and mode) and the range of a set of data

4. ________ Calculate the probability of an event and explain the possible outcomes

5. ________ Recognize and apply probabilities in everyday situations

6. ________ Calculate the probability of an event and express outcome as a ratio,

decimal, and/or percent as appropriate to the situation

7. ________ Identify and describe permutations or combinations using the Counting

Principle or a tree diagram

8.________ Use theoretical and experimental probability representing everyday

situations and analyze grading scales, games of chance, and other real life

experiences

## 2008 Mathematics Curriculum Algebra I

Diocese of Richmond

A. Working With Real Numbers

1. ________ Identify, distinguish among, compare, order, and use various subsets of the

real number system:

· _____natural numbers

· _____whole numbers

· _____integers

· _____rational numbers

· _____irrational numbers

· _____real numbers

2. ________ Graph real numbers on the number line

3. ________ Understand basic algebraic properties and use them efficiently to simplify

algebraic expressions:

· _____reflexive, symmetric, and transitive properties

· _____associative properties

· _____commutative properties

· _____closure properties

· _____identity properties

· _____property of reciprocals

· _____property of opposites

· _____property of opposites of a sum

· _____multiplicative and additive properties of equalities and

inequalities

4. ________ Apply the order of operations to simplify and evaluate expressions with and

without variables and grouping symbols involving:

· _____ fractions

· _____decimals

· _____negatives

· _____absolute value

· _____exponents

B. Solving Equations and Problems

1. ________Use appropriate algebraic vocabulary:

· _____equation

· _____solve

· _____like (similar) terms

· _____combine like terms

· _____replacement set

· _____solution set

2. ________ Translate verbal statements into algebraic expressions / equations and vice

versa

3. ________ Solve equations in one variable by applying real number properties

4. ________ Solve multiple variable equations for a specific variable (literal equations)

5. ________ Solve equations and problems with variables on both sides

6. ________ Solve real-life application problems including the following types:

· _____multi-step problems

· _____age problems (including those involving age now, age in the

past, and age in the future)

· _____percent problems

· _____consecutive integers / multiples

· _____rate-time-distance problems:

o _____motion in the same direction

o _____motion in opposite directions

o _____round trip problems

· _____area / perimeter / angle measures

· _____problems that do not have a solution

C. Polynomials

1. ________ Use appropriate algebraic vocabulary:

· _____monomial, binomial, trinomial, polynomial

· _____degree of a variable in a monomial

· _____degree of a monomial

· _____degree of a constant term

· _____degree of a polynomial

2. ________ Write a polynomial is ascending / descending order of a specified variable

3. ________ Add and subtract polynomials

4. ________ Multiply monomials using the rules of exponents to include:

· _____raising a power to a given power

· _____raising a product to a given power

5. ________Find products in the following ways:

· _____multiply a polynomial by a monomial

· _____multiply two binomials (using FOIL or similar method)

· _____multiply a polynomial by a binomial

D. Factoring Polynomials

1. ________ Find quotients and factors as follows:

· _____find the GCF of several integers

· _____simplify quotients of monomials

· _____divide polynomials by monomials

· _____find the monomial factor (GCF) of a polynomial

2. ________ Use factoring patterns as follows:

· _____difference of two perfect squares

· _____perfect square trinomials

· _____factor by grouping terms

· _____apply factoring patterns for x² + bx + c, where c is positive / negative

· _____apply factoring patterns for ax² + bx + c, where c is positive / negative

3. ________ Use factoring in solving polynomial equations

4. ________ Solve application problems by writing and factoring quadratic equations

E. Rational Expressions and Equations

1. ________ Simplify rational expressions

2. ________ Multiply rational expressions

3. ________ Divide rational expressions

4. ________ Add and subtract rational expressions with like denominators

5. ________ Add and subtract rational expressions with unlike denominators

6. ________ Solve equations involving rational expressions

7. ________ Evaluate exponential expressions containing negative and zero exponents

8. ________ Understand, interpret, and apply scientific notation

F. Applying Rational Expressions

1. ________ Solve problems involving ratio and proportion

2. ________ Solve equations with fractional coefficients and corresponding application

problems

3. ________ Work with percents and decimals

4. ________ Solve problems involving percents and decimals:

· _____percent of change

· _____mixture problems

G. Introduction to Functions

1. ________ Use appropriate algebraic vocabulary:

· _____relation

· _____function

· _____domain

· _____range

· _____coordinate plane

· _____horizontal axis

· _____vertical axis

· _____ordered pair

· _____origin

· _____quadrant

2. ________ Understand what a function is and define a function by using tables and

graphs

3. ________ Identify the domain and range of a function

H. Linear Equations

1. ________ Use appropriate algebraic vocabulary:

· _____linear equation

· _____slope

· _____x and y intercepts

· _____slope-intercept form of an equation

· _____standard / general form of an equation

2. ________ Identify a linear equation

3. ________ Differentiate between linear equations written in standard / general form and

those written in slope-intercept form

4. ________ Transform linear equations from one form to another

5. ________ Understand and use the slope-intercept method of graphing a linear equation

6. ________ Understand and use the x and y intercept method of graphing a linear equation

7. ________ Determine the slope of a line when given the graph of the line

8. ________ Determine the slope of a line algebraically using the slope formula when

given two points

9. ________ Determine the equation of a line when given:

· _____the slope and the y-intercept

· _____the slope and one point on the line

· _____two points on the line

10. ________ Determine the midpoint of a line segment

11. ________ Determine the distance between two points

I. Systems of Linear Equations

1. ________ Solve systems of linear equations in two variables by using:

· _____graphs

· _____linear combinations

· _____substitution method

2. ________ Understand that solution sets of systems of linear equations can result in:

· _____a single ordered pair (intersecting lines)

· _____the empty set (parallel lines)

· _____infinitely many ordered pairs (coincident lines)

3. ________ Understand the relationship between:

· _____parallel lines (same slope)

· _____perpendicular lines (slopes with negative reciprocals)

4. ________ Solve real-life application problems using systems of linear equations:

· _____wind and water current problems

· _____other types of applicable problems

J. Inequalities

1. ________ Solve and graph inequalities in one variable on a number line

2. ________ Solve and graph combined inequalities involving both “and” / “or” situations

3. ________ Solve and graph absolute value equations

4. ________ Solve and graph absolute value inequalities involving both “and” / “or”

situations

5. ________ Solve and graph linear inequalities in two variables

6. ________ Solve and graph systems of linear inequalities by graphing

K. Rational and Irrational Numbers

1. ________ Express rational numbers as decimals or fractions

2. ________ Find square roots of numbers that have rational square roots

3. ________ Master the first 20 squares, the first 6 cubes, and the first 3 fifths

4. ________ Simplify radicals

5. ________ Work with problems containing radical expressions in the following ways:

· _____simplify products and quotients of radicals

· _____simplify sums and differences of radicals

· _____multiply binomials containing square-root radicals

· _____rationalize binomial denominators

· _____solve radical equations

6. ________ Use the Pythagorean Theorem to solve geometric problems

L. Quadratic Functions

1. ________ Solve quadratic equations by finding square roots

2. ________ Solve quadratic equations by factoring and using the zero product property

3. ________ Solve quadratic equations by using the quadratic formula

4. ________ Solve application problems by writing and factoring quadratic equations

**2008 Mathematics Curriculum Geometry **

Diocese of Richmond

A. Basic Concepts

1. ________ Recognize the characteristics of points, lines, planes, segments, and rays

2. ________ Use the distance formula to measure distances on a line or a coordinate plane

3. ________ Know the basic classifications of angles

4. ________ Measure segments and angles

5. ________ Recognize the characteristics of vertical, complementary, supplementary, and

adjacent angles

6. ________ Use protractor to measure angles

7. ________ Use a ruler to measure line segments

8. ________ Use constructions to form geometric shapes with compass and straight edge

9. ________ Use a compass to measure relative lengths

10. ________ Observe a pattern, and then find a general rule based on the pattern

11. ________ Use models to develop conjecture

12. ________ Participate in cooperative learning

13. ________ Draw and label figures and diagrams

B. Reasoning and Proofs

1. ________ Identify the following different forms of a conditional statement:

• _____conditional

• _____hypothesis

• _____conclusion

• _____ if-then

• _____counterexample

• _____converse

• _____inverse

• _____contrapositive

2. ________ Recognize and use definitions and biconditional statements

3. ________ Use symbolic notation to represent the following logical statements:

• _____equivalent statements

• _____logical argument

• _____inductive and deductive reasoning

• _____Law of Syllogism and Detachment

4. ________ Use the following properties efficiently:

• _____properties of equality

• _____transitive, symmetric, and reflexive properties

• _____transitive, symmetric, and reflexive properties

• _____distributive property

• _____substitution

5. ________ Use proofs to justify statements about congruent segments

6. ________ Use angle congruence properties to prove properties about special pairs of

angles

7. ________ Use accurate definitions of all terms.

C. Perpendicular and Parallel Lines

1. ________ Identify relationship between lines and angles formed when parallel lines are

cut by a transversal

2. ________ Prove results involving the following:

• _____parallel lines

• _____perpendicular lines

• _____parallel lines cut by a transversal

3. ________ Construct parallel lines using a straightedge and compass

4. ________ Find slope, slope formula, and slope-intercept form of an equation

5. ________ Use slope to identify perpendicular lines in a coordinate plane

D. Polygons

1. ________ Classify polygons using angle measures

2. ________ Summarize the properties of polygons and parallelograms in correct order (for

example: use Venn Diagrams or charts illustrating points, lines, and planes)

3. ________ Identify congruent figures

4. ________ Prove triangles are congruent

5. ________ Find the sum of the interior and exterior angles of any polygon

6. ________ Identify and know when to use SSS, SAS, ASA, AAS and

postulates

E. Properties of Triangles

1. ________ Know the special properties of perpendicular bisectors

2. ________ Use the properties of perpendicular bisectors and angle bisectors in a triangle

3. ________ Use the properties of medians and altitudes in a triangle

4. ________ Identify the mid-segments of a triangle and know their properties

5. ________ Use greatest, least, and exterior angle inequality to determine which side is the

longest of shortest in a triangle

6. ________ Know the Hinge Theorem

F. Quadrilaterals

1. ________ Identify, name, and describe the different types of polygons

2. ________ Find the sum of the measures of the interior angles of a quadrilateral

3. ________ Know the special properties of parallelograms

4. ________ Prove that quadrilaterals are parallelograms

5. ________ Use properties of rhombuses, rectangles, and squares

6. ________ Use the properties of trapezoids and kites

7. ________ Prove that a quadrilateral is a rhombus or a trapezoid

8. ________ Recognize the difference between perimeter and area and find the areas of

different quadrilaterals

G. Transformations

1. ________ Identify transformations in a coordinate plane

2. ________ Identify relationships between reflections and line symmetry

3. ________ Identify rotations in a plane

4. ________ Identify and use translations in a plane

5. ________ Identify glide reflections

H. Similarity

1. ________ Simplify proportions and use them to solve various types of problems:

• _____ratios

• _____proportions

• _____means

• _____extremes

• _____cross-products

• _____reciprocals

2. ________ Solve geometric mean problems

3. ________ Use properties of proportions to identify similar figures

4. ________ Use SSS and SAS similarity theorems to prove that two triangles are similar

5. ________ Use proportionality theorems to calculate segment lengths

6. ________ Identify dilations

I. Special Right Triangles

1. ________ Solve problems involving similar right triangles and the geometric mean

2. ________ Use the Pythagorean Theorem to solve real-life problems

3. ________ Use side lengths to classify triangles by their angle measure

4. ________ Use the converse of the Pythagorean theorem to prove right triangles

5. ________ Find side lengths of special right triangles. (45-45-90 triangle and 30-60-90

triangle)

6. ________ Find trigonometric functions (If this is not completed in Geometry, this must

be done in the Trigonometry curriculum.)

7. ________ Use right triangles to solve real–life problems

8. ________ Find the magnitude and direction of a vector (Complete if time permits.)

9. ________ Add vectors (Complete if time permits.)

J. Circles

1. ________ Know the segments and lines related to a circle

2. ________ Use properties of a tangent to a circle

3. ________ Use properties of arcs in a circle

4. ________ Recognize properties of inscribed angles and know how to use them to solve

problems

5. ________ Use the angles formed by tangents and chords to solve problems

6. ________ Find the lengths of segments of chords, tangents, and secants

7. ________ Know how to write the equation of a circle and use the equation and its graph

to solve problems

8. ________ Draw the locus of points that satisfy a given condition or two or more

conditions (Complete if time permits.)

K. Area of Polygons and Circles

1. ________ Find the measure of interior and exterior angles in polygons and use these to

solve problems

2. ________ Find the area of an equilateral triangle and other regular polygons

3. ________ Recognize the relationship between perimeters and areas of similar figures

4. ________ Find the circumference of a circle and the length of a circular arc

5. ________ Find the area of circles and sectors of circles in order to solve real-life

problems

6. ________ Find a geometric probability (Complete if time permits.)

L. Quadratic Functions

1. ________ Solve quadratic equations by finding square roots

2. ________ Solve quadratic equations by factoring and using the zero product property

3. ________ Solve quadratic equations by using the quadratic formula

4. ________ Solve application problems by writing and factoring quadratic equations

Diocese of Richmond

A. Basic Concepts

1. ________ Recognize the characteristics of points, lines, planes, segments, and rays

2. ________ Use the distance formula to measure distances on a line or a coordinate plane

3. ________ Know the basic classifications of angles

4. ________ Measure segments and angles

5. ________ Recognize the characteristics of vertical, complementary, supplementary, and

adjacent angles

6. ________ Use protractor to measure angles

7. ________ Use a ruler to measure line segments

8. ________ Use constructions to form geometric shapes with compass and straight edge

9. ________ Use a compass to measure relative lengths

10. ________ Observe a pattern, and then find a general rule based on the pattern

11. ________ Use models to develop conjecture

12. ________ Participate in cooperative learning

13. ________ Draw and label figures and diagrams

B. Reasoning and Proofs

1. ________ Identify the following different forms of a conditional statement:

• _____conditional

• _____hypothesis

• _____conclusion

• _____ if-then

• _____counterexample

• _____converse

• _____inverse

• _____contrapositive

2. ________ Recognize and use definitions and biconditional statements

3. ________ Use symbolic notation to represent the following logical statements:

• _____equivalent statements

• _____logical argument

• _____inductive and deductive reasoning

• _____Law of Syllogism and Detachment

4. ________ Use the following properties efficiently:

• _____properties of equality

• _____transitive, symmetric, and reflexive properties

• _____transitive, symmetric, and reflexive properties

• _____distributive property

• _____substitution

5. ________ Use proofs to justify statements about congruent segments

6. ________ Use angle congruence properties to prove properties about special pairs of

angles

7. ________ Use accurate definitions of all terms.

C. Perpendicular and Parallel Lines

1. ________ Identify relationship between lines and angles formed when parallel lines are

cut by a transversal

2. ________ Prove results involving the following:

• _____parallel lines

• _____perpendicular lines

• _____parallel lines cut by a transversal

3. ________ Construct parallel lines using a straightedge and compass

4. ________ Find slope, slope formula, and slope-intercept form of an equation

5. ________ Use slope to identify perpendicular lines in a coordinate plane

D. Polygons

1. ________ Classify polygons using angle measures

2. ________ Summarize the properties of polygons and parallelograms in correct order (for

example: use Venn Diagrams or charts illustrating points, lines, and planes)

3. ________ Identify congruent figures

4. ________ Prove triangles are congruent

5. ________ Find the sum of the interior and exterior angles of any polygon

6. ________ Identify and know when to use SSS, SAS, ASA, AAS and

postulates

E. Properties of Triangles

1. ________ Know the special properties of perpendicular bisectors

2. ________ Use the properties of perpendicular bisectors and angle bisectors in a triangle

3. ________ Use the properties of medians and altitudes in a triangle

4. ________ Identify the mid-segments of a triangle and know their properties

5. ________ Use greatest, least, and exterior angle inequality to determine which side is the

longest of shortest in a triangle

6. ________ Know the Hinge Theorem

F. Quadrilaterals

1. ________ Identify, name, and describe the different types of polygons

2. ________ Find the sum of the measures of the interior angles of a quadrilateral

3. ________ Know the special properties of parallelograms

4. ________ Prove that quadrilaterals are parallelograms

5. ________ Use properties of rhombuses, rectangles, and squares

6. ________ Use the properties of trapezoids and kites

7. ________ Prove that a quadrilateral is a rhombus or a trapezoid

8. ________ Recognize the difference between perimeter and area and find the areas of

different quadrilaterals

G. Transformations

1. ________ Identify transformations in a coordinate plane

2. ________ Identify relationships between reflections and line symmetry

3. ________ Identify rotations in a plane

4. ________ Identify and use translations in a plane

5. ________ Identify glide reflections

H. Similarity

1. ________ Simplify proportions and use them to solve various types of problems:

• _____ratios

• _____proportions

• _____means

• _____extremes

• _____cross-products

• _____reciprocals

2. ________ Solve geometric mean problems

3. ________ Use properties of proportions to identify similar figures

4. ________ Use SSS and SAS similarity theorems to prove that two triangles are similar

5. ________ Use proportionality theorems to calculate segment lengths

6. ________ Identify dilations

I. Special Right Triangles

1. ________ Solve problems involving similar right triangles and the geometric mean

2. ________ Use the Pythagorean Theorem to solve real-life problems

3. ________ Use side lengths to classify triangles by their angle measure

4. ________ Use the converse of the Pythagorean theorem to prove right triangles

5. ________ Find side lengths of special right triangles. (45-45-90 triangle and 30-60-90

triangle)

6. ________ Find trigonometric functions (If this is not completed in Geometry, this must

be done in the Trigonometry curriculum.)

7. ________ Use right triangles to solve real–life problems

8. ________ Find the magnitude and direction of a vector (Complete if time permits.)

9. ________ Add vectors (Complete if time permits.)

J. Circles

1. ________ Know the segments and lines related to a circle

2. ________ Use properties of a tangent to a circle

3. ________ Use properties of arcs in a circle

4. ________ Recognize properties of inscribed angles and know how to use them to solve

problems

5. ________ Use the angles formed by tangents and chords to solve problems

6. ________ Find the lengths of segments of chords, tangents, and secants

7. ________ Know how to write the equation of a circle and use the equation and its graph

to solve problems

8. ________ Draw the locus of points that satisfy a given condition or two or more

conditions (Complete if time permits.)

K. Area of Polygons and Circles

1. ________ Find the measure of interior and exterior angles in polygons and use these to

solve problems

2. ________ Find the area of an equilateral triangle and other regular polygons

3. ________ Recognize the relationship between perimeters and areas of similar figures

4. ________ Find the circumference of a circle and the length of a circular arc

5. ________ Find the area of circles and sectors of circles in order to solve real-life

problems

6. ________ Find a geometric probability (Complete if time permits.)

L. Quadratic Functions

1. ________ Solve quadratic equations by finding square roots

2. ________ Solve quadratic equations by factoring and using the zero product property

3. ________ Solve quadratic equations by using the quadratic formula

4. ________ Solve application problems by writing and factoring quadratic equations