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