IXL Skill Plan | Texas Essential Knowledge and Skills (TEKS): Grade 6

Texas Essential Knowledge and Skills (TEKS): Grade 6

Skills available for Texas sixth-grade math standards

Strand

Mathematical process standards
Number and operations
Proportionality
Expressions, equations, and relationships
Measurement and data
Personal financial literacy

Print skill plan

1	Mathematical process standards
1 The student uses mathematical processes to acquire and demonstrate mathematical understanding.
A apply mathematics to problems arising in everyday life, society, and the workplace;		Number and operations 1. Understand fractions as division: word problems 2. Multiply and divide decimals: word problems 3. Multiply fractions: word problems 4. Multiply mixed numbers: word problems 5. Divide fractions and mixed numbers: word problems 6. Absolute value and integers: word problems 7. Add and subtract integers: word problems 8. Compare and order rational numbers: word problems 9. Compare temperatures above and below zero 10. Divide fractions: word problems Proportionality 11. Write a ratio: word problems 12. Calculate speed, distance, or time: word problems 13. Compare ratios: word problems 14. Compare rates: word problems 15. Ratios and rates: word problems 16. Scale drawings: word problems 17. Compare percents and fractions: word problems 18. Solve percent word problems 19. Unit prices 20. Unit prices with fractions and decimals 21. Unit prices with customary unit conversions Expressions, equations, and relationships 22. Solve one-step equations: word problems 23. One-step inequalities: word problems 24. Identify independent and dependent variables: word problems 25. Relationships between two variables: word problems 26. Area of quadrilaterals and triangles: word problems 27. Volume of cubes and rectangular prisms: word problems Measurement and data 28. Coordinate planes as maps 29. Interpret line plots 30. Interpret categorical data 31. Interpret histograms 32. Interpret circle graphs 33. Interpret stem-and-leaf plots 34. Box plots 35. Identify statistical questions 36. Interpret charts and graphs to find mean, median, mode, and range 37. Interpret median and interquartile range Personal financial literacy 38. Check registers 39. Occupations, education, and income
A apply mathematics to problems arising in everyday life, society, and the workplace;
Number and operations 1. Understand fractions as division: word problems 2. Multiply and divide decimals: word problems 3. Multiply fractions: word problems 4. Multiply mixed numbers: word problems 5. Divide fractions and mixed numbers: word problems 6. Absolute value and integers: word problems 7. Add and subtract integers: word problems 8. Compare and order rational numbers: word problems 9. Compare temperatures above and below zero 10. Divide fractions: word problems Proportionality 11. Write a ratio: word problems 12. Calculate speed, distance, or time: word problems 13. Compare ratios: word problems 14. Compare rates: word problems 15. Ratios and rates: word problems 16. Scale drawings: word problems 17. Compare percents and fractions: word problems 18. Solve percent word problems 19. Unit prices 20. Unit prices with fractions and decimals 21. Unit prices with customary unit conversions Expressions, equations, and relationships 22. Solve one-step equations: word problems 23. One-step inequalities: word problems 24. Identify independent and dependent variables: word problems 25. Relationships between two variables: word problems 26. Area of quadrilaterals and triangles: word problems 27. Volume of cubes and rectangular prisms: word problems Measurement and data 28. Coordinate planes as maps 29. Interpret line plots 30. Interpret categorical data 31. Interpret histograms 32. Interpret circle graphs 33. Interpret stem-and-leaf plots 34. Box plots 35. Identify statistical questions 36. Interpret charts and graphs to find mean, median, mode, and range 37. Interpret median and interquartile range Personal financial literacy 38. Check registers 39. Occupations, education, and income

B use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;		Number and operations 1. Scaling whole numbers by fractions: justify your answer 2. Divide fractions and mixed numbers using models: word problems 3. Add and subtract integers: word problems Proportionality 4. Solve percent problems using strip models 5. Unit prices with customary unit conversions Expressions, equations, and relationships 6. Identify mistakes involving the order of operations 7. Write equivalent expressions using properties 8. Write and solve equations that represent diagrams 9. Solve one-step equations: word problems 10. One-step inequalities: word problems Measurement and data 11. Changes in mean and median 12. Interpret median and interquartile range Personal financial literacy 13. Compare checking accounts
B use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;
Number and operations 1. Scaling whole numbers by fractions: justify your answer 2. Divide fractions and mixed numbers using models: word problems 3. Add and subtract integers: word problems Proportionality 4. Solve percent problems using strip models 5. Unit prices with customary unit conversions Expressions, equations, and relationships 6. Identify mistakes involving the order of operations 7. Write equivalent expressions using properties 8. Write and solve equations that represent diagrams 9. Solve one-step equations: word problems 10. One-step inequalities: word problems Measurement and data 11. Changes in mean and median 12. Interpret median and interquartile range Personal financial literacy 13. Compare checking accounts

C select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;		Number and operations 1. Multiply two fractions using models 2. Estimate products of mixed numbers 3. Divide fractions and mixed numbers using models 4. Put integers in order 5. Add integers using counters 6. Subtract integers using counters 7. Subtract integers using number lines 8. Add and subtract integers: find the sign 9. Multiply integers: find the sign 10. Divide integers: find the sign 11. Rational numbers on number lines 12. Benchmark percents with strip models: multiples of 10, 20, 25, 33, and 50 13. Represent fractions using strip diagrams 14. Add two negative integers using number lines 15. Add two integers with different signs using number lines Proportionality 16. Solve percent problems using grid models 17. Solve percent problems using strip models Expressions, equations, and relationships 18. Multiply using the distributive property: area models 19. Factor variable expressions: area models 20. Model and solve equations using algebra tiles 21. Model and solve equations using diagrams 22. Write and solve equations that represent diagrams 23. Understanding area of a parallelogram 24. Understanding area of a triangle 25. Understanding area of a trapezoid 26. Evaluate numerical expressions involving integers
C select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;
Number and operations 1. Multiply two fractions using models 2. Estimate products of mixed numbers 3. Divide fractions and mixed numbers using models 4. Put integers in order 5. Add integers using counters 6. Subtract integers using counters 7. Subtract integers using number lines 8. Add and subtract integers: find the sign 9. Multiply integers: find the sign 10. Divide integers: find the sign 11. Rational numbers on number lines 12. Benchmark percents with strip models: multiples of 10, 20, 25, 33, and 50 13. Represent fractions using strip diagrams 14. Add two negative integers using number lines 15. Add two integers with different signs using number lines Proportionality 16. Solve percent problems using grid models 17. Solve percent problems using strip models Expressions, equations, and relationships 18. Multiply using the distributive property: area models 19. Factor variable expressions: area models 20. Model and solve equations using algebra tiles 21. Model and solve equations using diagrams 22. Write and solve equations that represent diagrams 23. Understanding area of a parallelogram 24. Understanding area of a triangle 25. Understanding area of a trapezoid 26. Evaluate numerical expressions involving integers

D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;		Proportionality 1. Convert fractions to percents using grid models 2. Solve percent problems using grid models 3. Solve percent problems using strip models Expressions, equations, and relationships 4. Identify equivalent expressions using strip models 5. Write equivalent expressions using properties 6. Identify independent and dependent variables in tables and graphs 7. Identify independent and dependent variables: word problems 8. Understanding area of a parallelogram 9. Understanding area of a triangle 10. Understanding area of a trapezoid Measurement and data 11. Describe distributions in line plots 12. Interpret median and interquartile range
D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;
Proportionality 1. Convert fractions to percents using grid models 2. Solve percent problems using grid models 3. Solve percent problems using strip models Expressions, equations, and relationships 4. Identify equivalent expressions using strip models 5. Write equivalent expressions using properties 6. Identify independent and dependent variables in tables and graphs 7. Identify independent and dependent variables: word problems 8. Understanding area of a parallelogram 9. Understanding area of a triangle 10. Understanding area of a trapezoid Measurement and data 11. Describe distributions in line plots 12. Interpret median and interquartile range

E create and use representations to organize, record, and communicate mathematical ideas;		Number and operations 1. Understand fractions as division: word problems 2. Multiply fractions greater than one using models 3. Divide fractions and mixed numbers using models: word problems 4. Absolute value of integers on number lines 5. Add integers using counters 6. Subtract integers using counters 7. Subtract integers using number lines 8. Understand multiplying by a negative integer using a number line 9. Compare and order rational numbers using number lines 10. Classify rational numbers using a diagram 11. Add two negative integers using number lines 12. Add two integers with different signs using number lines Proportionality 13. Ratio tables 14. Ratios and rates: complete a table and make a graph 15. Represent percents with grid models, decimals, and fractions 16. Write an equation from a graph using a table Expressions, equations, and relationships 17. Write multiplication expressions using exponents 18. Prime factorization with exponents 19. Identify equivalent expressions using strip models 20. Multiply using the distributive property: area models 21. Factor variable expressions: area models 22. Write a one-step equation: word problems 23. Which word problem matches the one-step equation? 24. Relationships between two variables: word problems 25. Write a two-variable equation from a table 26. Complete a table and make a graph: word problems Measurement and data 27. Create line plots 28. Interpret line plots 29. Create and interpret line plots with fractions 30. Create frequency tables 31. Interpret categorical data 32. Create histograms 33. Interpret histograms 34. Interpret circle graphs 35. Create stem-and-leaf plots 36. Interpret stem-and-leaf plots 37. Box plots 38. Interpret charts and graphs to find mean, median, mode, and range Personal financial literacy 39. Check registers
E create and use representations to organize, record, and communicate mathematical ideas;
Number and operations 1. Understand fractions as division: word problems 2. Multiply fractions greater than one using models 3. Divide fractions and mixed numbers using models: word problems 4. Absolute value of integers on number lines 5. Add integers using counters 6. Subtract integers using counters 7. Subtract integers using number lines 8. Understand multiplying by a negative integer using a number line 9. Compare and order rational numbers using number lines 10. Classify rational numbers using a diagram 11. Add two negative integers using number lines 12. Add two integers with different signs using number lines Proportionality 13. Ratio tables 14. Ratios and rates: complete a table and make a graph 15. Represent percents with grid models, decimals, and fractions 16. Write an equation from a graph using a table Expressions, equations, and relationships 17. Write multiplication expressions using exponents 18. Prime factorization with exponents 19. Identify equivalent expressions using strip models 20. Multiply using the distributive property: area models 21. Factor variable expressions: area models 22. Write a one-step equation: word problems 23. Which word problem matches the one-step equation? 24. Relationships between two variables: word problems 25. Write a two-variable equation from a table 26. Complete a table and make a graph: word problems Measurement and data 27. Create line plots 28. Interpret line plots 29. Create and interpret line plots with fractions 30. Create frequency tables 31. Interpret categorical data 32. Create histograms 33. Interpret histograms 34. Interpret circle graphs 35. Create stem-and-leaf plots 36. Interpret stem-and-leaf plots 37. Box plots 38. Interpret charts and graphs to find mean, median, mode, and range Personal financial literacy 39. Check registers

F analyze mathematical relationships to connect and communicate mathematical ideas; and		Number and operations 1. Relate division and fractions 2. Convert fractions to decimals 3. Convert decimals to fractions 4. Scaling whole numbers by fractions: justify your answer 5. Understanding absolute value 6. Compare and order rational numbers: word problems Proportionality 7. Unit rates 8. Compare ratios: word problems 9. Compare rates: word problems 10. Ratios and rates: word problems 11. Represent percents with grid models, decimals, and fractions 12. Convert between percents, fractions, and decimals: word problems 13. Convert customary and metric units using proportions 14. Additive and multiplicative relationships Expressions, equations, and relationships 15. Identify equivalent expressions II 16. Write a one-step equation: word problems 17. Which word problem matches the one-step equation? 18. Write an equation from a graph using a table 19. Understanding area of a parallelogram 20. Understanding area of a triangle 21. Understanding area of a trapezoid Measurement and data 22. Coordinate planes as maps 23. Describe distributions in line plots 24. Interpret median and interquartile range
F analyze mathematical relationships to connect and communicate mathematical ideas; and
Number and operations 1. Relate division and fractions 2. Convert fractions to decimals 3. Convert decimals to fractions 4. Scaling whole numbers by fractions: justify your answer 5. Understanding absolute value 6. Compare and order rational numbers: word problems Proportionality 7. Unit rates 8. Compare ratios: word problems 9. Compare rates: word problems 10. Ratios and rates: word problems 11. Represent percents with grid models, decimals, and fractions 12. Convert between percents, fractions, and decimals: word problems 13. Convert customary and metric units using proportions 14. Additive and multiplicative relationships Expressions, equations, and relationships 15. Identify equivalent expressions II 16. Write a one-step equation: word problems 17. Which word problem matches the one-step equation? 18. Write an equation from a graph using a table 19. Understanding area of a parallelogram 20. Understanding area of a triangle 21. Understanding area of a trapezoid Measurement and data 22. Coordinate planes as maps 23. Describe distributions in line plots 24. Interpret median and interquartile range

G display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.		Number and operations 1. Scaling whole numbers by fractions: justify your answer 2. Add and subtract integers: word problems 3. Compare and order rational numbers: word problems Proportionality 4. Unit rates Expressions, equations, and relationships 5. Identify mistakes involving the order of operations 6. Write equivalent expressions using properties 7. Which word problem matches the one-step equation? 8. Identify independent and dependent variables in tables and graphs 9. Identify independent and dependent variables: word problems Measurement and data 10. Describe distributions in line plots 11. Interpret median and interquartile range
G display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Number and operations 1. Scaling whole numbers by fractions: justify your answer 2. Add and subtract integers: word problems 3. Compare and order rational numbers: word problems Proportionality 4. Unit rates Expressions, equations, and relationships 5. Identify mistakes involving the order of operations 6. Write equivalent expressions using properties 7. Which word problem matches the one-step equation? 8. Identify independent and dependent variables in tables and graphs 9. Identify independent and dependent variables: word problems Measurement and data 10. Describe distributions in line plots 11. Interpret median and interquartile range

2-3	Number and operations
2 The student applies mathematical process standards to represent and use rational numbers in a variety of forms.
A classify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers;		1. Classify rational numbers using a diagram 2. Classify numbers
A classify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers;
1. Classify rational numbers using a diagram 2. Classify numbers

B identify a number, its opposite, and its absolute value;		1. Understanding opposite integers 2. Understanding absolute value 3. Absolute value of integers on number lines 4. Absolute value 5. Absolute value and integers: word problems 6. Absolute value of rational numbers 7. Absolute values and opposites of rational numbers
B identify a number, its opposite, and its absolute value;
1. Understanding opposite integers 2. Understanding absolute value 3. Absolute value of integers on number lines 4. Absolute value 5. Absolute value and integers: word problems 6. Absolute value of rational numbers 7. Absolute values and opposites of rational numbers

C locate, compare, and order integers and rational numbers using a number line;		Rational numbers 1. Rational numbers on number lines 2. Compare and order rational numbers using number lines Integers 3. Integers on number lines 4. Graph integers on horizontal and vertical number lines 5. Compare integers 6. Put integers in order
C locate, compare, and order integers and rational numbers using a number line;
Rational numbers 1. Rational numbers on number lines 2. Compare and order rational numbers using number lines Integers 3. Integers on number lines 4. Graph integers on horizontal and vertical number lines 5. Compare integers 6. Put integers in order

D order a set of rational numbers arising from mathematical and real-world contexts; and		Positive rational numbers 1. Put a mix of decimals and fractions in order 2. Put a mix of decimals, fractions, and mixed numbers in order Integers 3. Put integers in order 4. Integer inequalities with absolute values Rational numbers 5. Rational numbers: equal or not equal 6. Compare rational numbers 7. Put rational numbers in order Real-world contexts 8. Compare and order rational numbers: word problems 9. Compare temperatures above and below zero
D order a set of rational numbers arising from mathematical and real-world contexts; and
Positive rational numbers 1. Put a mix of decimals and fractions in order 2. Put a mix of decimals, fractions, and mixed numbers in order Integers 3. Put integers in order 4. Integer inequalities with absolute values Rational numbers 5. Rational numbers: equal or not equal 6. Compare rational numbers 7. Put rational numbers in order Real-world contexts 8. Compare and order rational numbers: word problems 9. Compare temperatures above and below zero

E extend representations for division to include fraction notation such as a/b represents the same number as a ÷ b where b ≠ 0.		Representations for division 1. Relate division and fractions 2. Understand fractions as division: word problems 3. Write rational numbers in the form a/b Convert decimals and fractions 4. Convert between improper fractions and mixed numbers 5. Convert fractions to decimals 6. Convert decimals to fractions 7. Convert between fractions and repeating decimals 8. Convert between decimals and fractions 9. Convert between decimals and mixed numbers
E extend representations for division to include fraction notation such as a/b represents the same number as a ÷ b where b ≠ 0.
Representations for division 1. Relate division and fractions 2. Understand fractions as division: word problems 3. Write rational numbers in the form a/b Convert decimals and fractions 4. Convert between improper fractions and mixed numbers 5. Convert fractions to decimals 6. Convert decimals to fractions 7. Convert between fractions and repeating decimals 8. Convert between decimals and fractions 9. Convert between decimals and mixed numbers

Checkpoint opportunity		• Coming soon: Checkpoint: Classify and rewrite rational numbers • Coming soon: Checkpoint: Positive and negative numbers
Checkpoint opportunity
• Coming soon: Checkpoint: Classify and rewrite rational numbers • Coming soon: Checkpoint: Positive and negative numbers
3 The student applies mathematical process standards to represent addition, subtraction, multiplication, and division while solving problems and justifying solutions.
A recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values;		1. Reciprocals 2. Divide fractions using models 3. Divide fractions and mixed numbers using models
A recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values;
1. Reciprocals 2. Divide fractions using models 3. Divide fractions and mixed numbers using models

B determine, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, including values greater than or less than one;		1. Scaling whole numbers by fractions: justify your answer 2. Scaling by fractions and mixed numbers 3. Estimate products of mixed numbers
B determine, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, including values greater than or less than one;
1. Scaling whole numbers by fractions: justify your answer 2. Scaling by fractions and mixed numbers 3. Estimate products of mixed numbers

C represent integer operations with concrete models and connect the actions with the models to standardized algorithms;		1. Add integers using counters 2. Subtract integers using counters 3. Subtract integers using number lines 4. Understand multiplying by a negative integer using a number line 5. Add two negative integers using number lines 6. Add two integers with different signs using number lines
C represent integer operations with concrete models and connect the actions with the models to standardized algorithms;
1. Add integers using counters 2. Subtract integers using counters 3. Subtract integers using number lines 4. Understand multiplying by a negative integer using a number line 5. Add two negative integers using number lines 6. Add two integers with different signs using number lines

D add, subtract, multiply, and divide integers fluently; and		Add and subtract 1. Add integers 2. Subtract integers 3. Add and subtract integers: find the sign 4. Add and subtract integers: word problems 5. Add and subtract integers: input/output tables 6. Add three or more integers Multiply and divide 7. Multiply integers: find the sign 8. Multiply integers 9. Divide integers: find the sign 10. Divide integers Mixed operations 11. Add, subtract, multiply, or divide two integers
D add, subtract, multiply, and divide integers fluently; and
Add and subtract 1. Add integers 2. Subtract integers 3. Add and subtract integers: find the sign 4. Add and subtract integers: word problems 5. Add and subtract integers: input/output tables 6. Add three or more integers Multiply and divide 7. Multiply integers: find the sign 8. Multiply integers 9. Divide integers: find the sign 10. Divide integers Mixed operations 11. Add, subtract, multiply, or divide two integers

E multiply and divide positive rational numbers fluently.		Multiply and divide decimals 1. Multiply decimals 2. Divide decimals by whole numbers 3. Divide decimals by whole numbers: word problems 4. Multiply and divide decimals by powers of ten 5. Division with decimal divisors 6. Multiply and divide decimals: word problems 7. Divide decimals Multiply fractions and whole numbers 8. Multiply fractions and whole numbers 9. Multiply fractions by whole numbers: word problems Multiply fractions 10. Multiply two fractions using models 11. Multiply fractions greater than one using models 12. Multiply two fractions 13. Multiply fractions: word problems Multiply mixed numbers 14. Multiply mixed numbers 15. Multiply mixed numbers: word problems 16. Multiply three or more mixed numbers, fractions, and/or whole numbers Divide fractions and whole numbers 17. Divide whole numbers and fractions using models 18. Divide fractions by whole numbers in recipes Divide fractions 19. Divide fractions using models 20. Divide fractions 21. Divide fractions: word problems Divide fractions and mixed numbers 22. Divide fractions and mixed numbers using models 23. Divide fractions and mixed numbers 24. Divide fractions and mixed numbers using models: word problems 25. Divide fractions and mixed numbers: word problems
E multiply and divide positive rational numbers fluently.
Multiply and divide decimals 1. Multiply decimals 2. Divide decimals by whole numbers 3. Divide decimals by whole numbers: word problems 4. Multiply and divide decimals by powers of ten 5. Division with decimal divisors 6. Multiply and divide decimals: word problems 7. Divide decimals Multiply fractions and whole numbers 8. Multiply fractions and whole numbers 9. Multiply fractions by whole numbers: word problems Multiply fractions 10. Multiply two fractions using models 11. Multiply fractions greater than one using models 12. Multiply two fractions 13. Multiply fractions: word problems Multiply mixed numbers 14. Multiply mixed numbers 15. Multiply mixed numbers: word problems 16. Multiply three or more mixed numbers, fractions, and/or whole numbers Divide fractions and whole numbers 17. Divide whole numbers and fractions using models 18. Divide fractions by whole numbers in recipes Divide fractions 19. Divide fractions using models 20. Divide fractions 21. Divide fractions: word problems Divide fractions and mixed numbers 22. Divide fractions and mixed numbers using models 23. Divide fractions and mixed numbers 24. Divide fractions and mixed numbers using models: word problems 25. Divide fractions and mixed numbers: word problems

Checkpoint opportunity		1. Checkpoint: Multiply and divide fractions 2. Checkpoint: Multiply and divide decimals • Coming soon: Checkpoint: Integer operations
Checkpoint opportunity
1. Checkpoint: Multiply and divide fractions 2. Checkpoint: Multiply and divide decimals • Coming soon: Checkpoint: Integer operations

4-5	Proportionality
4 The student applies mathematical process standards to develop an understanding of proportional relationships in problem situations.
A compare two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x + a in order to differentiate between additive and multiplicative relationships;		1. Solve one-step equations: word problems 2. Write an equation from a graph using a table 3. Write a two-variable equation 4. Additive and multiplicative relationships
A compare two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x + a in order to differentiate between additive and multiplicative relationships;
1. Solve one-step equations: word problems 2. Write an equation from a graph using a table 3. Write a two-variable equation 4. Additive and multiplicative relationships

B apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates;		Equivalent ratios 1. Identify equivalent ratios 2. Write an equivalent ratio 3. Equivalent ratios: word problems Rates 4. Unit rates 5. Rates: word problems 6. Unit prices with fractions and decimals Comparison problems 7. Compare ratios: word problems 8. Compare rates: word problems 9. Compare percents and fractions: word problems Proportions 10. Do the ratios form a proportion? 11. Solve the proportion Ratios and rates 12. Calculate speed, distance, or time: word problems 13. Ratios and rates: word problems
B apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates;
Equivalent ratios 1. Identify equivalent ratios 2. Write an equivalent ratio 3. Equivalent ratios: word problems Rates 4. Unit rates 5. Rates: word problems 6. Unit prices with fractions and decimals Comparison problems 7. Compare ratios: word problems 8. Compare rates: word problems 9. Compare percents and fractions: word problems Proportions 10. Do the ratios form a proportion? 11. Solve the proportion Ratios and rates 12. Calculate speed, distance, or time: word problems 13. Ratios and rates: word problems

C give examples of ratios as multiplicative comparisons of two quantities describing the same attribute;		1. Write a ratio: word problems 2. Write an equivalent ratio 3. Ratio tables
C give examples of ratios as multiplicative comparisons of two quantities describing the same attribute;
1. Write a ratio: word problems 2. Write an equivalent ratio 3. Ratio tables

D give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients;		1. Unit rates 2. Unit prices 3. Unit prices with customary unit conversions
D give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients;
1. Unit rates 2. Unit prices 3. Unit prices with customary unit conversions

E represent ratios and percents with concrete models, fractions, and decimals;		Ratios 1. Write a ratio using a colon 2. Write a ratio using a fraction 3. Which model represents the ratio? Percents 4. What percentage is illustrated? 5. Represent percents with grid models, decimals, and fractions 6. Convert between percents, fractions, and decimals
E represent ratios and percents with concrete models, fractions, and decimals;
Ratios 1. Write a ratio using a colon 2. Write a ratio using a fraction 3. Which model represents the ratio? Percents 4. What percentage is illustrated? 5. Represent percents with grid models, decimals, and fractions 6. Convert between percents, fractions, and decimals

F represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers;		Fractions 1. Fractions on number lines 2. Represent fractions using strip diagrams Percents 3. What percentage is illustrated? 4. Benchmark percents with strip models: multiples of 10, 20, 25, 33, and 50 5. Graph percents on number lines Fractions and percents 6. Convert fractions to percents using grid models 7. Represent percents with grid models, decimals, and fractions
F represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers;
Fractions 1. Fractions on number lines 2. Represent fractions using strip diagrams Percents 3. What percentage is illustrated? 4. Benchmark percents with strip models: multiples of 10, 20, 25, 33, and 50 5. Graph percents on number lines Fractions and percents 6. Convert fractions to percents using grid models 7. Represent percents with grid models, decimals, and fractions

G generate equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money; and		1. Equivalent ratios: word problems 2. Convert between percents, fractions, and decimals: word problems 3. Fractions of a group: word problems
G generate equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money; and
1. Equivalent ratios: word problems 2. Convert between percents, fractions, and decimals: word problems 3. Fractions of a group: word problems

H convert units within a measurement system, including the use of proportions and unit rates.		Customary units 1. Convert and compare customary units 2. Convert, compare, add, and subtract mixed customary units 3. Customary unit conversions involving fractions and mixed numbers 4. Unit prices with customary unit conversions Metric units 5. Convert and compare metric units Customary and metric units 6. Convert customary and metric units using proportions 7. Convert metric and customary units using conversion factors
H convert units within a measurement system, including the use of proportions and unit rates.
Customary units 1. Convert and compare customary units 2. Convert, compare, add, and subtract mixed customary units 3. Customary unit conversions involving fractions and mixed numbers 4. Unit prices with customary unit conversions Metric units 5. Convert and compare metric units Customary and metric units 6. Convert customary and metric units using proportions 7. Convert metric and customary units using conversion factors
5 The student applies mathematical process standards to solve problems involving proportional relationships.
A represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions;		Ratios 1. Ratio tables Rates 2. Unit rates 3. Rates: word problems 4. Ratios and rates: word problems Proportions 5. Do the ratios form a proportion? Scale drawings 6. Scale drawings: word problems Graphs 7. Ratios and rates: complete a table and make a graph
A represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions;
Ratios 1. Ratio tables Rates 2. Unit rates 3. Rates: word problems 4. Ratios and rates: word problems Proportions 5. Do the ratios form a proportion? Scale drawings 6. Scale drawings: word problems Graphs 7. Ratios and rates: complete a table and make a graph

B solve real-world problems to find the whole given a part and the percent, to find the part given the whole and the percent, and to find the percent given the part and the whole, including the use of concrete and pictorial models; and		Find the whole 1. Find the total given a part and a percent Find the part 2. Percents of numbers and money amounts 3. Percents of numbers: word problems 4. Percents of numbers: fractional and decimal percents Find the percent 5. Find what percent one number is of another 6. Find what percent one number is of another: word problems Mixed percent problems 7. Solve percent problems using grid models 8. Solve percent problems using strip models 9. Solve percent problems 10. Solve percent word problems
B solve real-world problems to find the whole given a part and the percent, to find the part given the whole and the percent, and to find the percent given the part and the whole, including the use of concrete and pictorial models; and
Find the whole 1. Find the total given a part and a percent Find the part 2. Percents of numbers and money amounts 3. Percents of numbers: word problems 4. Percents of numbers: fractional and decimal percents Find the percent 5. Find what percent one number is of another 6. Find what percent one number is of another: word problems Mixed percent problems 7. Solve percent problems using grid models 8. Solve percent problems using strip models 9. Solve percent problems 10. Solve percent word problems

C use equivalent fractions, decimals, and percents to show equal parts of the same whole.		1. Represent percents with grid models, decimals, and fractions
C use equivalent fractions, decimals, and percents to show equal parts of the same whole.
1. Represent percents with grid models, decimals, and fractions

Checkpoint opportunity		1. Checkpoint: Ratio concepts 2. Checkpoint: Unit rates 3. Checkpoint: Percents
Checkpoint opportunity
1. Checkpoint: Ratio concepts 2. Checkpoint: Unit rates 3. Checkpoint: Percents

6-10	Expressions, equations, and relationships
6 The student applies mathematical process standards to use multiple representations to describe algebraic relationships.
A identify independent and dependent quantities from tables and graphs;		1. Identify independent and dependent variables in tables and graphs 2. Identify independent and dependent variables: word problems
A identify independent and dependent quantities from tables and graphs;
1. Identify independent and dependent variables in tables and graphs 2. Identify independent and dependent variables: word problems

B write an equation that represents the relationship between independent and dependent quantities from a table; and		1. Write a two-variable equation from a table
B write an equation that represents the relationship between independent and dependent quantities from a table; and
1. Write a two-variable equation from a table

C represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b.		Make a table 1. Complete a table for a two-variable relationship Make a graph 2. Identify the graph of an equation 3. Graph a relationship between two variables Write an equation 4. Write an equation from a graph using a table 5. Relationships between two variables: word problems 6. Write a two-variable equation Word problems 7. Complete a table and make a graph: word problems Tables and graphs 8. Identify independent and dependent variables in tables and graphs 9. Complete a table and graph a two-variable equation
C represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b.
Make a table 1. Complete a table for a two-variable relationship Make a graph 2. Identify the graph of an equation 3. Graph a relationship between two variables Write an equation 4. Write an equation from a graph using a table 5. Relationships between two variables: word problems 6. Write a two-variable equation Word problems 7. Complete a table and make a graph: word problems Tables and graphs 8. Identify independent and dependent variables in tables and graphs 9. Complete a table and graph a two-variable equation

Checkpoint opportunity		• Coming soon: Checkpoint: Two-variable relationships
Checkpoint opportunity
• Coming soon: Checkpoint: Two-variable relationships
7 The student applies mathematical process standards to develop concepts of expressions and equations.
A generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization;		Whole number exponents 1. Write multiplication expressions using exponents 2. Write powers of ten with exponents 3. Evaluate powers with integer, decimal, and fractional bases Prime factorization 4. Prime factorization 5. Prime factorization with exponents Order of operations 6. Evaluate numerical expressions involving whole numbers 7. Identify mistakes involving the order of operations 8. Evaluate numerical expressions involving integers
A generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization;
Whole number exponents 1. Write multiplication expressions using exponents 2. Write powers of ten with exponents 3. Evaluate powers with integer, decimal, and fractional bases Prime factorization 4. Prime factorization 5. Prime factorization with exponents Order of operations 6. Evaluate numerical expressions involving whole numbers 7. Identify mistakes involving the order of operations 8. Evaluate numerical expressions involving integers

B distinguish between expressions and equations verbally, numerically, and algebraically;		1. Write variable expressions: one operation 2. Write variable expressions: two operations 3. Write an equation from words 4. Identify expressions and equations
B distinguish between expressions and equations verbally, numerically, and algebraically;
1. Write variable expressions: one operation 2. Write variable expressions: two operations 3. Write an equation from words 4. Identify expressions and equations

C determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations; and		1. Identify equivalent expressions using strip models 2. Identify equivalent expressions I 3. Identify equivalent expressions II 4. Identify equivalent expressions using algebra tiles
C determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations; and
1. Identify equivalent expressions using strip models 2. Identify equivalent expressions I 3. Identify equivalent expressions II 4. Identify equivalent expressions using algebra tiles

D generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties.		Properties of operations 1. Properties of addition 2. Properties of multiplication Equivalent expressions 3. Multiply using the distributive property: area models 4. Multiply using the distributive property 5. Factor numerical expressions using the distributive property 6. Factor variable expressions: area models 7. Factor variable expressions using the distributive property 8. Write equivalent expressions using properties 9. Combine like terms 10. Add and subtract like terms
D generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties.
Properties of operations 1. Properties of addition 2. Properties of multiplication Equivalent expressions 3. Multiply using the distributive property: area models 4. Multiply using the distributive property 5. Factor numerical expressions using the distributive property 6. Factor variable expressions: area models 7. Factor variable expressions using the distributive property 8. Write equivalent expressions using properties 9. Combine like terms 10. Add and subtract like terms

Checkpoint opportunity		1. Checkpoint: Numerical expressions with exponents • Coming soon: Checkpoint: Expressions with variables
Checkpoint opportunity
1. Checkpoint: Numerical expressions with exponents • Coming soon: Checkpoint: Expressions with variables
8 The student applies mathematical process standards to use geometry to represent relationships and solve problems.
A extend previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle;		1. Triangle inequality 2. Find missing angles in triangles 3. Find missing angles in special triangles 4. Relationship between sides and angles in a triangle
A extend previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle;
1. Triangle inequality 2. Find missing angles in triangles 3. Find missing angles in special triangles 4. Relationship between sides and angles in a triangle

B model area formulas for parallelograms, trapezoids, and triangles by decomposing and rearranging parts of these shapes;		1. Understanding area of a parallelogram 2. Understanding area of a triangle 3. Understanding area of a trapezoid
B model area formulas for parallelograms, trapezoids, and triangles by decomposing and rearranging parts of these shapes;
1. Understanding area of a parallelogram 2. Understanding area of a triangle 3. Understanding area of a trapezoid

C write equations that represent problems related to the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers; and		1. Area of quadrilaterals and triangles: word problems 2. Volume of cubes and rectangular prisms: word problems
C write equations that represent problems related to the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers; and
1. Area of quadrilaterals and triangles: word problems 2. Volume of cubes and rectangular prisms: word problems

D determine solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers.		Quadrilaterals 1. Area of rectangles and squares 2. Area of parallelograms 3. Area of trapezoids 4. Area of quadrilaterals Triangles 5. Area of triangles Compound figures 6. Area of compound figures 7. Area of compound figures with triangles Shaded regions 8. Area between two rectangles 9. Area between two triangles Rectangular prisms 10. Volume of cubes and rectangular prisms Word problems 11. Area of quadrilaterals and triangles: word problems 12. Volume of cubes and rectangular prisms: word problems
D determine solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers.
Quadrilaterals 1. Area of rectangles and squares 2. Area of parallelograms 3. Area of trapezoids 4. Area of quadrilaterals Triangles 5. Area of triangles Compound figures 6. Area of compound figures 7. Area of compound figures with triangles Shaded regions 8. Area between two rectangles 9. Area between two triangles Rectangular prisms 10. Volume of cubes and rectangular prisms Word problems 11. Area of quadrilaterals and triangles: word problems 12. Volume of cubes and rectangular prisms: word problems

Checkpoint opportunity		• Coming soon: Checkpoint: Properties of triangles • Coming soon: Checkpoint: Area of polygons • Coming soon: Checkpoint: Volume
Checkpoint opportunity
• Coming soon: Checkpoint: Properties of triangles • Coming soon: Checkpoint: Area of polygons • Coming soon: Checkpoint: Volume
9 The student applies mathematical process standards to use equations and inequalities to represent situations.
A write one-variable, one-step equations and inequalities to represent constraints or conditions within problems;		Expressions 1. Write variable expressions: one operation Equations 2. Write an equation from words 3. Write a one-step equation: word problems Inequalities 4. One-step inequalities: word problems
A write one-variable, one-step equations and inequalities to represent constraints or conditions within problems;
Expressions 1. Write variable expressions: one operation Equations 2. Write an equation from words 3. Write a one-step equation: word problems Inequalities 4. One-step inequalities: word problems

B represent solutions for one-variable, one-step equations and inequalities on number lines; and		Equations 1. Solve one-step addition and subtraction equations and graph their solutions 2. Solve one-step multiplication and division equations and graph their solutions Inequalities 3. Graph inequalities on number lines 4. Write inequalities from number lines 5. Graph solutions to one-step inequalities 6. Solve and graph one-step addition and subtraction inequalities 7. Solve and graph one-step multiplication and division inequalities with positive numbers 8. Solve and graph one-step multiplication and division inequalities with rational numbers
B represent solutions for one-variable, one-step equations and inequalities on number lines; and
Equations 1. Solve one-step addition and subtraction equations and graph their solutions 2. Solve one-step multiplication and division equations and graph their solutions Inequalities 3. Graph inequalities on number lines 4. Write inequalities from number lines 5. Graph solutions to one-step inequalities 6. Solve and graph one-step addition and subtraction inequalities 7. Solve and graph one-step multiplication and division inequalities with positive numbers 8. Solve and graph one-step multiplication and division inequalities with rational numbers

C write corresponding real-world problems given one-variable, one-step equations or inequalities.		1. Which word problem matches the one-step equation?
C write corresponding real-world problems given one-variable, one-step equations or inequalities.
1. Which word problem matches the one-step equation?
10 The student applies mathematical process standards to use equations and inequalities to solve problems.
A model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts; and		Equation models 1. Model and solve equations using algebra tiles 2. Model and solve equations using diagrams 3. Write and solve equations that represent diagrams Solve equations 4. Solve one-step equations with whole numbers 5. Solve one-step addition and subtraction equations with decimals and fractions 6. Solve one-step multiplication and division equations with decimals and fractions 7. Solve one-step equations with decimals and fractions 8. Solve one-step addition and subtraction equations: word problems 9. Solve one-step multiplication and division equations: word problems 10. Solve one-step equations: word problems Solve inequalities 11. Solve one-step inequalities 12. One-step inequalities: word problems Write equations 13. Write a one-step equation: word problems
A model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts; and
Equation models 1. Model and solve equations using algebra tiles 2. Model and solve equations using diagrams 3. Write and solve equations that represent diagrams Solve equations 4. Solve one-step equations with whole numbers 5. Solve one-step addition and subtraction equations with decimals and fractions 6. Solve one-step multiplication and division equations with decimals and fractions 7. Solve one-step equations with decimals and fractions 8. Solve one-step addition and subtraction equations: word problems 9. Solve one-step multiplication and division equations: word problems 10. Solve one-step equations: word problems Solve inequalities 11. Solve one-step inequalities 12. One-step inequalities: word problems Write equations 13. Write a one-step equation: word problems

B determine if the given value(s) make(s) one-variable, one-step equations or inequalities true.		Equations 1. Does x satisfy an equation? 2. Which x satisfies an equation? Inequalities 3. Solutions to one-step inequalities
B determine if the given value(s) make(s) one-variable, one-step equations or inequalities true.
Equations 1. Does x satisfy an equation? 2. Which x satisfies an equation? Inequalities 3. Solutions to one-step inequalities

Checkpoint opportunity		1. Checkpoint: Understand and solve equations 2. Checkpoint: Solve inequalities
Checkpoint opportunity
1. Checkpoint: Understand and solve equations 2. Checkpoint: Solve inequalities

11-13	Measurement and data
11 The student applies mathematical process standards to use coordinate geometry to identify locations on a plane. The student is expected to graph points in all four quadrants using ordered pairs of rational numbers.
		1. Objects on a coordinate plane 2. Graph points on a coordinate plane 3. Quadrants 4. Coordinate planes as maps
12 The student applies mathematical process standards to use numerical or graphical representations to analyze problems.
A represent numeric data graphically, including dot plots, stem-and-leaf plots, histograms, and box plots;		Line plots 1. Create line plots 2. Create and interpret line plots with fractions Stem-and-leaf plots 3. Create stem-and-leaf plots Histograms 4. Create histograms Frequency tables 5. Create frequency tables Box plots 6. Box plots
A represent numeric data graphically, including dot plots, stem-and-leaf plots, histograms, and box plots;
Line plots 1. Create line plots 2. Create and interpret line plots with fractions Stem-and-leaf plots 3. Create stem-and-leaf plots Histograms 4. Create histograms Frequency tables 5. Create frequency tables Box plots 6. Box plots

B use the graphical representation of numeric data to describe the center, spread, and shape of the data distribution;		1. Box plots 2. Interpret charts and graphs to find mean, median, mode, and range 3. Describe distributions in line plots
B use the graphical representation of numeric data to describe the center, spread, and shape of the data distribution;
1. Box plots 2. Interpret charts and graphs to find mean, median, mode, and range 3. Describe distributions in line plots

C summarize numeric data with numerical summaries, including the mean and median (measures of center) and the range and interquartile range (IQR) (measures of spread), and use these summaries to describe the center, spread, and shape of the data distribution; and		Measures of center 1. Calculate mean and median 2. Mean and median: find the missing number 3. Changes in mean and median Measures of spread 4. Calculate range, quartiles, and interquartile range 5. Identify an outlier Measures of center and spread 6. Describe distributions in line plots 7. Interpret median and interquartile range
C summarize numeric data with numerical summaries, including the mean and median (measures of center) and the range and interquartile range (IQR) (measures of spread), and use these summaries to describe the center, spread, and shape of the data distribution; and
Measures of center 1. Calculate mean and median 2. Mean and median: find the missing number 3. Changes in mean and median Measures of spread 4. Calculate range, quartiles, and interquartile range 5. Identify an outlier Measures of center and spread 6. Describe distributions in line plots 7. Interpret median and interquartile range

D summarize categorical data with numerical and graphical summaries, including the mode, the percent of values in each category (relative frequency table), and the percent bar graph, and use these summaries to describe the data distribution.		1. Interpret categorical data 2. Create relative frequency tables 3. Create percent bar graphs 4. Interpret circle graphs
D summarize categorical data with numerical and graphical summaries, including the mode, the percent of values in each category (relative frequency table), and the percent bar graph, and use these summaries to describe the data distribution.
1. Interpret categorical data 2. Create relative frequency tables 3. Create percent bar graphs 4. Interpret circle graphs
13 The student applies mathematical process standards to use numerical or graphical representations to solve problems.
A interpret numeric data summarized in dot plots, stem-and-leaf plots, histograms, and box plots; and		Line plots 1. Interpret line plots 2. Create and interpret line plots with fractions Stem-and-leaf plots 3. Interpret stem-and-leaf plots Histograms 4. Interpret histograms Box-and-whisker plots 5. Box plots
A interpret numeric data summarized in dot plots, stem-and-leaf plots, histograms, and box plots; and
Line plots 1. Interpret line plots 2. Create and interpret line plots with fractions Stem-and-leaf plots 3. Interpret stem-and-leaf plots Histograms 4. Interpret histograms Box-and-whisker plots 5. Box plots

B distinguish between situations that yield data with and without variability.		1. Identify statistical questions
B distinguish between situations that yield data with and without variability.
1. Identify statistical questions

Checkpoint opportunity		• Coming soon: Checkpoint: Represent, summarize, and interpret data
Checkpoint opportunity
• Coming soon: Checkpoint: Represent, summarize, and interpret data

14	Personal financial literacy
14 The student applies mathematical process standards to develop an economic way of thinking and problem solving useful in one's life as a knowledgeable consumer and investor.
A compare the features and costs of a checking account and a debit card offered by different local financial institutions;		1. Compare checking accounts
A compare the features and costs of a checking account and a debit card offered by different local financial institutions;
1. Compare checking accounts

B distinguish between debit cards and credit cards;		1. Debit cards and credit cards
B distinguish between debit cards and credit cards;
1. Debit cards and credit cards

C balance a check register that includes deposits, withdrawals, and transfers;		1. Check registers
C balance a check register that includes deposits, withdrawals, and transfers;
1. Check registers

D explain why it is important to establish a positive credit history;		1. Credit reports
D explain why it is important to establish a positive credit history;
1. Credit reports

E describe the information in a credit report and how long it is retained;		1. Credit reports
E describe the information in a credit report and how long it is retained;
1. Credit reports

F describe the value of credit reports to borrowers and to lenders;		1. Credit reports
F describe the value of credit reports to borrowers and to lenders;
1. Credit reports

G explain various methods to pay for college, including through savings, grants, scholarships, student loans, and work-study; and		1. Paying for college
G explain various methods to pay for college, including through savings, grants, scholarships, student loans, and work-study; and
1. Paying for college

H compare the annual salary of several occupations requiring various levels of post-secondary education or vocational training and calculate the effects of the different annual salaries on lifetime income.		1. Occupations, education, and income
H compare the annual salary of several occupations requiring various levels of post-secondary education or vocational training and calculate the effects of the different annual salaries on lifetime income.
1. Occupations, education, and income