6th Grade Math (Texas TEKS)

111.26(b)(1) Mathematical process standards

• 111.26(b)(1) Student uses math processes to learn and show understanding through problem solving, tools, communication, representations, and justification.
• 111.26(b)(1)(A) Apply mathematics to problems arising in everyday life, society, and the workplace.
• 111.26(b)(1)(B) Use a problem-solving model: analyze information, plan, solve, justify, and evaluate reasonableness.
• 111.26(b)(1)(C) Select tools such as manipulatives, paper and pencil, or technology, and techniques such as mental math.
• 111.26(b)(1)(D) Communicate ideas, reasoning, and implications using multiple representations such as symbols, diagrams, graphs, and language.
• 111.26(b)(1)(E) Create and use representations to organize, record, and communicate mathematical ideas.
• 111.26(b)(1)(F) Analyze mathematical relationships to connect and communicate mathematical ideas.
• 111.26(b)(1)(G) Display, explain, and justify ideas and arguments using precise mathematical language, orally or in writing.

111.26(b)(2) Number and operations

• 111.26(b)(2) Student represents and uses rational numbers in varied forms, including classifying, locating, comparing, ordering, and extending division notation.
• 111.26(b)(2)(A) Classify whole numbers, integers, and rational numbers using a visual model such as a Venn diagram.
• 111.26(b)(2)(B) Identify a number, its opposite, and its absolute value.
• 111.26(b)(2)(C) Locate, compare, and order integers and rational numbers on a number line.
• 111.26(b)(2)(D) Order a set of rational numbers arising from mathematical and real-world contexts.
• 111.26(b)(2)(E) Extend division representations to fraction notation, where a/b equals a ÷ b and b is not zero.

111.26(b)(3) Number and operations

• 111.26(b)(3) Student applies operations to solve problems with rational numbers, using integer models, reciprocal relationships, multiplication effects, and fluent computation.
• 111.26(b)(3)(A) Recognize that dividing by a rational number and multiplying by its reciprocal give equivalent values.
• 111.26(b)(3)(B) Determine, with or without computation, whether multiplying by a fraction increases or decreases a quantity.
• 111.26(b)(3)(C) Represent integer operations with concrete models and connect those actions to standard algorithms.
• 111.26(b)(3)(D) Add, subtract, multiply, and divide integers fluently.
• 111.26(b)(3)(E) Multiply and divide positive rational numbers fluently.

111.26(b)(4) Proportionality

• 111.26(b)(4) Student understands proportional relationships by comparing rules, reasoning about ratios and rates, and converting fractions, decimals, percents, and units.
• 111.26(b)(4)(A) Compare two rules verbally, numerically, graphically, and symbolically to tell additive from multiplicative relationships.
• 111.26(b)(4)(B) Apply qualitative and quantitative reasoning to predict and compare real-world ratio and rate problems.
• 111.26(b)(4)(C) Give examples of ratios as multiplicative comparisons of two quantities describing the same attribute.
• 111.26(b)(4)(D) Give examples of rates as divisions of two quantities with different attributes, including rates as quotients.
• 111.26(b)(4)(E) Represent ratios and percents with concrete models, fractions, and decimals.
• 111.26(b)(4)(F) Represent benchmark fractions and percents using grids, strip diagrams, number lines, and numbers.
• 111.26(b)(4)(G) Generate equivalent fractions, decimals, and percents using real-world problems, including money problems.
• 111.26(b)(4)(H) Convert units within a measurement system using proportions and unit rates.

111.26(b)(5) Proportionality

• 111.26(b)(5) Student solves proportional problems using scale factors, tables, graphs, proportions, percent-finding tasks, and equivalent forms showing equal parts.
• 111.26(b)(5)(A) Represent ratio and rate problems using scale factors, tables, graphs, and proportions.
• 111.26(b)(5)(B) Solve real-world problems finding the whole, the part, or the percent, using concrete and pictorial models.
• 111.26(b)(5)(C) Use equivalent fractions, decimals, and percents to show equal parts of the same whole.

111.26(b)(6) Expressions, equations, and relationships

• 111.26(b)(6) Student uses multiple representations to describe algebraic relationships, identifying independent and dependent quantities and writing equations from tables and situations.
• 111.26(b)(6)(A) Identify independent and dependent quantities from tables and graphs.
• 111.26(b)(6)(B) Write an equation that represents the relationship between independent and dependent quantities from a table.
• 111.26(b)(6)(C) Represent situations using verbal descriptions, tables, graphs, and equations in the form y=kx or y=x+b.

111.26(b)(7) Expressions, equations, and relationships

• 111.26(b)(7) Student develops expressions and equations by generating equivalent numerical expressions, distinguishing expressions from equations, and verifying equivalence using properties.
• 111.26(b)(7)(A) Generate equivalent numerical expressions using order of operations, whole-number exponents, and prime factorization.
• 111.26(b)(7)(B) Distinguish between expressions and equations verbally, numerically, and algebraically.
• 111.26(b)(7)(C) Determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations.
• 111.26(b)(7)(D) Generate equivalent expressions using inverse, identity, commutative, associative, and distributive properties.

111.26(b)(8) Expressions, equations, and relationships

• 111.26(b)(8) Student uses geometry to represent relationships and solve problems about triangles, area and volume formulas, and related equations.
• 111.26(b)(8)(A) Extend knowledge of triangles to angle sums, side-angle relationships, and when three lengths form a triangle.
• 111.26(b)(8)(B) Model area formulas for parallelograms, trapezoids, and triangles by decomposing and rearranging shapes.
• 111.26(b)(8)(C) Write equations for area of rectangles, parallelograms, trapezoids, triangles, and volume of right rectangular prisms with positive rational dimensions.
• 111.26(b)(8)(D) Determine solutions for area and volume problems involving those shapes with positive rational dimensions.

111.26(b)(9) Expressions, equations, and relationships

• 111.26(b)(9) Student uses equations and inequalities to represent situations, including writing one-variable, one-step equations and inequalities and graphing their solutions.
• 111.26(b)(9)(A) Write one-variable, one-step equations and inequalities representing constraints within problems.
• 111.26(b)(9)(B) Represent solutions of one-variable, one-step equations and inequalities on number lines.
• 111.26(b)(9)(C) Write corresponding real-world problems given one-variable, one-step equations or inequalities.

111.26(b)(10) Expressions, equations, and relationships

• 111.26(b)(10) Student solves problems by modeling one-variable, one-step equations and inequalities and checking whether given values satisfy them.
• 111.26(b)(10)(A) Model and solve one-variable, one-step equations and inequalities representing problems, including geometric concepts.
• 111.26(b)(10)(B) Determine if given values make one-variable, one-step equations or inequalities true.

111.26(b)(11) Measurement and data

• 111.26(b)(11) Graph points in all four quadrants using ordered pairs of rational numbers.

111.26(b)(12) Measurement and data

• 111.26(b)(12) Student uses numerical and graphical representations to analyze problems, including summarizing data, describing distributions, and interpreting categorical data.
• 111.26(b)(12)(A) Represent numeric data graphically using dot plots, stem-and-leaf plots, histograms, and box plots.
• 111.26(b)(12)(B) Use graphical representations of numeric data to describe center, spread, and shape of distributions.
• 111.26(b)(12)(C) Summarize numeric data using mean, median, range, and IQR, and use these to describe distributions.
• 111.26(b)(12)(D) Summarize categorical data using mode, relative frequency tables, and percent bar graphs, and describe the distribution.

111.26(b)(13) Measurement and data

• 111.26(b)(13) Student uses numerical or graphical representations to solve problems, interpreting summarized numeric data and distinguishing data with and without variability.
• 111.26(b)(13)(A) Interpret numeric data summarized in dot plots, stem-and-leaf plots, histograms, and box plots.
• 111.26(b)(13)(B) Distinguish between situations that yield data with and without variability.

111.26(b)(14) Personal financial literacy

• 111.26(b)(14) Student develops economic thinking for consumer and investor decisions, including checking accounts, credit, credit reports, college financing, and salary effects.
• 111.26(b)(14)(A) Compare features and costs of checking accounts and debit cards from different local financial institutions.
• 111.26(b)(14)(B) Distinguish between debit cards and credit cards.
• 111.26(b)(14)(C) Balance a check register that includes deposits, withdrawals, and transfers.
• 111.26(b)(14)(D) Explain why establishing a positive credit history is important.
• 111.26(b)(14)(E) Describe information in a credit report and how long it is retained.
• 111.26(b)(14)(F) Describe the value of credit reports to borrowers and to lenders.
• 111.26(b)(14)(G) Explain methods to pay for college, including savings, grants, scholarships, student loans, and work-study.
• 111.26(b)(14)(H) Compare annual salaries of occupations requiring different education levels and calculate effects on lifetime income.