5th Grade Math (Texas TEKS)

111.7(b)(1) Mathematical process standards

• 111.7(b)(1) Students use problem solving, tools, representations, reasoning, and precise communication to acquire and demonstrate mathematical understanding.
• 111.7(b)(1)(A) Apply mathematics to problems arising in everyday life, society, and the workplace.
• 111.7(b)(1)(B) Use a problem-solving model: analyze information, plan, determine a solution, justify it, and evaluate reasonableness.
• 111.7(b)(1)(C) Select appropriate tools and techniques, such as mental math, estimation, or number sense, to solve problems.
• 111.7(b)(1)(D) Communicate ideas and reasoning using multiple representations, such as symbols, diagrams, graphs, and language.
• 111.7(b)(1)(E) Create and use representations to organize, record, and communicate mathematical ideas.
• 111.7(b)(1)(F) Analyze mathematical relationships to connect and communicate mathematical ideas.
• 111.7(b)(1)(G) Display, explain, and justify ideas and arguments using precise mathematical language.

111.7(b)(2) Number and operations

• 111.7(b)(2) Students represent, compare, and order positive rational numbers and understand place value relationships.
• 111.7(b)(2)(A) Represent the value of decimal digits through thousandths using expanded notation and numerals.
• 111.7(b)(2)(B) Compare and order two decimals to thousandths, using the symbols >, <, or =.
• 111.7(b)(2)(C) Round decimals to the tenths or hundredths place.

111.7(b)(3) Number and operations

• 111.7(b)(3) Students compute fluently with whole numbers, decimals, and fractions using models, algorithms, and properties to solve problems.
• 111.7(b)(3)(A) Estimate solutions to real-world problems involving addition, subtraction, multiplication, or division.
• 111.7(b)(3)(B) Multiply a three-digit number by a two-digit number fluently using the standard algorithm.
• 111.7(b)(3)(C) Divide up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm.
• 111.7(b)(3)(D) Represent decimal multiplication with products to hundredths using objects and area models.
• 111.7(b)(3)(E) Solve decimal products to hundredths, including money, using place value and whole-number relationships.
• 111.7(b)(3)(F) Represent decimal quotients to hundredths with up to four-digit dividends using objects and pictorial models.
• 111.7(b)(3)(G) Solve decimal quotients to hundredths with up to four-digit dividends using strategies and algorithms.
• 111.7(b)(3)(H) Represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole.
• 111.7(b)(3)(I) Represent and solve multiplication of a whole number and a fraction referring to the same whole.
• 111.7(b)(3)(J) Represent dividing a unit fraction by a whole number and a whole number by a unit fraction.
• 111.7(b)(3)(K) Add and subtract positive rational numbers fluently.
• 111.7(b)(3)(L) Divide whole numbers by unit fractions and unit fractions by whole numbers.

111.7(b)(4) Algebraic reasoning

• 111.7(b)(4) Students develop concepts of expressions and equations, identify number types, and analyze numerical patterns.
• 111.7(b)(4)(A) Identify prime and composite numbers.
• 111.7(b)(4)(B) Represent and solve multi-step whole-number problems using equations with a letter for the unknown.
• 111.7(b)(4)(C) Generate a numerical pattern from a rule in the form y = ax or y = x + a, and graph it.
• 111.7(b)(4)(D) Recognize the difference between additive and multiplicative numerical patterns in tables or graphs.
• 111.7(b)(4)(E) Describe the meaning of parentheses and brackets in a numeric expression.
• 111.7(b)(4)(F) Simplify numerical expressions without exponents, including up to two levels of grouping.
• 111.7(b)(4)(G) Use objects and pictorial models to develop volume formulas for rectangular prisms and cubes.
• 111.7(b)(4)(H) Represent and solve problems related to perimeter, area, and volume.

111.7(b)(5) Geometry and measurement

• 111.7(b)(5) Classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on attributes and properties.

111.7(b)(6) Geometry and measurement

• 111.7(b)(6) Students understand, recognize, and quantify volume of three-dimensional figures using unit cubes.
• 111.7(b)(6)(A) Recognize a unit cube as one cubic unit and measure volume as the number of unit cubes needed to fill a figure.
• 111.7(b)(6)(B) Determine the volume of a rectangular prism with whole-number sides using layers times unit cubes in the base.

111.7(b)(7) Geometry and measurement

• 111.7(b)(7) Solve problems by calculating conversions within the customary or metric measurement system.

111.7(b)(8) Geometry and measurement

• 111.7(b)(8) Students identify locations on a coordinate plane and graph ordered pairs in the first quadrant.
• 111.7(b)(8)(A) Describe coordinate plane attributes: perpendicular axes, the origin, and x- and y-coordinate movement from the origin.
• 111.7(b)(8)(B) Describe the process for graphing ordered pairs of numbers in the first quadrant.
• 111.7(b)(8)(C) Graph first-quadrant ordered pairs from problems, number patterns, or input-output tables.

111.7(b)(9) Data analysis

• 111.7(b)(9) Students collect, organize, display, and interpret data to solve problems.
• 111.7(b)(9)(A) Represent categorical data with bar graphs or frequency tables, and numerical data with dot plots or stem-and-leaf plots.
• 111.7(b)(9)(B) Represent discrete paired data on a scatterplot.
• 111.7(b)(9)(C) Solve one- and two-step problems using frequency tables, dot plots, bar graphs, stem-and-leaf plots, or scatterplots.

111.7(b)(10) Personal financial literacy

• 111.7(b)(10) Students manage financial resources effectively by understanding taxes, payment methods, financial records, and budgeting.
• 111.7(b)(10)(A) Define income tax, payroll tax, sales tax, and property tax.
• 111.7(b)(10)(B) Explain the difference between gross income and net income.
• 111.7(b)(10)(C) Identify advantages and disadvantages of payment methods, such as check, credit card, debit card, and electronic payments.
• 111.7(b)(10)(D) Develop a system for keeping and using financial records.
• 111.7(b)(10)(E) Describe actions that might be taken to balance a budget when expenses exceed income.
• 111.7(b)(10)(F) Balance a simple budget.