5th Grade
5th Grade
Embedded Files
Mathematics
Mathematics
Introduction
Introduction
(1) The desire to achieve educational excellence is the driving force behind the Texas essential knowledge and skills for mathematics, guided by the college and career readiness standards. By embedding statistics, probability, and finance, while focusing on computational thinking, mathematical fluency, and solid understanding, Texas will lead the way in mathematics education and prepare all Texas students for the challenges they will face in the 21st century.
(2) The process standards describe ways in which students are expected to engage in the content. The placement of the process standards at the beginning of the knowledge and skills listed for each grade and course is intentional. The process standards weave the other knowledge and skills together so that students may be successful problem solvers and use mathematics efficiently and effectively in daily life. The process standards are integrated at every grade level and course. When possible, students will apply mathematics to problems arising in everyday life, society, and the workplace. Students will 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. Students will select appropriate tools such as real objects, manipulatives, algorithms, paper and pencil, and technology and techniques such as mental math, estimation, number sense, and generalization and abstraction to solve problems. Students will effectively communicate mathematical ideas, reasoning, and their implications using multiple representations such as symbols, diagrams, graphs, computer programs, and language. Students will use mathematical relationships to generate solutions and make connections and predictions. Students will analyze mathematical relationships to connect and communicate mathematical ideas. Students will display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
(3) For students to become fluent in mathematics, students must develop a robust sense of number. The National Research Council's report, "Adding It Up," defines procedural fluency as "skill in carrying out procedures flexibly, accurately, efficiently, and appropriately." As students develop procedural fluency, they must also realize that true problem solving may take time, effort, and perseverance. Students in Grade 5 are expected to perform their work without the use of calculators.
(4) The primary focal areas in Grade 5 are solving problems involving all four operations with positive rational numbers, determining and generating formulas and solutions to expressions, and extending measurement to area and volume. These focal areas are supported throughout the mathematical strands of number and operations, algebraic reasoning, geometry and measurement, and data analysis. In Grades 3-5, the number set is limited to positive rational numbers. In number and operations, students will apply place value and identify part-to-whole relationships and equivalence. In algebraic reasoning, students will represent and solve problems with expressions and equations, build foundations of functions through patterning, identify prime and composite numbers, and use the order of operations. In geometry and measurement, students will classify two-dimensional figures, connect geometric attributes to the measures of three-dimensional figures, use units of measure, and represent location using a coordinate plane. In data analysis, students will represent and interpret data.
Unit 01: Extending Whole Number Operations
Unit 01: Extending Whole Number Operations
(13 classes for the entire unit)
(13 classes for the entire unit)
Students work toward becoming fluent when solving whole number addition, subtraction, and multiplication problems and proficient when solving whole number division problems. Estimating solutions to problems involving all four operations becomes embedded within one- and two-step real-world contexts to help determine the reasonableness of solutions. The number set for multiplication grows to three-digit by two-digit factors while the number set for division becomes four-digit dividends by two-digit divisors. Using the standard algorithm becomes a focus for both multiplication and division.
TEKS in this unit: 5.1A, 5.1B, 5.1C, 5.1D, 5.1E, 5.1F, 5.1G, 5.3A, 5.3B, 5.3C, 5.3K
GoMath!: Module 2
Unit 02: Algebraic Reasoning
Unit 02: Algebraic Reasoning
(12 classes for the entire unit)
(12 classes for the entire unit)
Students are introduced to the properties of prime and composite numbers. Students are encouraged to use previous understandings of representing products using arrays and area models to help support new learning and to identify prime and composite numbers by analyzing their factors. Students examine the meaning of grouping symbols within a numeric expression and simplify numerical expressions based on socially constructed conventions. In addition, students represent and solve multi-step problems algebraically using an equation with a letter representing the unknown. All operations within this unit are limited to whole numbers.
TEKS in this unit: 5.1A, 5.1B, 5.1C, 5.1D, 5.1E, 5.1F, 5.1G, 5.4A, 5.4B, 5.4E, 5.4F
GoMath!: Modules 7, 8, 9, 10
Unit 03: Financial Literacy
Unit 03: Financial Literacy
(5 classes for the entire unit)
(5 classes for the entire unit)
Students define different types of taxes including income tax, sales tax, property tax, and payroll tax. Students take a closer look at payroll tax when they investigate the differences between gross income and net income. They also compare and contrast various methods of payment including checks, credit cards, debit cards, and electronic payments. Students develop a system for keeping financial records with regards to income and expenses and balance a simple budget. The concept of negative values is abstractly embedded within balancing budgets as students are expected to describe the actions that might be taken should expenses exceed the income. The financial literacy expectations within this unit deepen student knowledge of income, taxes, payments, and methods to keep track of financial input and output.
TEKS in this unit: 5.1A, 5.1B, 5.1C, 5.1D, 5.1E, 5.1F, 5.1G, 5.10A, 5.10B, 5.10C, 5.10D, 5.10E, 5.10F
GoMath!: Module 17
Unit 04: Extending Decimals
Unit 04: Extending Decimals
(6 classes for the entire unit)
(6 classes for the entire unit)
Students are formally introduced to the thousandths place. Students build upon the idea that our base-10 place value system extends infinitely to very small values as well as very large values, and that each place-value position is one-tenth the value of the place to its left and 10 times the value of the place to its right. Students relate previous representations of decimals to the hundredths with concrete and pictorial models to develop their conceptual knowledge of decimals through the thousandths. Students are expected to use expanded notation and numerals to represent the value of a decimal through the thousandths. Students use comparison symbols to compare and order decimals to the thousandths and round decimals to the tenths or hundredths place. Students continue to estimate solutions and extend addition and subtraction with decimals to include the thousandths place. Numerical expressions are revisited as a means for students to communicate their solution process and to solve problem situations involving decimals.
TEKS in this unit: 5.1A, 5.1B, 5.1C, 5.1D, 5.1E, 5.1F, 5.1G, 5.2A, 5.2B, 5.2C, 5.3A, 5.3K, 5.4F
GoMath!: Modules 1, 3, 4
Unit 05: Decimal Multiplication and Division
Unit 05: Decimal Multiplication and Division
(14 classes for the entire unit)
(14 classes for the entire unit)
Students represent multiplicative structures (multiplication and division) of problem situations with products and decimals to the hundredths with the use of concrete objects, pictorial models, and area models. These models serve as a bridge between whole-number multiplication and division and should help students to assimilate new understandings involving decimal multiplication and division. There is an emphasis on representing multiplication and division before solving for products and quotients of decimals to allow for the development of the conceptual understanding before procedural understanding. Students are expected to estimate to determine products and quotients, solve for products and quotients, and simplify numerical expressions that include multiplication and division of whole numbers and decimals. The number set within this unit is limited to products and quotients to the hundredths. Factors may include decimals through the thousandths place as long as the product is only through the hundredths place. Division is limited to four-digit dividends and two-digit whole number divisors.
TEKS in this unit: 5.1A, 5.1B, 5.1C, 5.1D, 5.1E, 5.1F, 5.1G, 5.3A, 5.3D, 5.3E, 5.3F, 5.3G, 5.4F
GoMath!: Modules 3, 4
Unit 06: Addition and Subtraction of Fractions
Unit 06: Addition and Subtraction of Fractions
(13 classes for the entire unit)
(13 classes for the entire unit)
Students extend previous understandings of adding and subtracting whole numbers and decimals with the expectation of developing fluency in adding and subtracting positive rational numbers, including fractions. Students continue to estimate solutions to mathematical and real-world problems to determine the reasonableness of solutions. Concrete objects, pictorial models, and properties of operations are used to represent and solve problems involving adding and/or subtracting fractions with unequal denominators referring to the same whole. Previous grade level expectations regarding adding and subtracting fractions with equal denominators using models that build to the number line serve as a bridge to adding and subtracting fractions with unequal denominators. Students also continue to simplify numerical expressions that involve adding and subtracting fractions with unequal denominators.
TEKS in this unit: 5.1A, 5.1B, 5.1C, 5.1D, 5.1E, 5.1F, 5.1G, 5.3A, 5.3H, 5.3K, 5.4F
GoMath!: Module 5
Unit 07: Multiplication and Division of Whole Numbers by a Fraction
Unit 07: Multiplication and Division of Whole Numbers by a Fraction
(12 classes for the entire unit)
(12 classes for the entire unit)
Students represent a product of whole number and a fraction referring to the same whole using concrete and pictorial models, including area models and strip diagrams. Concrete and pictorial models, including area models and strip diagrams, are also used to represent the division of a whole number by a unit fraction and the division of a unit fraction by a whole number. Students continue to estimate solutions to mathematical and real-world problems to determine the reasonableness of solutions. Students also continue to simplify numerical expressions that involve all operations with whole numbers, decimals, and fractions. This unit concludes the formal study of operations with whole numbers, fractions, and decimals in Grade 5.
TEKS in this unit: 5.1A, 5.1B, 5.1C, 5.1D, 5.1E, 5.1F, 5.1G, 5.3A, 5.3I, 5.3J, 5.3L, 5.4F
GoMath!: Module 6
Unit 08: Geometry and Measurement
Unit 08: Geometry and Measurement
(15 classes for the entire unit)
(15 classes for the entire unit)
Students are introduced to the concept of volume as a three-dimensional measure. Students are expected to understand the concept that a cube with a side length of one unit is a unit cube having one cubic unit of volume, and the volume of a three-dimensional figure as the number of unit cubes (n cubic units) needed to fill the figure with no gaps or overlaps. Students use objects and pictorial models to develop the formulas for volume of a rectangular prism (V = l × w × h and V = Bh), including the special form for the volume of a cube (V = s × s × s). Grade 5 is the first grade level where students are formally introduced to formulas for volume as seen on the STAAR Grade 5 Mathematics Reference Materials. Students use these formulas to represent and solve problems related to perimeter and/or area and volume. Formulas are used to establish the concept that the volume of a rectangular prism with whole number side lengths is related to the number of layers times the number of unit cubes in the area of the base. Students extend previous knowledge of classifying two-dimensional figures based on the presence or absence of parallel or perpendicular lines or angles of a specified size to formally classify two-dimensional figures into a hierarchy of sets and subsets using graphic organizers. Students extend previous work with conversions to solve problems by calculating conversions within a measurement system. Measurements for side lengths of two- or three-dimensional figures and measurement conversions may include positive rational numbers within the number system and operational limitations for the grade level.
TEKS in this unit: 5.1A, 5.1B, 5.1C, 5.1D, 5.1E, 5.1F, 5.1G, 5.4G, 5.4H, 5.5A, 5.6A, 5.6B, 5.7A
GoMath!: Modules 11, 12, 13
Unit 09: Patterns on a Coordinate Plane
Unit 09: Patterns on a Coordinate Plane
(10 classes for the entire unit)
(10 classes for the entire unit)
Students are introduced to the coordinate plane and its key attributes including the axes and origin. Students analyze the process for graphing ordered pairs in the first quadrant of the coordinate plane and identify the first number in an ordered pair as the x-coordinate that indicates the movement parallel to the x-axis starting at the origin and the second number in the ordered pair as the y-coordinate that indicates the movement parallel to the y-axis starting at the origin. Although graphing is limited to the Quadrant I of the coordinate plane, ordered pairs may include any positive rational number, including fractions and decimals. Students are expected to graph ordered pairs in the first quadrant of the coordinate plane that are generated from number patterns or an input-output table. Number patterns are examined closely as students recognize the difference between additive and multiplicative numerical patterns when given in a table or graph. Students use input-output tables and graphs to generate numerical patterns when given a rule in the form y = ax (multiplicative numerical pattern) or y = a + x (additive numerical pattern).
TEKS in this unit: 5.1A, 5.1B, 5.1C, 5.1D, 5.1E, 5.1F, 5.1G, 5.4C, 5.4D, 5.8A, 5.8B, 5.8C
GoMath!: Module 14
Unit 10: Representing Data
Unit 10: Representing Data
(10 classes for the entire unit)
(10 classes for the entire unit)
Students represent categorical data with bar graphs and frequency tables. Numerical data, including data sets of measurements in fractions or decimals, is represented with dot plots or stem-and-leaf plots. Students are introduced to scatterplots as a means to represent discrete paired data. Students utilize all of these graphical representations to solve one- and two-step problems.
TEKS in this unit: 5.1A, 5.1B, 5.1C, 5.1D, 5.1E, 5.1F, 5.1G, 5.9A, 5.9B, 5.9C
GoMath!: Modules 15, 16
Unit 11: Making Connections
Unit 11: Making Connections
(10 classes for the entire unit)
(10 classes for the entire unit)
Students revisit representing and solving problems involving addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations. Students also solve addition and subtraction situations involving positive rational numbers. Students revisit representing and solving problems involving the multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models. Students continue multiplication as they solve for products of decimals to the hundredths, including situations involving money, using strategies based on place-value understandings, properties of operations, and the relationship of decimal multiplication to the multiplication of whole numbers. Students revisit division as they solve for quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using strategies and algorithms, including the standard algorithm. They divide whole numbers by unit fractions and unit fractions by whole numbers. Students continue to simplify numerical expressions that do not involve exponents, including up to two levels of grouping.
TEKS in this unit: 5.1A, 5.1B, 5.1C, 5.1D, 5.1E, 5.1F, 5.1G, 5.3E, 5.3G, 5.3I, 5.3K, 5.3L, 5.4F
GoMath!: Modules 10, 15, 16
Unit 12: Essential Understandings of Decimals
Unit 12: Essential Understandings of Decimals
(12 classes for the entire unit)
(12 classes for the entire unit)
Students revisit and solidify essential understandings of decimals. Students estimate to determine the reasonableness of sums, differences, products, and quotients. They solve situations involving addition and subtraction of decimals through the thousandths. Students represent multiplicative structures (multiplication and division) involving products and quotients using concrete objects, pictorial models, and area models. Factors may include decimals through the thousandths place as long as the product is only through the hundredths place. Division is limited to four-digit dividends and two-digit whole number divisors, with quotients limited to the hundredths. Simplifying numerical expressions is revisited as a means for students to communicate their solution process and to solve problem situations involving decimals.
TEKS in this unit: 5.1A, 5.1B, 5.1C, 5.1D, 5.1E, 5.1F, 5.1G, 5.3A, 5.3D, 5.3E, 5.3F, 5.3G, 5.3K, 5.4F
GoMath!: Modules 1, 3, 4
Unit 13: Essential Understandings of Fractions
Unit 13: Essential Understandings of Fractions
(13 classes for the entire unit)
(13 classes for the entire unit)
Students revisit and solidify essential understandings of fractions. Students estimate to determine the reasonableness of solutions to mathematical and real-world problems involving addition, subtraction, multiplication, and division. Students represent and solve addition and subtraction of fractions with unequal denominators using concrete objects, pictorial models, and properties of operations to build to the expectation of adding and subtracting positive rational numbers fluently. Students use concrete objects and pictorial models to multiply a whole number by a fraction and divide a whole number by a unit fraction and a unit fraction by a whole number. Throughout the unit, students simplify numerical expressions that do not involve exponents.
TEKS in this unit: 5.1A, 5.1B, 5.1C, 5.1D, 5.1E, 5.1F, 5.1G, 5.3A, 5.3H, 5.3I, 5.3J, 5.3K, 5.3L, 5.4F
GoMath!: Modules 5, 6
Texas Essential Knowledge & Skills (TEKS)
Texas Essential Knowledge & Skills (TEKS)
TEKS - Math - G5.pdfPage updated
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