3rd Grade
Mathematics
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 3 are expected to perform their work without the use of calculators.
(4) The primary focal areas in Grade 3 are place value, operations of whole numbers, and understanding fractional units. 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 focus on applying place value, comparing and ordering whole numbers, connecting multiplication and division, and understanding and representing fractions as numbers and equivalent fractions. In algebraic reasoning, students will use multiple representations of problem situations, determine missing values in number sentences, and represent real-world relationships using number pairs in a table and verbal descriptions. In geometry and measurement, students will identify and classify two-dimensional figures according to common attributes, decompose composite figures formed by rectangles to determine area, determine the perimeter of polygons, solve problems involving time, and measure liquid volume (capacity) or weight. In data analysis, students will represent and interpret data.
Unit 01: Foundations of Number
(8 classes for the entire unit)
Students extend their understanding of the thousands period to include the ten thousands and hundred thousands places. Students compose and decompose numbers through 100,000 as so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using concrete objects (e.g., proportional objects such as base-10 blocks, non-proportional objects such as place value disks, etc.), pictorial models (e.g., base-10 representations with place value charts, place value disk representations with place value charts, open number lines, etc.), and numerical representations (e.g., expanded notation, word form, standard form, etc.). Expanded notation introduces the × symbol as a means of representing the value of a digit as so many ten thousands, so many thousands, etc. Emphasis is on symbolically representing “5 × 100” stated as “5 groups of 100” or “5 hundreds.” While examining the magnitude of 100,000, students begin to describe the mathematical relationship between the digits in a number such as the value of each place-value position is 10 times the value of the place to the right. Students continue to build their understanding of the base-10 place value system using multiples of ten and equivalent compositions and decompositions of numbers of the same value. Students also compare and order whole numbers up to 100,000 and represent the comparisons using words and symbols. Ordering three or more numbers may include situations involving quantifying descriptors to specify ordering greatest to least or least to greatest and may involve the location of the numbers on a number line.
TEKS in this unit: 3.1A, 3.1B, 3.1C, 3.1D, 3.1E, 3.1F, 3.1G, 3.2A, 3.2B, 3.2D
GoMath!: Module 1
Unit 02: Addition and Subtraction
(17 classes for the entire unit)
Students begin by building an understanding of why estimation is a valuable tool for everyday experiences. Number lines and place value relationships are used to round numbers to the nearest 10 or 100. Students analyze numbers in a problem situation to determine the most efficient estimation strategy to use, rounding or compatible numbers. Students use their estimation and mental math strategies to justify the reasonableness of their solutions. Addition and subtraction skills are advanced through solving one- and two-step problem situations that promote the use of place value, properties of operations, and the examination of different representations of the solution process (e.g., base-10 blocks, open number lines, pictorial models, and/or equations). Extensions of these operations include determining the value of a collection of coins and bills as well as determining the perimeter of a polygon.
TEKS in this unit: 3.1A, 3.1B, 3.1C, 3.1D, 3.1E, 3.1F, 3.1G, 3.2C, 3.4A, 3.4B, 3.4C, 3.5A, 3.7B
GoMath!: Modules 4, 5
Unit 03: Building an Understanding of Multiplication
(12 classes for the entire unit)
Students represent multiplication facts through the use of context. These contextual situations provide real-life experiences and enable students to construct multiplication models (concrete, pictorial, and area models), equal groups, arrays, strip diagrams, and equations in a relevant way. Students also explore the commutative (if the order of the factors are changed, the product remains the same), associative (if three or more factors are multiplied, they can be grouped in any order, and the product will remain the same), and distributive (if multiplying a number by a sum of numbers, the product will be the same as multiplying the number by each addend and then adding the products together) properties of multiplication in order to provide the foundation needed to learn, retain, and apply basic multiplication facts up to 10 × 10. By applying the commutative property of multiplication the number of basic facts needing to be recalled is reduced by half. The distributive and associative properties of multiplication also aid in developing automatic recall of facts, or automaticity, by allowing students to decompose a factor(s), find known partial products, and compose the partial products to determine the total product (e.g., if a student knows that 2 × 9 = 18, then they can use the commutative property and doubling to find the product of 9 × 4). Although not expected to learn these properties of multiplication by name, students are expected to be able to analyze, describe, and represent these strategies. Students understanding of multiplication is strengthened by solving one-step problems, including problems involving area of rectangles, and making sense of meaningful, efficient representations and strategies.
TEKS in this unit: 3.1A, 3.1B, 3.1C, 3.1D, 3.1E, 3.1F, 3.1G, 3.4D, 3.4E, 3.4F, 3.4K, 3.5B, 3.5C, 3.6C
GoMath!: Module 6
Unit 04: Data Analysis
(6 classes for the entire unit)
Students collect, organize, represent, and summarize a categorical data set with multiple categories using a frequency table, dot plot, pictograph, and bar graph with scaled intervals. Previous understandings of pictographs and bar graphs are reviewed. For the first time, students explore dot plots, which are graphical representations to organize data that uses dots (or Xs) to show the frequency that each category occurs. Students are also formally introduced to frequency tables, which organize data by category and use tally marks, summarized with numbers, to indicate the frequency of data for each category. Students analyze and compare the data representations and determine which representation most efficiently summarizes a specific aspect of the given data. Students create horizontally or vertically oriented bar graphs and pictographs using scaled intervals. Students also create pictographs and dot plots where each symbol may represent one or more units of data and where partial symbols may be used to accurately represent the data count. While examining the similarities and differences between pictographs and dot plots, students recognize one significant difference between a pictograph and a dot plot is the arrangement of categories. Categories in a pictograph may be arbitrarily ordered and may be placed on either a horizontal or vertical axis. Whereas in a dot plot, categories are not arbitrary, meaning there is an organized or sequential arrangement (e.g., days of the week, months of the year, ranges of number in sequential order, etc.), and categories are always listed along a horizontal axis.
TEKS in this unit: 3.1A, 3.1B, 3.1C, 3.1D, 3.1E, 3.1F, 3.1G, 3.8A
GoMath!: Module 19
Unit 05: Relating Multiplication to Division
(7 classes for the entire unit)
Students use their understandings of multiplication as the framework for developing an understanding of division. Students use the sharing or partitioning model, as well as the repeated subtraction model, to connect understandings about multiplication to division. For the first time, students are introduced to the divisibility rules and use the divisibility rule of 2 and/or partitioning into two equal groups to determine if a number is odd or even. Through concrete and pictorial models of equal groups, arrays, and area models, students explore the mathematical relationships within and between multiplication and division. Students use multiplication and division facts, to construe division models (e.g., the product of a multiplication fact becomes the dividend in its related division fact). This inverse relationship between multiplication and division provides a mathematical foundation for learning basic facts families. Various strategies, including the inverse relationship, are applied to solve contextual one-step multiplication and division problems with products and dividends within 100.
TEKS in this unit: 3.1A, 3.1B, 3.1C, 3.1D, 3.1E, 3.1F, 3.1G, 3.4F, 3.4G, 3.4H, 3.4I, 3.4J, 3.4K, 3.5D
GoMath!: Module 14
Unit 06: Representing Fractions
(10 classes for the entire unit)
Students represent and explain fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 as single numbers defined by the relationship between the part (the numerator) and the whole (the denominator). Students use symbolic notation to describe fractions represented using concrete objects, pictorial models (including strip diagrams), and number lines. Students explain the unit fraction as one part of a whole that has been partitioned into equal parts and use this understanding to compose and decompose a fraction as a sum of unit fractions. Unit fractions include denominators of 2, 3, 4, 6, and 8 but are not limited to these values. Additionally, students demonstrate their fractional understanding by determining a corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given a specified point on a number line. While examining the number line, students represent the fractions halves, fourths, and eighths as distances from zero on the number line that may include fractions greater than 1. Students also solve problems that involve partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions with denominators of 2, 3, 4, 6, and 8. Solutions to problems may include fractions greater than 1 written as improper fractions or mixed numbers.
TEKS in this unit: 3.1A, 3.1B, 3.1C, 3.1D, 3.1E, 3.1F, 3.1G, 3.3A, 3.3B, 3.3C, 3.3D, 3.3E, 3.7A
GoMath!: Module 2
Unit 07: Application of Multiplication and Division
(10 classes for the entire unit)
Students extend their understanding of multiplication and division and the mathematical relationships between these operations as they represent multiplication and division of a two-digit number by a one-digit number using arrays, area models, strip diagrams, and equations. Students use the commutative (if the order of the factors are changed, the product remains the same), associative (if three or more factors are multiplied, they can be grouped in any order, and the product will remain the same), and distributive (if multiplying a number by a sum of numbers, the product will be the same as multiplying the number by each addend and then adding the products together) properties of multiplication, mental math, partial products, and the standard multiplication algorithm to represent and solve one- and two-step multiplication and division problem situations within 100. Multiplication problems include determining area of rectangles. Students explore both partitive and quotative (measurement) division problems and use divisibility generalizations to determine if a number is odd or even.
TEKS in this unit: 3.1A, 3.1B, 3.1C, 3.1D, 3.1E, 3.1F, 3.1G, 3.4G, 3.4I, 3.4J, 3.4K, 3.5B, 3.6C
GoMath!: Modules 6, 7, 8, 9, 10, 11, 12, 13, 14
Unit 08: Personal Financial Literacy
(5 classes for the entire unit)
Students explore concepts and decisions related to future financial security. Students explore how skills and education needed for jobs may impact potential income earned, as well as how scarcity or availability of resources may impact cost. Students identify and discuss decisions related to planned and unplanned spending, including the responsibilities and costs of spending using credit. Students list reasons to save and explain the benefits of saving (e.g., saving for college, surviving hard financial times, being prepared for unforeseen expenses, setting goals, etc.). Students also identify decisions regarding charitable giving.
TEKS in this unit: 3.1A, 3.1B, 3.1G, 3.9A, 3.9B, 3.9C, 3.9D, 3.9E, 3.9F
GoMath!: Module 20
Unit 09: Algebraic Reasoning – All Operations
(13 classes for the entire unit)
Students gain fluency, efficiency, and accuracy while solving one- and two-step problems involving addition and subtraction with sums and minuends within 1,000 and multiplication and division with products and dividends within 100. Students build on previous understandings of strategies based on place value, properties of operations, and pictorial representations to reason through and solve real-world problem situations. Students explain their reasoning and solution strategies using expressions, equations, and precise mathematical language. Through repeated exposure and practice, students solidify their understanding of the standard algorithm to solve problems involving multiplication of a two-digit number by a one-digit number and develop fluency using standard algorithms to solve addition and subtraction problems. Students experience various real-world situations that involve various operations, including decomposing composite figures to determine area using the additive property of area (the sum of the areas of each non-overlapping region of a composite figure equals the area of the original figure) to determine to area of the original figure. Real-world numerical relationships are presented using input-output tables. Students explore number pairs in tables to determine additive and multiplicative patterns that exist and represent the pattern (or process) using equations and expressions. Students also revisit summarizing a set of data using a frequency table, dot plot, pictograph, or bar graph. Students use these data representations to solve one- or two-step problems involving the categorical data represented.
TEKS in this unit: 3.1A, 3.1B, 3.1C, 3.1D, 3.1E, 3.1F, 3.1G, 3.4A, 3.4G, 3.4K, 3.5A, 3.5B, 3.5D, 3.5E, 3.6D, 3.8A, 3.8B
GoMath!: Module 14
Unit 10: Two- and Three-Dimensional Figures
(10 classes for the entire unit)
Students continue to develop their understanding of geometric figures by sorting and classifying two- and three-dimensional figures that may vary in size, shape, and orientation based on attributes using formal geometric language. Students focus their exploration of two-dimensional figures as they explore subcategories of quadrilaterals, including rhombuses, parallelograms, trapezoids, rectangles, and squares. Students use formal language to describe the attributes and properties of each subcategory of quadrilaterals as well as recognizing and drawing quadrilaterals that do not fit into any of the subcategories. Students also apply previous understanding of area and fractions to their exploration of two-dimensional figures. Students decompose two congruent two-dimensional figures into parts with equal areas and express the area of each part as a unit fraction of the whole. Students discover that equal shares of the same whole do not always have the same shape but are equal if the areas of each part are equal. A solid understanding of the properties and attributes of geometric figures is critical to students’ future success in the study of geometry.
TEKS in this unit: 3.1A, 3.1B, 3.1C, 3.1D, 3.1E, 3.1F, 3.1G, 3.6A, 3.6B, 3.6E
GoMath!: Module 15
Unit 11: Fractions – Equivalency and Comparisons
(12 classes for the entire unit)
Students represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using objects, pictorial models (including strip diagrams and area models), and number lines. Students explain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model. Students learn the role of the numerator and the role of the denominator. Understandings of the numerator and denominator assist students when comparing fractions with denominators of 2, 3, 4, 6, and 8 but not limited to these values. Strategies that students begin to develop when comparing fractions include comparing the size of the numerators when the denominators are the same, comparing the size of the denominators when the numerators are the same, and comparing the size of parts and the number of equal sized parts considered when the numerators and/or denominators are not the same. With extensive exploration, students develop fractional reasoning skills about the size of a fraction. For instance, students realize the smaller the number in the denominator, the larger the size of equal pieces; whereas, the larger the number in the numerator, the more equal size pieces being considered. A common misunderstanding when comparing fractions is to compare the numerators of the fractions only with no consideration of the denominators of the fractions or vice versa. Students develop an understanding that although a fraction is composed of a number in the numerator and a number in the denominator, together they represent a single value. Students also justify the comparison of fractions using symbols, words, objects, and pictorial models.
TEKS in this unit: 3.1A, 3.1B, 3.1C, 3.1D, 3.1E, 3.1F, 3.1G, 3.3F, 3.3G, 3.3H
GoMath!: Module 3
Unit 12: Measurement
(12 classes for the entire unit)
Students determine the area of rectangles and squares with whole number side lengths by multiplying the number of rows by the number of unit squares in each row. Students extend their knowledge of area to determining the area of composite figures by decomposing composite figures into non-overlapping rectangles and using the additive property of area to determine the area of the original figure. Students determine the perimeter of polygons with given side lengths as well as by measuring side lengths with both customary and metric measures. They also extend their understanding of perimeter by finding a missing length when given the perimeter of a polygon and the remaining side lengths and by applying geometric attributes to determine a missing side length. Students determine and use appropriate customary and metric units of measure, including distinguishing between fluid ounces for measuring liquid volume (capacity) and ounces for measuring weight, and determine liquid volume (capacity) and weight in problem situations. Although Grade 3 students do not convert between units of measure, relationships between the sizes of units are established in order to select an appropriate unit for efficiency and precision. In this unit, students also solve problems involving addition and subtraction of time intervals in minutes, finding an ending time when given a start time and an interval of time, and finding a start time when given an end time and an interval of time. When solving time problems, students should experience situations that require knowing there are 60 minutes in one hour. Problems may be solved using pictorial models and tools such as analog or digital clocks and/or number lines. Throughout the unit, students should experience appropriate abbreviations for all units of measure.
TEKS in this unit: 3.1A, 3.1B, 3.1C, 3.1D, 3.1E, 3.1F, 3.1G, 3.6C, 3.6D, 3.7B, 3.7C, 3.7D, 3.7E
GoMath!: Modules 16, 17, 18
Unit 13: Essential Operational Understandings
(10 classes for the entire unit)
Students revisit and solidify essential understandings of operational understandings. Students apply their understanding of place value, properties of operations (associative, commutative, and distributive properties of multiplication), and whole number operational relationships (addition, subtraction, multiplication, and division) to solve one- and two-step, real-world problem situations that include interpreting categorical data from a graph (frequency tables, dot plots, pictographs, and bar graphs). Students demonstrate their understanding of solution strategies by selecting appropriate tools, models (pictorial models, number lines, arrays, area models, equal group models), and equations to represent problems and solutions. Students analyze a variety of solutions in order to justify and evaluate the reasonableness of a solution.
TEKS in this unit: 3.1A, 3.1B, 3.1C, 3.1D, 3.1E, 3.1F, 3.1G, 3.4A, 3.4K, 3.5A, 3.5B, 3.8B
GoMath!: Modules 4, 5, 6, 10, 14
Unit 14: Essential Fractional Understandings
(7 classes for the entire unit)
Students revisit and solidify essential understandings of fractions. Students represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 and compare fractions with denominators including but not limited to 2, 3, 4, 6, and 8 presented in real-world situations. Students determine the corresponding fraction less than or equal to one when given a specific point on a number line. Students use number lines, as well as other objects and pictorial models, to represent equivalent fractions. They also explain that two fractions are equivalent if and only if they both represent the same point on the number line or represent the same portion of a same size whole for an area model. Students compare two fractions with like numerators or like denominators in problems by reasoning about their sizes and justify their conclusions using symbols, words, objects, and pictorial models. Students also solve real-world problem situations involving partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions less than or greater than 1 with denominators of 2, 3, 4, 6, and 8.
TEKS in this unit: 3.1A, 3.1B, 3.1C, 3.1D, 3.1E, 3.1F, 3.1G, 3.3B, 3.3E, 3.3F, 3.3G, 3.3H
GoMath!: Modules 2, 3
Unit 15: Measurable Attributes of Geometric Figures
(5 classes for the entire unit)
Students revisit the concepts of area and perimeter presented in real-world problem situations. Repeated practice and solid understanding of these concepts is critical to future success with numerous geometry and measurement concepts. Students use multiplication related to the number of rows times the number of unit squares in each row to determine the area of rectangles and squares with whole unit side lengths. Students also explore the relationship between the perimeters of many different polygonal figures (including regular and irregular figures) in order to generalize a method for finding the perimeter of any polygon or the side length of a polygon when given the perimeter and the remaining side lengths.
TEKS in this unit: 3.1A, 3.1B, 3.1C, 3.1D, 3.1E, 3.1F, 3.1G, 3.6C, 3.7B
GoMath!: Modules 16, 17
Texas Essential Knowledge & Skills (TEKS)
TEKS - Math - G3.pdf