4th Grade
4th 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 4 are expected to perform their work without the use of calculators.
(4) The primary focal areas in Grade 4 are use of operations, fractions, and decimals and describing and analyzing geometry and measurement. 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 represent points on a number line that correspond to a given fraction or terminating decimal. In algebraic reasoning, students will represent and solve multi-step problems involving the four operations with whole numbers with expressions and equations and generate and analyze patterns. In geometry and measurement, students will classify two-dimensional figures, measure angles, and convert units of measure. In data analysis, students will represent and interpret data.
Unit 01: Place Value of Whole Numbers and Decimals
Unit 01: Place Value of Whole Numbers and Decimals
(10 classes for the entire unit)
(10 classes for the entire unit)
Students extend their understanding of patterns in place value to represent the value of the digits in whole numbers through one billion and decimals to the hundredths using expanded notation and numerals. Students further generalize the value of each place-value position as 10 times the value of the place to its right and as one-tenth of the value of the place to its left. Students compare and order whole numbers to one billion and represent comparisons using symbols. Ordering three or more numbers may include situations involving quantifying descriptors (e.g., between two given numbers, greatest/least, ascending/descending, tallest/shortest, warmest/coldest, fastest/slowest, longest/shortest, heaviest/lightest, closest/farthest, oldest/youngest, etc.) and may involve the location of the numbers on a number line. Students represent decimals, including tenths and hundredths, using concrete and visual models (e.g., number lines, decimal disks, decimal grids, base-10 blocks) and money. Students also determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line. Comparing and ordering decimals to the hundredths is accomplished using concrete and visual models (e.g., place-value charts, number lines, decimal disks, decimal grids, base-10 blocks, money, etc.).
TEKS in this unit: 4.1A, 4.1B, 4.1C, 4.1D, 4.1E, 4.1F, 4.1G, 4.2A, 4.2B, 4.2C, 4.2E, 4.2F, 4.2H, 4.3G
GoMath!: Modules 1, 2
Unit 02: Addition and Subtraction of Whole Numbers and Decimals
Unit 02: Addition and Subtraction of Whole Numbers and Decimals
(7 classes for the entire unit)
(7 classes for the entire unit)
Students extend their understanding of rounding to numbers in the hundred thousands using their choice of strategies (e.g., number lines or numerical methods based on place value). Mathematical and real-world problem situations are analyzed for vocabulary that indicates estimation and for whether compatible numbers exist that could be used to find a reasonable estimate. Students develop the ability to recognize vocabulary descriptors that describe the effects of the adjustment on the estimation compared to the actual solution (e.g., about, close, little more/little less, around, approximately, estimated, etc.). Grade 4 students make connections between place value and the standard algorithms for adding and subtracting whole numbers to adding and subtracting decimals, including tenths and hundredths. They relate addition and subtraction of decimals to the hundredths place using concrete objects and pictorial models (e.g., tenths and hundredths grids, number lines, base-10 blocks, etc.) to the standard algorithm for adding and subtracting decimals. Skill with the standard algorithm for the addition and subtraction of decimals is applied as students determine profit from single or multiple sources for incomes and/or expenses. Also included in the unit is the expectation that students describe the basic purpose of financial institutions, including keeping money safe, borrowing money, and lending money.
TEKS in this unit: 4.1A, 4.1B, 4.1C, 4.1D, 4.1E, 4.1F, 4.1G, 4.2D, 4.4A, 4.4G, 4.10B, 4.10E
GoMath!: Module 6
Unit 03: Multiplication of Whole Numbers
Unit 03: Multiplication of Whole Numbers
(8 classes for the entire unit)
(8 classes for the entire unit)
Students determine products of a number by 10 or 100 using properties of operations (commutative and distributive properties) and place value understandings. Multiple representations of products of 2 two-digit numbers are used (e.g., arrays, area models, or equations), including representing the products for perfect squares through 15 by 15. Grade 4 students use strategies (e.g., mental math, partial products, and the commutative, associative, and distributive properties) and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. These understandings build the students’ capacity to fluently solve one-, two-, and multistep problems using combinations of addition, subtraction, and multiplication. They also represent problem situations using strip diagrams and equations with a letter standing for the unknown quantity. Students use rounding and compatible numbers to find estimates and justify reasonableness for solutions to problems involving these three operations.
TEKS in this unit: 4.1A, 4.1B, 4.1C, 4.1D, 4.1E, 4.1F, 4.1G, 4.4B, 4.4C, 4.4D, 4.4G, 4.4H, 4.5A
GoMath!: Modules 7, 8
Unit 04: Division of Whole Numbers
Unit 04: Division of Whole Numbers
(11 classes for the entire unit)
(11 classes for the entire unit)
Students represent quotients of up to four-digit whole number dividends by one-digit whole number divisors using arrays, area models, and equations. As students experience various division strategies and algorithms, including the standard algorithm, they begin to develop fluency of the operation of division. Students are expected to solve fluently one- and two-step problems involving division, including the interpretation of remainders. This unit also includes representing division problem situations using strip diagrams and equations with a letter standing for the unknown quantity. Students continue to use estimation, rounding and compatible numbers, to find estimates and justify reasonableness for solutions to problems involving division.
TEKS in this unit: 4.1A, 4.1B, 4.1C, 4.1D, 4.1E, 4.1F, 4.1G, 4.4E, 4.4F, 4.4G, 4.4H, 4.5A
GoMath!: Modules 9, 10
Unit 05: All Operations
Unit 05: All Operations
(14 classes for the entire unit)
(14 classes for the entire unit)
Students apply previously learned concepts to solve one-, two-, or multi-step problems involving addition and subtraction of whole numbers and decimals to the hundredths place, multiplication of whole numbers up to two-digit factors and up to four-digit factors by one-digit factors, and division of whole numbers up to four-digit dividends by one-digit divisors with remainders in appropriate contexts. Students examine financial literacy situations that involve calculating a profit and learn to distinguish between fixed and variable expenses. Representations of these real-life situations that continue to be utilized include strip diagrams and equations with a letter standing for the unknown quantity. This unit further requires students to represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule. These identified rules incorporate an algebraic understanding of the relationship of the values in the resulting sequence and their position in the sequence.
TEKS in this unit: 4.1A, 4.1B, 4.1C, 4.1D, 4.1E, 4.1F, 4.1G, 4.4A, 4.4H, 4.5A, 4.5B, 4.10A, 4.10B
GoMath!: Modules 6, 7, 8, 9, 10, 11
Unit 06: Fractions
Unit 06: Fractions
(18 classes for the entire unit)
(18 classes for the entire unit)
Students relate their understanding of decimal numbers to fractions that name tenths and hundredths, and represent both types of numbers as distances from zero on a number line. Along with representing fractions (including those that represent values greater than one) as sums of unit fractions, students decompose fractions into sums of fractions with the same denominator using concrete and pictorial models and record the results with symbolic representations. These expectations support understanding as students represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations. Students use benchmark fractions of 0, 1/4, 1/2, 3/4, and 1, referring to the same whole, to evaluate the reasonableness of sums and differences of fractions that may or may not have equal denominators. Using a variety of methods to determine equivalence of two fractions underlies students’ abilities to compare two fractions with different numerators and different denominators and represent those comparisons using symbols.
TEKS in this unit: 4.1A, 4.1B, 4.1C, 4.1D, 4.1E, 4.1F, 4.1G, 4.2G, 4.3A, 4.3B, 4.3C, 4.3D, 4.3E, 4.3F, 4.3G
GoMath!: Modules 3, 4, 5
Unit 07: Data Representations
Unit 07: Data Representations
(7 classes for the entire unit)
(7 classes for the entire unit)
Students represent data on a frequency table, dot plot, or stem-and-leaf plot marked with whole numbers and fractions. Students examine the characteristics of each data representation, as well as compare the similarities and differences between them. Adequate understandings of these data representations allow students to solve one- and two-step problems using data in whole number, decimal, and fraction form in a frequency table, dot plot, or stem-and-leaf plot.
TEKS in this unit: 4.1A, 4.1B, 4.1C, 4.1D, 4.1E, 4.1F, 4.1G, 4.9A, 4.9B
GoMath!: Module 17
Unit 08: Measurement
Unit 08: Measurement
(14 classes for the entire unit)
(14 classes for the entire unit)
Students begin the formal introduction to formulas to determine the perimeter and area of rectangles and squares. Students use models to determine the formulas for the perimeter of a rectangle (l + w + l + w or 2l + 2w), including the special form for perimeter of a square (4s) and the area of a rectangle (l × w). In order to develop the formulas for perimeter and area, students identify parallel and perpendicular lines. Grade 4 is the first grade level where students are formally introduced to formulas as seen on the STAAR Grade 4 Mathematics Reference Materials. Students are expected to solve problems related to perimeter and area of rectangles where dimensions are whole numbers. In addition to solving problems involving length, students also solve problems that deal with measurements of intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, and/or division as appropriate. Students identify relative sizes of measurement units within the customary and metric systems and apply this knowledge to conversion of measurements within the same measurement system, customary or metric. Conversions are limited to one-step from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table.
TEKS in this unit: 4.1A, 4.1B, 4.1C, 4.1D, 4.1E, 4.1F, 4.1G, 4.5C, 4.5D, 4.6A, 4.8A, 4.8B, 4.8C
GoMath!: Modules 14, 15
Unit 09: Geometry – Points, Lines, and Angles
Unit 09: Geometry – Points, Lines, and Angles
(11 classes for the entire unit)
(11 classes for the entire unit)
Students examine the foundations of geometry by identifying points, lines, line segments, rays, angles, and perpendicular and parallel lines. These concepts are essential for the ability to classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Although students have recognized examples of quadrilaterals in previous grade levels, students are expected to use formal geometric language such as parallel, perpendicular, acute, obtuse, and right angle to classify two-dimensional figures. Additionally, students apply knowledge of right angles to identify acute, right, and obtuse triangles. Symmetry is explored within two-dimensional figures as students identify and draw one or more lines of symmetry, if they exist, for two-dimensional figures.
TEKS in this unit: 4.1A, 4.1B, 4.1C, 4.1D, 4.1E, 4.1F, 4.1G, 4.6A, 4.6B, 4.6C, 4.6D
GoMath!: Module 13
Unit 10: Geometry – Measuring Angles
Unit 10: Geometry – Measuring Angles
(11 classes for the entire unit)
(11 classes for the entire unit)
Students illustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle that is "cut out" by the rays of the angle. They also illustrate degrees as the units used to measure an angle, where 1/360 of any circle is one degree and an angle that "cuts" n/360 out of any circle whose center is at the angle's vertex has a measure of n degrees. Using a protractor, students determine the approximate measures of angles in degrees to the nearest whole number and draw angles of a specified measure. Given one or both angle measures, students determine the measure of an unknown angle formed by two non-overlapping adjacent angles. The concepts of complementary and supplementary angles are embedded within the study of adjacent angles. Within this unit, all angle measures are limited to whole numbers.
TEKS in this unit: 4.1A, 4.1B, 4.1C, 4.1D, 4.1E, 4.1F, 4.1G, 4.7A, 4.7B, 4.7C, 4.7D, 4.7E
GoMath!: Module 14
Unit 11: Making Connections
Unit 11: Making Connections
(14 classes for the entire unit)
(14 classes for the entire unit)
Students revisit previously studied concepts, operations, multiple representations, and measurement. Students add and subtract whole numbers, decimals, and fractions with like denominators, solve problem situations involving the four operations, and represent those situations using strip diagrams and equations. Students represent real-world problem situations using input-output tables and numerical expressions to generate a number pattern that follows a given rule. Students solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate. They also solve problems related to perimeter and area of rectangles where dimensions are whole numbers. Students represent data in a frequency table, dot plot, or stem-and-leaf plot marked with whole numbers, decimals, and fractions. Students are expected to solve one- and two-step problems, including situations involving the data representations.
TEKS in this unit: 4.1A, 4.1B, 4.1C, 4.1D, 4.1E, 4.1F, 4.1G, 4.3E, 4.4A, 4.4H, 4.5A, 4.5B, 4.5D, 4.8C, 4.9A, 4.9B
GoMath!: Modules 3, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17
Unit 12: Essential Understandings of Fractions
Unit 12: Essential Understandings of Fractions
(15 classes for the entire unit)
(15 classes for the entire unit)
Students revisit and solidify essential understandings of fractions. They relate their understanding of decimal numbers to fractions that name tenths and hundredths, and represent both types of numbers as distances from zero on a number line. Along with representing fractions, including improper fractions as sums of unit fractions, students decompose fractions into sums of fractions with the same denominator using concrete and pictorial models and record their results with symbolic representations. These expectations support student understanding as they represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations. Students use benchmark fractions 0, 1/4, 1/2, 3/4, and 1, referring to the same whole, to evaluate the reasonableness of sums and differences of fractions that may or may not have equal denominators. Using a variety of methods to determine equivalence of two fractions, students compare two fractions with different numerators and different denominators and represent those comparisons using the symbols >, <, or =.
TEKS in this unit: 4.1A, 4.1B, 4.1C, 4.1D, 4.1E, 4.1F, 4.1G, 4.2G, 4.3A, 4.3B, 4.3C, 4.3D, 4.3E, 4.3F, 4.3G
GoMath!: Module 3
Unit 13: Essential Understandings of All Operations
Unit 13: Essential Understandings of All Operations
(10 classes for the entire unit)
(10 classes for the entire unit)
Students revisit and solidify essential understandings of all operations to solve one-, two-, or multistep problems. Students apply concepts of addition and subtraction of whole numbers and decimals to solve problems, including situations involving calculating profit. Students apply concepts of multiplication and division of whole numbers to solve problems, including division situations that require interpreting remainders. Students also demonstrate solving problems involving intervals of time and money. Financial understandings are discussed and examined by comparing advantages and disadvantages of saving operations; distinguishing between fixed and variable expenses; describing how to allocate a weekly allowance among spending, saving, including for college, and sharing; and describing the basic purpose of financial institutions, including keeping money safe, borrowing money, and lending.
TEKS in this unit: 4.1A, 4.1B, 4.1C, 4.1D, 4.1E, 4.1F, 4.1G, 4.4A, 4.4H, 4.8C, 4.10A, 4.10B, 4.10C, 4.10D, 4.10E
GoMath!: Modules 6, 7, 8, 9, 10, 18
Texas Essential Knowledge & Skills (TEKS)
Texas Essential Knowledge & Skills (TEKS)
TEKS - Math - G4.pdfPage updated
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