2nd Grade
2nd 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 2 are expected to perform their work without the use of calculators.
(4) The primary focal areas in Grade 2 are making comparisons within the base-10 place value system, solving problems with addition and subtraction within 1,000, and building foundations for multiplication.
(A) Students develop an understanding of the base-10 place value system and place value concepts. The students' understanding of base-10 place value includes ideas of counting in units and multiples of thousands, hundreds, tens, and ones and a grasp of number relationships, which students demonstrate in a variety of ways.
(B) Students identify situations in which addition and subtraction are useful to solve problems. Students develop a variety of strategies to use efficient, accurate, and generalizable methods to add and subtract multi-digit whole numbers.
(C) Students use the relationship between skip counting and equal groups of objects to represent the addition or subtraction of equivalent sets, which builds a strong foundation for multiplication and division.
Unit 01: Foundations of Number
Unit 01: Foundations of Number
(15 classes for the entire unit)
(15 classes for the entire unit)
Students extend their understanding of the base-10 place value system to include the thousands period and numbers up to 1,200. Students compose and decompose numbers through 1,200 in more than one way as a sum of so many one 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 form, word form, standard form, etc.). Students use place value relationships in order to generate numbers that are more or less than a given number using tools such as a hundreds chart or base-10 blocks. Students compare whole numbers up to 1,200 and represent the comparison using comparative language and symbols. Students use number lines, including open number lines, to locate, name, and represent the order of these numbers.
TEKS in this unit: 2.1A, 2.1B, 2.1C, 2.1D, 2.1E, 2.1F, 2.1G, 2.2A, 2.2B, 2.2C, 2.2D, 2.2E, 2.2F
GoMath!: Modules 1, 2, 3
Unit 02: Number Relationships
Unit 02: Number Relationships
(10 classes for the entire unit)
(10 classes for the entire unit)
Students focus on developing mathematical strategies based on patterns and number sense to strengthen their understanding of number relationships and fluency with computations. Students explore number relationships in strategies based on place value and properties of operations in order to develop automaticity in the recall of basic addition and subtraction facts, meaning executing the fact with speed and accuracy with little or no conscious effort. Students use fact family relationships to solve problems with an unknown in any position, such as start unknown, change unknown, and result unknown problems. Students also mentally calculate sums and differences for numbers using place value as they explore “10/100 more/less” relationships. Students discover patterns in odd and even numbers through the pairing of objects and determining if the number can be paired without leftovers. Students use skip counting patterns and relationships between the values of coins to determine the value of a collection of like or mixed coins up to one dollar. Students extend their representation of the value of coins to include either the cent symbol notation or the dollar sign and decimal point notation.
TEKS in this unit: 2.1A, 2.1B, 2.1C, 2.1D, 2.1E, 2.1F, 2.1G, 2.4A, 2.5A, 2.5B, 2.7A, 2.7B, 2.7C
GoMath!: Modules 4, 5, 13
Unit 03: Addition and Subtraction without Algorithms
Unit 03: Addition and Subtraction without Algorithms
(25 classes for the entire unit)
(25 classes for the entire unit)
Students apply strategies based on place value and properties of operations to add up to four two-digit numbers or subtract two-digit numbers. Students also explore flexible methods and models to solve and represent addition and subtraction situations within 1,000, which may include up to three-digit numbers. Strategies may include mental math, concrete models, pictorial representations, number sentences, and open number lines. Addition and subtraction situations, where the unknown may be any one of the terms in the problem, should include numbers that require regrouping to solve the problem. The relationship between place value and each flexible method and/or model should be emphasized in order to prepare students for the transition to algorithms in Unit 06. Within this unit, students also experience generating addition and subtraction situations when given a number sentence involving addition or subtraction of numbers within 1,000. Continued use of basic addition and subtraction fact strategies to solve problems leads to automatic recall and fact fluency. Students revisit determining the value of a collection of coins up to one dollar using formal money notation, including the dollar symbol and decimal or the cent symbol. Students also experience exchange of coins to create sets of equivalent value and to create minimal sets of coins for a given value.
TEKS in this unit: 2.1A, 2.1B, 2.1C, 2.1D, 2.1E, 2.1F, 2.1G, 2.4A, 2.4B, 2.4C, 2.4D, 2.5A, 2.5B, 2.7C
GoMath!: Module 5
Unit 04: Two- and Three-Dimensional Figures
Unit 04: Two- and Three-Dimensional Figures
(10 classes for the entire unit)
(10 classes for the entire unit)
Students analyze attributes of two-dimensional shapes and three-dimensional solids in order to develop generalizations about their properties. Using formal geometric language, students classify and sort polygons with 12 or fewer sides by identifying the number of sides and number of vertices. Students understand that all two-dimensional polygons have a specific name based on the number of sides and vertices in the figure. It is also important that students are exposed to both regular figures where sides are the same length and irregular figures where sides are not the same length. Although students at this grade level are expected to use formal geometric language, the term “right angle” when referring to corners is not an expectation until Grade 4. However, teachers may begin to associate the words “square” and “right” when describing corners of two-dimensional figures. Students use attributes based on formal geometric language to classify and sort three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes as special rectangular prisms), triangular prisms, square pyramids, and triangular pyramids. Students develop spatial visualization skills, meaning the creation and manipulation of mental representations of shapes, as they investigate creating two-dimensional shapes based on given attributes of the figures. Spatial visualization is also reinforced as students compose two-dimensional shapes and three-dimensional solids with given properties or attributes. Students also decompose two-dimensional shapes into equal or unequal parts and use geometric attributes to identify and name the resulting parts.
TEKS in this unit: 2.1A, 2.1B, 2.1C, 2.1D, 2.1E, 2.1F, 2.1G, 2.8A, 2.8B, 2.8C, 2.8D, 2.8E
GoMath!: Modules 14, 15
Unit 05: Fractions
Unit 05: Fractions
(15 classes for the entire unit)
(15 classes for the entire unit)
Students continue to develop spatial visualization skills, meaning the creation and manipulation of mental representations of shapes, as they decompose two-dimensional figures and partition objects or sets of objects into two, four, or eight parts. Students analyze the resulting parts to determine if equal parts exist and name the fractional parts using words rather than symbols (e.g., one half or 1 of 2 equal parts rather than ). Although students have not yet learned about area of two-dimensional figures, students use direct comparison to understand that the equality of fractional parts is determined based on the size in area of the parts, meaning fractional parts of an object are the same size in area and may or may not be the same shape. Students may also experience fractional parts of a set of objects when the set is defined as the whole. Through exploration, students discover and explain the relationship between the number of fractional parts used to make a whole and the size of the parts. Using concrete models, students recognize how many parts it takes to equal one whole, and use this understanding to count fractional parts beyond one whole. Students make connections between counting whole numbers and counting fractional parts as well as extend their understanding of hierarchical inclusion, meaning each prior number in the counting sequence is included in the set as the set increases, to include the sequence of fractional parts.
TEKS in this unit: 2.1A, 2.1B, 2.1C, 2.1D, 2.1E, 2.1F, 2.1G, 2.3A, 2.3B, 2.3C, 2.3D, 2.8E
GoMath!: Modules 4
Unit 06: Addition and Subtraction with Algorithms
Unit 06: Addition and Subtraction with Algorithms
(15 classes for the entire unit)
(15 classes for the entire unit)
Students apply strategies based on place value and properties of operations to add up to four two-digit numbers or subtract two-digit numbers within 1,000 in real-world problem situations. Problem situations include distinguishing between deposits and withdrawals and calculating how money saved accumulates over time with deposits. Addition and subtraction situations, where the unknown may be any one of the terms in the problem, should include numbers that require regrouping to solve the problem. Students make connections between representing and solving addition and subtractions problems using flexible methods, concrete and pictorial models, and number sentences to mental strategies and algorithms based on knowledge of place value and properties of operations. Students generate and solve problem situations for a given number sentence involving addition and subtraction of whole numbers within 1,000. Students continue to apply basic addition and subtraction fact strategies to solve problems while working toward automatic recall and fact fluency, thus increasing efficiency with mental and algorithmic problem solving.
TEKS in this unit: 2.1A, 2.1B, 2.1C, 2.1D, 2.1E, 2.1F, 2.1G, 2.4A, 2.4B, 2.4C, 2.4D, 2.7C, 2.11A, 2.11C
GoMath!: Modules 6, 7, 8, 9, 10, 13
Unit 07: Data Analysis
Unit 07: Data Analysis
(10 classes for the entire unit)
(10 classes for the entire unit)
Students demonstrate prior understanding of the process and purpose of data collection. Students transition data representations from bar-type graphs to bar graphs and from picture graphs to pictographs. A bar graph is a graphical representation to organize data that uses solid bars that do not touch each other to show the frequency (number of times) that each category occurs. Each bar represents a category and each bar within the bar graph is independent from the other bars. Students determine the total frequency of each category, the length of each bar, by associating the end of each bar to the scale marked interval of the axis. Frequency values may be interval values on the axis or in-between interval values on the axis. A pictograph is a graphical representation to organize data that uses a picture or symbol, where each picture or symbol represents one or more than one unit of data, to show the frequency (number of times) that each category occurs. In a pictograph, the value of each picture or symbol is defined by the pictograph key. Students use skip counting or repeated addition to determine the frequency, the total value of all pictures (or symbols), including partial pictures (or partial symbols), within each category. Both vertical and horizontal orientations of bar graphs and pictographs with up to four categories and intervals of one, two, five, or ten are experienced during this unit. Students summarize the factual data and inferential data (existing data used to make predictions about future data) in bar graphs and pictographs to draw conclusions and make predictions. Students also generate and solve one-step word problems based on the information in bar graphs and pictographs with intervals of one.
TEKS in this unit: 2.1A, 2.1B, 2.1C, 2.1D, 2.1E, 2.1F, 2.1G, 2.10A, 2.10B, 2.10C, 2.10D
GoMath!: Module 19
Unit 08: Time
Unit 08: Time
(7 classes for the entire unit)
(7 classes for the entire unit)
Students extend their understanding of telling time to reading and writing time to the nearest one-minute increment using digital and analog clocks. Students understand that time is a measurement attribute used to describe the length of time increments. Students make connections between the marked and unmarked increments on a number line to the face of an analog clock in order to read time to the nearest minute. Students explore the continuous nature of time measurement as it applies to the rotation of hands on an analog clock and the rotation of the digits on a digital clock. Students use previous knowledge of fractions and their relationship between common terms used for describing time, such as “a quarter to,” “a quarter past,” or “half-past.” As students explore the concept of a 24-hour day, they are able to distinguish between a.m. and p.m. as they record time. Student understand a.m. as the time period from midnight until noon, and p.m. as the time period from noon to midnight, rather than daylight indicating a.m. and dark indicating p.m. Students are also exposed to a variety of common terms related to a.m. and p.m. (such as sunrise, sunset, dawn, dusk, evening, etc.) and common activities related to each time period.
TEKS in this unit: 2.1A, 2.1B, 2.1C, 2.1D, 2.1E, 2.1F, 2.1G, 2.9G
GoMath!: Module 18
Unit 09: Linear Measurement
Unit 09: Linear Measurement
(18 classes for the entire unit)
(18 classes for the entire unit)
Students begin exploring length using concrete models of standard units (inch, foot, yard, centimeter, meter, etc.) in the customary and metric measurement systems. This exploration of measuring length leads to developing an understanding of the purpose and need for using standard units of measure in society. Students use concrete tools to measure distances and record the measure to the nearest whole unit. Through the use of concrete models of standard units, students build a strong foundation for understanding the inverse relationship between the size of a unit and the number of units needed to equal the length of an object. Students review locating whole numbers on a number line and extend their understanding to representing whole number distances from zero or any given location on the number line. The relationship between the number line and standard measuring tools is applied as students transition to determining length to the nearest whole unit using rulers, yardsticks, meter sticks, and measuring tapes. Students apply their understanding of length, including estimating lengths, to problem-solving situations. Students use benchmarks to estimate solutions (e.g., a finger joint on a thumb is approximately 1 inch, the width of tip of a finger is approximately 1 centimeter, etc.) and use actual measurements to solve problems involving adding and/or subtracting lengths, including finding the distances around the outer edges of objects.
TEKS in this unit: 2.1A, 2.1B, 2.1C, 2.1D, 2.1E, 2.1F, 2.1G, 2.9A, 2.9B, 2.9C, 2.9D, 2.9E
GoMath!: Modules 16, 17
Unit 10: Contextual Multiplication and Division
Unit 10: Contextual Multiplication and Division
(15 classes for the entire unit)
(15 classes for the entire unit)
Students model, create, and describe contextual multiplication and division situations. Students use concrete and pictorial models to represent problem situations where equal grouping is involved. Students use repeated addition or skip counting to determine the total number of objects and describe these situations using language such as “3 equal groups of 5 is 15.” Students extend the understanding of equal grouping situations to include determining the area of a rectangle. Students use concrete models of square units to cover a rectangle with no gaps or overlays, count the number of square units, and describe the measurement using a number and the label “square units.” Students discover the relationship between a variety of equal group models and the arrangement of the objects in rows and columns to determine area. Recognizing this relationship is foundational for students’ understanding of arrays and area models and future learning. Students also use concrete and pictorial models to represent problem situations where a given amount is separated into equal-sized groups and the number of groups is unknown (quotative or measurement division) as well as where a given amount is shared equally among a known number of groups and the number of objects in each group is unknown (partitive division). Students describe these situations using language such as “15 separated into 3 equal groups makes 5 in each group” or “15 separated into equal groups of 5 makes 3 groups.” Repeated exposure to modeling and describing equal grouping situations leads students to the inverse relationship between repeated addition (multiplication) and repeated subtraction (division) that is similar to the inverse relationship between addition and subtraction.
TEKS in this unit: 2.1A, 2.1B, 2.1C, 2.1D, 2.1E, 2.1F, 2.1G, 2.6A, 2.6B, 2.9F
GoMath!: Module 12
Unit 11: Essential Fractional Understandings
Unit 11: Essential Fractional Understandings
(5 classes for the entire unit)
(5 classes for the entire unit)
Students revisit and solidify essential understandings of fractions. Students partition objects or sets of objects into equal parts and name the parts, including halves, fourths, and eighths, using words rather than symbols (e.g., one half or 1 out of 2 equal parts rather than ). Students use direct comparison to understand that the equality of fractional parts of an object is determined based on the size in area of the parts, meaning fractional parts of an object are the same size in area and may or may not be the same shape. Students may also experience fractional parts of a set of objects when the set is defined as the whole. Through repeated practice modeling and naming fractions, students recognize the inverse relationship between the number of parts and the size of each part and explain this relationship using appropriate mathematical language. Students determine how many parts it takes to equal one whole and use this understanding to count fractional parts. Students further their understanding of hierarchical inclusion (each prior number in the counting sequence is included in the set as the set increases) as they apply their understanding of counting whole numbers to counting fractional parts beyond one whole using words.
TEKS in this unit: 2.1A, 2.1B, 2.1C, 2.1D, 2.1E, 2.1F, 2.1G, 2.3A, 2.3B, 2.3C
GoMath!: Modules 4, 20
Unit 12: Personal Financial Literacy
Unit 12: Personal Financial Literacy
(5 classes for the entire unit)
(5 classes for the entire unit)
Students explore the connection between the concepts of responsible spending and money management in meaningful mathematics situations. Students explore accumulating money through saving, deposits and withdrawals, and examples of responsible lending and borrowing. Students differentiate between producers and consumers and then apply these roles to real-world situations as they calculate the cost to produce a simple item. Although the student expectations related to Personal Financial Literacy in Mathematics are similar to the student expectations related to Economics in Social Studies, they do not replace each other, rather they complement each other.
TEKS in this unit: 2.1A, 2.1B, 2.1C, 2.1D, 2.1E, 2.1F, 2.1G, 2.11A, 2.11B, 2.11C, 2.11D, 2.11E, 2.11F
GoMath!: Module 20
Texas Essential Knowledge and Skills (TEKS)
Texas Essential Knowledge and Skills (TEKS)
TEKS - Math - G2.pdfPage updated
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