Kindergarten
Kindergarten
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 Kindergarten are expected to perform their work without the use of calculators.
(4) The primary focal areas in Kindergarten are understanding counting and cardinality, understanding addition as joining and subtraction as separating, and comparing objects by measurable attributes.
(A) Students develop number and operations through several fundamental concepts. Students know number names and the counting sequence. Counting and cardinality lay a solid foundation for number. Students apply the principles of counting to make the connection between numbers and quantities.
(B) Students use meanings of numbers to create strategies for solving problems and responding to practical situations involving addition and subtraction.
(C) Students identify characteristics of objects that can be measured and directly compare objects according to these measurable attributes.
Unit 01: Introducing and Developing Numbers 0 – 5 and Reciting Numbers to 30
Unit 01: Introducing and Developing Numbers 0 – 5 and Reciting Numbers to 30
(15 classes for the entire unit)
(15 classes for the entire unit)
Students are introduced to the numbers 0 – 5. They use sets of objects up to 5 to develop an understanding of the concepts of cardinality, meaning that the last number said when counting a set of objects names the number of objects; hierarchical inclusion, meaning each prior number in the counting sequence is included in the set as the set increases; and conservation of set, meaning if the same number of objects are counted and then rearranged, the quantity of objects in the set does not change. Students apply cardinality, hierarchical inclusion, and conservation of set as they begin to grasp the true meaning of numbers. Students count forward and backward to 5 with and without objects, as well as read, write, and represent the numbers. Students also compose and decompose numbers up to 5 using objects and pictures, which parallels the development of subitizing, meaning instantly recognizing the number being represented by a small quantity of objects in random and organized arrangements. Students apply all of these skills as they consider magnitude, or relative size, to compare sets of objects up to 5 and generate a set of objects and pictures that is more than, less than, or equal to a given number. Students use comparative language to describe the comparison of numbers represented using objects, pictures, or numerals. When given a number up to 5, students are expected to generate a number that is one more than or one less than a given number. Along with the investigation of number and quantity, students are expected to recite numbers up to 30 by tens beginning with 10 and by ones beginning with any number. Practice with rote reciting of numbers and learning the correct sequence of numbers aids in developing the foundation for meaningful counting strategies.
TEKS in this unit: K.1A, K.1B, K.1C, K.1D, K.1E, K.1F, K.1G, K.2A, K.2B, K.2C, K.2D, K.2E, K.2F, K.2G, K.2H, K.2I, K.5A
GoMath!: Modules 1, 2, 3, 4, 5, 6, 7, 8
Unit 02: Introducing Contextual Sums and Minuends to 5
Unit 02: Introducing Contextual Sums and Minuends to 5
(10 classes for the entire unit)
(10 classes for the entire unit)
Students extend the use of counting concepts and mathematical relationships to develop the foundation of operations. Students use concrete objects, pictorial models, and acting out a situation to model and represent joining and separating problems. Students use these representations to solve contextual addition and subtraction problems involving sums and minuends up to 5. Students record their solution using a number sentence and orally explain their solution strategy. As students model, represent, and solve addition and subtraction problems, they begin to develop an understanding of the problem solving process that includes understanding the context of the problem situation and the question being asked, forming a plan or strategy, and using the plan or strategy to determine a solution. Although Kindergarten students are not expected to identify problem types by name, they begin to recognize contextual problems that represent joining action result unknown, separating action result unknown, and part-part-whole whole unknown situations.
TEKS in this unit: K.1A, K.1B, K.1C, K.1D, K.1E, K.1F, K.1G, K.3A, K.3B, K.3C
GoMath!: Modules 9, 11, 12
Unit 03: Introducing and Developing Numbers 6 – 10 and Reciting Numbers to 60
Unit 03: Introducing and Developing Numbers 6 – 10 and Reciting Numbers to 60
(14 classes for the entire unit)
(14 classes for the entire unit)
Students are introduced to the numbers 6 – 10. They use sets of objects up to 10 to further develop an understanding of the concepts of cardinality, meaning that the last number said when counting a set of objects names the number of objects; hierarchical inclusion, meaning each prior number in the counting sequence is included in the set as the set increases; and conservation of set, meaning if the same number of objects are counted and then rearranged, the quantity of objects in the set does not change. Students apply cardinality, hierarchical inclusion, and conservation of set as they continue to explore the true meaning of numbers. Students count forward and backward to 10 with and without objects, as well as read, write, and represent the numbers. Students also compose and decompose numbers up to 10 using objects and pictures, which parallels the development of subitizing, meaning instantly recognizing the number being represented by a small quantity of objects in random and organized arrangements. Students apply all of these skills as they consider magnitude, or relative size, to compare sets of objects up to 10 and generate a set of objects and pictures that is more than, less than, or equal to a given number. Students use comparative language to describe the comparison of numbers represented using objects, pictures, or numerals. When given a number up to 10, students are expected to generate a number that is one more than or one less than a given number. Along with the investigation of number and quantity, students are expected to recite numbers up to 60 by tens beginning with 10 and by ones beginning with any number. Practice with rote reciting of numbers and learning the correct sequence of numbers aids in developing the foundation for meaningful counting strategies.
TEKS in this unit: K.1A, K.1B, K.1C, K.1D, K.1E, K.1F, K.1G, K.2A, K.2B, K.2C, K.2D, K.2E, K.2F, K.2G, K.2H, K.2I, K.5A
GoMath!: Modules 4, 5, 6
Unit 04: Contextual Sums and Minuends to 5
Unit 04: Contextual Sums and Minuends to 5
(5 classes for the entire unit)
(5 classes for the entire unit)
Students revisit contextual sums and minuends to 5. Repeated exposure to real-world problem situations further develops students’ understanding of the problem-solving process. Although Kindergarten students are not expected to identify problem types by name, they continue to examine the context of the problem situation to distinguish between joining action result unknown, separating action result unknown, and part-part-whole whole unknown situations and the operation needed to solve the problem. Students explore a variety of strategies and representations with emphasis on orally explaining models and representations and justifying solution strategies.
TEKS in this unit: K.1A, K.1B, K.1C, K.1D, K.1E, K.1F, K.1G, K.3A, K.3B, K.3C
GoMath!: Modules 9, 11, 12
Unit 05: Data Analysis with Numbers 0 – 10
Unit 05: Data Analysis with Numbers 0 – 10
(6 classes for the entire unit)
(6 classes for the entire unit)
Students extend their knowledge about counting and comparing numbers using graphing situations where numbers represent categorical data, meaning data that represents the attributes of a group of people, events, or objects. Data may be collected from posing a question and taking a survey or based on the attributes of a collection of objects or pictures. Students sort and organize the data into two or three categories. The organized data is used to create real-object and picture graphs, and these graphs are examined to understand the components of graphing (e.g., title, labels of categories, what each cell or picture represents, etc.). Both real-object and picture graphs should be constructed side-by-side with horizontal and vertical orientations so that students are provided opportunities to compare and contrast both graphs, discussing their similarities and differences. Students use the data within the graphs to compare categories up to 10 and describe the data using comparative language. Students draw conclusions to answer questions and summarize the data represented in real-object and picture graphs.
TEKS in this unit: K.1A, K.1B, K.1C, K.1D, K.1E, K.1F, K.1G, K.8A, K.8B, K.8C
GoMath!: Modules 4, 5, 6, 20
Unit 06: Introducing and Developing Numbers 11 – 15 and Reciting Numbers to 90
Unit 06: Introducing and Developing Numbers 11 – 15 and Reciting Numbers to 90
(15 classes for the entire unit)
(15 classes for the entire unit)
Students are introduced to the number 11 – 15. They use sets of objects up to 15 to develop an understanding of the concepts of cardinality, meaning that the last number said when counting a set of objects names the number of objects; hierarchical inclusion, meaning each prior number in the counting sequence is included in the set as the set increases; and conservation of set, meaning if the same number of objects are counted and then rearranged, the quantity of objects in the set does not change. Students apply cardinality, hierarchical inclusion, and conservation of set as they continue to explore the true meaning of numbers. Students count forward and backward to 15 with and without objects, as well as read, write, and represent the numbers. Students also compose and decompose numbers up to 10 using objects and pictures, which parallels the development of subitizing, meaning instantly recognizing the number being represented by a small quantity of objects in random and organized arrangements. Students apply all of these skills as they consider magnitude, or relative size, to compare sets of objects up to 15 and generate a set of objects and pictures that is more than, less than, or equal to a given number. Students use comparative language to describe the comparison of numbers represented using objects, pictures, or numerals. When given a number up to 15, students are expected to generate a number that is one more than or one less than a given number. Along with the investigation of number and quantity, students are expected to recite numbers up to 90 by tens beginning with 10 and by ones beginning with any number. Practice with rote reciting of numbers and learning the correct sequence of numbers aids in developing the foundation for meaningful counting strategies.
TEKS in this unit: K.1A, K.1B, K.1C, K.1D, K.1E, K.1F, K.1G, K.2A, K.2B, K.2C, K.2D, K.2E, K.2F, K.2G, K.2H, K.2I, K.5A
GoMath!: Modules 7, 8
Unit 07: Introducing Contextual Sums and Minuends to 10
Unit 07: Introducing Contextual Sums and Minuends to 10
(10 classes for the entire unit)
(10 classes for the entire unit)
Students extend contextual sums and minuends to 10 to develop the foundation of operations. Students use concrete objects, pictorial models, and acting out a situation to model and represent joining and separating problems. Students use these representations to solve contextual addition and subtraction problems involving sums and minuends up to 10. Students record their solution using a number sentence and orally explain their solution strategy. As students model, represent, and solve addition and subtraction problems, they begin to develop an understanding of the problem solving process that includes understanding the context of the problem situation and the question being asked, forming a plan or strategy, and using the plan or strategy to determine a solution. Although Kindergarten students are not expected to identify problem types by name, they begin to recognize contextual problems that represent joining action result unknown, separating action result unknown, and part-part-whole whole unknown situations.
TEKS in this unit: K.1A, K.1B, K.1C, K.1D, K.1E, K.1F, K.1G, K.3A, K.3B, K.3C
GoMath!: Modules 9, 10, 11, 12, 13, 14
Unit 08: Introducing and Developing Numbers 16 – 20 and Reciting Numbers to at Least 100
Unit 08: Introducing and Developing Numbers 16 – 20 and Reciting Numbers to at Least 100
(14 classes for the entire unit)
(14 classes for the entire unit)
Students are introduced to the numbers 16 – 20. They use sets of objects up to 20 to further develop an understanding of the concepts of cardinality, meaning that the last number said when counting a set of objects names the number of objects; hierarchical inclusion, meaning each prior number in the counting sequence is included in the set as the set increases; and conservation of set, meaning if the same number of objects are counted and then rearranged, the quantity of objects in the set does not change. Students apply cardinality, hierarchical inclusion, and conservation of set as they continue to explore the true meaning of numbers. Students count forward and backward to 20 with and without objects, as well as read, write, and represent the numbers. Students also compose and decompose numbers up to 10 using objects and pictures, which parallels the development of subitizing, meaning instantly recognizing the number being represented by a small quantity of objects in random and organized arrangements. Students apply all of these skills as they consider magnitude, or relative size, to compare sets of objects up to 20 and generate a set of objects and pictures that is more than, less than, or equal to a given number. Students use comparative language to describe the comparison of numbers represented using objects, pictures, or numerals. When given a number up to 20, students are expected to generate a number that is one more than or one less than a given number. Along with the investigation of number and quantity, students are expected to recite numbers up to at least 100 by tens beginning with 10 and by ones beginning with any number. Students also extend reciting numbers to include reciting numbers by tens up to at least 100 beginning with any multiple of 10 (e.g., 10, 20, 30, 40, etc.). Practice with rote reciting of numbers and learning the correct sequence of numbers aids in developing the foundation for meaningful counting strategies.
TEKS in this unit: K.1A, K.1B, K.1C, K.1D, K.1E, K.1F, K.1G, K.2A, K.2B, K.2C, K.2D, K.2E, K.2F, K.2G, K.2H, K.2I, K.5A
GoMath!: Modules 8, 16
Unit 09: Contextual Sums and Minuends to 10
Unit 09: Contextual Sums and Minuends to 10
(5 classes for the entire unit)
(5 classes for the entire unit)
Students revisit contextual sums and minuends to 10. Repeated exposure to real-world problem situations further develops students’ understanding of the problem-solving process. Although Kindergarten students are not expected to identify problem types by name, they continue to examine the context of the problem situation to distinguish between joining action result unknown, separating action result unknown, and part-part-whole whole unknown situations and the operation needed to solve the problem. Students explore a variety of strategies and representations with emphasis on orally explaining models and representations and justifying solution strategies.
TEKS in this unit: K.1A, K.1B, K.1C, K.1D, K.1E, K.1F, K.1G, K.3A, K.3B, K.3C
GoMath!: Modules 9, 10, 11, 12, 13, 14
Unit 10: Data Analysis with Numbers 10 – 20
Unit 10: Data Analysis with Numbers 10 – 20
(6 classes for the entire unit)
(6 classes for the entire unit)
Students extend their knowledge about counting and comparing numbers from 0 – 20 using graphing situations where numbers represent categorical data, meaning data that represents the attributes of a group of people, events, or objects. Data may be collected from posing a question and taking a survey or based on the attributes of a collection of objects or pictures. Students sort and organize the data into two or three categories. The organized data is used to create real-object and picture graphs, and these graphs are examined to understand the components of graphing (e.g., title, labels of categories, what each cell or picture represents, etc.). Both real-object and picture graphs should be constructed side-by-side with horizontal and vertical orientations so that students are provided opportunities to compare and contrast both graphs, discussing their similarities and differences. Students use the data within the graphs to compare categories up to 20 and describe the data using comparative language. Students draw conclusions to answer questions and summarize the data represented in real-object and picture graphs.
TEKS in this unit: K.1A, K.1B, K.1C, K.1D, K.1E, K.1F, K.1G, K.8A, K.8B, K.8C
GoMath!: Modules 5, 6, 7, 8, 20
Unit 11: Geometry – Two-Dimensional Shapes
Unit 11: Geometry – Two-Dimensional Shapes
(9 classes for the entire unit)
(9 classes for the entire unit)
Students explore two-dimensional figures, including circles, triangles, rectangles, and squares as special rectangles. Students use their counting skills and number relationships to determine the number of sides and vertices for each shape. Students use these attributes to discern different shapes from one another, whereas orientation, color, texture, and size are not defining attributes of shapes. Informal and formal language is used interchangeably as students identify the attributes of two-dimensional shapes. Students examine the attributes and properties of two-dimensional figures to distinguish between regular or irregular figures. Students apply their knowledge from data analysis to sort and classify two-dimensional figures. Students also develop spatial reasoning and visualization skills to create circles, triangles, rectangles, and squares using a variety of materials and drawings.
TEKS in this unit: K.1A, K.1B, K.1C, K.1D, K.1E, K.1F, K.1G, K.6A, K.6D, K.6E, K.6F
GoMath!: Module 17
Unit 12: Geometry – Three-Dimensional Solids
Unit 12: Geometry – Three-Dimensional Solids
(9 classes for the entire unit)
(9 classes for the entire unit)
Students explore three-dimensional solids in the context of real world objects. Students use their knowledge of two-dimensional shapes to identify three-dimensional solids. Two-dimensional shapes found in real-world objects are identified as components of three-dimensional solids. Students also classify and sort a collection of three-dimensional objects and a mixed collection of two- and three-dimensional figures based on their geometric attributes rather than other features such as orientation, color, texture, or size.
TEKS in this unit: K.1A, K.1B, K.1C, K.1D, K.1E, K.1F, K.1G, K.6B, K.6C, K.6E
GoMath!: Module 18
Unit 13: Coin Identification
Unit 13: Coin Identification
(7 classes for the entire unit)
(7 classes for the entire unit)
Students explore traditional and special edition pennies, nickels, dimes, and quarters. Students use sorting and classifying skills to discern distinguishing features and identify U.S. coins by name. The emphasis in Kindergarten is on identification only and not on value, relationships, or counting collections.
TEKS in this unit: K.1A, K.1B, K.1C, K.1G, K.4A
GoMath!: Module 15
Unit 14: Measurable Attributes and Direct Comparisons
Unit 14: Measurable Attributes and Direct Comparisons
(8 classes for the entire unit)
(8 classes for the entire unit)
Students focus on identifying measurable attributes of objects, including length, capacity, and weight. Through repeated direct comparison opportunities, students develop an understanding of conservation (the length, capacity, or weight of an object does not change when the orientation of the object changes). Comparative language is used to describe the differences of the attributes between two objects. Students develop appropriate vocabulary for describing the differences for a specific measureable attribute versus a general term such as bigger. In Kindergarten, the focus of measurement is on direct comparisons using descriptive language rather than quantity. These direct comparisons begin to provide the foundational understanding that measurement involves a comparison of a measureable attribute of an object to a quantity of units of measurement.
TEKS in this unit: K.1A, K.1B, K.1C, K.1D, K.1E, K.1F, K.1G, K.7A, K.7B
GoMath!: Modules 19, 20
Unit 15: Numeracy
Unit 15: Numeracy
(12 classes for the entire unit)
(12 classes for the entire unit)
Students apply their knowledge of mathematical relationships to counting, problem solving, and graphing. Students increase their foundational understandings of the mathematical relationships that exist within numbers. Counting is no longer simply rote. It now involves an understanding of the relationship between the numbers in the counting sequence. Students acquire a mathematical understanding of how numbers increase by one during the forward count or decrease by one during the backward count. Because of this understanding, students are able to count forward and backward easily without the use of objects. The understanding of this relationship will also apply when reciting numbers by tens beginning with any multiple of 10 and by ones tens beginning with any given number, as well as when generating a number that is one more or one less than a given number. Students transition to reading, writing, and representing numerals without objects or pictures. Students also transition from one-to-one correspondence to working with number relationships. These mathematical relationships are applied when students generate and compare sets of objects or compare written numerals using comparative language. Students use the subitizing skills of instantly recognizing quantities as they compose and decompose numbers. An understanding of cardinality and conservation supports their work with addition and subtraction. This understanding that the last number names the set and that the arrangement of the set does not matter, allows students to perform operations with numbers with greater accuracy. Students demonstrate an understanding that joining represents addition situations while separating represents subtraction situations. Students are able to explain the strategies used to solve problems with sums and minuends to 10. Numeracy concepts extend into graphing. Students draw conclusions about data in both real-object and picture graphs.
TEKS in this unit: K.1A, K.1B, K.1C, K.1D, K.1E, K.1F, K.1G, K.2A, K.2B, K.2C, K.2D, K.2E, K.2F, K.2G, K.2H, K.2I, K.3A, K.3B, K.3C, K.5A, K.8C
GoMath!: Module 21
Unit 16: Personal Financial Literacy
Unit 16: Personal Financial Literacy
(5 classes for the entire unit)
(5 classes for the entire unit)
Students are introduced to the concept of income. Students identify ways to earn income at home and in the community. Students understand that money can be earned as income or received as a gift. Students will explore and list simple skills required for jobs for both children and adults. Students will also distinguish between wants and needs and identify income as a source to meet ones wants and needs. 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: K.1A, K.1B, K.1G, K.9A, K.9B, K.9C, K.9D
GoMath!: Module 21
Texas Essential Knowledge and Skills (TEKS)
Texas Essential Knowledge and Skills (TEKS)
TEKS - Math - K.pdfPage updated
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