Texas Essential Knowledge and Skills for Mathematics Grade 2 March 2015 Page 1
Grade 2 Mathematics The majority of the Grade 2 Mathematics TEKS standards will be fully covered by the Grade 2 Eureka Math curriculum, provided the recommendations listed are addressed. The primary areas where TEKS Grade 2 standards and Eureka Math do not align are in the domains of number and operations, geometry and measurement, and personal financial literacy. Standards for number and operations will require use of Eureka Math content from other grade levels to address these areas: the discrepancy between the maximum number of 1,000 for addition and subtraction, 100 for solving word problems, 1,200 for addition and subtraction problems, and 1,000 for word problems; fractions greater than one; partitioning and identifying eighths; the decimal point in a money context; and the creation of a situation for a given mathematical number sentence. In the domain of geometry and measurement, use of Eureka Math content from other grade levels will be needed to address these areas: geometric solids other than cubes, classifying and sorting polygons with more than six sides, area, and telling time to the one- minute increment. Personal financial literacy standards are not covered in Eureka Math. The detailed analysis of alignment is provided in the table below. With strategic placement of supplemental materials, Eureka Math can ensure students are successful in achieving the proficiencies of the TEKS standards while benefiting from the coherence and rigor of Eureka Math. Indicators Green indicates the TEKS standard is fully addressed in Eureka Math. Yellow indicates the TEKS standard may not be completely addressed in Eureka Math. Red indicates the TEKS standard is not addressed in Eureka Math. Blue indicates there is a discrepancy between the grade level at which this standard is addressed in TEKS and in Eureka Math. TEKS Domain TEKS Expectation Aligned Components of Eureka Math Mathematical process (1) Mathematical process standards. The student uses The lessons of every module contain sample Page 2
standards mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (A) apply mathematics to problems arising in everyday life, society, and the workplace; (B) 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; (C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems; student teacher dialogue in the conceptual development and debrief sections as well as questions to ask students on daily problem sets and homework that model, elicit, and assess the mathematical process standards. These standards are comparable to the CCSSM Standards for Mathematical Practice implemented by Eureka Math. Every module includes ample application problems. Every module models, elicits, and assesses students use of a problem- solving model that incorporates the elements required by this standard. Every module models, elicits, and assesses students capacity to use tools strategically as required by this standard. (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate; Every module models, elicits, and assesses students communication of mathematical ideas, reasoning, and their implications using multiple representations as identified in this standard. (E) create and use representations to organize, record, Every module models, elicits, and assesses students Page 3
and communicate mathematical ideas; (F) analyze mathematical relationships to connect and communicate mathematical ideas; and G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication. capacity to create and use representations as required by this standard. Every module models, elicits, and assesses students capacity to analyze mathematical relationships to connect and communicate mathematical ideas as required by this standard. Every module models, elicits, and assesses students capacity to display, explain, and justify mathematical ideas and arguments using precise language as required by this standard. Number and operations 2) The student applies mathematical process standards to understand how to represent and compare whole numbers, the relative position and magnitude of whole numbers, and relationships within the numeration system related to place value. The student is expected to: (A) use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum of so many thousands, hundreds, tens, and ones; G2 M4 Topic B: Strategies for Composing a Ten G2 M4 Topic C: Strategies for Decomposing a Ten G2 M4 Topic D: Strategies for Composing Tens and Hundreds G2 M4 Topic E: Strategies for Decomposing Tens and Hundreds G2 M4 Topic F: Student Explanations of Written Methods G2 M5: Addition and Subtraction Within 1,000 with Word Problems to 100 Page 4
Note: Numbers beyond 1,000 exceed the work of Grade 2 in Eureka Math. Support for this can be found in G3. G3 M2 Topic D: Two- and Three- Digit Measurement Addition using the Standard Algorithm G3 M2 Topic C: Two- and Three- Digit Subtraction using the Standard Algorithm (B) use standard, word, and expanded forms to represent numbers up to 1,200; (C) generate a number that is greater than or less than a given whole number up to 1,200; G2 M3 Lesson 6: Write base ten numbers in expanded form. G2 M3 Lesson 7: Write, read, and relate base ten numbers in all forms. G2 M3 Lesson 14: Model numbers with more than 9 ones or 9 tens; write in expanded, unit, standard, and word forms. Note: The work in Grade 2 offers instruction and practice with numbers up to 1,000. Consider extending the lessons to include instruction and practice with numbers up to 1,200 in order to meet this standard. G2 M3 Topic F: Comparing Two Three- Digit Numbers G2 M3 Topic G: Finding 1, 10, and 100 More or Less than a Number G2 M4 Lesson 1: Relate 1 more, 1 less, 10 more, and 10 less to addition and subtraction of 1 and 10. G2 M5 Lesson 1: Relate 10 more, 10 less, 100 more, and 100 less to addition and subtraction of 10 and 100. Note: The work in Grade 2 offers instruction and practice with numbers up to 1,000. Consider extending the lessons to include instruction and Page 5
practice with numbers up to 1,200 in order to meet this standard. (D) use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>, <, or =); (E) locate the position of a given whole number on an open number line; and (F) name the whole number that corresponds to a specific point on a number line. G2 M3 Topic F: Comparing Two Three- Digit Numbers G2 M3 Lesson 21: Complete a pattern counting up and down. Note: The work in Grade 2 offers instruction and practice with numbers up to 1,000. Consider extending the lessons to include instruction and practice with numbers up to 1,200 in order to meet this standard. G2 M3 Lesson 9: Count from $10 to $1,000 on the place value chart and the empty number line. G2 M7 Lesson 21: Identify unknown numbers on a number line diagram by using the distance between numbers and reference points. G2 M7 Lesson 22: Represent two- digit sums and differences involving length by using the ruler as a number line. G2 M7 Lessons 25-26: Draw a line plot to represent a given data set; answer questions and draw conclusions based on measurement data. G2 M2 Lesson 8: Solve addition and subtraction word problems using the ruler as a number line. G2 M7 Lesson 21: Identify unknown numbers on a number line diagram by using the distance between numbers and reference points. G2 M7 Lesson 22: Represent two- digit sums and differences involving length by using the ruler as a number line. Page 6
G2 M7 Lessons 25-26: Draw a line plot to represent a given data set; answer questions and draw conclusions based on measurement data. Note: This standard is addressed in the Meter Strip Addition and Meter Strip Subtraction fluencies, which are found throughout Grade 2 Modules 2 and 3. Number and operations (3) The student applies mathematical process standards to recognize and represent fractional units and communicates how they are used to name parts of a whole. The student is expected to: (A) partition objects into equal parts and name the parts, including halves, fourths, and eighths, using words; (B) explain that the more fractional parts used to make a whole, the smaller the part; and the fewer the fractional parts, the larger the part; G2 M8 Lessons 9-10: Partition circles and rectangles into equal parts, and describe those parts as halves, thirds, or fourths. G2 M8 Lesson 7-8: Interpret equal shares in composite shapes as halves, thirds, and fourths. Note: Eighths are not addressed in Grade 2 of Eureka Math. For additional support, see G3 M5: Fractions as Numbers on the Number Line G2 M8 Topic B: Composite Shapes and Fraction Concepts G2 M8 Topic C: Halves, Thirds, and Fourths of Circles and Rectangles G2 M8 Lesson 9-10: Partition circles and rectangles into equal parts, and describe those parts as halves, thirds, or fourths. Note: This standard is addressed in a measurement Page 7
context in G2 M2 Lesson 7: Measure and compare lengths using standard metric length units and non- standard length units; relate measurement to unit size and in G2 M7 Lesson 18: Measure an object twice using different units and compare; relate measurement to unit size. (C) use concrete models to count fractional parts beyond one whole using words and recognize how many parts it takes to equal one whole; and (D) identify examples and non- examples of halves, fourths, and eighths. G2 M8 Lesson 7-8: Interpret equal shares in composite shapes as halves, thirds, and fourths. G2 M8 Topic C: Halves, Thirds, and Fourths of Circles and Rectangles Note: Fractions greater than one exceed the Grade 2 standards in Eureka Math. For additional support, see G3 M5: Fractions as Numbers on the Number Line. G2 M8 Lesson 7-8: Interpret equal shares in composite shapes as halves, thirds, and fourths. G2 M8 Topic C: Halves, Thirds, and Fourths of Circles and Rectangles Notes: Eighths are not addressed in Grade 2 of Eureka Math. For additional support, see G3 M5: Fractions as Numbers on the Number Line. Number and operations (4) The student applies mathematical process standards to develop and use strategies and methods for whole number computations in order to solve addition and subtraction problems with efficiency and accuracy. The student is expected to: Page 8
(A) recall basic facts to add and subtract within 20 with automaticity; G2 M1 Topic A: Foundations for Addition and Subtraction Within 20 G2 M1 Topic B: Mental Strategies for Addition and Subtraction Within 20 Note: This standard is also addressed numerous times throughout the year during fluency activities. (B) add up to four two- digit numbers and subtract two- digit numbers using mental strategies and algorithms based on knowledge of place value and properties of operations; (C) solve one- step and multi- step word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value, including algorithms; and G2 M4 Topic A: Sums and Differences Within 100 G2 M4 Topic B: Strategies for Composing a Ten G2 M4 Topic C: Strategies for Decomposing a Ten G2 M4 Topic D: Strategies for Composing Tens and Hundreds G2 M4 Topic E: Strategies for Decomposing Tens and Hundreds G2 M5 Lesson 1: Relate 10 more, 10 less, 100 more, and 100 less to addition and subtraction of 10 and 100. G2 M5 Lesson 5: Use the associative property to make a hundred in one addend. G2 M5 Lesson 6: Use the associative property to subtract from three- digit numbers and verify solutions with addition. G2 M2 Topic D: Relate Addition and Subtraction to Length. G2 M4: Addition and Subtraction Within 200 with Word Problems to 100 G2 M5: Addition and Subtraction Within 1,000 with Word Problems to 100 G2 M6 Lesson 9: Solve Word Problems involving addition of equal groups in rows and columns. Page 9
G2 M7 Lesson 7: Solve word problems involving the total value of a group of coins. G2 M7 Lesson 8: Solve word problems involving the total value of a group of bills G2 M7 Lesson 9: Solve word problems involving different combinations of coins with the same total value. G2 M7 Lesson 12: Solve word problems involving different ways to make change from $1. G2 M7 Lesson 13: Solve two- step word problems involving dollars or cents with totals within $100 or $1. G2 M7 Lesson 20: Solve two- digit addition and subtraction word problems involving length by using tape diagrams and writing equations to represent the problem. Note: Word problems in Grade 2 Eureka Math are limited to within 100. Apart from the lessons specifically focused on problem solving, students address this standard on a daily basis when solving the Application Problem. (D) generate and solve problem situations for a given mathematical number sentence involving addition and subtraction of whole numbers within 1,000. G2 M7 Topic A: Problem Solving with Categorical Data Note: Students do not generate a situation for a given mathematical number sentence in Grade 2 Eureka Math. In Module 7, students generate questions based on the data in a given graph, but supplemental materials will be needed to address the intent of this standard. Also, please note that all data sets in Module 7 Topic A involve numbers Page 10
within 20. Number and operations (5) The student applies mathematical process standards to determine the value of coins in order to solve monetary transactions. The student is expected to: (A) determine the value of a collection of coins up to one dollar; and G2 M7 Lesson 6: Recognize the value of coins and count up to find their total value. G2 M7 Lesson 7: Solve word problems involving the total value of a group of coins. G2 M7 Lesson 9: Solve word problems involving different combinations of coins with the same total value. G2 M7 Lesson 10: Use the fewest number of coins to make a given value. Note: This standard is also addressed in numerous fluency activities throughout Grade 2 Modules 5, 6, and 7. (B) use the cent symbol, dollar sign, and the decimal point to name the value of a collection of coins. G2 M7 Topic B: Problem Solving with Coins and Bills 5A is also addressed in numerous fluency activities throughout Modules 5, 6, and 7. Note: The decimal point is not addressed in Grade 2 Eureka Math. It is found in G4 M6: Decimal Fractions. Number and operations (6) The student applies mathematical process standards to connect repeated addition and Page 11
subtraction to multiplication and division situations that involve equal groupings and shares. The student is expected to: (A) model, create, and describe contextual multiplication situations in which equivalent sets of concrete objects are joined; and (B) model, create, and describe contextual division situations in which a set of concrete objects is separated into equivalent sets. G2 M6 Topic A: Formation of Equal Groups G2 M6 Topic B: Arrays and Equal Groups G2 M6 Topic C: Rectangular Arrays as a Foundation for Multiplication and Division Note: In Eureka Math, Grade 2 Module 6 lays the foundation for multiplication and division and the relationship between the two operations through repeated addition and subtraction. Students do not multiply or divide in Grade 2. Support for the full intention of this standard can be found in Grade 3. G2 M6 Topic C: Rectangular Arrays as a Foundation for Multiplication and Division Algebraic reasoning (7) The student applies mathematical process standards to identify and apply number patterns within properties of numbers and operations in order to describe relationships. The student is expected to: (A) determine whether a number up to 40 is even or odd using pairings of objects to represent the number; G2 M6 Topic D: The Meaning of Even and Odd Numbers (B) use an understanding of place value to determine G2 M3 Topic G: Finding 1, 10, and 100 More or Less Page 12
the number that is 10 or 100 more or less than a given number up to 1,200; and Than a Number G2 M4 Lesson 1: Relate 1 more, 1 less, 10 more, and 10 less to addition and subtraction of 1 and 10. G2 M4 Lesson 2: Add and subtract multiples of 10 including counting on to subtract. G2 M4 Lesson 3: Add and subtract multiples of 10 and some ones within 100. G2 M5 Lesson 1: Relate 10 more, 10 less, 100 more, and 100 less to addition and subtraction of 10 and 100. G2 M5 Lesson 2: Add and subtract multiples of 100, including counting on to subtract. G2 M5 Lesson 3: Add multiples of 100 and some tens within 1,000. G2 M5 Lesson 4: Subtract multiples of 100 and some tens within 1,000. Note: Grade 2 Module 3: Place Value, Counting, and Comparison of Numbers to 1,000 provides support for this standard. This standard is also addressed in fluency activities, which are found throughout Grade 2 in Eureka Math. The work in Grade 2 offers instruction and practice with numbers up to 1,000. Consider extending the lessons to include instruction and practice with numbers up to 1,200 in order to meet this standard. (C) represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problem. G2 M4: Addition and Subtraction Within 200 with Word Problems to 100 G2 M5: Addition and Subtraction Within 1,000 with Word Problems to 100 Page 13
Note: This standard is addressed daily through the Application Problem component of Eureka Math. Page 14
Geometry and measurement (8) The student applies mathematical process standards to analyze attributes of two- dimensional shapes and three- dimensional solids to develop generalizations about their properties. The student is expected to: (A) create two- dimensional shapes based on given attributes, including number of sides and vertices; G2 M8 Topic: Attributes of Geometric Shapes G2 M8 Lesson 6: Combine shapes to create a composite shape; create a new shape from composite shapes. (B) classify and sort three- dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes as special rectangular prisms), and triangular prisms, based on attributes using formal geometric language; (C) classify and sort polygons with 12 or fewer sides according to attributes, including identifying the number of sides and number of vertices; G2 M8 Lesson 5: Relate the square to the cube, and describe the cube based on attributes. Note: Grade 2 in Eureka Math addresses the cube. Additional support to address the other three- dimensional solids can be found in GK Module 2 and G1 Module 5. G2 M8 Lesson 1: Describe two- dimensional shapes based on attributes. G2 M8 Lesson 2: Build, identify, and analyze two- dimensional shapes with specified attributes. G2 M8 Lesson 3: Use attributes to draw different polygons including triangles, quadrilaterals, pentagons, and hexagons. G2 M8 Lesson 4: Use attributes to identify and draw different quadrilaterals including rectangles, rhombuses, parallelograms, and trapezoids. G2 M8 Lesson 6: Combine shapes to create a composite shape; create a new shape from Page 15
composite shapes. (D) compose two- dimensional shapes and three- dimensional solids with given properties or attributes; and (E) decompose two- dimensional shapes such as cutting out a square from a rectangle, dividing a shape in half, or partitioning a rectangle into identical triangles and identify the resulting geometric parts. G2 M8 Topic A: Attributes of Geometric Shapes G2 M8 Lesson 6: Combine shapes to create a composite shape; create a new shape from composite shapes. G2 M6 Lesson 10: Use square tiles to compose a rectangle, and relate to the array model. G2 M6 Lesson 11: Use square tiles to compose a rectangle, and relate to the array model. G2 M6 Lesson 16: Use grid paper to create designs to develop spatial structuring. Note: Grade 2 in Eureka Math addresses the cube. Additional support to address the other three- dimensional solids can be found in GK Module 2 and G1 Module 5. In addition, while Module 6 addresses foundations of multiplication and division, it also provides support for composing two- dimensional shapes. G2 M8 Topic B: Composite Shapes and Fraction Concepts G2 M8 Topic C: Halves, Thirds, and Fourths of Circles and Rectangles G2 M6 Lesson 13: Use square tiles to decompose a rectangle. G2 M6 Lesson 14: Use scissors to partition a rectangle into same- size squares, and compose arrays with the squares. G2 M6 Lesson 15: Use math drawings to partition a rectangle with square tiles, and relate to repeated addition. Page 16
Note: While Module 6 addresses foundations of multiplication and division, it also provides support for decomposing two- dimensional shapes. Geometry and measurement (9) The student applies mathematical process standards to select and use units to describe length, area, and time. The student is expected to: (A) find the length of objects using concrete models for standard units of length; (B) describe the inverse relationship between the size of the unit and the number of units needed to equal the length of an object; G2 M2 Topic A: Understand Concepts About the Ruler G2 M2 Lesson 4: Measure various objects using centimeter rulers and meter sticks G2 M2 Topic C: Measure and Compare Lengths Using Different Length Units G2 M2 Lesson 9: Measure lengths of string using measurement tools, and use tape diagrams to represent and compare lengths G2 M7 Topic C: Creating an Inch Ruler G2 M7 Topic D: Measuring and Estimating Length Using Customary and Metric Units G2 M2 Lesson 4: Measure various objects using centimeter rulers and meter sticks. G2 M2 Lesson 7: Measure and compare lengths using standard metric length units and non- standard length units; relate measurement to unit size. G2 M2 Topic C: Measure and Compare Lengths Using Different Length Units G2 M7 Lesson 18: Measure an item twice using different length units and compare; relate measurement to unit size G2 M7 Topic D: Measuring and Estimating Length Page 17
Using Customary and Metric Units (C) represent whole numbers as distances from any given location on a number line; (D) determine the length of an object to the nearest marked unit using rulers, yardsticks, meter sticks, or measuring tapes; (E) determine a solution to a problem involving length, including estimating lengths; G2 M2 Lesson 8: Solve addition and subtraction word problems using the ruler as a number line. G2 M7 Lesson 21: Identify unknown numbers on a number line diagram by using the distance between numbers and reference points. G2 M7 Lesson 22: Represent two- digit sums and differences involving length by using the ruler as a number line. G2 M2 Topic A: Understand Concepts About the Ruler G2 M2 Lesson 4: Measure various objects using centimeter rulers and meter sticks. G2 M2 Topic C: Measure and Compare Lengths Using Different Length Units G2 M2 Lesson 9: Measure lengths of string using measurement tools, and use tape diagrams to represent and compare the lengths. G2 M7 Topic C: Creating an Inch Ruler G2 M7 Topic D: Measuring and Estimating Length Using Customary and Metric Units G2 Module 2: Addition and Subtraction of Length Units G2 M7 Topic C: Creating an Inch Ruler G2 M7 Topic D: Measuring and Estimating Length Using Customary and Metric Units G2 M7 Topic E: Problem Solving with Customary and Metric Units G2 M7 Topic F: Displaying Measurement Data Page 18
Note: Throughout the entire Eureka Math curriculum teachers will find that many of the Application Problems involve length. (F) use concrete models of square units to find the area of a rectangle by covering it with no gaps or overlaps, counting to find the total number of square units, and describing the measurement using a number and the unit; and (G) read and write time to the nearest one- minute increment using analog and digital clocks and distinguish between a.m. and p.m. G2 M6 Topic B: Arrays and Equal Groups G2 M6 Topic C: Rectangular Arrays as a Foundation for Multiplication and Division Note: Grade 2 Eureka Math does not address area. Additional support may be found in Grade 3 Module 4: Multiplication and Area. G2 M8 Topic D: Application of Fractions to Tell Time Note: Grade 2 Eureka Math teaches time to the nearest five- minute increment. Additional support may be found in G3 M2 Topic A: Time Measurement and Problem Solving. Page 19
Data analysis (10) The student applies mathematical process standards to organize data to make it useful for interpreting information and solving problems. The student is expected to: (A) explain that the length of a bar in a bar graph or the number of pictures in a pictograph represents the number of data points for a given category; G2 M7 Topic A: Problem Solving with Categorical Data (B) organize a collection of data with up to four categories using pictographs and bar graphs with intervals of one or more; G2 M7 Topic A: Problem Solving with Categorical Data Personal financial literacy (C) write and solve one- step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one; and (D) draw conclusions and make predictions from information in a graph. (11) The student applies mathematical process standards to manage one's financial resources effectively for lifetime financial security. The student is expected to: G2 M7 Topic A: Problem Solving with Categorical Data G2 M7 Topic A: Problem Solving with Categorical Data G2 M7 Topic F: Displaying Measurement Data Personal financial literacy standards are not covered in Eureka Math. (A) calculate how money saved can accumulate into a Page 20
larger amount over time; (B) explain that saving is an alternative to spending; (C) distinguish between a deposit and a withdrawal; (D) identify examples of borrowing and distinguish between responsible and irresponsible borrowing; (E) identify examples of lending and use concepts of benefits and costs to evaluate lending decisions; and (F) differentiate between producers and consumers and calculate the cost to produce a simple item. Page 21