Tab 1: Refinement in the Mathematics TEKS Table of Contents

Tab 1: Refinement in the Mathematics TEKS Table of Contents Master Materials List 1-ii What Are the Changes K-2? 1-1 Transparency 1 1-5 Transparency 2 1-6 Handout 1 1-7 Transparency 3 1-8 TEKS K-2 Significant Changes Guide 1-9 TEKS K-2 Significant Changes Chart 1-35 What Are the Changes 3-5? 1-40 Transparency 1 1-44 Transparency 2 1-45 Handout 1 1-46 Transparency 3 1-47 TEKS 3-5 Significant Changes Guide 1-48 Significant Changes Chart 3-5 1-72 K-8 Mathematics TEKS by Strand 1-78 K-12 Mathematics TEKS Marked Up Version 1-124 Tab 1: Refinement in the Mathematics TEKS: Table of Contents 1-i

Tab 1: Refinement in the Mathematics TEKS Master Materials List Chart paper Highlighters Markers K-8 Mathematics TEKS by strand K-12 Mathematics TEKS What Are the Changes K-2? Transparencies and Handout What Are the Changes 3-5? Transparencies and Handout The following materials are not within this tab of the notebook, but they can be accessed by clicking on the links below. K-8 TEKS by strand on mailing labels K-2 TEKS with a blank column for notes 3-5 TEKS with a blank column for notes K-2 Overview PowerPoint 3-5 Overview PowerPoint K-5 Overview PowerPoint Tab 1: Refinement in the Mathematics TEKS: Master Materials List 1-ii

Activity: Materials: What Are the Changes K-2? Chart paper K-8 TEKS by strand, two copies of the assigned strand per group, one for reference and one to cut up (pages 1-78 1-123) * K-8 TEKS by strand on mailing labels may be used instead of cutting the copies of the TEKS. The mailing labels are designed to fit on 1 by 4 Avery 5161 labels. * K-8 TEKS by strand mailing label template (see link above) may be copied onto cardstock, laminated, and cut apart so that participants can move items around during their discussions. K-12 TEKS, one per group (Tab 2) K-2 TEKS with a blank column for notes, one per participant Markers Highlighters K-2 Overview PowerPoint Transparencies 1, 2, 3 (pages 1-5, 1-6, & 1-8) Handout 1 (page 1-7) Overview: Grouping: Time: Participants will investigate the refinements to the Texas Essential Knowledge and Skills and consider implications to instruction. They will also look at the refinements vertically to understand how instruction at each grade level impacts and complements other grades. Special attention will be given to the implementation of new TEKS and the modifications that will need to take place to make sure all children receive instruction in the new concepts. Large group and small group 3 hours Lesson: Procedures 1. Share PowerPoint slides relevant to changes in the K-5 TEKS. Point out that this is just a sample of what will happen to the TEKS and the TAKS over the next two years and what needs to be taught for student success on TAKS. A K-2 version, a 3-5 version, and a K-5 version of the Overview PowerPoint are Notes The PowerPoint gives teachers a reason to want to do the articulation activity because it is just a sample of the critical changes to the TEKS and TAKS that will impact instruction in the classroom. What type of instructional strategies and questioning techniques must What Are the Changes K-2? 1-1

Procedures available so that you can decide which best meets the needs of your audience. See the Master Materials List (page 1-ii) for link information. See the speaker notes within the PowerPoint file for suggestions on points to bring out on some of the slides. 2. Sort teachers by grade level. Have each table of Kindergarten teachers number off from 1 to 6. Then repeat the process with 1 st and 2 nd grade teachers. 3. Assign teachers to groups as follows: 1. Number, operation, and quantitative reasoning 2. Patterns, relationships, and algebraic thinking 3. Geometry and spatial reasoning 4A. Measurement (linear measurement, area, capacity, and volume) 4B. Measurement (remaining measurement TEKS) 5. Probability and Statistics 4. Determine where each group will work and have teachers move. 5. Direct each group to study their assigned strand and identify the refinements to the TEKS in it. Each group will make a chart showing: the new or refined TEKS where the concept was introduced where the concept is mastered Notes teachers use to address the spirit of the TEKS? What should the culture of the mathematics classroom look like and sound like? Even though there is no TAKS test in K-2, teachers need to understand that the content from K-2 is tested in 3 rd grade. If a teacher teaches more than one grade then he/she must choose one of the grades for this activity. For everything to work smoothly, trainers should have at least 6 people in each grade level group. If there are not enough teachers from a particular grade level, ask for volunteers to work with the group that is too small. Use Transparency 1 (page 1-5) to assign participants to each strand. Note: Trainers will probably want to split measurement. Have one group do linear measurement, area, capacity, and volume, and the other group do everything else. Be sure everyone understands that they should also study the Introductory Paragraphs to see if there is anything there that could impact their work. Have someone from each group pick up the TEKS for its assigned strand. Use Transparency 2 (page 1-6) and make sure instructions are understood. Each group will have TEKS for the assigned strand for grades K-8 (pages 1-78 1-123). Suggest that groups cut apart one What Are the Changes K-2? 1-2

Procedures any gaps (These are places in the TEKS where a concept is addressed in the grade level before and grade level after, but not in grade being studied.) Encourage participants to follow a concept back to where it is first introduced and forward to mastery. Handout 1 (page 1-7) will help groups organize. Refer participants to this handout and complete one example with the large group to make sure that everyone understands the task. Because of the nature of the activity, some groups will finish before others. For those that finish early, have them look through the measurement TEKS or have them identify TEKS that will influence numerical fluency. 6. While in the strand groups, participants should look at the changes at each grade level and identify the most significant refinements by grade level. 7. Post vertical articulation charts around the room. Notes grade at a time. Also, since the K&S statement may be cut apart from the SE, suggest that they label each SE with the K&S number. (See the materials list for a link to masters for printing peel and stick labels.) A set of the K-12 TEKS (Tab 2) should also be provided so that participants can determine if something deleted was actually moved to a different strand. **If you are working with a group of novice teachers or teachers that have not been part of an alignment activity, you have the materials to do a complete alignment instead of just focusing on the refinements. This will take more time but will be very beneficial in the long run. Each person should record changes for his/her particular grade level to take back to the grade level group. The debriefing of this part of the activity could be each group reporting on their findings or a gallery walk. Note: If something is deleted from the TEKS, the group needs to determine whether it has moved to a different grade or strand or is really deleted. Also, if something is added, is it really new or moved from another strand or grade level? When debriefing this part of the activity, ask participants to stick to the changes instead of giving an overview of the strand. Make sure the instructional What Are the Changes K-2? 1-3

Procedures 8. After debriefing the vertical articulation work, ask participants to return to the grade-level tables. 9. At each table, the strand expert should debrief the rest of the team. 10. After each strand has been debriefed, each table will prepare a list of the most significant changes at that grade level and implications for the classroom and record the list on chart paper. 11. Debrief the activity by doing a gallery walk. After everyone has completed the walk, end with a general discussion of the most significant changes to the TEKS and the implications in the classroom. Notes implications of new material at all three grade levels is discussed. For example, 2006 first grade students will have to be taught the new Kindergarten measurement TEKS as well as the new 1 st grade measurement TEKS. Each table should have at least one expert per strand. For the groups with more than one expert on a strand, one should report to the group, and then the other should make any additions needed. This is a type of jig-saw activity. Use Transparency 3 (page 1-8). A guide (pages 1-9 1-34) that highlights the significant changes and a chart (page 1-35 1-39) with information about the type of changes and notes about those changes are provided for the trainers to use. The TEKS with the blank column is a good place for participants to make notes about significant changes. (See materials list for link to this version.) What Are the Changes K-2? 1-4

Based on your group number assignment, you will study the following strand. #1 Number, operation, and quantitative reasoning #2 Patterns, relationships, and algebraic thinking #3 Geometry and spatial reasoning #4A Measurement (linear measurement, area, capacity, and volume) #4B Measurement (remaining measurement TEKS) #5 Probability and Statistics In addition, each group will study the Introductory Paragraphs for grades K, 1, and 2 to look for references to their group s assigned content strand. Transparency 1 What Are the Changes K-2? 1-5

Study your assigned strand and the Introductory Paragraphs for grades K, 1, and 2. Identify the changes within the strand by grade level. On chart paper develop a vertical articulation for the TEKS that have been modified in the assigned strand. Trace each concept back to where it was first introduced. Be sure to note when a concept should be mastered. Use Handout #1 as a recording sheet. If a concept has been deleted, is it no longer a part of the TEKS, or has it been moved to another grade level or strand? If a concept has been added to your strand, is it really new or has it been moved from another grade level or strand? Transparency 2 What Are the Changes K-2? 1-6

TEKS Refinement and Implications for the Classroom New/Refined TEKS or Intro. Paragraph First Introduced (grade) Should be mastered (grade) Nature of change (New concept, deleted concept, clarify language, etc.) Implications for the Classroom Handout 1 What Are the Changes K-2? 1-7

Record most significant changes for your grade level (5 content strands) on chart paper. Post Transparency 3 What Are the Changes K-2? 1-8

TEKS K-2 Significant Changes This document is intended as a resource for the trainer and not necessarily to be copied for participants. However, different trainers have different styles, thus the document is formatted so that if it is copied on a black and white copier, the changes are still apparent. New refinements are in bold red and underlined, deletions are in plain blue text with a strike through. 111.12. Mathematics, Kindergarten. (a) Introduction. (2) Throughout mathematics in Kindergarten-Grade 2, students build a foundation of basic understandings in number, operation, and quantitative reasoning; patterns, relationships, and algebraic thinking; geometry and spatial reasoning; measurement; and probability and statistics. Students use numbers in ordering, labeling, and expressing quantities and relationships to solve problems and translate informal language into mathematical symbols. Students use patterns to describe objects, express relationships, make predictions, and solve problems as they build an understanding of number, operation, shape, and space. Students use informal language and observation of geometric properties to describe shapes, solids, and locations in the physical world and begin to develop measurement concepts as they identify and compare attributes of objects and situations. Students collect, organize, and display data and use information from graphs to answer questions, make summary statements, and make informal predictions based on their experiences. (2) Throughout mathematics in Kindergarten-Grade 2, students build a foundation of basic understandings in number, operation, and quantitative reasoning; patterns, relationships, and algebraic thinking; geometry and spatial reasoning; measurement; and probability and statistics. Students use numbers in ordering, labeling, and expressing quantities and relationships to solve problems and translate informal language into mathematical language and symbols. Students use objects to create and identify patterns and use those patterns to express relationships, make predictions, and solve problems as they build an understanding of number, operation, shape, and space. Students progress from informal to formal language to describe two- and three-dimensional geometric figures and likenesses in the physical world. Students begin to develop measurement concepts as they identify and compare attributes of objects and situations. Students collect, organize, and display data and use information from graphs to answer questions, make summary statements, and make informal predictions based on their experiences. The first change to occur is the addition of mathematical language. It is important for Kindergarten children to begin to hear the formal language of mathematics. As with learning any language, children need to build their mathematical vocabulary by hearing and seeing the words within the correct context. Secondly, as with the previous Texas Essential Knowledge and Skills, students are required to identify patterns, but to be developmentally appropriate students must also build/create patterns as well. Lastly, as with all mathematical concepts, it is important for students to identify geometric figures within their TEKS K-2 Significant Changes Guide 1-9

physical world. As children do this it is important that the correct vocabulary of two- and three-dimensional figures is used. This use of vocabulary is now aligned throughout the K-12 curriculum. (3) Throughout mathematics in Kindergarten-Grade 2, students develop numerical fluency with conceptual understanding and computational accuracy. Students in Kindergarten-Grade 2 use basic number sense to compose and decompose numbers in order to solve problems requiring precision, estimation, and reasonableness. By the end of Grade 2, students know basic addition and subtraction facts and are using them to work flexibly, efficiently, and accurately with numbers during addition and subtraction computation. This is a completely new statement and reflects the need for students to become numerically fluent. Children need much practice composing and decomposing numbers. This does not imply that students need to memorize facts. In fact, it is the complete opposite. Efficiency does not occur until flexibility and accuracy are mastered. Kindergarten students need to develop a strong foundation of number. Addition and subtraction facts should not be presented abstractly at this level. (4) (3) Problem solving, language and communication, connections within and outside mathematics, and formal and informal reasoning underlie all content areas in mathematics. Throughout mathematics in Kindergarten-Grade 2, students use these processes together with technology and other mathematical tools such as manipulative materials to develop conceptual understanding and solve meaningful problems as they do mathematics. This statement s change is the addition of meaningful contexts. Throughout mathematics, students need to see relevant, meaningful applications of mathematics to their world in ways that develop and reinforce the concepts they are learning. (b) Knowledge and skills. (K.1) Number, operation, and quantitative reasoning. The student uses numbers to name quantities. (B) use sets of concrete objects to represent quantities given in verbal or written form (through 9); (K.1) Number, operation, and quantitative reasoning. The student uses numbers to name quantities. (B) use sets of concrete objects to represent quantities given in verbal or written form (through 20); Previously students needed to use concrete objects to represent quantities to 9. They are now required to do the same thing with numbers through 20. Also, this now is aligned with the development of the formal language for numbers found in K.1.C (K.1) Number, operation, and quantitative reasoning. The student uses numbers to name quantities. (C) use numbers to describe how many objects are in a set (through 20) using verbal and symbolic descriptions As with the introductory paragraph, it is important for students to develop the formal mathematical language in verbal and written form. Children in Kindergarten must have an understanding of numbers through 20. TEKS K-2 Significant Changes Guide 1-10

(K.3) Number, operation, and quantitative reasoning. The student recognizes that there are quantities less than a whole. (A) share a whole by separating it into two equal parts; and The intention with this change is to be more specific about the fractions that are taught at the Kindergarten level. Children need to work on understanding the whole and separating the whole into two equal parts. This use of vocabulary also promotes composing and decomposing numbers like that addressed in Paragraph 3 in the Introduction. (K.4) Number, operation, and quantitative reasoning. The student models addition (joining) and subtraction (separating). The student is expected to model and create addition and subtraction problems in real situations with concrete objects. The refinements that occur with this expectation statement address informal vocabulary. The use of joining and separating allows for the development of the conceptual understanding of addition and subtraction. This use of vocabulary also promotes composing and decomposing numbers like that addressed in Paragraph 3 in the Introduction. (K.8) Geometry and spatial reasoning. The student uses attributes to determine how objects are alike and different. (C) sort objects according to their attributes and describe how those groups are formed. (K.8) Geometry and spatial reasoning. The student uses attributes to determine how objects are alike and different. (C) sort a variety of objects including two- and three-dimensional geometric figures according to their attributes and describe how the objects are sorted. The refinements in this statement are due to mathematical vocabulary, which allows for alignment, K-12. It is important for children to distinguish between two- and three-dimensional geometric figures. (K.9) Geometry and spatial reasoning. The student recognizes characteristics of shapes and solids. (K.9) Geometry and spatial reasoning. The student recognizes attributes of two- and three-dimensional geometric figures. The refinements in this statement are due to mathematical vocabulary, which allows for alignment, K-12. It is important for children to distinguish between two- and three-dimensional geometric figures. (K.9) Geometry and spatial reasoning. The student recognizes characteristics of shapes and solids. (A) describe and compare real-life objects or models of solids; (K.9) Geometry and spatial reasoning. The student recognizes attributes of two- and three-dimensional geometric figures. (A) describe and compare the attributes of real-life objects such as balls, boxes, cans, and cones or models of three-dimensional geometric figures; The refinements in this statement address formal mathematical language, giving examples of threedimensional objects and vocabulary appropriate for Kindergarten students. TEKS K-2 Significant Changes Guide 1-11

(K.9) Geometry and spatial reasoning. The student recognizes characteristics of shapes and solids. (B) recognize shapes in real-life objects or models of solids; (K.9) Geometry and spatial reasoning. The student recognizes attributes of two- and three-dimensional geometric figures. (B) recognize shapes in real-life three-dimensional geometric figures or models of threedimensional geometric figures; The refinements in this statement were made to formalize the mathematical vocabulary and align the TEKS K-12. (K.9) Geometry and spatial reasoning. The student recognizes characteristics of shapes and solids. (C) describe, identify, and compare circles, triangles, and rectangles, including squares. (K.9) Geometry and spatial reasoning. The student recognizes attributes of two- and three-dimensional geometric figures. (C) describe, identify, and compare circles, triangles, rectangles, and squares (a special type of rectangle). Refinements in K.9.C include modifications in mathematical vocabulary. The expectation is that students will be able to define square as being a special type of rectangle. (K.10) Measurement. The student directly compares the uses attributes of such as length, weight, or capacity to compare and order objects. (K.10) Measurement. The student directly compares the [uses] attributes of length, area, weight/mass, capacity, and/or relative temperature. The student uses comparative language to solve problems and answer questions. There are many content refinements within this statement. Kindergarten students are now required to solve problems by comparing not only length and capacity, but also area and weight/mass. Students need to be actively engaged in hands-on learning when addressing this knowledge and skills statement. (K.10) Measurement. The student directly compares the uses attributes of such as length, weight, or capacity to compare and order objects. (A) compare and order two or three concrete objects according to length (shorter or longer), capacity (holds more or holds less), or weight (lighter or heavier); and (K.10) Measurement. The student directly compares the [uses] attributes of length, area, weight/mass, capacity, and/or relative temperature. The student uses comparative language to solve problems and answer questions. The student is expected to: (A) compare and order two or three concrete objects according to length (longer/shorter than, or the same); There are many refinements to the measurement strand for Kindergarten. This particular statement has been modified to only cover length. The wording has been changed so that correct grammar is used when comparing objects. TEKS K-2 Significant Changes Guide 1-12

(K.10) Measurement. The student uses attributes such as length, weight, or capacity to compare and order objects. (B) find concrete objects that are about the same as, less than, or greater than a given object according to length, capacity, or weight. (K.10) Measurement. The student directly compares the attributes of length, area, weight/mass, capacity, and/or relative temperature. The student uses comparative language to solve problems and answer questions. (B) compare the areas of two flat surfaces of two-dimensional figures (covers more, covers less, or covers the same); The old statement is now separated into new statements. This particular statement is a new concept being taught in Kindergarten. Students are now required to compare areas of two-dimensional figures. The use of the vocabulary and understanding of the concepts of covers more, covers less, and covers the same is very important for the foundation of measurement of area. (K.10) Measurement. The student directly compares the attributes of length, area, weight/mass, capacity, and/or relative temperature. The student uses comparative language to solve problems and answer questions. (C) compare two containers according to capacity (holds more, holds less, or holds the same); This statement was originally included in K.10.A (old) and K.10.B (old). Children need to continue to solve problems involving comparison of capacity. The wording has been changed so that correct grammar is used when comparing objects. (K.10) Measurement. The student directly compares the attributes of length, area, weight/mass, capacity, and/or relative temperature. The student uses comparative language to solve problems and answer questions. (D) compare two objects according to weight/mass (heavier than, lighter than or equal to); and It is now required to compare weight/mass instead of just weight. It is important for teachers to understand the difference. The wording has been changed so that correct grammar is used when comparing objects. (K.10) Measurement. The student directly compares the attributes of length, area, weight/mass, capacity, and/or relative temperature. The student uses comparative language to solve problems and answer questions. (E) compare situations or objects according to relative temperature (hotter/colder than, or the same as). This statement was moved from K.11.A The wording has been changed so that correct grammar is used when comparing objects. (K.11) Measurement. The student uses time and temperature to compare and order events, situations, and/or objects. (K.11) Measurement. The student uses time to describe, compare, and order events and situations. TEKS K-2 Significant Changes Guide 1-13

The knowledge and skills statement has changed because temperature has been moved to K.10. Students are also now required to describe events and situations. K.11) Measurement. The student uses time and temperature to compare, and order events, situations, and/or objects. (A) compare situations or objects according to temperature such as hotter or colder; Temperature has been moved to K.10. E (new). K.11) Measurement. The student uses time to describe, compare, and order events and situations. (A) compare events according to duration such as more time than or less time than; Since K.11.A (old) was moved to K.10.E, K.11.B (old) moved to K.10.A (new). Students are also required to describe events and situation when learning about time. (K.11) Measurement. The student uses time and temperature to compare and order events, situations, and/or objects. (C) sequence events; and (K.11) Measurement. The student uses time to describe, compare, and order events and situations. (B) sequence events (up to three); and TEK K.11.C (old) was re-lettered as K.11.B. Students now have to describe events and situations when sequencing up to three events or situations. Before there was no limit on the number of events that needed to be sequenced. (K.13) Underlying processes and mathematical tools. The student applies Kindergarten mathematics to solve problems connected to everyday experiences and activities in and outside of school. (B) use a problemsolving model, with guidance, that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; (K.13) Underlying processes and mathematical tools. The student applies Kindergarten mathematics to solve problems connected to everyday experiences and activities in and outside of school. (B) solve problems with guidance that incorporates the processes of understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; The refinements made to this statement are due to wording and make the statement clearer. The writers also wanted teachers to understand that solving problems encompasses the process skills of mathematics. (K.14) Underlying processes and mathematical tools. The student communicates about Kindergarten mathematics using informal language. (A) explain and record observations using objects, words, pictures, numbers, and technology; and TEKS K-2 Significant Changes Guide 1-14

(K.14) Underlying processes and mathematical tools. The student communicates about Kindergarten mathematics using informal language. (A) communicate mathematical ideas using objects, words, pictures, numbers, and technology; and The refinements to this statement broadens the possibilities of communication. (K.15) Underlying processes and mathematical tools. The student uses logical reasoning to make sense of his or her world. The student is expected to reason and support his or her thinking using objects, words, pictures, numbers, and technology. (K.15) Underlying processes and mathematical tools. The student uses logical reasoning. The student is expected to justify his or her thinking using objects, words, pictures, numbers, and technology. This statement s refinements consist of rewording and require justification of answers, a higher order thinking skill. 111.13. Mathematics, Grade 1. (a) Introduction. (1) Within a well-balanced mathematics curriculum, the primary focal points at Grade 1 are adding and subtracting whole numbers and organizing and analyzing data. (1) Within a well-balanced mathematics curriculum, the primary focal points at Grade 1 are building number sense through number relationships, adding and subtracting whole numbers, organizing and analyzing data, and working with two- and threedimensional geometric figures. This statement was changed with the addition of students investigating number relationships and working with two- and three-dimensional geometric figures. (2) Throughout mathematics in Kindergarten-Grade 2, students build a foundation of basic understandings in number, operation, and quantitative reasoning; patterns, relationships, and algebraic thinking; geometry and spatial reasoning; measurement; and probability and statistics. Students use numbers in ordering, labeling, and expressing quantities and relationships to solve problems and translate informal language into mathematical symbols. Students use patterns to describe objects, express relationships, make predictions, and solve problems as they build an understanding of number, operation, shape, and space. Students use informal language and observation of geometric properties to describe shapes, solids, and locations in the physical world and begin to develop measurement concepts as they identify and compare attributes of objects and situations. Students collect, organize, and display data and use information from graphs to answer questions, make summary statements, and make informal predictions based on their experiences. TEKS K-2 Significant Changes Guide 1-15

(2) Throughout mathematics in Kindergarten-Grade 2, students build a foundation of basic understandings in number, operation, and quantitative reasoning; patterns, relationships, and algebraic thinking; geometry and spatial reasoning; measurement; and probability and statistics. Students use numbers in ordering, labeling, and expressing quantities and relationships to solve problems and translate informal language into mathematical language and symbols. Students use objects to create and identify patterns and use those patterns to express relationships, make predictions, and solve problems as they build an understanding of number, operation, shape, and space. Students progress from informal to formal language to describe two- and three-dimensional geometric figures and likenesses in the physical world. Students begin to develop measurement concepts as they identify and compare attributes of objects and situations. Students collect, organize, and display data and use information from graphs to answer questions, make summary statements, and make informal predictions based on their experiences. The first change to occur is the addition of mathematical language. It is important for first grade children to begin to hear the formal language of mathematics. As with learning any language, children need to build their mathematical vocabulary by hearing and seeing the words within the correct context. Secondly, as with the previous Texas Essential Knowledge and Skills, students are required to identify patterns, but to be developmentally appropriate students must also build/create patterns as well. Lastly, as with all mathematical concepts, it is important for students to identify geometrical figures within their physical world. As children do this it is important that the correct vocabulary of two- and three-dimensional figures is used. This use of vocabulary is now aligned throughout the K-12 curriculum. (3) Throughout mathematics in Kindergarten-Grade 2, students develop numerical fluency with conceptual understanding and computational accuracy. Students in Kindergarten-Grade 2 use basic number sense to compose and decompose numbers in order to solve problems requiring precision, estimation, and reasonableness. By the end of Grade 2, students know basic addition and subtraction facts and are using them to work flexibly, efficiently, and accurately with numbers during addition and subtraction computation. This is a completely new statement and reflects the need for students to become numerically fluent. Children need much practice composing and decomposing numbers. This does not imply that students need to memorize facts. In fact, it is the complete opposite. Efficiency does not occur until flexibility and accuracy are mastered. First grade students need to develop a strong foundation of number. Addition and subtraction facts should not be presented abstractly at this level. (4) (3) Problem solving, language and communication, connections within and outside mathematics, and formal and informal reasoning underlie all content areas in mathematics. Throughout mathematics in Kindergarten-Grade 2, students use these processes together with technology and other mathematical tools such as manipulative materials to develop conceptual understanding and solve meaningful problems as they do mathematics. This statement s change is the addition of meaningful contexts. Throughout mathematics, students need to see relevant, meaningful applications of mathematics to their world in ways that develop and reinforce the concepts they are learning. TEKS K-2 Significant Changes Guide 1-16

(b) Knowledge and skills. (1.1) Number, operation, and quantitative reasoning. The student uses whole numbers to describe and compare quantities. (C) use words and numbers to describe the values of individual coins such as penny, nickel, dime, and quarter and their relationships; and (1.1) Number, operation, and quantitative reasoning. The student uses whole numbers to describe and compare quantities. (C) identify individual coins by name and value and describe relationships among them; and The change to this student expectation is rewording the statement and thus broadening the knowledge. It no longer specifies the coins that need to be taught. (1.2) Number, operation, and quantitative reasoning. The student uses pairs of whole numbers to describe fractional parts of whole objects or sets of objects. The student is expected to: (A) share a whole by separating it into equal parts and use appropriate language to describe the parts such as three out of four equal parts; and (1.2) Number, operation, and quantitative reasoning. The student uses pairs of whole numbers to describe fractional parts of whole objects or sets of objects. The student is expected to: (A) separate a whole into two, three, or four equal parts and use appropriate language to describe the parts such as three out of four equal parts; and The refinements made to this knowledge and skill are rewording for simplification. Added to the content is the specificity of two, three, or four equal parts of a whole. This use of vocabulary also promotes composing and decomposing numbers like that addressed in Paragraph 3 in the Introduction. (1.3) Number, operation, and quantitative reasoning. The student recognizes and solves problems in addition and subtraction situations. (B) learn and apply basic addition facts (sums to 18) using concrete models. (1.3) Number, operation, and quantitative reasoning. The student recognizes and solves problems in addition and subtraction situations. (B) use concrete and pictorial models to apply basic addition and subtraction facts (up to 9 + 9 = 18 and 18 9 = 9). Refinements to this student expectation are tremendous. First, students use concrete and pictorial models. This change is developmentally appropriate and very important for students to build a visualization of addition and subtraction facts. They are not to memorize facts without any connection to meaningful problem solving or concrete objects. The second change appears in the students investigating the relationship that occurs between addition and subtraction. This expectation promotes composing and decomposing numbers like that addressed in Paragraph 3 in the Introduction. (1.4) Patterns, relationships, and algebraic thinking. The student uses patterns to make predictions. The student is expected to (A) identify, describe, and extend concrete and pictorial patterns in order to make predictions and solve problems; and (B) use patterns to skip count by twos, fives, and tens. TEKS K-2 Significant Changes Guide 1-17

(1.4) Patterns, relationships, and algebraic thinking. The student uses repeating patterns and additive patterns to make predictions. The student is expected to identify, describe, and extend concrete and pictorial patterns in order to make predictions and solve problems. The new knowledge and skills statement is a rewrite of the original two student expectation statements. 1.4.A (old) is included and unchanged. The statement following what is expected of the student is the exact same statement as what appeared in 1.4.A. The change came in what could be found in statement 1.4.B. It originally [1.4.B (old)] stated skip counting by twos, fives, and tens. This statement has been moved to 1.5.A (new).yet, skip counting is considered an additive pattern. Thus, by changing the statement to repeating and additive patterns, the intention of what should be taught has broadened. This also includes examples like the stair problem included in this professional development. Be sure teachers understand that whatever pattern they are developing, it must be developmentally appropriate. (1.5) Patterns, relationships, and algebraic thinking. The student recognizes patterns in numbers and operations. (A) use patterns to skip count by twos, fives, and tens; This is a new statement for 1.5, but has only been moved from 1.4.B (old). (1.5) Patterns, relationships, and algebraic thinking. The student recognizes patterns in numbers and operations. The student is expected to (D) use patterns to develop strategies to solve basic addition and basic subtraction problems; and This is a new statement and is connected to 1.3.B (new). It is very important for students to understand the relationships that occur among operations. This is a major change for first graders. They are not to just memorize facts, but build a visualization of these facts through meaningful problem solving and the use of concrete objects. Strategies that are used during this professional development are research based and help students develop strategies that will help them use patterns and understand the relationships that exist between addition and subtraction. This concept helps develop numerical fluency by having students compose and decompose numbers like that addressed in Paragraph 3 in the Introduction. (1.6) Geometry and spatial reasoning. The student uses attributes to identify, compare, and contrast shapes and solids. (1.6) Geometry and spatial reasoning. The student uses attributes to identify twoand three-dimensional geometric figures. The student compares and contrasts two- and three-dimensional geometric figures or both. The refinements in this statement are due to mathematical vocabulary which allows for alignment, K-12. It is important for children to distinguish between two- and three-dimensional geometric figures. (1.6) Geometry and spatial reasoning. The student uses attributes to identify, compare, and contrast shapes and solids. [(A) describe and identify objects in order to sort them according to a given attribute using informal language;] TEKS K-2 Significant Changes Guide 1-18

(1.6) Geometry and spatial reasoning. The student uses attributes to identify, compare, and contrast shapes and solids. [(B)] identify circles, triangles, and rectangles, including squares, and describe the shape of balls, boxes, cans, and cones; and (1.6) Geometry and spatial reasoning. The student uses attributes to identify twoand three-dimensional geometric figures. The student compares and contrasts two- and three-dimensional geometric figures or both. (A) describe and identify two-dimensional geometric figures, including circles, triangles, rectangles, and squares (a special type of rectangle); There are several refinements that occur in 1.6. Beginning with 1.6.A (old) is moved to 1.6.C. Another change in this statement is due to vocabulary and now is aligned K-12. It is important for children to distinguish between two- and three-dimensional geometric figures by describing as well as identifying those figures. The original statement (1.6.B) included three-dimensional figures. Now, three-dimensional figures are covered in 1.6.B (new). (1.6) Geometry and spatial reasoning. The student uses attributes to identify twoand three-dimensional geometric figures. The student compares and contrasts two- and three-dimensional geometric figures or both. (B) describe and identify three-dimensional geometric figures, including spheres, rectangular prisms (including cubes), cylinders, and cones;. This is a new statement built from 1.6.B (old). One of the refinements in this statement is due to vocabulary and now is aligned K-12. It is important for children to distinguish between two- and threedimensional geometric figures by describing as well as identifying those figures. The three-dimensional figures that must be described and identified are specifically given so there is no question about the content that must be covered. (1.6) Geometry and spatial reasoning. The student uses attributes to identify twoand three-dimensional geometric figures. The student compares and contrasts two- and three-dimensional geometric figures or both. (C) describe and identify two- and three-dimensional geometric figures in order to sort them according to a given attribute using informal and formal language; and This statement was originally 1.6.A (old). It has been moved and now encompasses informal and formal language. The language has also changed so that it contains formal mathematical language. (1.6) Geometry and spatial reasoning. The student uses attributes to identify, compare, and contrast shapes and solids. (C) combine geometric shapes to make new geometric shapes using concrete models. (1.6) Geometry and spatial reasoning. The student uses attributes to identify twoand three-dimensional geometric figures. The student compares and contrasts two- and three-dimensional geometric figures or both. (D) use concrete models to combine two-dimensional geometric figures to make new geometric figures. There are two refinements to this student expectation statement. The first change is due to re-lettering because of the addition of one statement. The second change is due to mathematical vocabulary and now is aligned K-12. TEKS K-2 Significant Changes Guide 1-19

(1.7) Measurement. The student uses nonstandard units to describe length, weight, and capacity. (1.7) Measurement. The student directly compares the attributes of length, area, weight/mass, capacity, and temperature. The student uses comparative language to solve problems and answer questions. The student selects and uses nonstandard units to describe length. The refinements to this statement are tremendous. Students are to compare attributes of length, area, weight/mass, capacity, and temperature. This is in common with the measurement statement for Kindergarten. The students must do this comparing during problem solving situations. Instead of using nonstandard units to measure length, weight, and capacity, children are now only required to use nonstandard units to measure length. Students need to be actively engaged in hands-on learning when addressing this knowledge and skills statement. (1.7) Measurement. The student uses nonstandard units to describe length, weight, and capacity. (A) estimate and measure length, capacity, and weight of objects using nonstandard units and (1.7) Measurement. The student directly compares the attributes of length, area, weight/mass, capacity, and temperature. The student uses comparative language to solve problems and answer questions. The student selects and uses nonstandard units to describe length. (A) estimate and measure length using nonstandard units such as paper clips or sides of color tiles; This particular expectation deals only with estimating and measuring length. Examples of possible nonstandard units are given. The concept of capacity and weight has been deleted from this particular expectation. (1.7) Measurement. The student directly compares the attributes of length, area, weight/mass, capacity, and temperature. The student uses comparative language to solve problems and answer questions. The student selects and uses nonstandard units to describe length. (B) compare and order two or more concrete objects according to length (from longest to shortest); This is a new expectation and requires the student to compare and order two or more concrete objects according to length. This is further foundational work that was begun in Kindergarten. (1.7) Measurement. The student uses nonstandard units to describe length, weight, and capacity. (B) describe the relationship between the size of the unit and the number of units needed in a measurement. (1.7) Measurement. The student directly compares the attributes of length, area, weight/mass, capacity, and temperature. The student uses comparative language to solve problems and answer questions. The student selects and uses nonstandard units to describe length. The student is expected to (C) describe the relationship between the size of the unit and the number of units needed to measure the length of an object; TEKS K-2 Significant Changes Guide 1-20

With the addition of 1.7.B (new), 1.7.B (old) is now 1.7.C (new). The change in wording of the expectation is to specifically state the objects are to be physically measured, not just look at a picture to determine a measurement. (1.7) Measurement. The student directly compares the attributes of length, area, weight/mass, capacity, and temperature. The student uses comparative language to solve problems and answer questions. The student selects and uses nonstandard units to describe length. (D) compare and order the area of two or more two-dimensional surfaces (from covers the most to covers the least); This is not only a new statement, but a new concept. The comparison of area has not been an expectation of first graders before. Students are now required to compare areas of two-dimensional figures. The use of the vocabulary and understanding of the concepts of covers more, covers less, and covers the same is very important for the foundation of measurement of area. (1.7) Measurement. The student directly compares the attributes of length, area, weight/mass, capacity, and temperature. The student uses comparative language to solve problems and answer questions. The student selects and uses nonstandard units to describe length. (E) compare and order two or more containers according to capacity (from holds the most to holds the least); Even though the comparison of the capacity of containers was taught in Kindergarten prior to the TEKS refinement, the ordering of containers based on capacity was not an expectation for first graders. Instead, first graders were expected to estimate and measure the capacity of containers. This particular change makes the expectation developmentally appropriate for first graders. (1.7) Measurement. The student directly compares the attributes of length, area, weight/mass, capacity, and temperature. The student uses comparative language to solve problems and answer questions. The student selects and uses nonstandard units to describe length. (F) compare and order two or more objects according to weight/mass (from heaviest to lightest); and It is now required to compare weight/mass instead of just weight. It is important for teachers to understand the difference. The wording has been changed so that correct grammar is used when comparing objects. (1.7) Measurement. The student directly compares the attributes of length, area, weight/mass, capacity, and temperature. The student uses comparative language to solve problems and answer questions. The student selects and uses nonstandard units to describe length. (G) compare and order two or more objects according to relative temperature (from hottest to coldest). This is a new expectation as well. Previously students were expected to recognize temperatures such as hot/cold [1.8.A (old)]. Now, students have to compare and order objects according to relative temperature. Relative temperature is also a new vocabulary word using formal mathematical vocabulary. TEKS K-2 Significant Changes Guide 1-21

(1.8) Measurement. The student understands that time [and temperature] can be measured. (1.8) Measurement. The student understands that time can be measured. The student uses time to describe and compare situations. This knowledge and skills statement was refined by omitting temperature. Note: temperature was not deleted completely, but rather moved to 1.7 new. The students are now expected to use time to describe and compare situations and not just that time can be measured. (1.8) Measurement. The student understands that time [and temperature] can be measured. [(A) recognize temperatures such as a hot day or a cold day;] This expectation was moved to 1.7G new. (1.8) Measurement. The student understands that time [and temperature] can be measured. [(B) describe time on a clock using hours and half hours; and] (1.8) Measurement. The student understands that time can be measured. The student uses time to describe and compare situations. (B) read time to the hour and half-hour using analog and digital clocks. This expectation has been refined to include analog and digital clocks. Before the type of clock used was not designated. The expectation of students measuring to the hour and half-hour remains the same. (1.8) Measurement. The student understands that time [and temperature] can be measured. [(C)] order three or more events [by how much time they take.] (1.8) Measurement. The student understands that time can be measured. The student uses time to describe and compare situations. The students is expected to: (A) order three or more events according to duration; and Notice that the order of this expectation has been changed from 1.8C (old) to 1.8A (new). This expectation has been refined only by formalizing the language used. (1.11) Underlying processes and mathematical tools. The student applies Grade 1 mathematics to solve problems connected to everyday experiences and activities in and outside of school. (B) use a problem-solving model, with guidance as needed, that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; (1.11) Underlying processes and mathematical tools. The student applies Grade 1 mathematics to solve problems connected to everyday experiences and activities in and outside of school. (B) solve problems with guidance that incorporates the processes of understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; TEKS K-2 Significant Changes Guide 1-22