1 st Grade Math at a Glance
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- Ilene Morton
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2 1 st Grade Math at a Glance Grading Period All Grading Period 1 8/26 10/18 Grading Period 2 10/21 12/20 Grading Period 3 1/8 3/21 Grading Period 4 3/24 6/5 Unit Name Estimated Time Frame Start EDC (Daily) 177 Days 8/26 6/5 Problem Solving (Daily) 177 days 8/26 6/5 * Graphing (minimum 3 lessons per grading period: EDC; integrating lessons and envision) 177 days 8/26 6/5 * Graphing: EDC / start of school activities (Picture graphs; Creating and using tally marks for data 8/26 10/18 collection Numbers to 10 & Comparing and Ordering 10 days 8/26 9/9 Five and Ten Relationships 10 days 9/10 9/23 Understanding Addition & Subtraction 18 days 9/24 10/18 * Graphing/Picture graphs (Collect, sort, and organize data to create picture graphs; Generate questions and 10/21 12/20 answers from picture graphs created) Patterns & Geometry and Spatial Reasoning 10 days 10/21 11/1 Counting and Number Patterns to days 11/4 11/15 Counting Money and Time (included in EDC ) 10 days 11/18 12/6 Addition and Subtraction Strategies of Facts to days 12/9 12/20 * Graphing/Picture and Bar Graphs (Introduce bar graphs; Collect data up to 3 categories using tally 1/8 3/21 marks or T-charts) Comparing/Ordering Number to 100 (including number lines) 12 days 1/8 1/24 Fractions 10 days 1/27 2/7 Measurement 10 days 2/10 2/21 Tens and Ones 15 days 2/24 3/21 * Graphing/Picture and Bar Graphs (Draw conclusions and generate questions and answers using information 3/24 6/5 from picture and bar graphs) Addition and Subtraction Strategies of Facts to days 3/24 4/4 Adding and Subtracting with Tens and Ones 24 days 4/7 5/9 Probability: (Identify events as certain or impossible) 3 days 5/12 5/14 Strengthening First Grade Skills & Financial Literacy 15 days 5/15 6/5 End
3 Department of Curriculum and Instruction POWER STANDARDS Fort Bend Independent School District Grade 1 Content Math Content Standards Standard Objective. 1 Number, Operations, and Quantitative Reasoning 1.1 B Create sets of tens and ones using sets of concrete objects to describe, compare and order whole numbers 1.2 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 1.2B Use appropriate language to describe part of a set such as three out of the eight crayons are red 1.3 A Model and create addition and subtraction problem situations with concrete objects and write corresponding number sentences Standard Objective 2 Patterns, Relationships, and Algebraic Thinking 1.5 B Find patterns in numbers, including odd and even 1.5 D Use patterns to develop strategies to solve basic addition and basic subtraction problems Standard Objective 3 Geometry and Spatial Reasoning 1.6 C Describe and identify 2- and 3-dimensional geometric figures in order to sort them according to a given attribute using informal and formal language Standard Objective 4 Measurement 1.7 A Estimate and measure length using nonstandard units such as paper clips or sides of color tiles 1.7C Describe the relationship between the size of the unit and the number of units needed to measure the length of an object Standard Objective 5 Probability and Statistics 1.9B Use organized data to construct real-object graphs, picture graphs, and bar-type graphs 1.10 A Draw conclusions and answer questions using information organized in real-object graphs, picture graphs and bar-type graphs
4 District Assessment Blueprint 1 st Grade Math TEKS Grading Period Testing Window: December 2 20, A 1 Model and create addition and subtraction problem situations with concrete objects and write corresponding number sentences 1.5D 1 Use patterns to develop strategies to solve basic addition and basic subtraction problems 1.6C 2 Describe and identify 2 and 3 dimensional geometric figures in order to sort them according to a given attribute using informal and formal language 1.10A Year Draw conclusions and answer questions using Long information organized in real-object graphs, picture graphs and bar-type graphs (Tally charts and picture graphs) # of Items TEKS Grading Period Testing Window: April 21 May 9, B 3 Create sets of tens and ones using sets of concrete objects to describe, compare and order whole numbers 1.3A 4 Model and create addition and subtraction problem situations with concrete objects and write corresponding number sentences 1.5D 4 Use patterns to develop strategies to solve basic addition and basic subtraction problems (Facts to 18) 1.7C 3 Describe the relationship between the size of the unit and the number of units needed to measure the length of an object 1.10A Year Draw conclusions and answer questions using Long information organized in real-object graphs, picture graphs and bar-type graphs # of Items
5 First Grade Specificity Charts Mathematics Chapter 111 TEKS K-2 Introduction First Grade (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 twoand three-dimensional geometric figures. (2) Throughout mathematics in Kindergarten-Grade 2, students build a foundation of basic understanding 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 the 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. 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. (4) 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.
6 1.1 Number, operation, and quantitative reasoning. The student uses whole numbers to describe and compare quantities. The student is expected to: 1.1A Compare and order whole numbers up to 99 (less than, greater than, or equal to) using sets of concrete objects and pictorial models. recognize and generate equivalent forms for the same number using concrete models recognize and generate equivalent forms for the same number using pictorial models Connect concrete to pictorial by making pictorial representations to illustrate concrete examples (Ex. Draw a picture to represent a set of manipulatives.) Connect pictorial to concrete by making concrete examples to model pictorial representations (Ex. Use manipulatives to represent a set of pictorial objects.) Compare and order quantities from greatest to least and least to greatest. Compare or order up to three sets of concrete or pictorial objects in different formats (Ex. Vertically, horizontally, in boxes). compare and order using correct mathematical vocabulary (ex: 58 is greater than 49) Compare and order up to 2 numbers using symbols > = <.. compare equal to fewer fewer than greater than less less than more more than order Note: Address and review ordinal numbers 1.1B Create sets of tens and ones using concrete objects to describe, compare, and order whole numbers. use place value concepts to represent whole numbers using numerals, expanded notation and concrete models (example, 99 = 90 9) Connect concrete to pictorial by making pictorial representations to illustrate concrete examples (Ex. Draw a picture to represent a set of manipulatives.) Connect pictorial to concrete by making concrete examples to model pictorial representations (Ex. Use manipulatives to represent a set of pictorial objects.) create concrete and pictorial models that are more or less than a given model connect models to numbers to describe, compare and order up to 3 numbers digit compare
7 1.1C Identify individual coins by name and value and describe relationships among them Identify similarities and differences between pennies, nickels, dimes, and quarters (Ex. All coins say United States of America. Nickels say five cents. ) recognize the real and pictorial coins (front and back) sort, name, and compare coins (pennies, nickels, dimes, quarters) Find the value of a combination of coins only to understand relationships among coins: 1 dime is 2 nickels, 1 nickel and five pennies, or 10 pennies; 1 quarter = two dimes and a nickel (NOT finding the value of a random combination of mixed coins i.e.3dimes and 2 pennies equal 32 cents) use cent symbol with value find the value of sets of like coins (i.e. set of 5 nickels) pennies nickels dimes quarters cent Note: Money is introduced in first grade. 1.1D Read and write numbers to 99 to describe sets of concrete objects. Write a numeral to describe a set of concrete of pictorial objects Create a concrete or pictorial set to illustrate a numeral number digit numeral place value (10 s and 1 s)
8 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: 1.2A 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 represent commonly used fractions using words, concrete, and pictorial models recognize fractions are represented by equal size parts of a whole and of a set of objects create concrete and pictorial models of a whole separated into two, three, and four equal parts Simultaneously describe parts of a whole using symbols (1/2), informal language (one out of two equal parts), and formal language (one-half). fraction halves thirds fourths equal parts out of whole total 1.2B Use appropriate language to describe part of a set such as three out of the eight crayons is red. use "out of" when distinguishing part versus whole use a variety of concrete and pictorial objects to make a set up to 18 and divide it into fractional parts and put fractional parts together as a whole Use a variety of attributes to describe sets (i.e. color, shape, size, number of wheels)
9 1.3 Number, operation, and quantitative reasoning. The student recognizes and solves problems in addition and subtraction situations. The student is expected to: 1.3A Model and create addition and subtraction problem situations with concrete objects and write corresponding number sentences. model and explain addition or subtraction problems using concrete materials and pictures in contextual situations. analyze and explain that subtraction of whole numbers equals an answer smaller than or equal to the original number analyze and explain that addition of whole numbers equals an answer equal to or greater than the original number model real addition and subtraction situations when parts are unknown use equation (number sentence) to represent addition or subtraction situations sum difference subtraction addition combining separating plus two-digit minus even odd all together left in all equals number sentence count on count back 1.3B Use concrete objects and pictorial models to apply basic addition and subtraction facts (up to 9 9=18 and 18-9=9). Compose and decompose numbers into a maximum of two parts and Use different ways to express the same number (9 1 = 10, 5 5 = 10) Determine the results of adding or subtracting two even, two odd or an even and odd number Use multiple formats for solving addition and subtraction problems (i.e. number lines, counting on, concrete objects, pictures, etc.) facts fact families doubles doubles plus one Note: concrete instruction and application is most appropriate for first-grade; timed tests
10 and flash cards can be used only to reinforce skills, not used as an assessment tool. 1.4 Patterns, relationships, and algebraic thinking. The student uses repeating patterns and additive patterns to make predictions. The student is expected to: 1.4A Identify, describe, and extend concrete and pictorial patterns in order to make predictions and solve problems. demonstrate the difference between an additive (growing pattern) and repeating pattern using concrete objects create and extend additive and repeating patterns (Concrete and pictorial) Additive: ab, aab, aaab, aaaab or 2, 4, 6, 8, 10, 12 Repeating: abababab or or repeated shapes 1.5 Patterns, relationships, and algebraic thinking. The student recognizes patterns in numbers and operations. The student is expected to: 1.5A Use patterns to skip count by twos, fives, and tens. describe characteristics of concrete, pictorial, and numerical patterns create and extend patterns model skip counting using concrete objects, 100 s chart, money, T-chart, etc identify patterns in the environment Use patterns to solve problems involving skip counting by 2s, 5s, and 10s (i.e. 1 person has 2 eyes, 2 people have 4 eyes) repeating patterns similar patterns skip count 1.5B Find patterns in numbers, including odd and even. illustrate and explain the difference between odd and even identify pattern in the environment of even and odd (such as egg carton, sets of tricycle wheels, etc) identify even and odd on hundreds chart use real life examples to create and extend pattern Identify missing numbers in a series only using patterns on a hundreds chart growing patterns odd even 1.5C Compare and order whole numbers using place value. Use concrete models, numerals, pictures, and words to represent place value through 99 Use patterns to determine missing numbers (before, after, or between) in a given set of numbers Identify place value patterns on the 100 s chart before
11 after between 1.5D Use patterns to develop strategies to solve basic addition and basic subtraction problems. Create and extend addition and subtraction patterns (9 1 = 10, 9 2 = 11) use combining and separating strategies such as doubles plus or minus one, sums of ten, etc 1.5E Identify patterns in related addition and subtraction sentences (fact families for sums to 18) such as 2 3 = 5, 3 2 = 5, 5 2 = 3, and 5 3 = 2. develop strategies for addition and subtraction involving even and odd combinations such as even plus an even always equals an even sum generate another fact from that fact family when given one fact generate all members of the fact family
12 1.6 Geometry and spatial reasoning. The student uses attributes to identify two-and three-dimensional geometric figures. The student compares and contrasts twoand three-dimensional geometric figures or both. 1.6A Describe and identify two dimensional geometric figures including circles, triangles, rectangles, and squares (a special type of rectangle) Name circle, triangle, rectangle, square (special type of rectangle), hexagon, trapezoid, and rhombus (NOT diamond) identify symmetrical and nonsymmetrical shapes identify congruent shapes Compare and contrast two-dimensional geometric figures by attribute Connect concrete models to pictorial representations Vocabulary Congruent Symmetry Square Rectangle Triangle Hexagon Trapezoid Rhombus Circle 1.6B Describe and identify three-dimensional geometric figures, including spheres, rectangular prisms (including cubes), cylinders, and cones. identify symmetrical and nonsymmetrical shapes identify geometric figures in everyday life Sort a variety of polygons by attribute only, not by name Connect concrete models to pictorial representations Vocabulary circles spheres cones cubes cylinders pyramids rectangular prisms symmetry NOTE: 1 st grade introduces mathematical names of 3-D figures. Kinder introduces attributes only. 1.6C Describe and identify two- and three-dimensional geometric figures in order to sort them according to a given attribute using informal and formal language identify common attributes involving two- and three-dimensional geometric figures Connect concrete models to pictorial representations
13 attribute two-dimensional attributes (sides and vertices) polygons (a straight-sided closed figure) NONEXAMPLE: a circle three-dimensional attributes (faces, vertices, curves, edges) Note: The emphasis is on the attributes, not the names. The purpose is to sort. 1.6D Use concrete models to combine two-dimensional geometric figures to make new geometric figures. create and identify new shapes by combining existing shapes (Ex: two triangles make a parallelogram, etc) Connect concrete models to pictorial representations
14 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: 1.7A Estimate and measure length using nonstandard units such as paper clips and sides of color tiles. estimate before measuring with nonstandard units identify nonstandard tools used to measure length identify objects that have equal length compare lengths of different objects using nonstandard units use mathematical language to describe lengths such as "longer than" or "shorter than" begin to measure at the edge of the object being measured height longer than shorter than width length 1.7B Compare and order two or more concrete objects according to length (from longest to shortest) Directly compare the length of up to five objects to order length. Compare the length of up to three objects using non-standard units. length longest shortest 1.7C Describe the relationship between the size of the unit and the number of units needed to measure the length of an object. experience and understand that changing the size of a unit will change the number of units it takes to measure an object (i.e. it takes more paper clips than pencils to measure the length of a desk.) identify nonstandard tools used to measure length Note: Allow students to explore measurement using a ruler 1.7D Compare and order two or more two-dimensional surfaces (from covers the most to covers the least) stimate before determining area use various sizes of nonstandard units used to determine the area of one object Directly compare the area of up to 5 objects (i.e. by placing objects on top of each other.) Do not compare objects by using nonstandard units. area
15 1.7E Compare and order two or more containers according to capacity (from holds the most to holds the least) stimate before determining capacity use various sizes of nonstandard units used to determine the capacity of one container Directly compare the capacity of up to 5 containers (i.e. by pouring beans, cubes, or water from one container into another). Do not compare objects by using nonstandard units. capacity 1.7F Compare and order two or more objects according to weight/mass (from heaviest to lightest) stimate before determining weight/mass use various sizes of nonstandard units used to determine the weight/mass of one object Directly compare the weight/mass of up to 5 objects (i.e. by placing objects on a balance). Do not compare objects by using nonstandard units. balance heavier lighter mass scale weight 1.7G Compare and order two or more objects according to relative temperature (from hottest to coldest). estimate temperature before measuring identify hot and cold in everyday experiences identify the tool to measure temperature (thermometer) order objects in temperature from coldest to hottest or hottest to coldest the opposite of a hot summer day is a colder than coldest cooler hot hotter than hottest same as thermometer warmer Note: Introduce the thermometer.
16 1.8 Measurement. The student understands that time can be measured. The student uses time to describe and compare situations. The student is expected to: 1.8A Order three or more events according to duration. order three or more events according to duration order everyday events according to occurrence duration Note: Calendars and schedules may be addressed at this time. 1.8B Read time to the hour and half-hour using analog and digital clocks. identifies hour hand and minute hand models the direction that hands move on a clock understand the position of the hour hand according to the position of the minute hand (2:00 vs 2:30) digital analog hour o clock minute hand hour hand minute AM and PM Note: Writing time is introduced in 1st grade.
17 1.9 Probability and statistics. The student displays data in an organized form. The student is expected to: 1.9A Collect and sort data. Create different ways to collect and sort data.(surveys, tables, and tally marks) Tally mark Survey Table data 1.9B Use organized data to construct real object graphs, picture graphs, and bar-type graphs. create different ways to collect and sort data labels graphs appropriately including title, category labels, key (on picture graphs) construct both horizontal and vertical bar-type (NOT a bar graph with numbers, x-axis, and y-axis) graphs or picture Graphs bar- type graph (A bar-type graph does not have numbers. Students must count quantities of objects like post-it notes, cubes in a stack, boxes, etc.) picture graph key horizontal vertical 1.10 Probability and statistics. The student uses information from organized data. The student is expected to: 1.10A Draw conclusions and answer questions using information organized in real object graphs, picture graphs, and bar-type graphs. Ask student questions to compare quantities. (Ex.Which has more? How many more?) bar- type graph data more/most less/least same not included picture graph 1.10B Identify events as certain or impossible such as drawing a red crayon from a bag of green crayons. Included but not limited to: Connect concrete examples to pictorial representations. certain
18 impossible possible 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. The student is expected to: 1.11A Identify mathematics in everyday situations. Process skill to be addressed with relevant content. 1.11B 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. Process skill to be addressed with relevant content. 1.11C Select or develop an appropriate problem-solving plan or strategy including drawing a picture, looking for a pattern, systematic guessing and checking, or acting it out in order to solve a problem. Process skill to be addressed with relevant content. 1.11D Use tools such as real objects, manipulatives, and technology to solve problems. Process skill to be addressed with relevant content Underlying processes and mathematical tools. The student communicates about Grade 1 mathematics using informal language. The student is expected to: 1.12A Explain and record observations using objects, words, pictures, numbers, and technology. Process skill to be addressed with relevant content. 1.12B Relate everyday language to mathematical language and symbols. Process skill to be addressed with relevant content 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. 1.13A Justify his or her thinking using objects, words, pictures, numbers, and technology Process skill to be addressed with relevant content.
19 SIDE-BY-SIDE TEKS COMPARISON GRADE 1
20 The materials are copyrighted (c) and trademarked (tm) as the property of the Texas Education Agency (TEA) and may not be reproduced without the express written permission of TEA, except under the following conditions: Texas public school districts, charter schools, and Education Service Centers may reproduce and use copies of the Materials and Related Materials for the districts and schools educational use without obtaining permission from TEA. Residents of the state of Texas may reproduce and use copies of the Materials and Related Materials for individual personal use only without obtaining written permission of TEA. Any portion reproduced must be reproduced in its entirety and remain unedited, unaltered and unchanged in any way. No monetary charge can be made for the reproduced materials or any document containing them; however, a reasonable charge to cover only the cost of reproduction and distribution may be charged. Private entities or persons located in Texas that are not Texas public school districts, Texas Education Service Centers, or Texas charter schools or any entity, whether public or private, educational or non-educational, located outside the state of Texas MUST obtain written approval from TEA and will be required to enter into a license agreement that may involve the payment of a licensing fee or a royalty. For information contact: Office of Copyrights, Trademarks, License Agreements, and Royalties, Texas Education Agency, 1701 N. Congress Ave., Austin, TX ; phone: or ; copyrights@tea.state.tx.us Texas Education Agency All Rights Reserved Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Side-By-Side TEKS Comparison
21 Grade 1 Mathematics Current TEKS Revised TEKS (2012) Supporting Information Notes (a) Introduction. (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 three-dimensional geometric figures. (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 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 threedimensional 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. (a) 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. (a) Introduction. (4) The primary focal areas in Grade 1 are understanding and applying place value, solving problems involving addition and subtraction, and composing and decomposing two-dimensional shapes and three-dimensional solids. (A) Students use relationships within the numeration system to understand the sequential order of the counting numbers and their relative magnitude. (B) Students extend their use of addition and subtraction beyond the actions of joining and separating to include comparing and combining. Students use properties of operations and the relationship between addition and subtraction to solve problems. By comparing a variety of solution strategies, students use efficient, accurate, and generalizable methods to perform operations. (C) Students use basic shapes and spatial reasoning to model objects in their environment and construct more complex shapes. Students are able to identify, name, and describe basic twodimensional shapes and threedimensional solids. The definition of a well-balanced mathematics curriculum has expanded to include the CCRS. A focus on mathematical fluency and solid understanding allows for rich exploration of the primary focal points. The 2012 paragraph that highlights more specifics about grade 1 mathematics content follows paragraphs about the mathematical process standards and mathematical fluency. This supports the notion that the TEKS should be learned in a way that integrates the mathematical process standards in an effort to develop fluency. The 2012 paragraph has been updated to align to the 2012 grade 1 mathematics TEKS. The 2012 paragraph highlights focal areas or topics that receive emphasis in this grade level. These are different from focal points which are part of the Texas Response to Curriculum Focal Points [TXRCFP]. [A] curriculum focal point is not a single TEKS statement; a curriculum focal point is a mathematical idea or theme that is developed through appropriate arrangements of TEKS statements at that grade level that lead into a connected grouping of TEKS at the next grade level (TEA, 2010, p. 5). The focal areas are found within the focal points. The focal points may represent a subset of a focal area, or a focal area may represent a subset of a focal point. The focal points within the TXRCFP list related grade-level TEKS Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Side-by-Side TEKS Comparison 1
22 Grade 1 Mathematics Current TEKS Revised TEKS (2012) Supporting Information Notes The Revised TEKS (2012) include the use of the words automaticity, fluency / fluently, and proficiency with references to standard algorithms. Attention is being given to these descriptors to indicate benchmark levels of skill to inform intervention efforts at each grade level. These benchmark levels are aligned to national recommendations for the development of algebra readiness for enrollment in Algebra I. (a) Introduction. (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. (a) Introduction. (3) For students to become fluent in mathematics, students must develop a robust sense of number. The National Research Council s report, Adding It Up, defines procedural fluency as skill in carrying out procedures flexibly, accurately, efficiently, and appropriately. As students develop procedural fluency, they must also realize that true problem solving may take time, effort, and perseverance. Students in Grade 1 are expected to perform their work without the use of calculators. Automaticity refers to the rapid recall of facts and vocabulary. For example, we would expect a fifth-grade student to recall rapidly the sum of 5 and 3 or to identify rapidly a closed figure with 3 sides and 3 angles. To be mathematically proficient, students must develop conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition (National Research Council, 2001, p. 116). Procedural fluency refers to knowledge of procedures, knowledge of when and how to use them appropriately, and skill in performing them flexibly, accurately, and efficiently (National Research Council, 2001, p. 121). Students need to see that procedures can be developed that will solve entire classes of problems, not just individual problems (National Research Council, 2001, p. 121). Procedural fluency and conceptual understanding weave together to develop mathematical proficiency Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Side-by-Side TEKS Comparison 2
23 Grade 1 Mathematics Current TEKS Revised TEKS (2012) Supporting Information Notes (a) Introduction. (4) 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. (a) Introduction. (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, 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. (a) Introduction. (5) Statements that contain the word "including" reference content that must be mastered, while those containing the phrase "such as" are intended as possible illustrative examples. This 2012 paragraph occurs second in the Revised TEKS (2012) instead of fourth as in the current TEKS. This highlights the continued emphasis on process skills that now continue from Kindergarten through high school mathematics. The language of this 2012 introductory paragraph is very similar to the Mathematical Process Standard strand within the Revised TEKS (2012). This 2012 introductory paragraph includes generalization and abstraction with the text from 1(C). This 2012 introductory paragraph includes computer programs with the text from 1(D). This 2012 introductory paragraph states, students will use mathematical relationships to generate solutions and make connections and predictions instead of the text from 1(E). The State Board approved the retention of some such as statements within the TEKS where needed for clarification of content Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Side-by-Side TEKS Comparison 3
24 Grade 1 Mathematics Current TEKS: Number, operation, and quantitative reasoning 1(1)(A) Number, operation, and quantitative reasoning. The student uses whole numbers to describe and compare quantities. The student is expected to compare and order whole numbers up to 99 (less than, greater than, or equal to) using sets of concrete objects and pictorial models. Revised TEKS (2012) Supporting Information Notes This skill is not included within the Revised TEKS (2012). It is an instructional strategy that may be used to support the revised SE 1(2)(E) and 1(2)(F). Specificity is added to the use of concrete models or objects. These models are used to compose and decompose numbers in more than one way as a means to describe the value of whole numbers. 1(1)(B) Number, operation, and quantitative reasoning. The student uses whole numbers to describe and compare quantities. The student is expected to create sets of tens and ones using concrete objects to describe, compare, and order whole numbers. 1(2)(B) Number and operations. The standards 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 use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many hundreds, so many tens, and so many ones. Specificity has been added with "so many hundreds, so many tens, and so many ones." It may include decomposing 67 into 5 tens and 17 ones. It may also include decomposing 67 into the sum of 60, 10, and 7 to prepare for work with compatible numbers when adding whole numbers with fluency. The number has increased from up to 99 to up to 120. Students are expected to use pictorial models in addition to concrete models or objects. Comparing and ordering whole numbers using concrete objects is not included within the Revised TEKS (2012). 1(1)(C) Number, operation, and quantitative reasoning. The student uses whole numbers to describe and compare quantities. 1(4)(A) Number and operations. The standards to identify coins, their values, and the relationships among them in order to recognize the need for monetary transactions. The student is expected to identify U.S. coins including pennies, nickels, dimes, and quarters by value and describe the relationships among them. It is an instructional strategy that may be used to support the revised SE 1(2)(E) and 1(2)(F). Specificity has been added to indicate that coins are to be U.S. coins including pennies, nickels, dimes, and quarters Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Side-by-Side TEKS Comparison 4
25 Grade 1 Mathematics Current TEKS: Number, operation, and quantitative reasoning Revised TEKS (2012) Supporting Information Notes The student is expected to identify individual coins by name and value and describe relationships among them. 1(4)(B) Number and operations. The standards to identify coins, their values, and the relationships among them in order to recognize the need for monetary transactions. The revised SE expects students to label the value of a coin with the cent symbol. The student is expected to write a number with the cent symbol to describe the value of a coin. 1(1)(C) Number, operation, and quantitative reasoning. The student uses whole numbers to describe and compare quantities. The student is expected to identify individual coins by name and value and describe relationships among them. 1(1)(D) Number, operation, and quantitative reasoning. The student uses whole numbers to describe and compare quantities. The student is expected to read and write numbers to 99 to describe sets of concrete objects. 1(4)(C) Number and operations. The standards to identify coins, their values, and the relationships among them in order to recognize the need for monetary transactions. The student is expected to use relationships to count by twos, fives, and tens to determine the value of a collection of pennies, nickels, and/or dimes. 1(2)(C) Number and operations. The standards 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 use objects, pictures, and expanded and standard forms to represent numbers up to 120. Specificity has been added regarding the relationships among the coins with connections to skip counting. One may count nickels by fives and dimes by tens. One may count two pennies together to count by twos. With a collection of pennies, nickels, and dimes, a student may begin counting by tens to determine the value of the dimes, continue from that amount counting by fives to determine the value of the dimes and the nickels, and count by ones or twos to include the pennies in the value of the collection. The maximum value of the collection is 120 cents. Specificity has been added with what students are expected to write with the inclusion of expanded and standard forms. In addition to objects, students may use pictures to represent numbers. Representing numbers has increased from 99 to (2)(A) 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 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. 1(6)(G) Geometry and measurement. The standards to analyze attributes of twodimensional shapes and three-dimensional solids to develop generalizations about their properties. The student is expected to partition twodimensional figures into two and four fair shares or equal parts and describe the parts using words. Specificity has been added for the mathematical meaning of equal parts with fair shares or equal parts. Two dimensional figures include circles and rectangles. Describing the parts using words such as halves, fourths, or quarters and phrases such as half of. Separating a whole into three equal parts has moved to grade 3: Number and operations 3(3)(A) 2013 Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Side-by-Side TEKS Comparison 5
26 Grade 1 Mathematics Current TEKS: Number, operation, and quantitative reasoning Revised TEKS (2012) Supporting Information Notes 1(6)(H) Geometry and measurement. The standards to analyze attributes of twodimensional shapes and three-dimensional solids to develop generalizations about their properties. The student is expected to identify examples and non-examples of halves and fourths. Specificity has been added to illustrate how students might justify their thinking related to halves and fourths. A non-example of a half would be a twodimensional figure that has been partitioned into two unequal parts. The focus of this SE, given revised SE 1(6)(G), is on the fair sharing or equal parts of the two-dimensional figure. 1(2)(B) 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 use appropriate language to describe part of a set such as three out of the eight crayons are red. This skill is not included within the Revised TEKS (2012). 1(3)(A) Number and operations. The standards to develop and use strategies for whole number addition and subtraction computations in order to solve problems. Specificity has been added regarding the addition problems including the sum of a multiple of ten and a one-digit number up to 99. The student is expected to use concrete and pictorial models to determine the sum of a multiple of 10 and a one-digit number in problems up to 99. 1(3)(B) Number and operations. The standards to develop and use strategies for whole number addition and subtraction computations in order to solve problems. In addition to objects, students may use pictorial models to model and add whole numbers up to 99 with sums of multiples of 10 and one-digit numbers. 1(3)(A) Number, operation, and quantitative reasoning. The student recognizes and solves problems in addition and subtraction situations. The student is expected to model and create addition and subtraction problem situations with concrete objects and write corresponding number sentences. The student is expected to use objects and pictorial models to solve word problems involving joining, separating, and comparing sets within 20 and unknowns as any one of the terms in the problem such as 2 4 = [ ]; 3 [ ] = 7; and 5 = [ ] (3)(E) Number and operations. The standards to develop and use strategies for whole number addition and subtraction computations in order to solve problems. Specificity has been added regarding number sentences and the placement of the unknown. Specificity has been added regarding the description of addition as joining and subtraction as separating or comparing. Students may use pictorial models. Specificity has been added regarding the size of the sum or the original amount when subtracting as up to 20. The student is expected to explain strategies used to solve addition and subtraction problems up to 20 using spoken words, objects, pictorial models, and number sentences. When the current SE is paired with the current 1(12)(A), students are expected to explain and record observations which may include strategies Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Side-by-Side TEKS Comparison 6
27 Grade 1 Mathematics Current TEKS: Number, operation, and quantitative reasoning Revised TEKS (2012) Supporting Information Notes 1(3)(A) Number, operation, and quantitative reasoning. The student recognizes and solves problems in addition and subtraction situations. The student is expected to model and create addition and subtraction problem situations with concrete objects and write corresponding number sentences. 1(3)(A) Number, operation, and quantitative reasoning. The student recognizes and solves problems in addition and subtraction situations. The student is expected to model and create addition and subtraction problem situations with concrete objects and write corresponding number sentences. 1(3)(B) Number, operation, and quantitative reasoning. The student recognizes and solves problems in addition and subtraction situations. The student is expected to use concrete and pictorial models to apply basic addition and subtraction facts (up to 9 9 = 18 and 18 9 = 9). 1(3)(F) Number and operations. The standards to develop and use strategies for whole number addition and subtraction computations in order to solve problems. The student is expected to generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20. 1(5)(D) Algebraic reasoning. 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 represent word problems involving addition and subtraction of whole numbers to 20 using concrete and pictorial models and number sentences. 1(3)(C) Number and operations. The standards to develop and use strategies for whole number addition and subtraction computations in order to solve problems. The student is expected to compose 10 with two or more addends with and without concrete objects. 1(3)(D) Number and operations. The standards to develop and use strategies for whole number addition and subtraction computations in order to solve problems. The student is expected to apply basic fact strategies to add and subtract within 20 using strategies, including making 10 and decomposing a number leading to a 10. 1(2)(A) Number and operations. The standards 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 recognize instantly the quantity of structured arrangements. Students are expected to generate or create problem situations. Specificity has been added regarding the size of the sum or the original amount when subtracting as up to 20. Students are expected to solve the problem situations that they generate. Students are provided the number sentence for which they are writing a problem situation. Specificity has been added regarding the size of the sum or the original amount when subtracting as up to 20. The revised SE 1(3)(C) represents a subset of the current SE. The focus is on flexible thinking with composing 10 with two or more addends to support basic fact strategies such as making 10. Students are expected to compose 10 with and without concrete objects. Applying basic fact strategies with concrete and pictorial models is not included in the revised SE. Basic facts for addition and subtraction within 18 have been extended to basic facts for addition and subtraction within 20. Structured arrangements include ten frames and the arrangements of dots on randomnumber generators Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Side-by-Side TEKS Comparison 7
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