# SUPPORTING INFORMATION GRADE 1 - Education Service Center

## Transcript Of SUPPORTING INFORMATION GRADE 1 - Education Service Center

SUPPORTING INFORMATION

GRADE 1

Texas Education Agency

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.

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For information contact Office of Copyrights, Trademarks, License Agreements, and Royalties, Texas Education Agency, 1701 N. Congress Ave., Austin, TX 78701-1494; phone: 512-463-9041 email: [email protected]

©2017 Texas Education Agency All Rights Reserved 2017

©2017 Texas Education Agency. All Rights Reserved 2017

Mathematics TEKS: Supporting Information

Updated January 2019

Grade 1 – Mathematics

TEKS (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. (2) The process standards describe ways in which students are expected to engage in the content. The placement of the process standards at the beginning of the knowledge and skills listed for each grade and course is intentional. The process standards weave the other knowledge and skills together so that students may be successful problem solvers and use mathematics efficiently and effectively in daily life. The process standards are integrated at every grade level and course. When possible, students will apply mathematics to problems arising in everyday life, society, and the workplace. Students will use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. Students will select appropriate tools such as real objects, manipulatives, algorithms, paper and pencil, and technology and techniques such as mental math, estimation, number sense, and generalization and abstraction to solve problems. Students will effectively communicate mathematical ideas, reasoning, and their implications using multiple representations such as symbols, diagrams, graphs, computer programs, and language. Students will use mathematical relationships to generate solutions and make connections and predictions. Students will analyze mathematical relationships to connect and communicate mathematical ideas. Students will display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

(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.

Supporting Information

The definition of a well-balanced mathematics curriculum has expanded to include the Texas College and Career Readiness Standards (CCRS). A focus on mathematical fluency and solid understanding allows for rich exploration of the primary focal points.

This paragraph occurs second in the TEKS to highlight the continued emphasis on process skills that are now included from kindergarten through high school mathematics. This introductory paragraph includes generalization and abstraction with the text from (1)(C). This introductory paragraph includes computer programs with the text from 1(D). This introductory paragraph states, “Students will use mathematical relationships to generate solutions and make connections and predictions” instead of incorporating the text from (1)(E).

The TEKS 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. Automaticity refers to the rapid recall of facts and vocabulary. For example, we would expect a third-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.

©2017 Texas Education Agency. All Rights Reserved 2017

Mathematics TEKS: Supporting Information

Updated January 2019

1

Grade 1 – Mathematics

(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 two-dimensional shapes and three-dimensional solids.

(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 paragraph highlights more specifics about grade 1 mathematics content and 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.

This paragraph has been updated to align to the grade 1 mathematics TEKS.

This 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.

The State Board of Education approved the retention of some “such as” statements within the TEKS where needed for clarification of content.

The phrases “including” and “such as” should not be considered as limiting factors for the student expectations (SEs) in which they reside.

Additional Resources are available online including Interactive Mathematics Glossary Vertical Alignment Charts Texas Response to the Curriculum Focal Points, Revised 2013 Texas Mathematics Resource Page

©2017 Texas Education Agency. All Rights Reserved 2017

Mathematics TEKS: Supporting Information

Updated January 2019

2

Grade 1 – Mathematics

TEKS: Mathematical Process Standards.

1(1)(A) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.

The student is expected to apply mathematics to problems arising in everyday life, society, and the workplace.

1(1)(B) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.

The student is expected to 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. 1(1)(C) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.

The student is expected to select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems. 1(1)(D) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.

The student is expected to communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

1(1)(E) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.

The student is expected to create and use representations to organize, record, and communicate mathematical ideas.

1(1)(F) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.

The student is expected to analyze mathematical relationships to connect and communicate mathematical ideas.

1(1)(G) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.

The student is expected to display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Supporting Information This SE emphasizes application.

The opportunities for application have been consolidated into three areas: everyday life, society, and the workplace.

This SE, when paired with a content SE, allows for increased rigor through connections outside the discipline.

This SE describes the traditional problem-solving process used in mathematics and science.

Students are expected to use this process in a grade appropriate manner when solving problems that can be considered difficult relative to mathematical maturity.

The phrase “as appropriate” is included in the TEKS. This implies that students are assessing which tool(s) to apply rather than trying only one or all accessible tools.

“Paper and pencil” is included in the list of tools that still includes real objects, manipulatives, and technology.

Communication includes reasoning and the implications of mathematical ideas and reasoning.

The list of representations is summarized with “multiple representations” with specificity added for “symbols,” “graphs,” and “diagrams.”

The use of representations includes organizing and recording mathematical ideas in addition to communicating ideas.

As students use and create representations, it is implied that they will evaluate the effectiveness of their representations to ensure that they are communicating mathematical ideas clearly.

Students are expected to use appropriate mathematical vocabulary and phrasing when communicating mathematical ideas. The TEKS allow for additional means to analyze relationships and to form connections with mathematical ideas past forming conjectures about generalizations and sets of examples and non-examples.

Students are expected to form conjectures based on patterns or sets of examples and nonexamples. Students are expected to validate their conclusions with displays, explanations, and justifications. The conclusions should focus on mathematical ideas and arguments.

Displays could include diagrams, visual aids, written work, etc. The intention is to make one’s work visible to others so that explanations and justifications may be shared in written or oral form.

Precise mathematical language is expected. For example, students would use “vertex” instead of “corner” when referring to the point at which two edges intersect on a polygon.

©2017 Texas Education Agency. All Rights Reserved 2017

Mathematics TEKS: Supporting Information

Updated January 2019

3

Grade 1 – Mathematics

TEKS: Number and Operations.

1(2)(A) Number and operations. The student applies mathematical process 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.

Supporting Information This SE extends K(2)(C), where students are asked to recognize small quantities in organized and random arrangements.

The number of items should be ten or less.

When paired with 1(1)(G), a student may be asked to explain the thinking he or she used to subitize the number.

Structured arrangements include ten frames and the arrangements of dots on random number generators. For example, when shown an arrangement with two “parts,” a student might justify his or her thinking by saying, “I recognize five, and then I added two more.”

1(2)(B) Number and operations. The student applies mathematical process 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. 1(2)(C) Number and operations. The student applies mathematical process 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. 1(2)(D) Number and operations. The student applies mathematical process 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 generate a number that is greater than or less than a given whole number up to 120.

1(2)(E) Number and operations. The student applies mathematical process 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 place value to compare whole numbers up to 120 using comparative language.

1(2)(F) Number and operations. The student applies mathematical process 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 order whole numbers up to 120 using place value and open number lines. 1(2)(G) Number and operations. The student applies mathematical process 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 represent the comparison of two numbers to 100 using the symbols >, <, or =.

This use of structured arrangements builds students’ conceptual understandings of the part-whole relationship of numbers (5 and 2 compose to 7) and basic facts (5 + 2 or 2 + 5). These concrete and pictorial models are used to compose and decompose numbers in more than one way as a means to describe the value of whole numbers.

“So many hundreds, so many tens, and so many ones" may include using models to decompose 67 into 5 tens and 17 ones. It may also include models to decompose 67 into the sum of 50, 10, and 7.

This SE allows students to incorporate 1(1)(D) through the use of multiple representations of a number by using concrete models, pictorial models, standard form (119), and expanded form (119 = 100 + 10 + 9).

This SE extends K(2)(F), where students are expected to generate a number that is one more or one less than another number up to 20.

Students may be expected to use comparative language such as greater than, less than, or equal to in order to compare numbers using place value. The comparison may occur in ones, tens, or hundreds. For example, given the numbers 87 and 64, a student would describe 64 as having the lesser value because the value of the 6 in the tens place is 60, while having an 8 in the tens place is 80, and 60 is less than 80.

In comparing numbers up to 120, one may use the hundreds, tens, and ones places with a set of whole numbers like 118, 108, 98, and 89. Students may be expected to use place value to order numbers based on the value of the digits and use an open number line, which builds to 2(2)(E), where students locate whole numbers on an open number line.

The use of an open number line supports student understanding related to the magnitude of number and the place-value relationship among numbers when locating a given number. Students are expected to extend their understanding of comparing numbers using comparative language in 1(2)(E). In this SE, student are expected to compare two numbers using the symbols >, <, or =.

This SE complements 1(2)(D), 1(2)(E), and 1(2)(F).

©2017 Texas Education Agency. All Rights Reserved 2017

Mathematics TEKS: Supporting Information

Updated January 2019

4

Grade 1 – Mathematics

TEKS: Number and Operations. 1(3)(A) Number and operations. The student applies mathematical process standards to develop and use strategies for whole number addition and subtraction computations in order to solve problems.

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 student applies mathematical process standards to develop and use strategies for whole number addition and subtraction computations in order to solve problems.

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.

1(3)(C) Number and operations. The student applies mathematical process 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 student applies mathematical process 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, including making 10 and decomposing a number leading to a 10.

1(3)(E) Number and operations. The student applies mathematical process standards to develop and use strategies for whole number addition and subtraction computations in order to solve problems.

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. 1(3)(F) Number and operations. The student applies mathematical process 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.

Supporting Information

Students may use concrete and pictorial models to add whole numbers with sums up to 99. For example, to determine the sum of 60 + 7, a student would use a model to represent 6 tens and 7 ones.

This SE supports student understanding of place value and expanded form.

This SE extends K(3)(A), where students solve joining and separating problems with the result unknown. It also provides a context for 1(5)(F).

This SE extends students’ problem solving to address joining and separating actions with start, change, and result unknown. An example of a change unknown problem could be 3 + [ ] = 7. There were 3 birds in a tree. Some more birds came to join them. Now, there are 7 birds in the tree. How many birds came to join the birds that were there at the start? Students would then be asked to use objects or pictures to solve the problem.

The focus is on flexible thinking with composing 10 with two or more addends to support basic fact strategies such as “making 10.” For example, a student may compose 10 without objects using addends such a 4 + 6 = 10 or 4 + 1 + 5 = 10.

This SE supports 1(3)(C) by asking students to apply their understanding of composing 10 to solving problems based upon the basic facts of addition. For example, given the fact 7 + 8, a student may decompose 8 into 3 and 5 so that the 3 may be added to the 7 to make 10, then add the 10 and 5 to equal 15.

When paired with 1(1)(A), students may be asked to apply these basic facts to solve real-world word problems.

This SE builds to 2(4)(A), where students are expected to have automaticity of basic math facts. Students in first-grade are not expected to have automaticity of basic facts. Basic facts of addition include all possible pairs of addends chosen from 1 to 10 including 10 + 10.

When the SE is paired with the 1(1)(E) and 1(1)(G), students are expected to explain and record observations, which may include strategies.

This SE extends K(3)(C). Word problem structures may include joining and separating (start, change, or result unknown) actions, additive comparisons, and part-part-whole relationships. Students are not expected to know this terminology.

Students must be provided with a mathematical number sentence (equation) in order to generate and then solve a problem situation.

To build upon SEs 1(3)(B) and 1(5)(F), the unknown may be in any one of the terms in the problem. Problem situation structures may also include additive comparisons and part-part-whole relationships. Students are not expected to know this terminology.

©2017 Texas Education Agency. All Rights Reserved 2017

Mathematics TEKS: Supporting Information

Updated January 2019

5

Grade 1 – Mathematics

TEKS: Number and Operations. 1(4)(A) Number and operations. The student applies mathematical process 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. 1(4)(B) Number and operations. The student applies mathematical process 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 write a number with the cent symbol to describe the value of a coin.

1(4)(C) Number and operations. The student applies mathematical process 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.

Supporting Information This SE extends K(4) by asking students to describe the relationship among the coins. For example, a quarter may be thought of as having the same value as 5 nickels or 25 pennies.

Students should be familiar with the basic attributes of each coin regardless of if the coin has traditional or other images.

The SE expects students to label the value of a coin with the cent symbol, such as a dime has a value of 10¢.

To use the relationships among the coins with connections to skip count, one may count nickels by fives and dimes by tens. One may count two pennies together to count by twos. In this way, this SE may support 1(5)(B).

A collection of coins used for skip counting should not include quarters in grade 1.

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.

©2017 Texas Education Agency. All Rights Reserved 2017

Mathematics TEKS: Supporting Information

Updated January 2019

6

Grade 1 – Mathematics

TEKS: Algebraic Reasoning. 1(5)(A) 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 recite numbers forward and backward from any given number between 1 and 120. 1(5)(B) 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 skip count by twos, fives, and tens to determine the total number of objects up to 120 in a set. 1(5)(C) 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 use relationships to determine the number that is 10 more and 10 less than a given number up to 120.

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 up to 20 using concrete and pictorial models and number sentences.

1(5)(E) 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 understand that the equal sign represents a relationship where expressions on each side of the equal sign represent the same value(s).

1(5)(F) 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 determine the unknown whole number in an addition or subtraction equation when the unknown may be any one of the three or four terms in the equation.

Supporting Information

This SE extends K(5), where students are expected to recite numbers up to at least 100 by ones and tens beginning with any given number. When reciting by tens, kindergarten students counted only multiples of 10: 60, 70, 80 . . .

The focus of counting is to determine the total number of objects in a set.

This SE supports 1(4)(C), where students skip count to find the value of a collection of coins.

This technique of counting may lead to the concept of multiplication in grade 3 [3(4)(E)].

The relationship that students use should focus on place value. For example, 99 = 90 + 9. If a student wants a number that is 10 more than 99, the student can think (90 + 10) + 9 or 100 + 9 or 109.

This SE supports 1(2)(D) and builds to 2(7)(B), where students determine numbers that are either 10 or 100 more or less than a given up to 1,200. For this SE, the student is not asked to solve the word problem. The student is asked to represent the context of the word problem using objects, pictures, and number sentences (equations).

Based upon 1(3)(B), these word problems may include the unknown as any one of the terms.

For example, Phoung has 12 pencils. She has some red pencils and 8 yellow pencils. How many red

pencils does Phoung have?

12 pencils

12 = 8 + ?

8 yellow pencils ? red pencils

Word problem structures may include joining and separating (start, change, or result unknown) actions, additive comparisons, and part-part-whole relationships. Students are not expected to know this terminology. This SE requires students to understand that the equal sign does not necessarily mean “find the answer.”

For example, in the problem 4 + 2 + 3 = [ ], the relationship may be 4 + 2 + 3 = 9 or 4 + 2 + 3 = 6 + 3. In both of these number sentences, the expressions on each side of the equal sign have a value of 9.

The understanding of this SE helps support 1(5)(F) as students are asked to determine the unknown equation (number sentence).

When paired with 1(1)(G), students may be expected to explain that 4 + 2 + 2 = 4 + 4 because the sum on each side of the equal sign is 8.

This SE allows students to apply their understanding of 1(5)(E).

Examples of equations with three terms and one unknown include 6 + [ ] = 14, 14 ‒ [ ] = 6, or 14 ‒ 6 = [ ].

Examples of equations with four terms include 6 + [ ] = 4 + 8.

©2017 Texas Education Agency. All Rights Reserved 2017

Mathematics TEKS: Supporting Information

Updated January 2019

7

Grade 1 – Mathematics

TEKS: Algebraic Reasoning.

Supporting Information This SE may require students to apply the understanding of properties of operations to problem situations when incorporating 1(1)(A) and 1(1)(C). For example, there are 2 books on Ms. Smith’s desk. After lunch, she placed 9 more books on her desk. How many books are on Ms. Smith’s desk now?

A student may solve this problem using the commutative property of addition. The problem may be solved as 2 + 9 = 11, or a student may understand that 9 + 2 = 11 and could use this to solve the problem. A student may also use a place-value strategy such as “make 10.” For example, 2 + 9 = 2 + (8 + 1) = (2 + 8) + 1 = 10 + 1 = 11

The SE also includes the addition and subtraction of three numbers. For example, students may be expected to add 3 + 8 + 6 using the associative property as 3 + (7 + 1) + 6 = (3 + 7) + 1 + 6 = 10 + (1 + 6) = 10 + 7 = 17.

The application of the properties of operations allow for the grouping and regrouping of numbers to develop a strong sense of place value and for creating groups of tens and ones.

Larry has 7 toys. He gives 3 to his sister. He gives 2 to his brother. How many does he have left?

1(5)(G) 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 apply properties of operations to add and subtract two or three numbers.

Maria has 9 cards. She gets two more, then gives away 1. How many cards does Maria have? 9 + 2 - 1 = 10

©2017 Texas Education Agency. All Rights Reserved 2017

Mathematics TEKS: Supporting Information

Updated January 2019

8

GRADE 1

Texas Education Agency

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 78701-1494; phone: 512-463-9041 email: [email protected]

©2017 Texas Education Agency All Rights Reserved 2017

©2017 Texas Education Agency. All Rights Reserved 2017

Mathematics TEKS: Supporting Information

Updated January 2019

Grade 1 – Mathematics

TEKS (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. (2) The process standards describe ways in which students are expected to engage in the content. The placement of the process standards at the beginning of the knowledge and skills listed for each grade and course is intentional. The process standards weave the other knowledge and skills together so that students may be successful problem solvers and use mathematics efficiently and effectively in daily life. The process standards are integrated at every grade level and course. When possible, students will apply mathematics to problems arising in everyday life, society, and the workplace. Students will use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. Students will select appropriate tools such as real objects, manipulatives, algorithms, paper and pencil, and technology and techniques such as mental math, estimation, number sense, and generalization and abstraction to solve problems. Students will effectively communicate mathematical ideas, reasoning, and their implications using multiple representations such as symbols, diagrams, graphs, computer programs, and language. Students will use mathematical relationships to generate solutions and make connections and predictions. Students will analyze mathematical relationships to connect and communicate mathematical ideas. Students will display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

(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.

Supporting Information

The definition of a well-balanced mathematics curriculum has expanded to include the Texas College and Career Readiness Standards (CCRS). A focus on mathematical fluency and solid understanding allows for rich exploration of the primary focal points.

This paragraph occurs second in the TEKS to highlight the continued emphasis on process skills that are now included from kindergarten through high school mathematics. This introductory paragraph includes generalization and abstraction with the text from (1)(C). This introductory paragraph includes computer programs with the text from 1(D). This introductory paragraph states, “Students will use mathematical relationships to generate solutions and make connections and predictions” instead of incorporating the text from (1)(E).

The TEKS 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. Automaticity refers to the rapid recall of facts and vocabulary. For example, we would expect a third-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.

©2017 Texas Education Agency. All Rights Reserved 2017

Mathematics TEKS: Supporting Information

Updated January 2019

1

Grade 1 – Mathematics

(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 two-dimensional shapes and three-dimensional solids.

(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 paragraph highlights more specifics about grade 1 mathematics content and 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.

This paragraph has been updated to align to the grade 1 mathematics TEKS.

This 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.

The State Board of Education approved the retention of some “such as” statements within the TEKS where needed for clarification of content.

The phrases “including” and “such as” should not be considered as limiting factors for the student expectations (SEs) in which they reside.

Additional Resources are available online including Interactive Mathematics Glossary Vertical Alignment Charts Texas Response to the Curriculum Focal Points, Revised 2013 Texas Mathematics Resource Page

©2017 Texas Education Agency. All Rights Reserved 2017

Mathematics TEKS: Supporting Information

Updated January 2019

2

Grade 1 – Mathematics

TEKS: Mathematical Process Standards.

1(1)(A) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.

The student is expected to apply mathematics to problems arising in everyday life, society, and the workplace.

1(1)(B) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.

The student is expected to 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. 1(1)(C) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.

The student is expected to select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems. 1(1)(D) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.

The student is expected to communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

1(1)(E) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.

The student is expected to create and use representations to organize, record, and communicate mathematical ideas.

1(1)(F) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.

The student is expected to analyze mathematical relationships to connect and communicate mathematical ideas.

1(1)(G) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.

The student is expected to display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Supporting Information This SE emphasizes application.

The opportunities for application have been consolidated into three areas: everyday life, society, and the workplace.

This SE, when paired with a content SE, allows for increased rigor through connections outside the discipline.

This SE describes the traditional problem-solving process used in mathematics and science.

Students are expected to use this process in a grade appropriate manner when solving problems that can be considered difficult relative to mathematical maturity.

The phrase “as appropriate” is included in the TEKS. This implies that students are assessing which tool(s) to apply rather than trying only one or all accessible tools.

“Paper and pencil” is included in the list of tools that still includes real objects, manipulatives, and technology.

Communication includes reasoning and the implications of mathematical ideas and reasoning.

The list of representations is summarized with “multiple representations” with specificity added for “symbols,” “graphs,” and “diagrams.”

The use of representations includes organizing and recording mathematical ideas in addition to communicating ideas.

As students use and create representations, it is implied that they will evaluate the effectiveness of their representations to ensure that they are communicating mathematical ideas clearly.

Students are expected to use appropriate mathematical vocabulary and phrasing when communicating mathematical ideas. The TEKS allow for additional means to analyze relationships and to form connections with mathematical ideas past forming conjectures about generalizations and sets of examples and non-examples.

Students are expected to form conjectures based on patterns or sets of examples and nonexamples. Students are expected to validate their conclusions with displays, explanations, and justifications. The conclusions should focus on mathematical ideas and arguments.

Displays could include diagrams, visual aids, written work, etc. The intention is to make one’s work visible to others so that explanations and justifications may be shared in written or oral form.

Precise mathematical language is expected. For example, students would use “vertex” instead of “corner” when referring to the point at which two edges intersect on a polygon.

©2017 Texas Education Agency. All Rights Reserved 2017

Mathematics TEKS: Supporting Information

Updated January 2019

3

Grade 1 – Mathematics

TEKS: Number and Operations.

1(2)(A) Number and operations. The student applies mathematical process 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.

Supporting Information This SE extends K(2)(C), where students are asked to recognize small quantities in organized and random arrangements.

The number of items should be ten or less.

When paired with 1(1)(G), a student may be asked to explain the thinking he or she used to subitize the number.

Structured arrangements include ten frames and the arrangements of dots on random number generators. For example, when shown an arrangement with two “parts,” a student might justify his or her thinking by saying, “I recognize five, and then I added two more.”

1(2)(B) Number and operations. The student applies mathematical process 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. 1(2)(C) Number and operations. The student applies mathematical process 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. 1(2)(D) Number and operations. The student applies mathematical process 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 generate a number that is greater than or less than a given whole number up to 120.

1(2)(E) Number and operations. The student applies mathematical process 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 place value to compare whole numbers up to 120 using comparative language.

1(2)(F) Number and operations. The student applies mathematical process 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 order whole numbers up to 120 using place value and open number lines. 1(2)(G) Number and operations. The student applies mathematical process 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 represent the comparison of two numbers to 100 using the symbols >, <, or =.

This use of structured arrangements builds students’ conceptual understandings of the part-whole relationship of numbers (5 and 2 compose to 7) and basic facts (5 + 2 or 2 + 5). These concrete and pictorial models are used to compose and decompose numbers in more than one way as a means to describe the value of whole numbers.

“So many hundreds, so many tens, and so many ones" may include using models to decompose 67 into 5 tens and 17 ones. It may also include models to decompose 67 into the sum of 50, 10, and 7.

This SE allows students to incorporate 1(1)(D) through the use of multiple representations of a number by using concrete models, pictorial models, standard form (119), and expanded form (119 = 100 + 10 + 9).

This SE extends K(2)(F), where students are expected to generate a number that is one more or one less than another number up to 20.

Students may be expected to use comparative language such as greater than, less than, or equal to in order to compare numbers using place value. The comparison may occur in ones, tens, or hundreds. For example, given the numbers 87 and 64, a student would describe 64 as having the lesser value because the value of the 6 in the tens place is 60, while having an 8 in the tens place is 80, and 60 is less than 80.

In comparing numbers up to 120, one may use the hundreds, tens, and ones places with a set of whole numbers like 118, 108, 98, and 89. Students may be expected to use place value to order numbers based on the value of the digits and use an open number line, which builds to 2(2)(E), where students locate whole numbers on an open number line.

The use of an open number line supports student understanding related to the magnitude of number and the place-value relationship among numbers when locating a given number. Students are expected to extend their understanding of comparing numbers using comparative language in 1(2)(E). In this SE, student are expected to compare two numbers using the symbols >, <, or =.

This SE complements 1(2)(D), 1(2)(E), and 1(2)(F).

©2017 Texas Education Agency. All Rights Reserved 2017

Mathematics TEKS: Supporting Information

Updated January 2019

4

Grade 1 – Mathematics

TEKS: Number and Operations. 1(3)(A) Number and operations. The student applies mathematical process standards to develop and use strategies for whole number addition and subtraction computations in order to solve problems.

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 student applies mathematical process standards to develop and use strategies for whole number addition and subtraction computations in order to solve problems.

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.

1(3)(C) Number and operations. The student applies mathematical process 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 student applies mathematical process 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, including making 10 and decomposing a number leading to a 10.

1(3)(E) Number and operations. The student applies mathematical process standards to develop and use strategies for whole number addition and subtraction computations in order to solve problems.

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. 1(3)(F) Number and operations. The student applies mathematical process 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.

Supporting Information

Students may use concrete and pictorial models to add whole numbers with sums up to 99. For example, to determine the sum of 60 + 7, a student would use a model to represent 6 tens and 7 ones.

This SE supports student understanding of place value and expanded form.

This SE extends K(3)(A), where students solve joining and separating problems with the result unknown. It also provides a context for 1(5)(F).

This SE extends students’ problem solving to address joining and separating actions with start, change, and result unknown. An example of a change unknown problem could be 3 + [ ] = 7. There were 3 birds in a tree. Some more birds came to join them. Now, there are 7 birds in the tree. How many birds came to join the birds that were there at the start? Students would then be asked to use objects or pictures to solve the problem.

The focus is on flexible thinking with composing 10 with two or more addends to support basic fact strategies such as “making 10.” For example, a student may compose 10 without objects using addends such a 4 + 6 = 10 or 4 + 1 + 5 = 10.

This SE supports 1(3)(C) by asking students to apply their understanding of composing 10 to solving problems based upon the basic facts of addition. For example, given the fact 7 + 8, a student may decompose 8 into 3 and 5 so that the 3 may be added to the 7 to make 10, then add the 10 and 5 to equal 15.

When paired with 1(1)(A), students may be asked to apply these basic facts to solve real-world word problems.

This SE builds to 2(4)(A), where students are expected to have automaticity of basic math facts. Students in first-grade are not expected to have automaticity of basic facts. Basic facts of addition include all possible pairs of addends chosen from 1 to 10 including 10 + 10.

When the SE is paired with the 1(1)(E) and 1(1)(G), students are expected to explain and record observations, which may include strategies.

This SE extends K(3)(C). Word problem structures may include joining and separating (start, change, or result unknown) actions, additive comparisons, and part-part-whole relationships. Students are not expected to know this terminology.

Students must be provided with a mathematical number sentence (equation) in order to generate and then solve a problem situation.

To build upon SEs 1(3)(B) and 1(5)(F), the unknown may be in any one of the terms in the problem. Problem situation structures may also include additive comparisons and part-part-whole relationships. Students are not expected to know this terminology.

©2017 Texas Education Agency. All Rights Reserved 2017

Mathematics TEKS: Supporting Information

Updated January 2019

5

Grade 1 – Mathematics

TEKS: Number and Operations. 1(4)(A) Number and operations. The student applies mathematical process 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. 1(4)(B) Number and operations. The student applies mathematical process 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 write a number with the cent symbol to describe the value of a coin.

1(4)(C) Number and operations. The student applies mathematical process 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.

Supporting Information This SE extends K(4) by asking students to describe the relationship among the coins. For example, a quarter may be thought of as having the same value as 5 nickels or 25 pennies.

Students should be familiar with the basic attributes of each coin regardless of if the coin has traditional or other images.

The SE expects students to label the value of a coin with the cent symbol, such as a dime has a value of 10¢.

To use the relationships among the coins with connections to skip count, one may count nickels by fives and dimes by tens. One may count two pennies together to count by twos. In this way, this SE may support 1(5)(B).

A collection of coins used for skip counting should not include quarters in grade 1.

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.

©2017 Texas Education Agency. All Rights Reserved 2017

Mathematics TEKS: Supporting Information

Updated January 2019

6

Grade 1 – Mathematics

TEKS: Algebraic Reasoning. 1(5)(A) 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 recite numbers forward and backward from any given number between 1 and 120. 1(5)(B) 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 skip count by twos, fives, and tens to determine the total number of objects up to 120 in a set. 1(5)(C) 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 use relationships to determine the number that is 10 more and 10 less than a given number up to 120.

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 up to 20 using concrete and pictorial models and number sentences.

1(5)(E) 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 understand that the equal sign represents a relationship where expressions on each side of the equal sign represent the same value(s).

1(5)(F) 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 determine the unknown whole number in an addition or subtraction equation when the unknown may be any one of the three or four terms in the equation.

Supporting Information

This SE extends K(5), where students are expected to recite numbers up to at least 100 by ones and tens beginning with any given number. When reciting by tens, kindergarten students counted only multiples of 10: 60, 70, 80 . . .

The focus of counting is to determine the total number of objects in a set.

This SE supports 1(4)(C), where students skip count to find the value of a collection of coins.

This technique of counting may lead to the concept of multiplication in grade 3 [3(4)(E)].

The relationship that students use should focus on place value. For example, 99 = 90 + 9. If a student wants a number that is 10 more than 99, the student can think (90 + 10) + 9 or 100 + 9 or 109.

This SE supports 1(2)(D) and builds to 2(7)(B), where students determine numbers that are either 10 or 100 more or less than a given up to 1,200. For this SE, the student is not asked to solve the word problem. The student is asked to represent the context of the word problem using objects, pictures, and number sentences (equations).

Based upon 1(3)(B), these word problems may include the unknown as any one of the terms.

For example, Phoung has 12 pencils. She has some red pencils and 8 yellow pencils. How many red

pencils does Phoung have?

12 pencils

12 = 8 + ?

8 yellow pencils ? red pencils

Word problem structures may include joining and separating (start, change, or result unknown) actions, additive comparisons, and part-part-whole relationships. Students are not expected to know this terminology. This SE requires students to understand that the equal sign does not necessarily mean “find the answer.”

For example, in the problem 4 + 2 + 3 = [ ], the relationship may be 4 + 2 + 3 = 9 or 4 + 2 + 3 = 6 + 3. In both of these number sentences, the expressions on each side of the equal sign have a value of 9.

The understanding of this SE helps support 1(5)(F) as students are asked to determine the unknown equation (number sentence).

When paired with 1(1)(G), students may be expected to explain that 4 + 2 + 2 = 4 + 4 because the sum on each side of the equal sign is 8.

This SE allows students to apply their understanding of 1(5)(E).

Examples of equations with three terms and one unknown include 6 + [ ] = 14, 14 ‒ [ ] = 6, or 14 ‒ 6 = [ ].

Examples of equations with four terms include 6 + [ ] = 4 + 8.

©2017 Texas Education Agency. All Rights Reserved 2017

Mathematics TEKS: Supporting Information

Updated January 2019

7

Grade 1 – Mathematics

TEKS: Algebraic Reasoning.

Supporting Information This SE may require students to apply the understanding of properties of operations to problem situations when incorporating 1(1)(A) and 1(1)(C). For example, there are 2 books on Ms. Smith’s desk. After lunch, she placed 9 more books on her desk. How many books are on Ms. Smith’s desk now?

A student may solve this problem using the commutative property of addition. The problem may be solved as 2 + 9 = 11, or a student may understand that 9 + 2 = 11 and could use this to solve the problem. A student may also use a place-value strategy such as “make 10.” For example, 2 + 9 = 2 + (8 + 1) = (2 + 8) + 1 = 10 + 1 = 11

The SE also includes the addition and subtraction of three numbers. For example, students may be expected to add 3 + 8 + 6 using the associative property as 3 + (7 + 1) + 6 = (3 + 7) + 1 + 6 = 10 + (1 + 6) = 10 + 7 = 17.

The application of the properties of operations allow for the grouping and regrouping of numbers to develop a strong sense of place value and for creating groups of tens and ones.

Larry has 7 toys. He gives 3 to his sister. He gives 2 to his brother. How many does he have left?

1(5)(G) 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 apply properties of operations to add and subtract two or three numbers.

Maria has 9 cards. She gets two more, then gives away 1. How many cards does Maria have? 9 + 2 - 1 = 10

©2017 Texas Education Agency. All Rights Reserved 2017

Mathematics TEKS: Supporting Information

Updated January 2019

8