Math, Grades 3-5 TEKS and TAKS Alignment

Transcription

1 Mathematics, Grade Mathematics, Grade Mathematics, Grade 5. (a) Introduction. (1) Within a well-balanced mathematics curriculum, the primary focal points are multiplying and dividing whole numbers, connecting fraction symbols to fractional quantities, and standardizing language and procedures in geometry and measurement. comparing and ordering fractions and decimals, applying multiplication and division, and developing ideas related to congruence and symmetry. comparing and contrasting lengths, area, and volume of geometric shapes and solids; representing and interpreting data in graphs, charts, and tables; and applying whole number operations in a variety of contexts. (2) Throughout mathematics in Grades 3-5, students build a foundation of basic understandings in number, operation, and quantitative reasoning; use algorithms for addition, subtraction, multiplication, and division as generalizations connected to concrete experiences; and they concretely develop basic concepts of fractions and decimals. patterns, relationships, and algebraic thinking; appropriate language and organizational structures such as tables and charts to represent and communicate relationships, make predictions, and solve problems geometry and spatial reasoning; select and use formal language to describe their reasoning as they identify, compare, and classify shapes and solids measurement; use numbers, standard units, and measurement tools to describe and compare objects, make estimates, and solve application problems probability and statistics. organize data, choose an appropriate method to display the data, and interpret the data to make decisions and predictions and solve problems. (3) Problem solving, language and communication, connections within and outside mathematics, and formal and informal reasoning underlie all content areas in mathematics. Throughout mathematics in Grades 3-5, students USE THESE PROCESSES TOGETHER WITH TECHNOLOGY AND OTHER MATHEMATICAL TOOLS SUCH AS MANIPULATIVE MATERIALS TO DEVELOP CONCEPTUAL UNDERSTANDING AND SOLVE PROBLEMS AS THEY DO MATHEMATICS. Key for TEKS and TAKS: Yellow Highlight: Focus for grade level Underlined: Knowledge and skills statement Red Italics: Student performance expectation - what students will do to show proficiency of the math TEKS BLUE ALL CAPS: Process skills *: Math TAKS objective [Brackets]: Not specifically tested on TAKS Source: The provisions of this adopted to be effective September 1, 1998, 22 TexReg Reformatted by Authentic Learning, Inc. Page 1

2 (b) Knowledge and skills. (3.1) Number, operation, and quantitative The student uses place value to communicate about increasingly large whole numbers in verbal and written form, including money. (A)* use place value to read, write (in symbols and words), and describe the value of whole numbers through 999,999 (B)* use place value to compare and order whole numbers through 9,999 (C)* determine the value of a collection of coins and bills (3.2) Number, operation, and quantitative The student uses fraction names and symbols to describe fractional parts of whole objects or sets of objects. (A) construct concrete models of fractions (B)* compare fractional parts of whole objects or sets of objects in a problem situation using [concrete] models (C)* use fraction names and symbols to describe fractional parts of whole objects or sets of objects with denominators of 12 or less (D) construct concrete models of equivalent fractions for fractional parts of whole objects Math, Grades 3-5 TEKS and TAKS Alignment (4.1) Number, operation, and quantitative (5.1) Number, operation, and quantitative The student uses place value to represent whole numbers and decimals. (A)* use place value to read, write, compare, and order whole numbers through the millions place (B) use place value to read, write, compare, and order decimals involving tenths and hundredths, including money, using concrete models (4.2) Number, operation, and quantitative The student describes and compares fractional parts of whole objects or sets of objects. (A)* generate equivalent fractions using [concrete] and pictorial models (B)* model fraction quantities greater than one using [concrete materials and] pictures (C)* compare and order fractions using [concrete and] pictorial models (D)* relate decimals to fractions that name tenths and hundredths using models (A)* use place value to read, write, compare, and order whole numbers through the billions place (B)* use place value to read, write, compare, and order decimals through the thousandths place (5.2) Number, operation, and quantitative The student uses fractions in problem-solving situations. (A)* generate equivalent fractions (B)* compare two fractional quantities in problem-solving situations using a variety of methods, including common denominators (C)* use models to relate decimals to fractions that name tenths, hundredths, and thousandths Source: The provisions of this adopted to be effective September 1, 1998, 22 TexReg Reformatted by Authentic Learning, Inc. Page 2

3 (3.3) Number, operation, and quantitative The student adds and subtracts to solve meaningful problems involving whole numbers. (A)* model addition and subtraction using pictures, words, and numbers (B)* select addition or subtraction and use the operation to solve problems involving whole numbers through 999 (3.4) Number, operation, and quantitative The student recognizes and solves problems in multiplication and division situations. (A) learn and apply multiplication facts through the tens using concrete models (B)* solve and record multiplication problems (one-digit multiplier) (C)* use models to solve division problems and use number sentences to record the solutions Math, Grades 3-5 TEKS and TAKS Alignment (4.3) Number, operation, and quantitative The student adds and subtracts to solve meaningful problems involving whole numbers and decimals. (A)* use addition and subtraction to solve problems involving whole numbers (B)* add and subtract decimals to the hundredths place using [concrete and] pictorial models (4.4) Number, operation, and quantitative The student multiplies and divides to solve meaningful problems involving whole numbers and decimals. (A)* model factors and products using arrays and area models (B)* represent multiplication and division situations in picture, word, and number form (C)* recall and apply multiplication facts through 12 x 12 (D)* use multiplication to solve problems involving two-digit numbers (E)* use division to solve problems involving one-digit divisors (5.3) Number, operation, and quantitative The student adds, subtracts, multiplies, and divides to solve meaningful problems. (A)* use addition and subtraction to solve problems involving whole numbers and decimals (B)* use multiplication to solve problems involving whole numbers (no more than three digits times two digits without technology) (C)* use division to solve problems involving whole numbers (no more than two-digit divisors and three-digit dividends without technology) (D)* identify prime factors of a whole number and common factors of a set of whole numbers (E)* model and record addition and subtraction of fractions with like denominators in problem-solving situations Source: The provisions of this adopted to be effective September 1, 1998, 22 TexReg Reformatted by Authentic Learning, Inc. Page 3

4 (3.5) Number, operation, and quantitative (4.5) Number, operation, and quantitative The student estimates to determine reasonable results. (A)* round two-digit numbers to the nearest ten (A)* round whole numbers to the nearest ten, and three-digit numbers to the nearest hundred, or thousand to approximate hundred reasonable results in problem situations (B)* estimate sums and differences beyond basic facts (3.6) Patterns, relationships, and algebraic thinking. The student uses patterns to solve problems. (A)* identify and extend whole-number and geometric patterns to make predictions and solve problems (B)* identify patterns in multiplication facts using [concrete objects,] pictorial models, [or technology] (C)* identify patterns in related multiplication and division sentences (fact families) such as 2 x 3 = 6, 3 x 2 = 6, 6 2 = 3, 6 3 = 2 (3.7) Patterns, relationships, and algebraic thinking. The student uses lists, tables, and charts to express patterns and relationships. (A)* generate a table of paired numbers based on a real-life situation such as insects and legs (B)* identify patterns in a table of related number pairs based on a real-life situation and extend the table. (B)* estimate a product or quotient beyond basic facts (4.6) Patterns, relationships, and algebraic thinking. The student uses patterns in multiplication and division. (C)* use patterns to multiply by 10 and 100 (A) use patterns to develop strategies to remember basic multiplication facts (B)* solve division problems related to multiplication facts (fact families) such as 9 x 9 = 81 and 81 9 = 9 (4.7) Patterns, relationships, and algebraic thinking. The student uses organizational structures to analyze and describe patterns and relationships. (A)* describe the relationship between two sets of related data such as ordered pairs in a table (5.4) Number, operation, and quantitative (A)* round whole numbers and decimals through tenths to approximate reasonable results in problem situations (B)* estimate to solve problems where exact answers are not required (5.5) Patterns, relationships, and algebraic thinking. The student makes generalizations based on observed patterns and relationships. (A)* use concrete objects or pictures to make generalizations about determining all possible combinations (B)* use lists, tables, charts, and diagrams to find patterns and make generalizations such as a procedure for determining equivalent fractions (C)* identify prime and composite numbers using [concrete] models and patterns in factor pairs (5.6) Patterns, relationships, and algebraic thinking. The student describes relationships mathematically. (A)* select from and use diagrams and number sentences to represent real-life situations Source: The provisions of this adopted to be effective September 1, 1998, 22 TexReg Reformatted by Authentic Learning, Inc. Page 4

5 (3.8) Geometry and spatial The student uses formal geometric vocabulary. (A)* name, describe, and compare shapes and solids using formal geometric vocabulary (3.9) Geometry and spatial The student recognizes congruence and symmetry. (A)* identify congruent shapes (B) create shapes with lines of symmetry using concrete models and technology (C)* identify lines of symmetry in shapes (3.10) Geometry and spatial The student recognizes that numbers can be represented by points on a line. (A)* locate and name points on a line using whole numbers [and fractions such as halves]. (4.8) Geometry and spatial The student identifies and describes lines, shapes, and solids using formal geometric language. (A)* identify right, acute, and obtuse angles (B)* identify models of parallel and perpendicular lines (C)* describe shapes and solids in terms of vertices, edges, and faces (4.9) Geometry and spatial The student connects transformations to congruence and symmetry. (A) demonstrate translations, reflections, and rotations using concrete models (B)* use translations, reflections, and rotations to verify that two shapes are congruent (C)* use reflections to verify that a shape has symmetry (4.10) Geometry and spatial The student recognizes the connection between numbers and points on a number line. (A)* locate and name points on a number line using whole numbers, fractions such as halves and fourths, and decimals such as tenths. (5.7) Geometry and spatial The student generates geometric definitions using critical attributes. (A)* identify critical attributes including parallel, perpendicular, and congruent parts of geometric shapes and solids (B)* use critical attributes to define geometric shapes or solids (5.8) Geometry and spatial The student models transformations. (A)* sketch the results of translations, rotations, and reflections (B)* describe the transformation that generates one figure from the other when given two congruent figures (5.9) Geometry and spatial The student recognizes the connection between ordered pairs of numbers and locations of points on a plane. (A)* locate and name points on a coordinate grid using ordered pairs of whole numbers. Source: The provisions of this adopted to be effective September 1, 1998, 22 TexReg Reformatted by Authentic Learning, Inc. Page 5

6 (3.11) Measurement. The student selects and uses appropriate units and procedures to measure length and area. (A)* estimate and measure lengths using standard units such as inch, foot, yard, centimeter, [decimeter,] and meter (B)* use linear measure to find the perimeter of a shape (C)* use [concrete] models of square units to determine the area of shapes Math, Grades 3-5 TEKS and TAKS Alignment (4.11) Measurement. The student selects and uses appropriate units and procedures to measure weight and capacity. (A)* estimate [and measure] weight using standard units including ounces, pounds, grams, and kilograms (B)* estimate [and measure] capacity using standard units including milliliters, liters, cups, pints, quarts, and gallons (5.10) Measurement. The student selects and uses appropriate units and procedures to measure volume. (A)* measure volume using [concrete] models of cubic units (B) estimate volume in cubic units (3.12) Measurement. The student measures time and temperature. (A)* tell and write time shown on traditional and digital clocks (B)* use a thermometer to measure temperature (3.13) Measurement. (4.12) Measurement. (5.11) Measurement. The student applies measurement concepts. (A)* measure to solve problems involving length, area, temperature, and time (A)* measure to solve problems involving length, including perimeter, time, temperature, and area (A)* measure to solve problems involving length (including perimeter), weight, capacity, time, temperature, and area (B)* describe numerical relationships between units of measure within the same measurement system such as an inch is one-twelfth of a foot Source: The provisions of this adopted to be effective September 1, 1998, 22 TexReg Reformatted by Authentic Learning, Inc. Page 6

7 (3.14) Probability and statistics. The student solves problems by collecting, organizing, displaying, and interpreting sets of data. (A)* collect, organize, record, and display (A)* list all possible outcomes of a probability data in pictographs and bar graphs experiment such as tossing a coin where each picture or cell might represent more than one piece of data (B)* interpret information from pictographs and bar graphs (C)* use data to describe events as more likely, less likely, or equally likely (5.12) Probability and statistics. The student describes and predicts the results of a probability experiment. (A)* use fractions to describe the results of an experiment (B)* use experimental results to make predictions (4.13) Probability and statistics. (5.13) Probability and statistics. (B)* use a pair of numbers to compare favorable outcomes to all possible outcomes such as four heads out of six tosses of a coin (C)* interpret bar graphs (A)* use tables of related number pairs to make line graphs (B)* describe characteristics of data presented in tables and graphs including the shape and spread of the data and the middle number (C)* graph a given set of data using an appropriate graphical representation such as a picture or line Source: The provisions of this adopted to be effective September 1, 1998, 22 TexReg Reformatted by Authentic Learning, Inc. Page 7

8 (3.15) Underlying processes and (4.14) Underlying processes and (5.14) Underlying processes and The student APPLIES MATHEMATICS TO SOLVE PROBLEMS CONNECTED TO EVERYDAY EXPERIENCES AND ACTIVITIES IN AND OUTSIDE OF SCHOOL. (A)* IDENTIFY THE MATHEMATICS IN EVERYDAY SITUATIONS (B)* USE A PROBLEM-SOLVING MODEL THAT INCORPORATES UNDERSTANDING THE PROBLEM, MAKING A PLAN, CARRYING OUT THE PLAN, AND EVALUATING THE SOLUTION FOR REASONABLENESS (C)* SELECT OR DEVELOP AN APPROPRIATE PROBLEM-SOLVING STRATEGY, INCLUDING DRAWING A PICTURE, LOOKING FOR A PATTERN, SYSTEMATIC GUESSING AND CHECKING, ACTING IT OUT, MAKING A TABLE, WORKING A SIMPLER PROBLEM, OR WORKING BACKWARDS TO SOLVE A PROBLEM (D) USE TOOLS such as real objects, manipulatives, and technology TO SOLVE PROBLEMS (3.16) Underlying processes and (4.15) Underlying processes and The student COMMUNICATES ABOUT MATHEMATICS USING INFORMAL LANGUAGE. (A) EXPLAIN AND RECORD OBSERVATIONS USING OBJECTS, WORDS, PICTURES, NUMBERS, AND TECHNOLOGY (B)* RELATE INFORMAL LANGUAGE TO MATHEMATICAL LANGUAGE AND SYMBOLS (3.17) Underlying processes and (4.16) Underlying processes and The student USES LOGICAL REASONING TO MAKE SENSE OF HIS OR HER WORLD. (A)* MAKE GENERALIZATIONS FROM PATTERNS OR SETS OF EXAMPLES AND NONEXAMPLES (B) JUSTIFY WHY AN ANSWER IS REASONABLE AND EXPLAIN THE SOLUTION PROCESS. (5.15) Underlying processes and (5.16)Underlying processes and Source: The provisions of this adopted to be effective September 1, 1998, 22 TexReg Reformatted by Authentic Learning, Inc. Page 8