1 Mathematics, Grade Mathematics, Grade Mathematics, Grade 3. (a) Introduction. (1) Within a well-balanced mathematics curriculum, the primary focal points are adding and subtracting whole numbers and organizing and analyzing data. comparing and ordering whole numbers, applying addition and subtraction, and using measurement processes. multiplying and dividing whole numbers, connecting fraction symbols to fractional quantities, and standardizing language and procedures in geometry and measurement. (2) Throughout mathematics in Grades 1-3, students build a foundation of basic understandings in number, operation, and quantitative reasoning; use numbers in ordering, labeling, and expressing quantities and relationships to solve problems and translate informal language into mathematical symbols. patterns, relationships, and algebraic thinking; use patterns to describe objects, express relationships, make predictions, and solve problems as they build an understanding of number, operation, shape, and space. geometry and spatial reasoning; use informal language and observation of geometric properties to describe shapes, solids, and locations in the physical world. measurement; to develop measurement concepts as they identify and compare attributes of objects and situations. probability and statistics; 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) 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 1-3, 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: Highlight: Focus for grade level Underlined: Knowledge and skills statement Italics: Student performance expectation - what students will do to show proficiency of the math TEKS ALL CAPS: Process skills *: Math TAKS objective +: TEKS that support Grade 3 TAKS objectives [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. (1.1) Number, operation, and quantitative reasoning. The student uses whole numbers to describe and compare quantities. (A)+ compare and order whole numbers up to 99 (less than, greater than, or equal to) using sets of concrete objects and pictorial models (D)+ read and write numbers to 99 to describe sets of concrete objects (B)+ create sets of tens and ones using concrete objects to describe, compare, and order whole numbers (C)+ use words and numbers to describe the values of individual coins such as penny, nickel, dime, and quarter and their relationships (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. (A)+ share a whole by separating it into equal parts and use appropriate language to describe the parts such as three out of four equal parts (B)+ use appropriate language to describe part of a set such as three out of the eight crayons are red Math, Grades 1-3 TEKS and TAKS Alignment (2.1) Number, operation, and quantitative reasoning. The student understands how place value is used to represent whole numbers. (A)+ use concrete models to represent, compare, and order whole numbers (through 999), read the numbers, and record the comparisons using numbers and symbols (>, <, =) (2.2) Number, operation, and quantitative reasoning. The student uses fraction words to name parts of whole objects or sets of objects. (A)+ name fractional parts of a whole object (not to exceed twelfths) when given a concrete representation (B)+ name fractional parts of a set of objects (not to exceed twelfths) when given a concrete representation (3.1) Number, operation, and quantitative reasoning. 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 reasoning. 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 Source: The provisions of this adopted to be effective September 1, 1998, 22 TexReg Reformatted by Authentic Learning, Inc. Page 2
3 (1.3) Number, operation, and quantitative reasoning. The student recognizes and solves problems in addition and subtraction situations. (B)+ learn and apply basic addition facts (sums to 18) using concrete models (A)+ model and create addition and subtraction problem situations with concrete objects and write corresponding number sentences Math, Grades 1-3 TEKS and TAKS Alignment (2.3) Number, operation, and quantitative reasoning. The student adds and subtracts whole numbers to solve problems. (A)+ recall and apply basic addition facts (sums to 18) (B)+ select addition or subtraction and solve problems using two-digit numbers, whether or not regrouping is necessary (C)+ determine the value of a collection of coins less than one dollar (2.4) Number, operation, and quantitative reasoning. The student models multiplication and division. (A)+ model, create, and describe multiplication situations in which equivalent sets of concrete objects are joined (B)+ model, create, and describe division situations in which a set of concrete objects is separated into equivalent sets (3.3) Number, operation, and quantitative reasoning. 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 reasoning. 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 (3.5) Number, operation, and quantitative reasoning. The student estimates to determine reasonable results. (A)* round two-digit numbers to the nearest ten and three-digit numbers to the nearest hundred (B)* estimate sums and differences beyond basic facts Source: The provisions of this adopted to be effective September 1, 1998, 22 TexReg Reformatted by Authentic Learning, Inc. Page 3
4 (1.5) Patterns, relationships, and algebraic thinking. The student recognizes patterns in numbers and operations. (A)+ find patterns in numbers, including odd and even (B)+ compare and order whole numbers using place value (C)+ identify patterns in related addition and subtraction sentences (fact families for sums to 18) such as = 5, = 5, 5 2 = 3, and 5 3 = 2 (1.4) Patterns, relationships, and algebraic thinking. The student uses patterns to make predictions. (A)+ identify, describe, and extend concrete and pictorial patterns in order to make predictions and solve problems (B)+ use patterns to skip count by twos, fives, and tens (2.5) Patterns, relationships, and algebraic thinking. The student uses patterns in numbers and operations. (A)+ find patterns in numbers such as in a 100s chart (B)+ use patterns in place value to compare and order whole numbers through 999 (C)+ use patterns to develop strategies to remember basic addition facts (D)+ solve subtraction problems related to addition facts (fact families) such as = 17, = 17, 17 8 = 9, and 17 9 = 8 (2.6) Patterns, relationships, and algebraic thinking. The student uses patterns to describe relationships and make predictions. (A)+ generate a list of paired numbers based on a real-life situation such as number of tricycles related to number of wheels (B)+ identify patterns in a list of related number pairs based on a real-life situation and extend the list (C)+ identify, describe, and extend patterns to make predictions and solve problems (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 Source: The provisions of this adopted to be effective September 1, 1998, 22 TexReg Reformatted by Authentic Learning, Inc. Page 4
5 (1.6) Geometry and spatial reasoning. The student uses attributes to identify, compare, and contrast shapes and solids. (A)+ describe and identify objects in order to sort them according to a given attribute using informal language (B)+ identify circles, triangles, and rectangles, including squares, and describe the shape of balls, boxes, cans, and cones (C)+ combine geometric shapes to make new geometric shapes using concrete models (1.7) Measurement. The student uses nonstandard units to describe length, weight, and capacity. (A)+ estimate and measure length, capacity, and weight of objects using nonstandard units (B)+ describe the relationship between the size of the unit and the number of units needed in a measurement (2.7) Geometry and spatial reasoning. The student uses attributes to identify, compare, and contrast shapes and solids. (A)+ identify attributes of any shape or solid (B)+ use attributes to describe how two shapes or two solids are alike or different (3.8) Geometry and spatial reasoning. The student uses formal geometric vocabulary. (A)* name, describe, and compare shapes and solids using formal geometric vocabulary (3.9) Geometry and spatial reasoning. The student recognizes congruence and symmetry. (A)* identify congruent shapes (C)* identify lines of symmetry in shapes (C)+ cut geometric shapes apart and identify (B) create shapes with lines of symmetry the new shapes made using concrete models and technology (2.8) Geometry and spatial reasoning. (3.10) Geometry and spatial reasoning. The student recognizes that numbers can be represented by points on a line. (A)+ use whole numbers to locate and name (A)* locate and name points on a line using points on a line whole numbers [and fractions such as halves] (2.9) Measurement. The student recognizes and uses models that approximate standard units (metric and customary) of length, weight, capacity, and time. (A)+ identify concrete models that approximate standard units of length, capacity, and weight (B)+ measure length, capacity, and weight using concrete models that approximate standard units (C)+ describe activities that take approximately one second, one minute, and one hour (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 Source: The provisions of this adopted to be effective September 1, 1998, 22 TexReg Reformatted by Authentic Learning, Inc. Page 5
6 (1.8) Measurement. The student understands that time and temperature can be measured. Math, Grades 1-3 TEKS and TAKS Alignment (2.10) Measurement. The student uses standard tools to measure time and temperature. (A)+ read a thermometer to gather data (3.12) Measurement. The student measures time and temperature. (A)+ recognize temperatures such as a hot day or a cold day (B)* use a thermometer to measure temperature (B)+ describe time on a clock using hours and (B)+ describe time on a clock using hours and (A)* tell and write time shown on traditional half hours minutes and digital clocks (C)+ order three or more events by how much (3.13) Measurement. The student applies time they take measurement concepts. (A)* measure to solve problems involving length, area, temperature, and time (1.9) Probability and statistics. The student (2.11) Probability and statistics. The student (3.14) Probability and statistics. The student displays data in an organized form. organizes data to make it useful for solves problems by collecting, organizing, interpreting information. displaying, and interpreting sets of data. (A)+ collect and sort data (A)+ construct picture graphs and bar-type (A)* collect, organize, record, and display data graphs in pictographs and bar graphs where each picture or cell might represent more than one piece of data (B)+ use organized data to construct real object graphs, picture graphs, and bar- type graphs (1.10) Probability and statistics. The student uses information from organized data. (A)+ draw conclusions and answer questions using information organized in realobject graphs, picture graphs, and bartype graphs (B)+ identify events as certain or impossible such as drawing a red crayon from a bag of green crayons (B)+ draw conclusions and answer questions (B)* interpret information from pictographs based on picture graphs and bar-type and bar graphs graphs (C)+ use data to describe events as more likely (C)* use data to describe events as more likely, or less likely such as drawing a certain less likely, or equally likely color crayon from a bag of seven red crayons and three green crayons Source: The provisions of this adopted to be effective September 1, 1998, 22 TexReg Reformatted by Authentic Learning, Inc. Page 6
7 (1.11) Underlying processes and (2.12) Underlying processes and (3.15) Underlying processes and The student APPLIES MATHEMATICS TO SOLVE PROBLEMS CONNECTED TO EVERYDAY EXPERIENCES AND ACTIVITIES IN AND OUTSIDE OF SCHOOL. (A)* IDENTIFY MATHEMATICS IN EVERYDAY SITUATIONS (B)+ USE A PROBLEM-SOLVING MODEL, WITH GUIDANCE AS NEEDED, THAT (B)* USE A PROBLEM-SOLVING MODEL THAT INCORPORATES UNDERSTANDING THE PROBLEM, MAKING A PLAN, CARRYING OUT THE PLAN, AND EVALUATING THE SOLUTION FOR INCORPORATES UNDERSTANDING THE REASONABLENESS 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, OR ACTING IT OUT IN ORDER TO SOLVE A PROBLEM (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 (1.12) Underlying processes and (2.13) Underlying processes and (3.16) 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 EVERYDAY LANGUAGE TO MATHEMATICAL LANGUAGE AND SYMBOLS (1.13) Underlying processes and (2.14) Underlying processes and The student USES LOGICAL REASONING TO MAKE SENSE OF HIS OR HER WORLD. (A) REASON AND SUPPORT HIS OR HER THINKING USING OBJECTS, WORDS, PICTURES, NUMBERS, AND TECHNOLOGY (3.17) Underlying processes and (A)* MAKE GENERALIZATIONS FROM PATTERNS OR SETS OF EXAMPLES AND NONEXAMPLES (B) JUSTIFY WHY AN ANSWER IS REASONABLE AND EXPLAIN THE SOLUTION PROCESS Source: The provisions of this adopted to be effective September 1, 1998, 22 TexReg Reformatted by Authentic Learning, Inc. Page 7
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