Web viewsolve problems that incorporate the process of understanding the problem, making a plan, carrying out the plan, and evaluating the solution of reasonableness

Green: Remaining/Clarified Content (content/cognitive changes) Blue: New Content Yellow: Shifted Content (down 1+ grade levels)

3.1/4.1/5.1 The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

Instructional Considerations

Current TEKS New 4th grade TEKS 2013-14 2014-15 Current TEKS New 5th grade TEKS

3.14A/4.14A /5.14A identify the mathematics in everyday situations

3.1A/4.1A/5.1A apply mathematics to problems arising in everyday life, society, and the workplace

3.14B/4.14B/5.14B solve problems that incorporate the process of understanding the problem, making a plan, carrying out the plan, and evaluating the solution of reasonableness

3.14C/4.14C/5.14C select or develop and appropriate problem-solving plan or strategy including drawing a picture, looking for a pattern, systematic guessing and checking, acting it, making a table, working a simpler problem, or working backwards to solve a problem

3.1B/4.1B/5.1B 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

Copyright©2013 ESC Region 13


3.1/4.1/5.1 The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:



3.14D/4.14D/5.14D use tools such as real objects, manipulatives, and technology to solve problems

3.1C/4.1C/5.1C select tools, including real objects, manipulatives, paper/pencil, and technology, as appropriate and techniques, including mental math, estimation, and number sense, as appropriate to solve problems

3.15A/4.15A/5.15A explain and record observations using objects, words, pictures, numbers, and technology

3.1D/4.1D/5.1D communicate mathematical ideas, reasoning, and their implications using multiple representation, including symbols, diagrams, graphs, and language as appropriate



3.1/4.1/5.1 The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to



3.15B/4.15B/5.15B relate informal language to mathematical language and symbols

3.1E/4.1E/5.1E create and use representations to organize, record and communicate mathematical ideas

3.16A/4.16A/5.16A make generalizations about patterns or sets of examples and non-examples

3.1F/4.1F/5.1F analyze mathematical relationships to connect and communicate mathematical ideas

3.16B/4.16B/5.16B justify why an answer is reasonable and explain the solution process

3.1G/4.1G/5.1G display, explain and justify mathematical ideas and arguments using precise mathematical language in written or oral communications



4.2 The student applies mathematical process standards to represent, compare, and order whole numbers and decimals and understand relationships related to place value. The student is expected to:



4.2A interpret the value of each place-value position as ten times the position to the right and as one-tenth of the value of the place to its left

5.1B use place value to read, write, compare, and order decimals through the thousandths place

5.2A represent the value of the digit in decimals through the thousandths using expanded notation and numerals

4.1A use place value to read, write, compare, and order whole numbers through 999,999,999

4.1B use place value to read, write, compare, and order decimals involving tenths and hundredths, including money, using concrete objects and pictorial models

4.2B represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals



4.1A use place value to read, write, compare, and order whole numbers through 999,999,999

4.2C compare and order whole numbers to 1,000,000,000 and represent comparisons using the symbols <, >, or =


5.2B compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or =



4.2 The student applies mathematical process standards to represent, compare, and order whole numbers and decimals and understand relationships related to place value. The student is expected to:



4.5A round whole numbers to the nearest ten, hundred, or thousand to approximate reasonable results in problem situations

4.2D round whole numbers to a given place value through the hundred thousands place

5.4A use strategies including rounding and compatible numbers to estimate solutions to addition subtraction, multiplication, and division problems

5.2C round decimals to tenths or hundredths

4.1B use place value to read, write, compare, and order decimals involving tenths and hundredths, including money, using concrete objects and pictorial models

4.2E represent decimals, including tenths and hundredths, using concrete and visual models and money

4.2F compare and order decimals using concrete and visual models to hundredths



4.2D relate decimals to fractions that name tenths and hundredths using concrete objects and pictorial models

4.2G relate decimals to fractions that name tenths and hundredths

NONE

4.10A locate and name points on a number line using whole numbers, fractions such as halves and fourths, and decimals such as tenths

4.2H determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line

NONE



4.3 The student applies mathematical process standards to represent and generate fractions to solve problems. The student is expected to:



4.3A represent a fraction a/b as a sum of fractions 1/b, where a and b are whole numbers and b>0, including when a>b

NONE

4.3B decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations

NONE

4.3C determine if two given fractions are equivalent using a variety of methods

NONE






5.2A generate a fraction equivalent to a given fraction such as 1/2 and 3/6 or 4/12 and 1/3

5.2B generate a mixed number equivalent to a given improper fraction or generate an improper fraction equivalent to a given mixed number

5.2C compare two fractional quantities in problem-solving situations using a variety of methods, including common denominators.

4.3D compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or <

NONE

5.3E model situations using addition and/or subtraction involving fractions with like denominators using concrete objects, pictures, words, and numbers

4.3E represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations

5.3H represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects, pictorial models, and properties of operations






4.3F evaluate the reasonableness of sums and differences of fractions using benchmark fractions 0, ¼, ½, ¾, and 1, referring to the same whole

5.3A use addition and subtraction to solve problems involving whole numbers and decimals

5.3K add and subtract positive rational numbers fluently

4.10A locate and name points on a number line using whole numbers, fractions such as halves and fourths, and decimals such as tenths (Geometry and Spatial Reasoning Strand)

4.3G represent fractions and decimals to the tenths or hundredths as distances from zero on a number line

NONE



4.4 The student applies mathematical process standards to develop and use strategies and methods for whole number computations and decimal sums and differences in order to solve problems with efficiency and accuracy. The student is expected to:



4.3A use addition and subtraction to solve problems involving whole numbers

5.3A use addition and subtraction to solve problems involving whole numbers and decimals

4.4A add and subtract whole numbers and decimals to the hundredths place using the standard algorithm

5.4A use strategies including rounding and compatible numbers to estimate solutions to addition, subtraction, multiplication, and division problems

5.3A estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division

4.6B use patterns to multiply by 10 and 100 (Patterns, Relationships, and Algebraic Thinking)

4.4B determine products of a number and 10 or 100 using properties of operations and place value understanding

5.3B use multiplication to solve problems involving whole numbers (no more than three digits times two digits without technology)

5.3B multiply with fluency a three-digit number by a two-digit number using the standard algorithm



4.4A model factors and products using arrays and area models

4.4B represent multiplication and division situations in picture, word, and number form

4.4C represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 x 15

5.3B use multiplication to solve problems involving whole numbers (no more than three digits times two digits without technology)





4.4D use multiplication to solve problems (no more than two digits times two digits without technology)

4.4D use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number; strategies may include mental math, partial products, and the commutative, associative, and distributive properties

5.3B use multiplication to solve problems involving whole numbers (no more than threedigits times two digits without technology)





4.4E represent the quotient of up to a four-digit whole number divided by a one-digit whole number using arrays, area models, or equations

5.3C use division to solve problems involving whole numbers (no more than two-digitdivisors and three-digit dividends without technology) including interpreting the remainder within a given context

5.3C solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm

4.4E use division to solve problems (no more than one-digit divisors and three-digit dividends without technology)

4.4F use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor

5.3C use division to solve problems involving whole numbers (no more than two-digitdivisors and three-digit dividends without technology) including interpreting the remainder within a given context

5.3C solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm






4.5B use strategies including rounding and compatible numbers to estimate solutions to multiplication and division problems

4.4G round to the nearest 10, 100 or 1,000 or use compatible numbers, to estimate solutions involving whole numbers

5.4A use strategies including rounding and compatible numbers to estimate solutions to addition, subtraction, multiplication, and division problems

5.2C round decimals to tenths or hundredths


4.4D use multiplication to solve problems (no more than two digits times two digits without technology)

5.3C use division to solve problems involving whole numbers (no more than two-digit divisors and three-digit dividends without technology) including interpreting the remainder within a given context

4.4H solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders

5.3B use multiplication to solve problems involving whole numbers (no more than threedigits times two digits without technology)


4.5 The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to: Instructional Considerations





4.5A represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with a letter standing for the unknown quantity

5.6 select from and use diagrams and equations such as y = 5 + 3 to represent meaningful problem situations

5.4B represent and solve multistep problems involving the four operations with the whole numbers using equations with a letter standing for the unknown quantity

4.7A describe the relationship between two sets of related data such as ordered pairs in a table

4.5B represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequence and their position in the sequence

5.5A describe the relationship between sets of data in graphic organizers such as lists, tables, charts, and diagrams

5.4C generate a numerical pattern when given a rule in the form y=ax or y = x + a and graph

5.4D recognize the difference between additive and multiplicative numerical patterns give in a table or graph

4.5 The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to: Instructional Considerations




4.11A estimate to use measurement tools to determine length (including perimeter), area, capacity, and weight/mass using standard units SI (metric) and customary

5.10B connect models for perimeter, area, and volume with their respective formulas

4.5C use models to determine the formulas for the perimeter of a rectangle (l + w + l+ w or 2l + 2w), including the special form for perimeter of a square (4s) and the area of a rectangle (l x w)

5.10B connect models for perimeter, area, and volume with their respective formulas(Measurement Strand)

5.4G use concrete objects and pictorial models to develop the formulas for the volume of a rectangular prism, including the special form for a cube (V = l x w x h, V = s x s x s, and V=Bh)

4.11A estimate and use measurement tools to determine length (including perimeter), area, capacity, and weight/mass using standard units SI (metric) and customary (Measurement Strand)

4.5D solve problems related to perimeter and area of rectangles where dimensions are whole numbers

5.10C select and use appropriate units and formulas to measure length, perimeter, area and volume

5.4H represent and solve problems related to perimeter and/or area and related to volume

4.6 The student applies mathematical process standards to analyze geometric attributes in order to develop generalizations about their properties. The student is expected to:





4.8B identify and describe parallel and intersecting (including perpendicular) lines using concrete objects and pictorial models

4.6A identify points, lines, line segments, rays, angles, and perpendicular and parallel lines

NONE

4.9C use reflections to verify that a shape has symmetry

4.6B identify and draw one or more lines of symmetry, if they exist, for a two-dimensional figure

NONE

4.8A identify and describe right, acute, and obtuse angles

4.6C apply knowledge of right angles to identify acute, right, and obtuse triangles

NONE

4.8C use essential attributes to define two- and three-dimensional geometric figures

6.6B identify relationships involving angles in triangles and quadrilaterals

7.6B use properties to classify triangles and quadrilaterals

4.6D classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size

5.7A identify essential attributes including parallel, perpendicular, and congruent parts of two- and three-dimensional geometric figures

5.5A classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties

4.7 The student applies mathematical process standards to solve problems involving angles less than or equal to 180 degrees. The student is expected to:





6.8C measure angles 4.7A illustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle that is “cut out” by the rays of the angle; angle measures are limited to whole numbers

NONE

6.8C measure angles 4.7B illustrate degrees as the units used to measure an angle, where 1/360 of any circle is 1 degree and an angle that “cuts” n/360 out of any circle whose center is at the angle’s vertex has a measure of n degrees; angle measures are limited to whole numbers

NONE

4.7 The student applies mathematical process standards to solve problems involving angles less than or equal to 180 degrees. The student is expected to:





6.8C measure angles 4.7C determine the approximate measures of angles in degrees to the nearest whole number using a protractor

NONE

6.8C measure angles 4.7D draw an angle with a given measure

NONE

7.6A use angle measurements to classify pairs of angles as complementary or supplementary

4.7E determine the measure of an unknown angle formed by two non-overlapping adjacent angles given one or both angles measures

NONE

4.8 The student applies mathematical process standards to select appropriate customary and metric units, strategies, and tools to solve problems involving measurement. The student is expected to:





4.11B perform simple conversions between different units of length, between different units of capacity, and between different units of weight within the customary measurement system

4.8A identify relative sizes of measurement units within the customary and metric systems

5.10A perform simple conversions within the same measurement system (SI (metric) or customary)

5.7A solve problems by calculating conversions within a measurement system, customary or metric

4.11B perform simple conversions between different units of length, between different units of capacity, and between different units of weight within the customary measurement system

4.8B convert measurements within the same measurement system, customary or metric, from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table



4.11A estimate and use measurement tools to determine length (including perimeter), area, capacity and weight/mass using standard units SI (metric) and customary.

4.8C solve problems that deal with measurement of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate



4.8 The student applies mathematical process standards to solve problems by collecting, organizing, displaying, and interpreting data. The student is expected to:





4.9A - represent data on a frequency table, dot plot or stem-and-leaf plot marked with whole numbers and fractions.

5.9A – represent categorical data with bar graphs or frequency tables and numerical data, including data sets of measurements in fractions or decimals, with dot plots or stem-and-leaf plots.

4.9B - solve one-and two-step problems using data in whole number, decimal, and fraction form in a frequency table, dot plot, or stem-and-leaf-plot.

5.9C – solve one- and two-step problems using data from a frequency table, dot plot, bar graph, stem-and-leaf plot, or scatterplot.



GRADE 4 - DELETED CONTENT

4.2A use concrete objects and pictorial models to generate equivalent fractions

4.2B model fraction quantities greater than one using concrete objects and pictorial models

4.2C compare and order fractions using concrete objects and pictorial models

4.3B add and subtract decimals to the hundredths place using concrete objects and pictorial models

4.4C recall and apply multiplication facts through 12 x 12

4.6A use patterns and relationships to develop strategies to remember basic multiplication and division facts (such as the patterns in related multiplication and division number sentences (fact families) such as 9 x 9 = 81 and 81÷ 9 = 9

4.9A demonstrate translations, reflections, and rotations using concrete models

4.9B use translations, reflections, and rotations to verify that two shapes are congruent

4.11C use concrete models of standard cubic units to measure volume

4.11D estimate volume in cubic units

4.11E explain the difference between weight and mass

4.12A use a thermometer to measure temperature and changes in temperature

4.13A use concrete objects or pictures to make generalizations about determining all possible combinations of a given set of data or of objects in a problem situation


Documents

Web viewsolve problems that incorporate the process of understanding the problem, making a plan, carrying out the plan, and evaluating the solution of reasonableness