TEKS Student Expectations

MATHEMATICS

Vertical Alignment

 

Number, operation, and quantitative reasoning.

The student uses numbers to name quantities.  The student is expected to:

use one-to-one correspondence and language to describe relative sizes

(K.1)    (A)       Kindergarten:       use one-to-one correspondence and language such as more than, same number as, or two less to describe relative sizes of sets of concrete objects

(1.1)     (A)       First grade:          compare whole numbers up to 99 (less than, greater than, or equal to) using sets of concrete objects and pictorial models

                        Second grade:     compare whole numbers up to 999 (less than, greater than, or equal to) using sets of concrete objects and pictorial models

                        Third grade:         compare whole numbers up to 9,999 (less than, greater than, or equal to) using sets of concrete objects and pictorial models

 

use place value to describe, compare, and order whole numbers using concrete models

(K.1)    (B)       Kindergarten:       use sets of concrete objects to represent quantities given in verbal or written form (through 9) (DVISD expectation: use place value to create sets of tens and ones using concrete objects to describe, compare, and order whole numbers to 99)

(1.1)     (B)       First grade:          use place value to create sets of tens and ones using concrete objects to describe, compare, and order whole numbers (DVISD expectation:  use place value to create sets of tens, ones, and hundreds using concrete objects to describe, compare, and order whole numbers)

                        Second grade:     (DVISD expectation:  use place value to create sets of tens, ones, hundreds, and thousands using concrete objects to describe, compare, and order whole numbers)

 

use numbers to describe how many objects are in a set

(K.1)    (C)       Kindergarten:       use numbers to describe how many objects are in a set of 20

                       

use place value to read, write (in symbols and words)

.                       Kindergarten:       (DVISD expectation:  use place value to read, write (in symbols and words), and describe the value of whole numbers through 999)

(1.1)     (D)       First grade:          (DVISD expectation:  use place value to read, write (in symbols and words), and describe the value of whole numbers through 999 with the ability to recognize up to 9,999)

(2.1)                 Second grade:     (DVISD expectation:  use place value to read, write (in symbols and words), and describe the value of whole numbers through 99,999)

(3.1)     (A)       Third grade:       use place value to read, write (in symbols and words), and describe the value of whole numbers through 999,999

(4.1)     (A)       Fourth grade:    use place value to read and write whole numbers through the millions place

(5.1)     (A)       Fifth grade:        use place value to read and write whole numbers through the billions place

 

use place value to compare and order whole numbers

                        Kindergarten:       (DVISD expectation:  use place value to compare and order whole numbers through 99)

(1.1)     (C)       First grade:          use words and numbers to describe the values of individual coins such as penny, nickel, dime, and quarter and their relationship (DVISD expectation:  use place value to compare and order whole numbers through 99 with the ability to recognize up to 999)

(2.1)                 Second grade:     use place value to compare and order whole numbers through 999 and:  use place value to compare and order whole numbers through 9,999)

(3.1)     (B)       Third grade:         use place value to compare and order whole numbers through 9,999 (DVISD expectation:  use place value to compare and order whole numbers through 999,999

(4.1)     (A)       Fourth grade:    use place value to compare and order whole numbers through the millions place

(5.1)     (A)       Fifth grade:        use place value to compare and order whole numbers through the billions place

 

determine the value of a collection of coins and bills

                        Kindergarten:       (DVISD expectation: determine the value of a collection of coins (pennies, nickels, dimes, and quarters)

(1.1)     (C)       First grade:          use words and numbers to describe the values of individual coins such as penny, nickel, dime, and quarter and their relationships (DVISD expectation: determine the value of individual coins (pennies, nickels, dimes, and quarters) and their relationships with half dollars and one dollar bills)

(2.3)     (C)       Second grade:     determine the value of a collections of coins less than one dollar (DVISD expectation:  determine the value of a collection of coins and bills (pennies, nickels, dimes, quarters, half dollars, and ones, fives, tens, and twenties dollar bills)

(3.1)     (C)       Third grade:      determine the value of a collection of coins and bills (pennies, nickels, dimes, quarters, half dollars, and ones, fives, tens, and twenties, fifties, and one hundred dollar bills)

                        Fourth grade:       (DVISD expectation: continue use of money to determine the value of a collection of coins and bills)

                        Fifth grade:          (DVISD expectation: continue use of money to relate decimals to real-life situations)

 

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

                        Second grade:     (DVISD expectation: read and write decimals through the tenths place)

                        Third grade:         (DVISD read and write decimals through the hundredths place)

(4.1)     (B)       Fourth grade:       use place value to read, write, compare, and order decimals involving tenths and hundredths, including money, using concrete models

(5.1)     (B)       Fifth grade:        use place value to read, write, compare, and order decimals through the thousandths place

 

compare and order non-negative rational numbers

                        Fourth grade:       (DVISD expectation: introduce non-negative rational numbers)

                        Fifth grade:          (DVISD expectation: compare and order non-negative rational numbersand integers)

(6.1)     (A)       Sixth grade:       compare and order positive rational numbers through models

(7.1)     (A)       Seventh grade:  compare and order positive rational numbers

generate equivalent forms of rational numbers

                        Fifth grade:          (DVISD expectation: generate equivalent forms of rational numbers including whole numbers, fractions, and decimals)

(6.1)     (B)       Sixth grade:       generate equivalent forms of rational numbers including whole numbers, fractions, and decimals

 

use integers to represent real-life situations

                        Fourth grade:       (DVISD expectation: introduce integers)

                        Fifth grade:          (DVISD expectation: use integers to represent real-life situations)

(6.1)     (C)       Sixth grade:       use integers to represent real-life situations (DVISD expectation: use models to add and subtract integers)

 

write prime factorizations using exponents

                        Fifth grade:          (DVISD expectation: write prime factorizations using exponents)

(6.1)     (D)       Sixth grade:       write prime factorizations using exponents

 

identify factors and multiples including common factors and common multiples

                        Fifth grade:          (DVISD expectation: identify factors and multiples including common factors and common multiples)

(6.1)     (E)       Sixth grade:       identify factors and multiples including common factors and common multiples

 

convert between fractions, decimals, whole numbers, and percents mentally, on paper [or with a calculator]

                        Fifth grade:          (DVISD expectation: convert between fractions, decimals and whole numbers mentally, on paper [or with a calculator])

                        Sixth grade:         (DVISD expectation: convert between fractions, decimals, whole numbers, and percents mentally, on paper [or with a calculator])

(7.1)     (B)       Seventh grade:  convert between fractions, decimals, whole numbers, and percents mentally, on paper [or with a calculator]

 

represent squares and square roots using geometric models

                        Fifth grade:          (DVISD expectations: represent squares and square roots using geometric models)

                        Sixth grade:         (DVISD expectations: represent squares and square roots using geometric models)

(7.1)     (C)       Seventh grade:  represent squares and square roots using geometric models

 

The student describes order of events or objects.  The student is expected:

use language to describe relative positions in a sequence of events or objects

(K.2)    (A)       Kindergarten:       use language such as before and after to describe relative positions in a sequence of events and objects

 

name the ordinal positions in a sequence

(K.2)    (B)       Kindergarten:       name the ordinal positions in a sequence such as first, second, third, etc.

                        First grade:          (DVISD expectation: name the ordinal positions in a sequence through 10)

                        Second grade:     (DVISD expectation: name the ordinal positions in a sequence through 20)

Fractions

The student recognizes that there are quantities less than a whole and uses pairs of whole numbers to describe the parts of whole describe fractional parts of whole objects or sets of objects.  The student is expected to:

share a whole by separating it into equal parts

(K.3)    (A)       Kindergarten:       share a whole by separating it into equal parts

(1.2)     (A)       First grade:          share a whole by separating it into equal parts and uses appropriate language to describe the parts such as three out of four equal parts

                        Second grade:     (DVISD expectation: share a whole by separating it into equal parts and uses appropriate language to describe fractional parts with denominators up to and including eighths)

 

explain why a given part is half of the whole

(K.3)    (B)       Kindergarten:       explain why a given part is half of the whole

(1.2)     (B)       First grade:          use appropriate language to describe part of a set such as three out of eight crayons are red

                       

use fraction names and symbols to describe fractional parts of whole objects or sets of objects

                        Kindergarten:       (DVISD expectation: use fraction names and symbols to describe fractional parts of whole objects or sets of objects with denominators of 2)

                        First grade:          (DVISD expectation: use fraction names and symbols to describe fractional parts of whole objects or sets of objects with denominators of 2, 3, and 4 with the ability to recognize sixths and eighths)

(2.2)     (A)(B)  Second grade:     name fractional parts of a whole object or a set of objects (not to exceed twelfths) when given a concrete representation

(3.2)     (C)       Third grade:      use fraction names and symbols to describe fractional parts of whole objects or sets of objects with denominators of 12 or less

 

construct concrete models of fractions

                        Kindergarten:       (DVISD expectation: construct concrete models of fractions to represent halves)

                        First grade:          (DVISD expectation: construct concrete models of fractions to represent halves and fourths)

                        Second grade:     (DVISD expectation: construct concrete models of fractions to represent halves, thirds, fourths, and sixths)

(3.2)     (A)       Third grade:         construct concrete models of fractions

 

compare fractional parts of whole objects or sets of objects in a problem situation

                        Kindergarten:       (DVISD expectation: compare fractional parts of whole objects or sets of objects in a problem situation using [concrete] models (halves)

                        First grade:          (DVISD expectation: compare fractional parts of whole objects or sets of objects in a problem situation using [concrete] models (halves, thirds and fourths) with exposure to sixths and eighths)

                        Second grade:     (DVISD expectation: compare fractional parts of whole objects or sets of objects in a problem situation using [concrete] models (halves, thirds, fourths, sixths, eighths, and twelfths)

(3.2)     (B)       Third grade:      compare fractional parts of whole objects or sets of objects in a problem situation using [concrete] models (halves, thirds, fourths, sixths, eighths, and twelfths)

(4.2)     (C)       Fourth grade:    compare and order fractions using [concrete and] pictorial models

(5.2)     (B)       Fifth grade:          compare two fractional quantities in problem solving situations using a variety of methods, including common denominators

 

generate equivalent fractions using [concrete and] pictorial models

                        Second grade:     (DVISD expectation: identify equivalent fractions using halves and fourths)

                        Third grade:         (DVISD expectation: identify equivalent fractions using halves, thirds, fourths, sixths, and eighths)

(4.2)     (A)       Fourth grade:    generate equivalent fractions using [concrete and] pictorial models

(5.2)     (A)       Fifth grade:        generate equivalent fractions

 

model fraction quantities greater than one using [concrete materials and] pictures

                        Third grade:         (DVISD expectation: model fractional quantities of greater than one using [concrete materials and] pictures)

(4.2)     (B)       Fourth grade:    model fractional quantities of greater than one using [concrete materials and] pictures

 

compare and order fractions using [concrete and] pictorial models

                        Second grade:     (DVISD expectation: compare and order fractions using [concrete and] pictorial models using halves)

                        Third grade:         (DVISD expectation: compare and order fractions using [concrete and] pictorial models using halves and fourths)

(4.2)     (C)       Fourth grade:    compare and order fractions using [concrete and] pictorial models

 

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

                        Fourth grade:       (DVISD expectation: compare two fractional quantities in problem-solving situations using a variety of methods)

(5.2)     (B)       Fifth grade:          compare two fractional quantities in problem-solving strategies using a variety of methods, including common denominators

 

relate decimals to fractions using models

                        Second grade:     (DVISD expectation: identify tenths)

                        Third grade:         (DVISD expectation: identify tenths and hundredths)

(4.2)     (D)       Fourth grade:    relate decimals to fractions that name tenths and hundredths using models

(5.2)     (C)       Fifth grade:        use models to relate decimals to fractions that name tenths, hundredths, and thousandths

 

Operations

The student models addition, and subtraction, model and create addition and subtraction problems in real situations with concrete objects.  The student is expected to:

model and create addition and subtraction problem situations with concrete objects and write corresponding number sentences

(K.4)                Kindergarten:       model and create addition and subtraction problem situations with concrete objects and write corresponding number sentences

(1.3)     (A)       First grade           model and create addition and subtraction problem situations with concrete objects and write corresponding number sentences

 

 

learn and apply basic addition facts

                        Kindergarten:       (DVISD expectation: learn and apply basic addition facts to 10)

(1.3)     (B)       First grade:          learn and apply basic addition facts (sums to 18) using concrete models

(2.3)     (A)       Second grade:     recall and apply basic addition facts (sums to 18)

 

The student adds and subtracts to solve meaningful problems involving whole numbers (K-3).  The student adds, subtracts, multiplies, and divides to solve meaningful problems and justify solutions involving whole numbers and decimals (4-8).  The student is expected to:

use addition and subtraction

(K.4)    .           Kindergarten:       model addition and subtraction using pictures, words, and numbers (DVISD expectation: model addition and subtraction with numbers to 10)

                        First grade:          (DVISD expectation: model addition and subtraction using pictures, words, and numbers with numbers to 100)

                        Second grade:     (DVISD expectation: model addition and subtraction using pictures, words, and numbers with numbers to 1,000)

(3.3)     (A)       Third grade:      model addition and subtraction using pictures, words, and numbers

                        Fourth grade:       (DVISD expectation: model addition and subtraction involving fractions with models, using pictures words, and numbers)

                        Fifth grade:          (DVISD expectation: model addition and subtraction involving fractions with models, using pictures words, and numbers)

6.2)      (A)       Sixth grade:         model addition and subtraction involving fractions with models, using pictures words, and numbers

 

use addition and subtraction to solve problems

                        Kindergarten:       (DVISD expectation: model addition and subtraction using concrete models  to solve problems involving whole numbers to 20)

                        First grade:          (DVISD expectation: use addition and subtraction to solve problems involving whole numbers to 100)

                        Second grade:     (DVISD expectation: use addition and subtraction to solve problems involving whole numbers to 1,000)

                        Third grade:       use addition and subtraction to solve problems involving whole numbers

(4.3)     (A)       Fourth grade:    use addition and subtraction to solve problems involving whole numbers

(5.3)     (A)       Fifth grade:        use addition and subtraction to solve problems involving whole numbers and decimals

(6.2)     (B)       Sixth grade:         use addition and subtraction to solve problems involving fractions and decimals

 

select addition or subtraction and use the operation to solve problems

                        Kindergarten:       (DVISD expectation: select addition or subtraction and use the operation to solve problems involving whole numbers through 18)

.                       First grade:          (DVISD expectation: select addition or subtraction and use the operation to solve problems involving whole numbers through 99 without regrouping)

(2.3)     (B)       Second grade:     select addition or subtraction and solve problems using two-digit numbers, whether or not regrouping is necessary (DVISD expectation: select addition or subtraction and use the operation to solve problems involving whole numbers through 999)

(3.3)     (B)       Third grade:      select addition or subtraction and use the operation to solve problems involving whole numbers through 999 (DVISD expectation: select addition or subtraction and use the operation to solve problems involving whole numbers through   9,999)

 

add and subtract decimals

                        First grade:          (DVISD expectation: add and subtract money using combinations of pennies, nickels, dimes, and quarters)

                        Second grade:     (DVISD expectation: add and subtract money using dollars and cents)

                        Third grade:         (DVISD expectation: add and subtract decimals to the tenths place using [concrete and] pictorial models, including dollars and cents)

(4.3)     (B)       Fourth grade:    add and subtract decimals to the hundredths place using [concrete and] pictorial models (DVISD expectation: includes dollars and cents)

(5.3)     (A)       Fifth grade:        use addition and subtraction to solve problems involving decimals (DVISD expectation: includes dollars and cents)

                                                  

model and record addition and subtraction of fractions with like denominators in problem-solving situations

                        Fourth grade:       (DVISD expectation: model and record addition and subtraction of fractions with like denominators in problem-solving situations)

(5.3)     (E)       Fifth grade:        model and record addition and subtraction of fractions with like denominators in problem-solving situations

 

The student recognizes and solves problems in multiplication and division situations (3).  The student multiplies and divides to solve meaningful problems involving whole numbers (4-8).  The student is expected to:

solve and record multiplication problems (one-digit multiplier)

(K.1)    (B)       Kindergarten:       introduce the concept of groups or sets

                        First grade:          (DVISD expectation: use a graphic representation to make equal groups to identify how many in all)

                        Second grade:     (DVISD expectation: solve and record multiplication problems using one digit multipliers)

(3.4)     (B)       Third grade:      solve and record multiplication problems (one-digit multiplier)

(4.4)     (D)       Fourth grade:    use multiplication to solve problems involving two-digit numbers

(5.3)     (B)       Fifth grade:          use multiplication to solve problems involving whole numbers (no more than 3-digit times 2-digit)

           

use models to solve division problems and use number sentences to record the solutions

                        First grade:          (DVISD expectation: use a graphic representation to separate a group of objects to identify how many equal groups)

(2.4)     (B)       Second grade:     model, create, and describe division situations in which a set of concrete objects is separated into equivalent sets

(3.4)     (C)       Third grade:      use models to solve division problems and use number sentences to record the solutions

(4.4)     (E)       Fourth grade:    use division to solve problems involving one-digit divisors

 

model factors and products

                        Second grade:     (DVISD expectation: use arrays for multiplication with multiplies up to 10)

                        Third grade:         (DVISD expectation: use arrays for multiplication with multipliers up to 12)

(4.4)     (A)       Fourth grade:    model factors and products using arrays and area models

recall and apply multiplication facts

                        Second grade:     (DVISD expectation: recall multiplication facts through 5 x 5)

(3.4)     (A)       Third grade:         learn and apply multiplication facts through the tens using concrete models

(4.4)     (C)       Fourth grade:    recall and apply multiplication facts through 12 x 12

 

represent multiplication and division situations

                        Second grade:     (DVISD expectation: identify multiplication and division situations using pictorial models)

                        Third grade:         (DVISD expectation: represent multiplication and division situations in picture, word, and number form)

(4.4)     (B)       Fourth grade:    represent multiplication and division situations in picture, word, and number form

                        Fifth grade:          (DVISD expectation: represent multiplication situations involving fractions)

                        Sixth grade:         (DVISD expectation: represent multiplication and division situations involving fractions and decimals with [concrete] models, pictures, words, and numbers)

(7.2)     (A)       Seventh grade:  represent multiplication and division situations involving fractions and decimals with [concrete] models, pictures, words, and numbers

 

use division to solve problems

                        Third grade:         (DVISD expectation: use division to solve problems involving whole numbers (no more than one-digit divisors and two-digit dividends)

                        Fourth grade:       (DVISD expectation: use division to solve problems involving whole numbers (no more than one-digit divisors and three-digit dividends without technology)

(5.3)     (C)       Fifth grade:        use division to solve problems involving whole numbers (no more than two-digit divisors and three-digit dividends without technology)

 

use multiplication and division to solve problems including situations involving equivalent ratios and rates

                        Fifth grade:          (DVISD expectation: use multiplication and division of whole numbers to solve problems including situations involving equivalent ratios and rates)

(6.2)     (C)       Sixth grade:       use multiplication and division of whole numbers to solve problems including situations involving equivalent ratios and rates

(7.1)     (D)       Seventh grade:  use division to find unit rates and rations in proportional relationships such as speed, density, price, recipes, and student-teacher ratio

 

identify prime factors of a whole number and common factors of a set of whole numbers

                        Fourth grade:       (DVISD expectation: identify prime factors of a whole number and common factors of a set of whole numbers)

(5.3)     (D)       Fifth grade:        identify prime factors of a whole number and common factors of a set of whole numbers

(6.1)     (E)       Sixth grade:       identify factors and multiples including common factors and common multiples

 

Quantitative reasoning.

The student estimates to determine reasonable results.  The student is expected to:

round two-digit numbers to the nearest ten and three-digit numbers to the nearest hundred

                        Kindergarten:       (DVISD expectation: round one-digit numbers to ten)

                        First grade:          (DVISD expectation: round two-digit numbers to the nearest ten)

                        Second grade:     (DVISD expectation: round two-digit numbers to the nearest ten and three-digit numbers to the nearest hundred)

(3.5)     (B)       Third grade:      round two-digit numbers to the nearest ten and three-digit numbers to the nearest hundred

(4.4)     (A)       Fourth grade:    round whole numbers to the nearest ten, hundred, or thousand to approximate reasonable results in problem situations

(5.4)     (A)       Fifth grade:        round whole numbers and decimals through tenths to approximate reasonable results in problem situations

                        Sixth grade:         (DVISD expectation: round whole numbers and decimals through hundredths to approximate reasonable results in problem situations)

 

estimate sums and differences beyond basic facts

                        First grade:          (DVISD expectation: identify the better estimate when using 10 as a referent)

                        Second grade:     (DVISD expectation: estimate sums and differences beyond basic facts)

(3.5)     (B)       Third grade:      estimate sums and differences beyond basic facts

 

estimate a product or quotient beyond basic facts

                        Third grade:         (DVISD expectation: estimate a product or quotient beyond basic facts)

(4.5)     (B)       Fourth grade:    estimate a product or quotient beyond basic facts

 

estimate to solve problems where exact answers are not required

                        Fourth grade:       (DVISD expectation: estimate to solve problems where exact answers are not required)

(5.4)     (B)       Fifth grade:        estimate to solve problems where exact answers are not required

(6.2)     (D)       Sixth grade:       estimate and round to approximate reasonable results and to solve problems where exact answers are not required

(7.2)     (G)       Seventh grade:  determine the reasonableness of a solution to a problem

 

 

Patterns, relationships, and algebraic thinking.

The student uses patterns to solve problems (K-3).  The student makes generalizations based on observed patterns and relationships.  The student is expected to:

identify, extend, and create patterns

(K.4)                Kindergarten:       identify, extend, and create patterns of sounds, physical movement, and concrete models

 

identify patterns

                        Kindergarten:       (DVISD expectation: skip count by 2’s to 20 and by 5’s and 10’s to 100)

(1.4)     (B)       First grade:          use patterns to skip count by twos, fives, and tens

(2.5)     (C)       Second grade:     use patterns to develop strategies to remember basic addition facts

(3.6)     (B)       Third grade:      identify patterns in multiplication facts using [concrete objects,] pictorial models, [or technology]

(4.6)     (C)       Fourth grade:    use patterns to multiple by 10 and 100

 

find patterns in numbers

(1.5)     (A)       First grade:          find patterns in numbers, including odd and even

(2.5)     (A)       Second grade:     find patterns in numbers such as in a 100’s chart

compare and order whole numbers using place value

(K.6)    (B)       Kindergarten:       count by ones to 100

(1.5)     (B)       First grade:          compare and order whole numbers using place value

(2.5)     (B)       Second grade:     use patterns in place value to compare and order whole numbers through 999

 

identify and extend whole-number and geometric patterns to make predictions and solve problems

(K.6)    (A)       Kindergarten:       use patterns to predict what comes next, including cause-and-effect relationships (DVISD expectation: identify and extend patterns AB, ABC, ABB)

(1.4)     (A)       First grade:          identify, describe, and extend concrete and pictorial patterns in order to make predictions and solve problems

(2.6)     (C)       Second grade:     identify, describe, and expand whole number and geometric patterns to make predictions and solve problems

(3.6)     (A)       Third grade:      identify and extend whole number and geometric patterns to make predictions and solve problems

 

identify patterns in related sentences (fact families)

(1.5)     (C)       First grade:          identify patterns in related addition and subtraction sentences (fact families for sums to 18) such as such as 2 + 3 = 6, 3 + 2 =6, 6 - 2 =3,

                                                   6 - 3 = 2

(2.5)     (D)       Second grade:     identify patterns in related addition and subtraction sentences (fact families) such as 2 + 3 = 6, 3 + 2 =6, 6 - 2 =3, 6 - 3 = 2

(3.6)     (C)       Third grade:      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

(4.6)     (B)       Fourth grade:    solve division problems related to multiplication facts (fact families) such as 9 x 9 = 81 and 81 ÷ 9 = 9

 

use [concrete objects or] pictures to make generalizations about determining all possible combinations

                        Second grade:     (DVISD expectation: use manipulatives to show different combinations for a given number)

                        Third grade:         (DVISD expectation: use manipulatives to show different combinations for a given number)

                        Fourth grade:       (DVISD expectation: use manipulatives to show different combinations for a given number)

 (5.5)    (A)       Fifth grade:       use [concrete objects or] pictures to make generalizations about determining all possible combinations

 

use lists, tables , charts, and diagrams to find patterns and make generalizations such as a procedure for determining equivalent fractions

                        Second grade:     (DVISD expectation: recognize and complete patterns in charts or tables using skip counting)

                        Third grade:         (DVISD expectation: recognize and complete patterns in charts or tables using skip counting)

                        Fourth grade:       (DVISD expectation: use lists, tables , charts, and diagrams to find patterns and make generalizations such as a procedure for determining equivalent fractions)

(5.5)     (B)       Fifth grade:        use lists, tables , charts, and diagrams to find patterns and make generalizations such as a procedure for determining equivalent fractions

identify prime and composite numbers using [concrete] models and patterns in factor pairs

                        Second grade:     (DVISD  expectation: use manipulatives to identify whether a number can be put into equal groups)

                        Third grade:         (DVISD expectation: identify whether a number can be put into equal groups)

                        Fourth grade:       (DVISD expectation: identify prime and composite numbers using [concrete] models and patterns in factor pairs)

(5.5)     (C)       Fifth grade:        identify prime and composite numbers using [concrete] models and patterns in factor pairs

 

Relationships

The student uses, lists, tables, and charts to express patterns and relationships (K-3).  The student uses organizational structures to analyze and describe patterns and relationships (4-8).  The student is expected to:

generate a table of paired numbers based on a real-life situation such as insects and legs

                        Kindergarten:       (DVISD expectation: generate a table of paired numbers using concrete materials or pictures)

                        First grade:          (DVISD expectation: sort objects into two categories and make a tally table)

(2.6)     (A)       Second grade:     generate a table of paired numbers based on a real-life situation such as number of tricycles related to number of wheels

(3.7)     (A)       Third grade:      generate a table of paired numbers based on a real-life situation such as insects and legs

 

identify patterns in a table of related number pairs based on a real-life situation and extend the table

                        Kindergarten:       (DVISD expectation: identify patterns and extend the table using concrete materials or pictures)

                        First grade:          (DVISD expectation: identify patterns in a table of related number pairs based on a real-life situation)

(2.6)     (B)       Second grade:     identify patterns in a table of related number pairs based on a real-life situation and extend the table

(3.7)     (B)       Third grade:      identify patterns in a table of related number pairs based on a real-life situation and extend the table

 

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

                        Kindergarten:       (DVISD expectation: compare two sets of data using concrete materials)

                        First grade:          (DVISD expectation: identify positions at intersections of lines on a grid)

                        Second grade:     (DVISD expectation: name points on a graph using ordered pairs)

                        Third grade:         (DVISD expectation: describe the relationship between two sets of related data such as ordered pairs in a table)

(4.7)     (A)       Fourth grade:    describe the relationship between two sets of related data such as ordered pairs in a table

 

select from and use diagrams and number sentences to represent real-life situations

                        Fourth grade:       (DVISD expectation: select from and use diagrams and number sentences to represent real-life situations)

(5.6)     (A)       Fifth grade:        select from and use diagrams and number sentences to represent real-life situations

 

The student solves problems involving proportional relationships.  The student is expected to:                

use ratios to describe proportional situations

                        Fifth grade:          (DVISD expectation: introduce the term ratio with examples related to fractions and decimals)

(6.3)     (A)       Sixth grade:       use ratios to describe proportional situations

 

represent ratios and percents with [concrete] models, fractions, and decimals

                        Fifth grade:          (DVISD expectation: introduce ratios)

(6.3)     (B)       Sixth grade:       represent ratios and percents with [concrete] models, fractions, and decimals

 

use ratios to make predictions in proportional situations

                        Fifth grade:          (DVISD expectation: introduce the concept of ratios)

(6.3)     (C)       Sixth grade:       use ratios to make predictions in proportional situations

 

Relationships

The student solves problems involving proportional relationships.  The student is expected to:

estimate and find solutions to application problems involving percent

                        Sixth grade:         (DVISD expectation: introduce the concept of percent)

 

estimate and find solutions to application problems involving proportional relationships such as similarity, scaling, unit costs, and related measurement units

                        Sixth grade:         (DVISD expectation: introduce the concept of proportional relationships)

 

The student uses letters as variables in mathematical expressions to describe how one quantity changes when a related quantity changes.  The student is expected to:

use tables and symbols to represent and describe proportional and other relationships involving conversions, sequences, perimeter, area, etc.

                        Fifth grade:          (DVISD expectation: introduce and use T-charts, tables, and symbols involving perimeter and area)

(6.4)     (A)       Sixth grade:       use tables and symbols to represent and describe proportional and other relationships involving conversions, sequences, perimeter, area, etc.

 

generate formulas to represent relationships and conversions involving perimeter, area, volume of a rectangular prism, etc., from a table of data

                        Fifth grade:          (DVISD expectation: set up and use formulas on formula chart)

(6.4)     (B)       Sixth grade:       generate formulas to represent relationships involving perimeter, area, volume of a rectangular prism, etc., from a table of data

 

graph data to demonstrate relationship in familiar concepts such as conversions, perimeter, area, circumference, volume, and scaling

                        Sixth grade:         (DVISD expectation: introduce graphing of data)

 

describe the relationship between the terms in a sequence and their positions in a sequence

                        Sixth grade:         (DVISD expectation: introduce the concept)

 

Algebraic thinking

The student uses letters to represent an unknown in an equation.  The student is expected to;

formulate an equation from a problem situation

                        Fifth grade:          (DVISD expectation: formulate and solve linear equations (ex. x-3=4)

(6.5)     (A)       Sixth grade:       formulate an equation from a problem situation

 

use [concrete] models to solve equations and use symbols to record the actions

                        Sixth grade:         (DVISD expectation: introduce the concept using [concrete] models to solve equations and use symbols to record the actions)

 

 

Geometry and spatial reasoning.

The student uses formal geometric vocabulary (K-3).  The fifth grade student generates geometric definitions using critical attributes.  The seventh grade student compares and classifies shapes and solids using geometric vocabulary and properties.  The student is expected to:

describe one object in relation to another in informal language

(K.7)    (A)       Kindergarten:       describe one object in relation to another in informal language such as over, under, above, and below

 

place an object in a specified position

(K.7)    (B)       Kindergarten:       place an object in a specified position

 

describe and identify an object in relation to another using formal language

(K.8)    (A)       Kindergarten:       describe and identify an object by its attributes using formal language

 

describe and identify an object by its attributes using informal language

(K.8)    (A)       Kindergarten:       describe and identify an object by its attributes using informal language

(1.6)     (A)       First grade:          describe and identify an object by its attributes using informal language

 

compare objects based on attribute

(K.8)    (B)       Kindergarten:       compare two objects based on their attributes

 

sort objects by attributes

(K.8)    (C)       Kindergarten:       sort objects according to their attributes and describe how those groups are formed

 

The student recognizes characteristics of shapes and solids.  The student is expected to:

describe and compare real-life objects or models of solids

(K.9)    (A)       Kindergarten:       describe and compare real-life objects or models of solids

                        First grade:          (DVISD expectation: introduce shapes and solids using the attributes to describe shapes)

(2.7)     (A)       Second grade:     identify attributes of shapes or solids

 

recognize shapes in real-life objects or models of solids

(K.9)    (B)       Kindergarten:       recognize shapes in real-life objects or models of solids

 

name, describe, and compare shapes and solids using formal geometric vocabulary

(K.9)    (C)       Kindergarten:       describe, identify, and compare circles, triangles, and rectangles including squares (DVISD expectation) name, describe and compare 2-dimentional and 3-dimentional shapes (circle, square, rectangle, triangle, prism, cylinder, cone, pyramid, cube, sphere)

(1.6)     (B)       First grade:          identify circles, triangles, and rectangles, including squares, and describe the shape of balls, boxes, cans, and cones (DVISD expectation: name and describe basic 2-dimentional and 3-dimentional shapes and solids according to a given attribute using formal geometric vocabulary)

(2.7)     (A)       Second grade:     use attributes to describe how two shapes or two solids are alike or different

(3.8)                 Third grade:      name, describe, and compare shapes and solids using formal geometric vocabulary

           

identify critical attributes including parallel, perpendicular, and congruent parts of geometric shapes and solids

                        Second grade:     (DVISD expectation: introduce concept and vocabulary of parallel, perpendicular, and congruent)

                        Third grade:         (DVISD expectation: name and describe congruent parts)

                        Fourth grade:       (DVISD expectation: name, describe, and compare parallel, perpendicular, and congruent parts of geometric shapes and solids using geometric vocabulary)

(5.7)     (A)       Fifth grade:        identify critical attributes including parallel, perpendicular, and congruent parts of geometric shapes and solids

 

use critical attributes to define geometric shapes or solids

                        Third grade:         (DVISD expectation: introduce attributes for geometric shapes and solids)

                        Fourth grade:       (DVISD expectation: identify critical attributes of geometric shapes and solids)

(5.7)     (B)       Fifth grade:        use critical attributes to define geometric shapes or solids

 

use properties to classify shapes including triangles, quadrilaterals, pentagons, and circles

                        Sixth grade:         (DVISD expectation: classify shapes)

 

use properties to classify solids, including pyramids, cones, prisms, and cylinders

                        Sixth grade:         (DVISD expectation: introduce properties to classify solids, including pyramids, cones, prisms, and cylinders)

 

use critical attributes to define similarity

(2.7)     (B)       Second grade:     use critical attributes to define similarity

                        Third grade:         (DVISD expectation: use critical attributes to define similarity)

                        Fourth grade:       (DVISD expectation: use critical attributes to define similarity)

                        Fifth grade:          (DVISD expectation: use critical attributes to define similarity)

                        Sixth grade:         (DVISD expectation: use critical attributes to define similarity)

 

The student recognizes congruency and symmetry (K-3).  The fourth grade student identifies and describes lines, shapes, and solids using formal geometric language.  In the fifth grade, the student models transformations.  The student is expected to:

congruency

                        Kindergarten:       (DVISD expectation: identify congruent shapes)

                        First grade:          (DVISD expectation: identify and construct congruent figures)

                        Second grade:     (DVISD expectation: identify and construct congruent figures)

 

(3.9)     (A)       Third grade:      identify congruent shapes

(4.9)     (B)       Fourth grade:    use translations, reflections, and rotations to verify that two shapes are congruent

(5.8)     (A)       Fifth grade:        identify critical attributes including parallel, perpendicular, and congruent parts of geometric shapes and solids

 

lines of symmetry

(3.9)     (B)       Third grade:         create shapes using concrete models and technology

 

symmetry

                        Kindergarten:       (DVISD expectation: identify lines of symmetry in shapes)

                        First grade:          (DVISD expectation: identify lines of symmetry in shapes)

                        Second grade:     (DVISD expectation: identify lines of symmetry in shapes)

(3.9)     (C)       Third grade:      identify lines of symmetry in shapes

(5.8)     (B)       Fifth grade:        use critical attributes to define geometric shapes or solids

 

demonstrate translations, reflections, and rotations

(4.9)     (A)       Fourth grade:       demonstrate translations, reflections, and rotations using concrete models

(5.8)     (A)       Fifth grade:          sketch the results of translations, rotations, and reflections

 

use translations, reflections, and rotations

(4.9)     (B)       Fourth grade:       use translations, reflections, and rotations to verify that two shapes are congruent

(5.8)     (B)       Fifth grade:          describe the transformation that generates one figure from the other when given two congruent figures

 

use reflections to verify that shape has symmetry

(4.9)     (C)       Fourth grade:      use reflections to verify that a shape has symmetry

 

The student identifies and describes lines, shapes, and solids using formal geometric language.  The student in sixth grade uses geometric vocabulary to describe angles, polygons, and circles.  The student is expected to:

identify right, acute, and obtuse angles

                        First grade:          (DVISD expectation: sort plane figures by the umbers of sides and corners)

                        Second grade:     (DVISD expectation: identify corners and vertices)

                        Third grade:         (DVISD expectation: identify angles)

(4.8)     (A)       Fourth grade:    identify right, acute, and obtuse angles

                        Fifth grade:          identify and review right, acute, and obtuse angles and introduce measurement of angles

(6.6)     (A)       Sixth grade:       use angle measurements to classify angles as acute, obtuse, or right

 

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

                        Sixth grade:         (DVISD expectation: introduce complementary and supplementary angles)

 

identify models of parallel and perpendicular lines

                        Kindergarten:       (DVISD expectation: identify parallel lines)

                        First grade:          (DVISD expectation: introduce the vocabulary and a model of parallel and perpendicular)

                        Second grade:     (DVISD expectation: introduce parallel lines using shapes)

                        Third grade:         (DVISD expectation: introduce models of parallel and perpendicular lines)

(4.8)     (B)       Fourth grade:    identify models of parallel and perpendicular lines

describe shapes and solids in terms of vertices, edges, and faces

(K.8)    (A)       Kindergarten:       describe shapes and solids in terms of edges

                        First grade:          (DVISD expectation: sort and classify solid figures by the number of faces)

(2.7)     (C)       Second grade:     describe shapes and solids in terms of vertices, edges, and faces

                        Third grade:         (DVISD expectation: describe shapes and solids in terms of vertices, edges, and faces)

(4.8)     (C)       Fourth grade:    describe shapes and solids in terms of vertices, edges, and faces

 

identify relationships involving angles in triangles and quadrilaterals

                        Fifth grade:          (DVISD expectation: introduce triangles as 180° and quadrilaterals as 360°)

(6.6)     (B)       Sixth grade:       identify relationships involving angles in triangles and quadrilaterals

 

describe the relationship between radius, diameter, ad circumference of a circle

                        Fourth grade:       (DVISD expectation: introduce parts of a circle)

                        Fifth grade:          (DVISD expectation: use terms of radius, diameter, and circumference of a circle and introduce basic formulas for parts of circles)

(6.6)     (C)       Sixth grade:       describe the relationship between radius, diameter, and circumference of a circle

 

The student recognizes that numbers can be represented by points on a line (K-3).  The fourth grade student recognizes the connection between numbers and points on a number line.  The student in the fifth grade recognizes the connection between ordered pairs of numbers and locations of points on a plane.  The seventh grade student uses coordinate geometry to describe location on a plane.  The student is expected to:

locate and name points on a line using whole numbers [and fractions such as halves]

                        Kindergarten:       (DVISD expectation: locate and name points on a line to 20)

                        First grade:          (DVISD expectation: locate and name points on a line using whole numbers (before, after, and in between) from 0-99)

                        Second grade:     (DVISD expectation: locate and name points on a line using whole numbers)

(3.10)               Third grade:      locate and name points on a line using whole numbers [and fractions such as halves]

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

 

locate and name points on a coordinate grid                       

                        Second grade:     (DVISD expectation: locate points on a coordinate grid using ordered pairs of whole numbers)

                        Third grade:         (DVISD expectation: locate points on a coordinate grid using ordered pairs of whole numbers)

                        Fourth grade:       (DVISD expectation: locate and name points on a coordinate grid using ordered pairs of whole numbers)

(5.9)     (A)       Fifth grade:        locate and name points on a coordinate grid using ordered pairs of whole numbers

(6.7)     (A)       Sixth grade:       locate and name points on a coordinate plane using ordered pairs of non-negative rational numbers

 

 

graph translations on a coordinate plane

                        Fifth grade:          (DVISD expectation: identify translations on x coordinate plane)

                        Sixth grade:         (DVISD expectation: identify translations on x coordinate plane)

 

The student uses geometry to model and describe the physical world.  The student is expected to:

combine geometric shapes to make new shapes

(1.6)     (A)       First grade:          combine geometric shapes to make new geometric shapes using concrete models

(2.7)     (C)       Second grade:     cut geometric shapes apart and identify the new shapes made

 

sketch a solid when given the top, side, and front views

                        Third grade:         (DVISD expectation: identify solids when given faces)

                        Fourth grade:       (DVISD expectation: identify solids when given faces)

                        Fifth grade:          (DVISD expectation: identify solids when given faces)

                        Sixth grade:         (DVISD expectation: sketch a solid when given the top, side, and front views)

 

make a net (two-dimensional model) of the surface area of a solid:

                        Sixth grade:         (DVISD expectation: make a net (two-dimensional model) of the surface area of a solid)

 

use geometric concepts and properties to solve problems to solve problems in fields such as art and architecture

                        Sixth grade:         (DVISD expectation: use geometric concepts and properties to solve problems to solve problems in fields such as art and architecture)

 

                       

Measurement.

The student selects and uses appropriate units and procedures to measure length and area.  The student is expected to:

compare and order concrete objects

(K.10)              Kindergarten:       compare and order two or three concrete objects according to length, (shorter or longer), capacity (holds more or less), or weight (lighter or heavier)

(1.7)     (B)       First grade:          describe the relationship between the size of the unit and the number of units needed in a measurement

 

identify concrete models that approximate standard units of length, capacity, and weight

(2.9)     (A)       Second grade:     identify concrete models that approximate standard units of length, capacity, and weight

 

find concrete objects that are about the same as, less than, or greater than a given object according to length, capacity, or weight

(K.10)  (B)       Kindergarten:       find concrete objects that are about the same as, less than, or greater than a given object according to length, capacity, or weight

                        First grade:          (DVISD expectation: identify tool for measuring length, capacity, and weight using concrete models that approximate standard units)

(2.9)     (A)       Second grade:     measure length, capacity, and weight using concrete models that approximate standard units             

                       

estimate and measure lengths using standard units such as inch, foot, yard, centimeter, [decimeter,] and meter

                        Kindergarten:       (DVISD expectation: estimate and measure lengths using inch and foot)

(1.7)     (A)       First grade:          estimate and measure length, capacity, and weight of objects using nonstandard units (DVISD expectation: estimate and measure lengths using standard units such as inch, foot, yard, centimeter, [decimeter,] and meter)

(2.9)     (A)(B)  Second grade:     estimate and measure lengths using standard units such as inch, foot, yard, centimeter, [decimeter,] and meter

(3.11)   (A)       Third grade:      estimate and measure lengths using standard units such as inch, foot, yard, centimeter, [decimeter,] and meter

 

estimate [and measure] weight using standard units including ounces, pounds, grams, and kilograms

(K.10)  (B)       Kindergarten:       (DVISD expectation: estimate and measure weight using pounds)

                        First grade:          (DVISD expectation: estimate and compare weights using heavier and lighter)

                        Second grade:     (DVISD expectation: measure weight using standard units including ounces, pounds, grams, and kilograms)

 (4.11)  (A)       Third grade:      estimate [and measure] weight using standard units including ounces, pounds, grams, and kilograms

 

estimate [and measure] capacity using standard units including milliliters, liters, cups, pints, quarts, and gallons

(K.10)  (B)       Kindergarten:       estimate and measure capacity using cups

                        First grade:          (DVISD expectation: estimate and measure capacity using cups)

                        Second grade:     (DVISD expectation: measure capacity using standard units including milliliters, liters, cups, pints, quarts, and gallons)

(4.12)   (A)       Third grade:      estimate [and measure] capacity using standard units including milliliters, liters, cups, pints, quarts, and gallons

 

use linear measure to find the perimeter of a shape

            `           Kindergarten:       (DVISD expectation: introduce the term perimeter)

                        First grade:          (DVISD expectation: given the linear measurement the student will be able to find the perimeter)

                        Second grade:     (DVISD expectation: use linear measure to find the perimeter of a shape including equalateral shapes given the measurement to only two sides)

(3.11)   (B)       Third grade:      use linear measure to find the perimeter of a shape

 

use [concrete] models of square units to determine the area of shapes

                        First grade:          (DVISD expectation: make a model to build cube structures)

                        Second grade:     (DVISD expectation: use [concrete] models of square units to determine the area of shapes)

(3.11)   (C)       Third grade:      use [concrete] models of square units to determine the area of shapes

 

measure volume using [concrete] models of cubic units

                        First grade:          (DVISD expectation: estimate and measure capacity using cups)

                        Second grade:     (DVISD expectation: measure volume using [concrete] models of cubic units)

(3.10)   (A)       Third grade:      measure volume using [concrete] models of cubic units

                        Fourth grade:       (DVISD expectation: measure volume in cubic units)

(5.10)   (B)       Fifth grade:          (DVISD expectation: estimate volume in cubic units)

 

The student measures time and temperature.  The student is expected to:

tell and write time shown on traditional and digital clocks

(K.11)  (B)       Kindergarten:       compare events according to duration such as more time than or less time than (DVISD expectation: tell and write time on traditional and digital clocks to the hour)

(1.8)     (B)       First grade:          describe time on a clock using hours and half hours

(2.10)   (B)       Second grade:     describe time on a clock using hours and minutes (DVISD expectation:  tell and write time shown on traditional and digital to the minute, quarter past, half past, and quarter till)

(3.12)   (A)       Third grade:      tell and write time shown on traditional and digital clocks

 

sequence events

(K.11)  (C)       Kindergarten:       sequence events

(1.8)     (C)       First grade:          order three or more events by how much time they take

(2.9)     (C)       Second grade:     describe activities that that take approximately on second, one minute, and one hour sequence events

 

read a calendar

(K.11)  (D)       Kindergarten:       read a calendar using days, weeks, and months

 

use a thermometer to measure temperature

(K.11)  (A)       Kindergarten:       compare situations or objects according to temperature such as hotter or colder (DVISD expectation: use a thermometer to measure hot and cold temperatures)

(1.8)     (A)       First grade:          recognize temperatures such as a hot day or a cold day (DVISD expectation: identify a thermometer as a tool for measuring temperature)

(2.10)   (A)       Second grade:     use a thermometer to measure temperature

(3.12)   (B)       Third grade:      use a thermometer to measure temperature

 

The student applies measurement concepts (K-5).  The sixth grade student solves application problems involving estimation and measurement of length, area, time, temperature, capacity, weight, and angles.  The student is expected to:

measure to solve problems

(K.10)  (A)       Kindergarten:       estimate and measure length

                        First grade:          (DVISD expectation: measure length, area, time, temperature, capacity, and weight)

(2.9)     (B)(C)  Second grade:     measure to solve problems involving length, [area,] temperature, and time

(3.13)   (A)       Third grade:      measure to solve problems involving length, [area,] temperature, and time

(4.12)   (B)       Fourth grade:    measure to solve problems involving length, including perimeter, time, temperature, and area

(5.11)   (A)       Fifth grade:        measure to solve problems involving length (including perimeter), weight, capacity, time, temperature, and area

 

describe numerical relationships between units of measure within the same measurement system such as an inch is one-twelfth of a foot

                        Third grade:         (DVISD expectation: introduce 12 inches = 1 foot, 6 inches = ½, and 3 feet = 1 yard)

                        Fourth grade:       (DVISD expectation: describe numerical relationships between units of measure within the same measurement system such as 6 inches equals one foot)

(5.11)   (B)       Fifth grade:        describe numerical relationships between units of measure within the same measurement system such as an inch is one-twelfth of a foot

 

estimate measurements and evaluate reasonableness of results

                        Fifth grade           (DVISD expectation: introduce estimating measurements and evaluating reasonableness of results)

(6.8)     (A)       Sixth grade:       estimate measurements and evaluate reasonableness of results

 

The student uses attributes such as length, weight, or capacity to compare and order objects.  The student is expected to:

compare and order two or three concrete objects according to length (shorter or longer), capacity (holds more or holds less), or weight (lighter or heavier)

(K.10)  (A)       Kindergarten:       compare and order two or three concrete objects according to length (shorter or longer), capacity (holds more or holds less), or weight (lighter or heavier)

                       

find concrete objects that are about the same as, less than, or greater than a given object according to length, capacity, or weight

(K.10)  (B)       Kindergarten:       find concrete objects that are about the same as, less than, or greater than a given object according to length, capacity, or weight

 

select and use appropriate units, tools, or formulas to measure and to solve problems involving length (including perimeter and circumference), area, time, temperature, capacity, and weight

                        Third grade:         (DVISD expectation: select appropriate units and tools to measure objects involving length (including perimeter), time, temperature, capacity, and weight)

                        Fourth grade:       (DVISD expectation: select appropriate units and tools to measure objects involving length (including perimeter), time, temperature, capacity, and weight)

                        Fifth grade:          (DVISD expectation: select appropriate units and tools to measure objects involving length (including perimeter), time, temperature, capacity, and weight)

(6.8)     (B)       Sixth grade:       select and use appropriate units, tools, or formulas to measure and to solve problems involving length (including perimeter), area, time, temperature, capacity, and weight

 

measure angles

                        Fifth grade:          (DVISD expectation: introduce concept of measuring angles)

(6.8)     (C)       Sixth grade:       measure angles

 

convert measures within the same measurement system (customary and metric) based on relationships between units

                        Fifth grade:          (DVISD expectation: convert measures within the same measurement system (customary and metric) based on relationships between units)

(6.8)     (D)       Sixth grade:       convert measures within the same measurement system (customary and metric) based on relationships between units

 

The student solves application problems involving estimation and measurement.  The student is expected to:

estimate measurements and solve application problems involving length (including perimeter and circumference), area, and volume

                        Fifth grade:          (DVISD expectation: introduce estimating measurements and solving application problems involving length (including perimeter and circumference), area, and volume)

                        Sixth grade:         (DVISD expectation: estimate measurements and solve application problems involving length (including perimeter and circumference), area, and volume)

 

 

Probability and statistics.

The student solves problems by collecting, organizing, displaying, and interpreting sets of data.  The student is expected to:

collect and sort data

(K.9)    (A)       Kindergarten:       collect and sort data (DVISD expectation: collect data using tally marks)

(1.9)     (A)       First grade:          collect and sort data

(

[collect,] organize, record, and display data in pictographs and bar graphs

(K.12)  (A)       Kindergarten:       construct graphs using real objects or pictures in order to answer questions

                                                   (DVISD expectation: organize, record, and display data in pictographs and bar graphs where each picture or cell might represent more than one piece of data)

(1.9)     (B)       First grade:          use organized data to construct real object graphs, picture graphs, and bar-type graphs (DVISD expectation: [collect,] organize, record, and display data in pictographs and bar graphs)

(2.11)   (A)       Second grade:     construct picture graphs and bar-type graphs

(3.14)   (A)       Third grade:      [collect,] organize, record, and display data in pictographs and bar graphs where each picture or cell might represent more than one piece of data

 

interpret information from pictographs and bar graphs

(K.12)  (B)       Kindergarten:       use information from a graph of real objects or pictures in order to answer questions (from pictographs and bar graphs)

(1.10)   (A)       First grade:          draw conclusions and answer questions using information organized in real-object graphs, picture graphs, and bar-type graphs  (DVISD expectation: interpret data from pictographs, bar graphs, and tally tables)

(2.11)   (B)       Second grade:     draw conclusions and answer questions based on picture graphs and bar-type graphs

(3.14)   (B)       Third grade:      interpret information from pictographs and bar graphs

(4.13)   (C)       Fourth grade:    interpret bar graphs

 

use data to describe events as more likely, less likely, or equally likely

(1.10)   (B)       First grade:          identify events as certain or impossible such as drawing a red crayon from a bag of green crayons

(2.11)   (C)       Second grade:     use data to describe events as more likely or less likely such as drawing a certain color crayon from a bag of seven red crayon and three green crayons

(3.14)   (C)       Third grade:      use data to describe events as more likely, less likely, or equally likely

 

list all possible outcomes of a probability experiment such as tossing a coin

                        Second grade:     (DVISD expectation: introduce concept of listing all possible outcomes of a probability experiment such as tossing a coin)

                        Third grade:         (DVISD expectation: list all possible outcomes of a probability experiment such as tossing a coin)

(4.13)   (A)       Fourth grade:    list all possible outcomes of a probability experiment such as tossing a coin

 

use a pair of numbers to compare favorable outcomes to all possible outcomes such as four heads out of six tosses of a coin

                        Third grade:         (DVISD expectation: use a pair of numbers to compare favorable outcomes to all possible outcomes such as four heads out of six tosses of a coin)

(4.13)   (C)       Fourth grade:    use a pair of numbers to compare favorable outcomes to all possible outcomes such as four heads out of six tosses of a coin

 

The student describes and predicts the results of a probability.  The student is expected to:

use fractions to describe the results of an experiment

                        Fourth grade:       introduce fractions to describe results of an experiment

(5.12)   (A)       Fifth grade:        use fractions to describe the results of an experiment

 

use experimental results to make predictions

                        Fourth grade:       (DVISD expectation: use experimental results to make predictions)

(5.12)   (B)       Fifth grade:        use experimental results to make predictions

 

The student solves problems by collecting, organizing, displaying, and interpreting sets of data.  The seventh grade student understands that the way a set of data is displayed influences its interpretation.  The student is expected to:

use tables of related number pairs to make line graphs

                        Third grade:         (DVISD expectation: introduce ordered pairs)

                        Fourth grade:       (DVISD expectation: introduce number pairs to make line graphs)

(5.13)   (A)       Fifth grade:        use tables of related number pairs to make line graphs

 

describe characteristics of data presented in tables and graphs including the shape and spread of the data and the middle number

                        Fourth grade:       (DVISD expectation: introduce characteristics of data presented in tables and graphs including the shape and spread of the data and the middle number)

(5.13)   (B)       Fifth grade:        describe characteristics of data presented in tables and graphs including the shape and spread of the data and the middle number

 

 

graph a given set of data using an appropriate graphical representation such as a picture or line

                        Third grade:         (DVISD expectation: graph collected data)

                        Fourth grade:       (DVISD expectation: graph a given set)

(5.13)   (C)       Fifth grade:        graph a given set of data using an appropriate graphical representation such as a picture or line

(6.10)   (D)       Sixth grade:         solves problems by collecting, organizing, displaying and interpreting graphs

(7.11)   (A)       Seventh grade:  select and use an appropriate representation for presenting collected data and justify the selection

 

make inferences and convincing arguments based on an analysis of given or collected data

                        Sixth grade:         (DVISD expectation: make inferences and convincing arguments based on an analysis of given or collected data)

 

The student uses experimental and theoretical probability to make predictions.  The student is expected to:

construct sample spaces using lists, tree diagrams, and combinations

                        Fifth grade:          (DVISD expectation: introduce sample spaces using lists, tree diagrams, and combinations)

(6.9)     (A)       Sixth grade:       construct sample spaces using lists, tree diagrams, and combinations

 

find the probabilities of a simple event and its complement and describe the relationship between the two

                        Fifth grade:          (DVISD expectation: find the probability of a simple event)

(6.9)     (B)       Sixth grade:       find the probabilities of a simple event and its complement and describe the relationship between the two

 

The student uses statistical representations to analyze data. The seventh grade student uses measures of central tendency and range to describe a set of data.  The student is expected to:

[draw and] compare different graphical representations of the same data

(4.13)   (C)       Fourth grade;       interpret bar graphs

                        Fifth grade:          (DVISD expectation: interpret and construct bar and line graphs)

(6.10)   (A)       Sixth grade:       [draw and] compare different graphical representations of the same data

 

use median, mode, and range to describe data

                        Fifth grade:          (DVISD expectation: use median, mode, and range to describe data (and mean)

(6.10)   (B)       Sixth grade:       use median, mode, and range to describe data (and mean)

(7.12)   (A)       Seventh grade:  describe a set of data using mean, median, mode, and range

 

choose among mean, median, mode , or range to describe a set of data and justify the choice for a particular situation

                        Fifth grade:          (DVISD expectation: choose among mean, median, and mode)

                        Sixth grade:         (DVISD expectation: choose among mean, median, mode, or range to describe a set of data and justify the choice for a particular situation)

 

sketch circle graphs to display data

                        Fourth grade:       (DVISD expectation: interpret circle graph information)

                        Fifth grade:          (DVISD expectation: interpret circle graph information)

(6.10)   (C)       Sixth grade:       sketch circle graphs to display data

 

solve problems by collecting, organizing, displaying, and interpreting data

                        Fourth grade:       (DVISD expectation: introduce collecting, organizing, displaying, and interpreting data)

                        Fifth grade:          (DVISD expectation: solve problems by collecting, organizing, displaying, and interpreting data)

(6.10)   (D)       Sixth grade:       solve problems by collecting, organizing, displaying, and interpreting data

 

 

Underlying processes and mathematical tools.

The student applies mathematics to solve problems connected to everyday experiences and activities in and outside of school 3-5).  The sixth grade student applies mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school.  The student is expected to:

(K.13)  (A)       Kindergarten:       identify the mathematics in everyday situations

(1.11)   (A)       First grade:          identify the mathematics in everyday situations

(2.12)   (A)       Second grade:     identify the mathematics in everyday situations

(3.15)   (A)       Third grade:      identify the mathematics in everyday situations

(4.14)   (A)       Fourth grade:    identify the mathematics in everyday situations

(5.14)   (A)       Fifth grade:        identify the mathematics in everyday situations

(6.11)   (A)       Sixth grade:       identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics

 

use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness

(K.13)  (B)       Kindergarten:       use a problem-solving model, with guidance, that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness

(1.11)   (B)       First grade:          use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness

(2.12)   (B)       Second grade:     use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness

(3.15)   (B)       Third grade:      use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness

(4.14)   (B)       Fourth grade:    use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness

(5.14)   (B)       Fifth grade:        use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness

(6.11)   (B)       Sixth grade:       use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness

 

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

(K.13)  (C)       Kindergarten:       select or develop an appropriate problem-solving strategy, including drawing a picture, looking for a pattern, systematic guessing and checking or acting it out to solve a problem

(1.11)   (C)       First grade:          select or develop an appropriate problem-solving strategy, including drawing a picture, looking for a pattern, systematic guessing and checking or acting it out to solve a problem

(2.12)   (C)       Second grade:     select or develop an appropriate problem-solving strategy, including drawing a picture, looking for a pattern, systemic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem

(3.15)   (C)       Third grade:      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

(4.14)   (C)       Fourth grade:    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

(5.14)   (C)       Fifth grade:        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

(6.11)   (C)       Sixth grade:       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

 

use tools such as real objects, manipulatives, and technology to solve problems

(K.13)  (D)       Kindergarten:       use tools such as real objects, manipulatives, and technology to solve problems

(1.11)   (D)       First grade:          use tools such as real objects, manipulatives, and technology to solve problems

(2.12)     (D)       Second grade:     use tools such as real objects, manipulatives, and technology to solve problems

(3.15)   (D)       Thirds grade:       use tools such as real objects, manipulatives, and technology to solve problems

(4.14)   (D)       Fourth grade:       use tools such as real objects, manipulatives, and technology to solve problems

(5.14)   (D)       Fifth grade:          use tools such as real objects, manipulatives, and technology to solve problems

(6.11)   (D)       Sixth grade:         select tools such as real objects, manipulatives, paper/pencil and technology or techniques such as mental math, estimation, and number sense to solve problems

 

The student communicates about mathematics using informal language (3-5).  The sixth grade student communicates about mathematics through informal through informal and mathematical language, representations, and models.  The student is expected to:

relate informal language to mathematical language and symbols

(K.14)  (B)       Kindergarten:       relate informal language to mathematical language

(1.12)   (B)       First grade:          relate informal language to mathematical language

(2.13)   (B)       Second grade:     relate informal language to mathematical language and symbols

(3.16)   (B)       Third grade:      relate informal language to mathematical language and symbols

(4.15)   (B)       Fourth grade:    relate informal language to mathematical language and symbols

(5.15)   (B)       Fifth grade:        relate informal language to mathematical language and symbols

(6.12)   (A)       Sixth grade:       communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models

 

explain and record observations using objects, words, pictures, numbers and technologies

(K.14)  (A)       Kindergarten:       explain and record observations using objects, words, pictures, numbers and technologies

(1.12)   (A)       First grade:          explain and record observations using objects, words, pictures, numbers and technologies

                        Second grade:     explain and record observations using objects, words, pictures, numbers and technologies

(3.16)   (A)       Third grade:         explain and record observations using objects, words, pictures, numbers and technologies

(4.15)   (A)       Fourth grade:       explain and record observations using objects, words, pictures, numbers and technologies

(5.15)   (B)       Fifth grade:          explain and record observations using objects, words, pictures, numbers and technologies

 

evaluate the effectiveness of different representations to communicate ideas

(6.12)   (B)       Sixth grade:         evaluate the effectiveness of different representations to communicate ideas

 

Underlying processes and mathematical tools.

The student uses logical reasoning to make sense of his of her world (3-5).  The sixth grade student uses logical reasoning to make conjectures and verify conclusions.  The student is expected to:

make generalizations from patterns or sets of examples and nonexamples

(K.15)              Kindergarten:       (DVISD expectation: make generalizations from patterns or sets of examples and nonexamples (Venn diagrams)

(1.13)               First grade:          use reason to support his or her thinking using objects, words, pictures, numbers and technology

                        Second grade:     use reason to support his or her thinking using objects, words, pictures, numbers and technology

(3.17)   (A)       Third grade:      make generalizations from patterns or sets of examples and nonexamples

(4.16)   (A)       Fourth grade:    make generalizations from patterns or sets of examples and nonexamples

(5.16)   (A)       Fifth grade:        make generalizations from patterns or sets of examples and nonexamples

(6.13)   (A)       Sixth grade:       make conjectures from patterns or sets of examples and nonexamples

 

validate his/her conclusions using mathematical properties and relationships

(K.15)              Kindergarten:       reason and support his or her thinking using objects, words, pictures, numbers, and technology

(1.13)               First grade:          reason and support his or her thinking using objects, words, pictures, numbers, and technology

(2.14)               Second grade:     reason and support his or her thinking using objects, words, pictures, numbers, and technology

(3.17)   (B)       Third grade:         justify why an answer is reasonable and explain the solution process

(4.16)   (B)       Fourth grade:       justify why an answer is reasonable and explain the solution process

(5.16)   (B)       Fifth grade:          justify why an answer is reasonable and explain the solution process

(6.13)   (B)       Sixth grade:         validate his/her conclusions using mathematical properties and relationships