TEKS Student Expectations
MATHEMATICS
Number, operation, and
quantitative reasoning.
The student uses numbers to name quantities. The student is expected to:
(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
(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)
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:
(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)
(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
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
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