Use
words, actions, pictures, and concrete objects to solve
problems.

D

Use
pictures or objects to show one more or one less than
any number to 99.

I

Estimate the number of objects in a group and explain
the reasoning for the estimate.

I

Explain
and justify solutions and strategies in problem solving.

I

Add and
subtract up to two-digit whole numbers using various
strategies (e.g., counting up or back, taking away,
doubles plus one, comparison, number relationships, and
modeling).

Match
the spoken or written word names and concrete or
pictorial representations (parts of regions or parts of
sets of objects) of halves, thirds, and fourths.

I

Compare
the unit fractions 1/2, 1/3, and 1/4.

D

Determine the value of a collection of coins up to
$1.00.

Use
concrete or pictorial representations to compare and
order commonly used fractions.

D

Use
concrete and pictorial representations to compare
decimals.

D

Use
various models and equivalent forms to represent, order,
and compare whole numbers and commonly used fractions
and mixed numbers (e.g., number lines, base ten blocks,
expanded notation, Venn diagrams, and hundreds boards).

A

Represent whole numbers up to 10,000 in expanded form
(1,000’s + 100’s +10’s +1’s).

Select
appropriate methods and tools for computing with whole
numbers (e.g., mental computation, estimation,
calculators, paper and pencil, guess and check).

A

Solve
one-step real-world problems involving addition or
subtraction of whole numbers and/or decimals.

Read
and write numbersfrom
millions to thousandths.

A

Identify the place value of a given digit from millions
to thousandths.

A

Represent whole numbers and two-place decimals in
expanded form.

A

Represent, compare, and order whole numbers and decimals
to thousandths.

D

Order
and compare (<, >, or =) whole numbers, fractions, mixed
numbers, and decimals using models (e.g., number lines,
base ten blocks, Venn diagrams, and hundreds boards).

A

Compare
and order fractions using the appropriate symbol (<, >,
and =).

D

Demonstrate knowledge and understanding of grade level
mathematical terms.

D

Represent proper fractions, improper fractions, and
mixed numbers using concrete objects, pictures, and the
number line.

A

Connect
symbolic representations of proper and improper
fractions to models of proper and improper fractions.

A

Represent numbers as both improper fractions and mixed
numbers.

D

Identify and change improper fractions to mixed numbers
and vice versa.

A

Generate equivalent forms of commonly used fractions,
decimals, and percents (e.g., 1/10, 1/4, 1/2, .75, 50%).

D

Recognize relationships among commonly used fractions
and decimals.

A

Multiply a fraction by a multiple of its denominator
(denominator less than or equal to 10).

M

Use
commutative, associative, and identity properties.

D

Explain
and demonstrate the inverse nature of addition and
subtraction.

D

Explain
and demonstrate the inverse nature of multiplication and
division.

D

Explain
how addition, subtraction, multiplication, and division
affect the size and order of numbers.

D

Select
appropriate methods and tools for computations (e.g.,
mental computation, estimation, calculators, and paper
and pencil).

I

Explain
why one form of a number might be more useful for
computation than another form.

A

Use
estimation to determine a reasonable solution to a whole
number computation.

A

Add,
subtract, multiply, and divide whole numbers
(multipliers and divisors no more than two-digits).

A

Add,
subtract, and multiply decimals.

A

Add and
subtract commonly used fractions.

D

Identify missing information and/or too much information
in real-world problems.

A

Solve
one- or two-step real-world problems involving addition,
subtraction, and/or multiplication of whole numbers and
decimals.

D

Solve
real-world problems using decimals (including money),
fractions, and percents.

Connect rational numbers to
locations on a number line.

A

Connect percents greater
than 100 and percents less than one to real-world
situations.

A

Use ratios to represent
quantitative relationships.

D

Understand and use ratios
and proportions to represent quantitative relationships.

A

Identify the opposite and
the reciprocal of a rational number.

D

Use concrete, pictorial, and
symbolic representations for integers, including
locations on a number line.

D

Apply number theory concepts
to solve problems (e.g., divisibility, factors,
multiples, composite numbers, prime numbers, prime
factorization, and relatively prime).

Apply order of operations
when computing with decimals and fractions.

M

Understand and use the
inverse relationships of addition and subtraction and
multiplication and division to simplify computations and
solve problems.

D

Select and use appropriate
methods and tools for computing with whole numbers,
fractions, decimals, percents, and integers in problem
solving situations (e.g., mental computation,
estimation, calculators, number line, computers, and
paper and pencil).

D

Analyze procedures for
computing with fractions, decimals, and integers.

D

Estimate the results of
rational number computations in real-world situations.

A

Use estimation strategies to
select a reasonable solution to a computation involving
rational numbers.

D

Determine if the results of
rational number estimates and computations are
reasonable.

A

Select a reasonable solution
to a real-world division problem in which the remainder
must be considered.

A

Solve one- and two-step
real-world problems involving whole numbers, fractions,
and decimals.

Use
exponents to express a monomial written in expanded
form.

A

Determine the square roots of perfect squares (<169).

D

Use a
variety of models to demonstrate the relationships
within the real number system (e.g., Venn diagrams and
webs).

A

Work
flexibly with fractions, decimals, and percents to solve
one- and two-step word problems.

D

Compare
and order fractions, decimals, and percents.

A

Compare
rational numbers using the appropriate symbol (<, >, and
=).

D

Locate
and specify whole numbers, fractions, decimals,
percents, and integers on the number line.

A

Determine the approximate locations of rational numbers
on a number line.

D

Develop
meaning for percents greater than 100 and less than one
and identify examples.

M

Use
appropriate mathematical language and symbols to express
numerical relationships (e.g., <, >, and =).

D

Understand and use ratios and proportions to represent
quantitative relationships.

A

Use
ratios and proportions to represent real-world
situations (i.e., scale drawings and probability).

A

Use
exponential, scientific, and calculator notation to
represent large numbers in real-world situations.

A

Identify the opposite and the reciprocal of a rational
number.

M

Use
concrete, pictorial, and symbolic representations of
integers.

D

Apply
number theory concepts to solve problems (e.g.,
divisibility, factors, multiples, composite numbers,
prime numbers, prime factorization, and relatively
prime).

D

Understand the meaning and effects of arithmetic
operations with fractions, decimals, and integers.

M

Use the
associative and commutative properties of addition and
multiplication to simplify computations with integers,
fractions, and decimals.

D

Use the
distributive property to simplify computations with
integers, fractions, and decimals.

A

Apply
order of operations in computing with rational numbers
using no more than two parentheses and exponents 1 and
2.

Understand and use the inverse relationships of addition
and subtraction, multiplication and division, and
squaring and finding square roots to simplify
computations and to solve problems.

D

Select
and use appropriate methods and tools for computing with
whole numbers, fractions, decimals, percents, and
integers in problem-solving situations (e.g., mental
computation, estimation, calculators, computers, and
paper and pencil).

A

Compute
efficiently and accurately with whole numbers,
fractions, decimals, and percents.

M

Develop
and analyze procedures for computing with fractions,
decimals, and integers.

A

Use
estimation strategies to select a reasonable solution to
a real-world problem involving computing with rational
numbers.

D

Judge
the reasonableness of the results of rational number
estimates and computations.