Vertical Alignment
Computation and Estimation
Prince William County Public Schools
NCTM Process Standards:
 Problem Solving
 Reasoning and Proof
 Communication
 Connections
 Representation
Mathematics
K-5
Big Ideas:
 Addition names the whole in terms of the parts, and subtraction names a
missing part. Addition and subtraction are inverse operations.
 Multiplication involves counting groups of like size and determining how
many are in all (multiplicative thinking). Division names a missing factor in
terms of the known factor and the product. Multiplication and division are
inverse operations.
 Addition and multiplication are related, as are subtraction and division.
 Models can be used to solve problems for all operations and to figure out
what operation is involved in a problem regardless of the size of the
numbers.
 Nearly all computational estimation involves replacing or substituting
difficult-to-handle numbers with close “nice” numbers so that the resulting
computation can be done mentally.
Grade 2
Kindergarten
Grade 1
K.6 Model adding and subtracting
whole numbers, using up to 10 concrete
objects.
1.4A Given a familiar problem
situation involving magnitude, select a
reasonable order of magnitude from
three given quantities: a one-digit
numeral, a two-digit numeral, and a
three-digit numeral (e.g., 5, 50, 500).
2.5 Recall addition facts with sums to
20 or less and the corresponding
subtraction facts.
1.4B Given a familiar problem
situation involving magnitude, explain
the reasonableness of the choice.
2.6B Find the sum of two whole
numbers whose sum is 99 or less, using
various methods of calculation.
1.5 Recall basic addition facts with
sums to 18 or less and the
corresponding subtraction facts.
2.7A Estimate the difference of two
whole numbers, each of which is 99 or
less.
1.6 Create and solve one-step story
and picture problems using basic
addition facts with sums to 18 or less
and the corresponding subtraction
facts.
2.7B Find the difference of two whole
numbers, each of which is 99 or less,
using various methods of calculation.
2.6A Estimate the sum of two whole
numbers whose sum is 99 or less.
2.8 Create and solve one- and two-step
addition and subtraction problems,
using data from simple tables, picture
graphs, and bar graphs.
2.9 Recognize and describe the related
facts that represent the inverse
relationship between addition and
subtraction.
Revised July 20, 2011
Grade 3
3.4 Estimate solutions to and solve
single-step and multistep problems
involving the sum or difference of two
whole numbers, each 9,999 or less, with
or without regrouping.
3.5 Recall multiplication facts through
the twelves table, and the corresponding
division facts.
3.6 Represent multiplication and
division, using area, set, and number
line models, and create and solve
problems that involve multiplication of
two whole numbers, one factor 99 or
less and the second factor 5 or less.
3.7 Add and subtract proper fractions
having like denominators of 12 or less.
Grade 4
4.4A Estimate sums, differences,
products, and quotients of whole
numbers.
4.4B Add, subtract, and multiply
whole numbers.
4.4C Divide whole numbers, finding
quotients with and without remainders.
4.4D Solve single-step and multistep
addition, subtraction, and
multiplication problems with whole
numbers.
4.5A Determine common multiples
and factors, including least common
multiple and greatest common factor.
4.5B Add and subtract fractions
having like and unlike denominators
that are limited to 2, 3, 4, 5, 6, 8, 10,
and 12, and simplify the resulting
fractions, using common multiples and
factors.
Grade 5
5.4 Create and solve single-step and
multistep practical problems involving
addition, subtraction, multiplication,
and division with and without
remainders of whole numbers.
5.5A Find the sum, difference, product,
and quotient of two numbers expressed
as decimals through thousandths
(divisors with only one non-zero digit).
5.5B Create and solve single-step and
multistep practical problems involving
decimals.
5.6 Solve single-step and multistep
practical problems involving addition
and subtraction with fractions and
mixed numbers and express answers in
simplest form.
5.7 Evaluate whole number numerical
expressions, using the order of
operations limited to parentheses,
addition, subtraction, multiplication,
and division.
4.5C Add and subtract with decimals.
4.5D Solve single-step and multistep
practical problems involving addition
and subtraction with fractions and with
decimals.
Revised July 20, 2011
Vertical Alignment:
Computation and Estimation
Prince William County Public Schools
NCTM Process Standards:
 Problem Solving
 Reasoning and Proof
 Communication
 Connections
 Representation
Grade 6
6.6A Multiply and divide fractions and
mixed numbers.
6.6B Estimate solutions and then solve
single-step and multi-step practical
problems involving addition,
subtraction, multiplication, and division
of fractions.
6.7 Solve single-step and multi-step
practical problems involving addition
subtraction, multiplication, and division
of decimals.
Mathematics
6–8
Big Ideas:
 Bringing meaning to why procedures work (or sense-making) is critical in
developing conceptual and algorithmic understanding of operations with
integers and rational numbers.
 Estimation is one strategy for solving a problem.
 There are real life situations when exact answers are appropriate and others
when estimates are equally appropriate.
 Making valid judgments regarding the reasonableness of an answer is part of
problem-solving.
 Skills with operations with whole numbers, fractions, and decimals are critical
in problem-solving and applications.
Grade 7
Grade 8
7.3A Model addition, subtraction,
multiplication, and division of
integers.
8.3A Solve practical problems
involving rational numbers, percents,
ratios, and proportions.
7.3B Add, subtract, multiply, and
divide integers.
8.3B Determine the percent increase or
decrease for a given situation.
7.4 The student will solve single-step
and multi-step problems, using
proportional reasoning.
8.4 Apply the order of operations to
evaluate algebraic expressions for
given replacement values of variables.
6.8 Evaluate whole number numerical
expressions, using order of operations.
Revised July 20, 2011