
Number Operations Continuum
Addition and Subtraction (Combining
and Comparing)
 Develops computation strategies for combining and comparing
based on number sense and number relationships.
 Uses landmark numbers (multiples of 10 and 100) in comparing
and combining quantities.
 Examines how parts and the whole are related in addition
and subtraction.
 Solves addition problems with multiple addends.
 Develops more than one way to solve a computation problem
and uses one method to check another.
 Solves compare and combine problems with strategies and records
with standard addition and subtraction notation.
 Makes comparisons of how things change over time.
 Learns to weigh with a pan balance.
 Explores number relationships in the context of time, money,
and linear measure.
 Uses important equivalencies of time, money, and linear measure.
 Estimates solutions that can be adjusted to construct an
exact solution.
 Reads and writes numbers in the hundreds and thousands.
 Develops strategies to combine and compare quantities in
the hundreds and thousands.
 Develops conjectures and predictions; evaluates data and
evidence.
 Collects, records, and graphs data.
 Describes and interprets data.
 Explores the mathematical characteristics of the calendar.
 Develops strategies for problems that combine addition and
subtraction.
Addition and Subtraction
(Money, Miles, and Large Numbers)
 Estimates sums, including total amounts of money.
 Explores strategies for comparing and combining numbers,
through hundreds and thousands.
 Uses landmark numbers (multiples of 10 or 0.10 and 100 or
1.00) to compare and find differences between two quantities.
 Uses standard addition and subtraction notation to record
combining and comparing situations.
 Uses the calculator to solve problems and interpret decimals
on the calculator as amounts of money.
 Estimates local distances in miles and tenths of miles: develops
a sense of about how long a mile and 1/10 of a mile are.
 Compares and combines decimal numbers and, later, quantities
with decimal portions.
 Sees the relationships of decimal parts to the whole.
 Measures distances on maps using a scale.
 Becomes familiar with common decimal and fraction equivalents.
 Considers whether events are likely or unlikely to occur
(Ten Minute Math).
Multiplication and Division
(Things That Come in Groups)
 Finds things that come in groups.
 Uses multiplication to mean groups.
 Recognizes that skip counting represents multiples of the
same number and has a connection to multiplication.
 Finds patterns in multiples of 2, 3, 4, 5, 6, 9, 10, 11,
and 12 by using the 100 chart and the calculator.
 Understands that number patterns can help in multiplication.
 Recognizes that multiplication can be used to find the area
of a rectangle.
 Uses arrays to skip count; multiplies and divides with skip
counting.
 Finds factor pairs.
 Understands relationships between multiplication and division.
 Identifies whether word problems can be solved using division
and/or multiplication.
 Uses multiplication and/or division notation to write number
sentences.
 Uses patterns to solve multiplication and division problems.
 Organizes and presents data in tables and line plots.
 Sorts out complex problems that require both multiplication
and addition.
 Describes events as likely and unlikely (Ten Minute Math).
Multiplication and Division
(Arrays and Shares)
 Uses skip counting as a model for multiplication.
 Sees multiplication as an accumulation of groups of a number.
 Looks for the multiplication patterns of numbers (including
patterns of multiples highlighted on the 100 chart).
 Uses known multiplication relationships to solve harder relationships.
 Uses an array as a model for multiplication.
 Recognizes prime numbers as those that each have only one
pair of factors and only one array.
 Understands how division notation represents a variety of
division situations (including sharing and partitioning situations).
 Determines what to do with leftovers in division, depending
on the situation.
 Partitions numbers to multiply them more easily (e.g., 7x23
can be 7x10 plus 7x10 plus 7x3).
 Learns about patterns that are useful for multiplying by
multiples of 10.
Multiplication and Division
(Packages and Groups)
 Looks for and uses multiplication patterns of numbers (e.g.,
identifies multiples of 5 by seeing that the units digit is either
a 5 or a 0).
 Finds multiples and becomes familiar with the multiples of
larger numbers (e.g., skip counting by 2digit numbers like 25).
 Identifies factors of larger numbers (including tripledigit
numbers).
 Uses familiar landmark numbers to solve problems (e.g., determining
whether the solution is greater than 100, 200, 300, etc., or
estimating 32x9 as 30x10 or 300).
 Partitions large numbers to multiply them more easily (e.g.,
24x8 is thought of as 20x8+4x8).
 Solves doubledigit multiplication problems (e.g., 32x21).
 Understands how division notation can represent a variety
of division situations, including sharing and grouping situations.
 Creates a context that is representative of a division equation
(e.g., represents 152÷4=38 with 152 apples divided into
38 packages of 4).
 Uses multiplication and division relationships in order to
solve problems.
 Describes features of data; interprets and poses questions
about data (Ten Minute Math).
 Recognizes and describes characteristics of numbers and relationships
among numbers (Ten Minute Math).
Computation and Estimation Strategies (Building
on Numbers You Know)
 Skip counts by 2, 3, and 4digit numbers (including landmark
numbers).
 Relates skip counting to multiplication and division.
 Finds and uses patterns in sequences of multiples.
 Reads, writes, and orders large numbers, and approximates
them to the nearest multiple of 100 or 1000.
 Develops strategies for determining and comparing distances
between numbers.
 Uses random digits to approximate 4 or 5digit numbers.
 Develops, records, explains, and compares strategies for
estimating and solving subtraction, multiplication, and division
problems in more than one way.
 Makes sense of remainders in a variety of contexts.
 Interprets, records, and uses division and multiplication
notation in a variety of situations.
 Understands and explains the relationships among the four
basic operations, and using those relationships to solve problems
and model situations.
 Develops reallife meaning for quantities in the thousands,
ten thousands, and hundred thousands, and begins to acquire a
sense of the size of 1,000,000.
 Breaks difficult computation problems into manageable parts.
 Uses a rectangular array model to represent factor pairs
of numbers 10,000 and larger.
 Visualizes ratios, makes predictions, and explores the relationship
of a sample to its group (Ten Minute Math).
 Develops concepts and language to communicate about shapes,
patterns, and visual images (Ten Minute Math).
