Number Operations Continuum
Addition and Subtraction (Combining
- 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
- 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
- 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
- Collects, records, and graphs data.
- Describes and interprets data.
- Explores the mathematical characteristics of the calendar.
- Develops strategies for problems that combine addition and
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
- Finds factor pairs.
- Understands relationships between multiplication and division.
- Identifies whether word problems can be solved using division
- Uses multiplication and/or division notation to write number
- 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
- 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 2-digit numbers like 25).
- Identifies factors of larger numbers (including triple-digit
- 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 double-digit 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
- 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 4-digit numbers (including landmark
- 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
- Uses random digits to approximate 4- or 5-digit 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 real-life 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).