Number Operations and Number
Sense Continuum
The following continuum is organized
in subgroups that represent units of the Investigations in
Number, Data, and Space curriculum materials published by
Dale Seymour. These objectives represent the three years of instruction
for grades 3, 4, and 5 for this strand. Some objectives that relate
to other strands are included to help students make connections
between strands of mathematics.
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
2-digit numbers like 25).
- Identifies factors of larger numbers
(including triple-digit 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 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 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 4-digit
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 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).
copyright ©
2000 by Russell
Yates