# 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.

(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.
• 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).

 Russell Yates - Resume Email graywolf@olympus.net