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).

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