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Multiplication and Division Concepts and Facts
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Recognize equal groups, repeated addition, arrays, and multiplicative comparisons as multiplication.
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Use patterns to find products with factors of 0, 1, 2, 5, and 9.
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Use the Distributive Property to find products by breaking unknown facts into known facts.
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Find products of factors 10, 11, and 12.
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Make tables and use them to solve word problems.
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Use sharing and repeated subtraction to solve word problems with division.
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Complete multiplication and division fact families, and write fact families for given numbers.
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Divide using a related multiplication fact.
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Give quotients of 0 when the number divided is 0, give a quotient of 1 when a number is divided by itself, and give the number divided as the quotient when dividing by 1.
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Write stories using given multiplication and division facts.
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Write and evaluate variable expressions that involve a single operation of multiplication or division.
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Find the rule for a pattern presented in a table, and use the rule to add inputs and outputs to the table.
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Find the solution to an equation by testing a set of values for the variable.
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PDE: Whole numbers
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PDE: Operation of addition
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PDE: Operation of subtraction
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PDE: Operation of multiplication
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PDE: Operation of division
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PDE: Money through the cent
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PDE: Concept of "missing element"
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PDE: Numerical Pattern
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PDE: Concept of "pattern rule"
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PDE: Numerical Pattern
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PDE: Numerical Pattern
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PDE: Concept of "expression"
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PDE: Concept of "equation"
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PDE: Concept of "missing number"
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PDE: Strategy - estimation
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PDE: Strategy - guess & check
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PDE: Equation
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PDE: Operation symbols (+, -, x, ÷, , =)
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PDE: Number sentences
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PDE: Whole numbers
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PDE: Operation of addition
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PDE: Operation of subtraction
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PDE: Operation of multiplication
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PDE: Operation of division
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PDE: Money through the cent
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PDE: Concept of "missing element"
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PDE: Numerical Pattern
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PDE: Concept of "pattern rule"
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PDE: Numerical Pattern
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PDE: Numerical Pattern
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PDE: Concept of "expression"
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PDE: Concept of "equation"
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PDE: Concept of "missing number"
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PDE: Strategy - estimation
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PDE: Strategy - guess & check
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PDE: Equation
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PDE: Operation symbols (+, -, x, ÷, , =)
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PDE: Number sentences
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PDE: Whole numbers
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PDE: Operation of addition
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PDE: Operation of subtraction
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PDE: Operation of multiplication
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PDE: Operation of division
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PDE: Concept of "analog time"
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PDE: Concept of "digital time"
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PDE: Concept of "minutes before the hour"
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PDE: Concept of "minutes after the hour"
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PDE: Concept of "elapsed time"
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PDE: Concept of "beginning time"
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PDE: Concept of "ending time"
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PDE: Ordered pair
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PDE: Simple grid
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PDE: Point or object on simple grid
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PDE: Concept of "data"
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PDE: Table
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PDE: Chart
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PDE: Bar graph
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PDE: Pictograph
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PDE: Concept of "data"
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PDE: Bar graph
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PDE: Pictograph
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PDE: Table
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PDE: Chart
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PDE: Bar graph
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PDE: Pictograph
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Array, factor, product
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Multiple, Zero, Property of Multiplication, Identity Property of Multiplication, Commutative Property of Multiplication
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Distributive Property
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Divide. divisor, dividend, quotient
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Fact family, inverse operations
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Variable (p.98)
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Equation (p.100), solution (p.100)
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PDE: Explain the solution to a two-step problem (limit to two-step problems -e.g , multiply then add - single digit multipiers and divisors)
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PDE: Solve up to two step problems involving subtraction with decimals (through tenths)
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PDE: Solve up to two step money problems involving addition (through cents).
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PDE: Solve up to two step money problems involving subtraction (through cents)
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PDE: Find a missing element in a numerical pattern (+.-, o x may be used - numerical patterns must be whole numbers)
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PDE: Extend a numerical pattern (+.-, o x may be used - numerical patterns must be whole numbers)
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PDE: Identify the rule for a numerical pattern shown (+. -, or x may be used - numerical patterns must be whole numbers.
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PDE: Replicate a numerical pattern showing 3 repetitions (+, -, or x may be used - numerical patterns must be whole numbers or money)
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PDE: Create a numerical pattern showing 3 repetitions (+, -, or x may be used - numerical patterns must be whole numbers or money)
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PDE: Correlate story situations with expressions (may use numbers and one operation +, -, or x; no variables)
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PDE: Correlate story situations with equations (may use numbers and one operation +. -, or x; no variables)
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PDE: Solve for a missing number in an equation (using estimation, guess & check, etc). May use +, -, or single digit multiplication or division
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PDE: Identify the missing symbol (+, -, x, ÷, , =) that makes a number sentence true (single digit x or ÷ only)
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PDE: Explain the solution to a two-step problem (limit to two-step problems -e.g , multiply then add - single digit multipiers and divisors)
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PDE: Solve up to two step problems involving subtraction with decimals (through tenths)
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PDE: Solve up to two step money problems involving addition (through cents).
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PDE: Solve up to two step money problems involving subtraction (through cents)
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PDE: Find a missing element in a numerical pattern (+.-, o x may be used - numerical patterns must be whole numbers)
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PDE: Extend a numerical pattern (+.-, o x may be used - numerical patterns must be whole numbers)
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PDE: Identify the rule for a numerical pattern shown (+. -, or x may be used - numerical patterns must be whole numbers.
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PDE: Replicate a numerical pattern showing 3 repetitions (+, -, or x may be used - numerical patterns must be whole numbers or money)
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PDE: Create a numerical pattern showing 3 repetitions (+, -, or x may be used - numerical patterns must be whole numbers or money)
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PDE: Correlate story situations with expressions (may use numbers and one operation +, -, or x; no variables)
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PDE: Correlate story situations with equations (may use numbers and one operation +. -, or x; no variables)
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PDE: Solve for a missing number in an equation (using estimation, guess & check, etc). May use +, -, or single digit multiplication or division
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PDE: Identify the missing symbol (+, -, x, ÷, , =) that makes a number sentence true (single digit x or ÷ only)
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PDE: Solve problems involving all operations with whole numbers (limit to two-step problems -e.g , multiply then add - single digit multipiers and divisors)
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PDE: Explain the solution to a two-step problem (limit to two-step problems -e.g , multiply then add - single digit multipiers and divisors)
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PDE: Match anoalog time (a picture of a clock) to the same time written in digital
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PDE: Construct analog time (a picture of a clock) to the same time written in digital
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PDE: Identify analog time as the amount of time before the hour (e.g., 2:50 is the same as 10 minutes before 3:00)
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PDE: Identify digital time as the amount of time before the hour (e.g., 2:50 is the same as 10 minutes before 3:00)
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PDE: Identify analog time as the amount of time after the hour (e.g., quarter past six is the same as 6:15)
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PDE: Identify digital time as the amount of time after the hour (e.g., quarter past six is the same as 6:15)
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PDE: Calculate the elapsed time, to the minute, in a given situation (limited to 2 adjacent hours)
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PDE: Determine the ending time, given the elapsed time (limited to 2 adjacent hours.)
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PDE: Determine the beginning time, given the elapsed time (limited to 2 adjacent hours)
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PDE: Match the ordered point with the appropriate point (or object) on a simple grid
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PDE: Plot the ordered point on a simple grid.
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PDE: Describe data shown in tables, charts, bar graphs or pictographs
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PDE: Interpret data shown in tables, charts, bar graphs or pictographs
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PDE: Answer questions based on data shown in tables, charts, bar graphs or pictographs.
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PDE: Graph data given the data (bar graph or pictograph - grid is provided)
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PDE: Complete a graph given the data (bar graph or pictograph - grid is provided)
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PDE: Translate information from one type of display to another (table, chart, bar graph or pictograph.
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M4.A.2.1 ~ Use operations to solve problems (may include word problems).
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M4.B.1.1 ~ Determine time and/or calculate elapsed time.
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M4.C.3.1 ~ Locate points on a simple grid.
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M4.D.1.1 ~ Recognize, describe, extend, create and/or replicate a variety of patterns.
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M4.D.1.2 ~ Apply simple function rules.
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M4.D.2.1 ~ Use numbers and symbols to model the concepts of expressions and/or equations.
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M4.D.2.2 ~ Determine the missing number or symbol in a number sentence.
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M4.E.1.1 ~ Interpret data shown on tables, charts, line graphs, bar graphs or pictographs.
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M4.E.1.2 ~ Organize or display data using tables, bar graphs, line graphs or pictographs.
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Tell time to the nearest 1 minute and 5 minutes using analog and digital clocks, and identify times as A.M. or P.M.
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Convert among different units of time, and compare measurements of time.
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Write comparison statements using data from tables and graphs.
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Find elapsed time, starting time, or ending time, given two of these
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Read, interpret, and make pictographs.
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Find dates on a calendar that are certain numbers of weeks before and after given dates.
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Read, interpret, and make line plots.
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Read, interpret, and make bar graphs.
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Locate and graph ordered pairs on a coordinate grid.
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Interpret and make line graphs.
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Use data in tables and tally charts to make line graphs, bar graphs, and pictographs to solve problems.
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Interpret survey results and make predictions based on those results.
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Analog clock, digital clock, A.M., P.M.
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Second, minute, hour, century, millennium. day, week, month, year, leap year, decade
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Elapsed time
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Ordinal numbers
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Data, pictograph, key
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Line plot, outlier
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Bar graph, scale, interval
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Coordinate grid, ordered pair, plot
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Line graph, trend
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Survey
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Scale (p.208)
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M4.B.1.1 ~ Determine time and/or calculate elapsed time.
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M4.C.3.1 ~ Locate points on a simple grid.
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M4.E.1.1 ~ Interpret data shown on tables, charts, line graphs, bar graphs or pictographs.
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M4.E.1.2 ~ Organize or display data using tables, bar graphs, line graphs or pictographs.
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