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## WA.4.1.Core Content: Multi-digit multiplication (Numbers, Operations, Algebra) Students learn basic multiplication facts and efficient procedures for multiplying two- and three-digit numbers. They explore the relationship between multiplication and division as they learn related division and multiplication facts in the same fact family. These skills, along with mental math and estimation, allow students to solve problems that call for multiplication. Building on an understanding of how multiplication and division relate to each other, students prepare to learn efficient procedures for division, which will be developed in fifth grade. Multiplication of whole numbers is not only a basic skill, it is also closely connected to Core Content in this grade level on area, and this connection reinforces understanding of both concepts. Multiplication is also central to students' study of many other topics in mathematics across the grades, including fractions, volume, and algebra.

Core Content: Multi-digit multiplication (Numbers, Operations, Algebra) Students learn basic multiplication facts and efficient procedures for multiplying two- and three-digit numbers. They explore the relationship between multiplication and division as they learn related division and multiplication facts in the same fact family. These skills, along with mental math and estimation, allow students to solve problems that call for multiplication. Building on an understanding of how multiplication and division relate to each other, students prepare to learn efficient procedures for division, which will be developed in fifth grade. Multiplication of whole numbers is not only a basic skill, it is also closely connected to Core Content in this grade level on area, and this connection reinforces understanding of both concepts. Multiplication is also central to students' study of many other topics in mathematics across the grades, including fractions, volume, and algebra.
4.1.A. Quickly recall multiplication facts through 10 x 10 and the related division facts.
Flip Charts Columns Across
Flip Charts Function Machine
Flip Charts Magic Squares
Flip Charts Math Grade 3
Flip Charts Math Grade 4
Flip Charts Math Grade 5
Vocabulary Terms Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Division
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiplication

4.1.B. Identify factors and multiples of a number.
Flip Charts Math Grade 5
Vocabulary Terms Common Factors
Quiz, Flash Cards, Worksheet, Game & Study Guide Common Factors

4.1.C. Represent multiplication of a two-digit number by a two-digit number with place value models.
Flip Charts Columns Across
Flip Charts Function Machine
Flip Charts Magic Squares
Flip Charts Math Grade 4
Flip Charts Math Grade 5
Vocabulary Terms Division
Vocabulary Terms More Multiplication
Vocabulary Terms Division/Multiplication
Vocabulary Terms Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Commutative/Associative Properties
Quiz, Flash Cards, Worksheet, Game & Study Guide Division
Quiz, Flash Cards, Worksheet, Game & Study Guide More Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Division/Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Odd/Even

4.1.D. Multiply by 10, 100, and 1,000.
Flip Charts Columns Across
Flip Charts Function Machine
Flip Charts Magic Squares
Flip Charts Math Grade 5
Vocabulary Terms Division/Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Division/Multiplication

4.1.E. Compare the values represented by digits in whole numbers using place value.
Flip Charts Box It Up
Flip Charts Math Grade 3
Flip Charts Math Grade 4
Vocabulary Terms Compare and Order Numbers
Vocabulary Terms Compare and Order Numbers
Vocabulary Terms Estimation
Vocabulary Terms Expanding Numbers
Vocabulary Terms Greater Than/Less Than
Vocabulary Terms Place Value
Vocabulary Terms Place Value
Vocabulary Terms Place Value
Vocabulary Terms Rounding Numbers
Vocabulary Terms Whole Numbers to Millions
Quiz, Flash Cards, Worksheet, Game & Study Guide Add/Subtract/Multiply/Divide Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Compare and Order Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Compare and Order Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Estimation
Quiz, Flash Cards, Worksheet, Game & Study Guide Expanding Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Exponential & Scientific Notation
Quiz, Flash Cards, Worksheet, Game & Study Guide Greater Than/Less Than
Quiz, Flash Cards, Worksheet, Game & Study Guide Number Words and Place Value
Quiz, Flash Cards, Worksheet, Game & Study Guide Ordering and Comparing Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Place Value
Quiz, Flash Cards, Worksheet, Game & Study Guide Place Value
Quiz, Flash Cards, Worksheet, Game & Study Guide Place Value
Quiz, Flash Cards, Worksheet, Game & Study Guide Rounding Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Rounding to Nearest 10
Quiz, Flash Cards, Worksheet, Game & Study Guide Whole Numbers to Millions

4.1.F. Fluently and accurately multiply up to a three-digit number by one- and two-digit numbers using the standard multiplication algorithm.
Flip Charts Columns Across
Flip Charts Function Machine
Flip Charts Magic Squares
Flip Charts Math Grade 4
Flip Charts Math Grade 5
Vocabulary Terms Division
Vocabulary Terms More Multiplication
Vocabulary Terms Multiplication
Vocabulary Terms Multiplication
Vocabulary Terms Division/Multiplication
Vocabulary Terms Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Commutative/Associative Properties
Quiz, Flash Cards, Worksheet, Game & Study Guide Division
Quiz, Flash Cards, Worksheet, Game & Study Guide More Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Division/Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Odd/Even

4.1.G. Mentally multiply two-digit numbers by numbers through 10 and by multiples of 10.
Flip Charts Columns Across
Flip Charts Function Machine
Flip Charts Magic Squares
Flip Charts Math Grade 4
Flip Charts Math Grade 5
Vocabulary Terms Multiplication
Vocabulary Terms Multiplication
Vocabulary Terms Division/Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Division/Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Odd/Even

4.1.H. Estimate products to approximate solutions to problems and determine reasonableness of answers.
Quiz, Flash Cards, Worksheet, Game & Study Guide Estimation

4.1.I. Solve single- and multi-step word problems involving multi-digit multiplication and verify the solutions.
Vocabulary Terms Problem Solving
Quiz, Flash Cards, Worksheet, Game & Study Guide Problem Solving
Quiz, Flash Cards, Worksheet, Game & Study Guide Word Problems

4.1.J. Solve single- and multi-step word problems involving division and verify the solutions.
Vocabulary Terms Problem Solving
Quiz, Flash Cards, Worksheet, Game & Study Guide Problem Solving
Quiz, Flash Cards, Worksheet, Game & Study Guide Word Problems

## WA.4.2.Core Content: Fractions, decimals, and mixed numbers (Numbers, Algebra) Students solidify and extend their understanding of fractions (including mixed numbers) to include decimals and the relationships between fractions and decimals. Students work with common factors and common multiples as preparation for learning procedures for fraction operations in grades five and six. When they are comfortable with and knowledgeable about fractions, students are likely to be successful with the challenging skills of learning how to add, subtract, multiply, and divide fractions.

Core Content: Fractions, decimals, and mixed numbers (Numbers, Algebra) Students solidify and extend their understanding of fractions (including mixed numbers) to include decimals and the relationships between fractions and decimals. Students work with common factors and common multiples as preparation for learning procedures for fraction operations in grades five and six. When they are comfortable with and knowledgeable about fractions, students are likely to be successful with the challenging skills of learning how to add, subtract, multiply, and divide fractions.
4.2.A. Represent decimals through hundredths with place value models, fraction equivalents, and the number line.
Flip Charts All About Decimals
Flip Charts All About Decimals
Flip Charts Box It Up
Flip Charts Math Grade 3
Flip Charts Math Grade 4
Vocabulary Terms Add/Subtract Decimals
Vocabulary Terms Decimals
Vocabulary Terms Decimals/Fractions
Vocabulary Terms Less Than, Greater Than
Vocabulary Terms Ordering Decimals
Vocabulary Terms Percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Add/Subtract Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Add/Subtract/Multiply/Divide Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Algebra
Quiz, Flash Cards, Worksheet, Game & Study Guide Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Decimals/Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Fractions/Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Less Than, Greater Than
Quiz, Flash Cards, Worksheet, Game & Study Guide Ordering Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Rounding

4.2.B. Read, write, compare, and order decimals through hundredths.
Flip Charts All About Decimals
Flip Charts All About Decimals
Flip Charts Math Grade 3
Vocabulary Terms Less Than, Greater Than
Vocabulary Terms Ordering Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Fractions/Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Less Than, Greater Than
Quiz, Flash Cards, Worksheet, Game & Study Guide Ordering Decimals

4.2.C. Convert a mixed number to a fraction and vice versa, and visually represent the number.
Flip Charts Math Grade 5
Flip Charts Our Atmosphere
Vocabulary Terms Simplify Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Adding Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Simplify Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Subtracting Fractions

4.2.D. Convert a decimal to a fraction and vice versa, and visually represent the number.
Flip Charts Box It Up
Vocabulary Terms Decimals/Fractions
Vocabulary Terms Percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Decimals/Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Percents

4.2.E. Compare and order decimals and fractions (including mixed numbers) on the number line, lists, and the symbols <, >, or =.
Flip Charts All About Decimals
Flip Charts All About Decimals
Flip Charts Box It Up
Flip Charts Math Grade 3
Flip Charts Triangle Tricks
Vocabulary Terms Comparing Fractions
Vocabulary Terms Less Than, Greater Than
Vocabulary Terms Ordering Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Algebra
Quiz, Flash Cards, Worksheet, Game & Study Guide Compare and Order Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Comparing Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Equivalent Fractions to 1/2
Quiz, Flash Cards, Worksheet, Game & Study Guide Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Fractions/Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Less Than, Greater Than
Quiz, Flash Cards, Worksheet, Game & Study Guide Ordering Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Ordering Fractions

4.2.F. Write a fraction equivalent to a given fraction.
Flip Charts Box It Up
Flip Charts Fraction Concepts
Flip Charts Fraction Concepts
Flip Charts Math Grade 3
Flip Charts Math Grade 4
Flip Charts Math Grade 5
Flip Charts Triangle Tricks
Vocabulary Terms Equivalent Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Equivalent Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Fractions/Decimals

4.2.G. Simplify fractions using common factors.
Flip Charts Box It Up
Flip Charts Fraction Concepts
Flip Charts Fraction Concepts
Flip Charts Math Grade 3
Flip Charts Math Grade 4
Flip Charts Math Grade 5
Flip Charts Our Atmosphere
Flip Charts Triangle Tricks
Vocabulary Terms Add/Subtract Fractions
Vocabulary Terms Equivalent Fractions
Vocabulary Terms Simplify Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Add/Subtract Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Adding Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Equivalent Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Number Line
Quiz, Flash Cards, Worksheet, Game & Study Guide Probability
Quiz, Flash Cards, Worksheet, Game & Study Guide Probability
Quiz, Flash Cards, Worksheet, Game & Study Guide Simplify Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Subtracting Fractions

4.2.H. Round fractions and decimals to the nearest whole number.
Flip Charts Box It Up
Flip Charts Math Grade 3
Flip Charts Triangle Tricks
Quiz, Flash Cards, Worksheet, Game & Study Guide Equivalent Fractions to 1/2
Quiz, Flash Cards, Worksheet, Game & Study Guide Rounding

4.2.I. Solve single- and multi-step word problems involving comparison of decimals and fractions (including mixed numbers), and verify the solutions.
Flip Charts All About Decimals
Flip Charts All About Decimals
Flip Charts Box It Up
Flip Charts Math Grade 3
Flip Charts Triangle Tricks
Vocabulary Terms Comparing Fractions
Vocabulary Terms Less Than, Greater Than
Vocabulary Terms Ordering Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Algebra
Quiz, Flash Cards, Worksheet, Game & Study Guide Compare and Order Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Comparing Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Equivalent Fractions to 1/2
Quiz, Flash Cards, Worksheet, Game & Study Guide Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Fractions/Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Less Than, Greater Than
Quiz, Flash Cards, Worksheet, Game & Study Guide Ordering Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Ordering Fractions

## WA.4.3.Core Content: Concept of area (Geometry/Measurement, Algebra) Students learn how to find the area of a rectangle as a basis for later work with areas of other geometric figures. They select appropriate units, tools, and strategies, including formulas, and use them to solve problems involving perimeter and area. Solving such problems helps students develop spatial skills, which are critical for dealing with a wide range of geometric concepts. The study of area is closely connected to Core Content on multiplication, and connections between these concepts should be emphasized whenever possible.

Core Content: Concept of area (Geometry/Measurement, Algebra) Students learn how to find the area of a rectangle as a basis for later work with areas of other geometric figures. They select appropriate units, tools, and strategies, including formulas, and use them to solve problems involving perimeter and area. Solving such problems helps students develop spatial skills, which are critical for dealing with a wide range of geometric concepts. The study of area is closely connected to Core Content on multiplication, and connections between these concepts should be emphasized whenever possible.
4.3.A. Determine congruence of two-dimensional figures.
Flip Charts Math Grade 5
Vocabulary Terms Congruent Shapes
Quiz, Flash Cards, Worksheet, Game & Study Guide Congruent Shapes
Quiz, Flash Cards, Worksheet, Game & Study Guide Congruent Shapes

4.3.B. Determine the approximate area of a figure using square units.
Flip Charts Math Grade 4
Quiz, Flash Cards, Worksheet, Game & Study Guide Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Area and Perimeter

4.3.C. Determine the perimeter and area of a rectangle using formulas, and explain why the formulas work.
Quiz, Flash Cards, Worksheet, Game & Study Guide Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Area and Perimeter

## WA.4.4.Additional Key Content (Geometry/Measurement, Algebra, Data/Statistics/Probability) Students use coordinate grids to connect numbers to basic ideas in algebra and geometry. This connection between algebra and geometry runs throughout advanced mathematics and allows students to use tools from one branch of mathematics to solve problems related to another branch. Students also extend and reinforce their work with whole numbers and fractions to describe sets of data and find simple probabilities. Students combine measurement work with their developing ideas about multiplication and division as they do basic measurement conversions. They begin to use algebraic notation while solving problems in preparation for formalizing algebraic thinking in later grades.

Additional Key Content (Geometry/Measurement, Algebra, Data/Statistics/Probability) Students use coordinate grids to connect numbers to basic ideas in algebra and geometry. This connection between algebra and geometry runs throughout advanced mathematics and allows students to use tools from one branch of mathematics to solve problems related to another branch. Students also extend and reinforce their work with whole numbers and fractions to describe sets of data and find simple probabilities. Students combine measurement work with their developing ideas about multiplication and division as they do basic measurement conversions. They begin to use algebraic notation while solving problems in preparation for formalizing algebraic thinking in later grades.
4.4.A. Represent an unknown quantity in simple expressions, equations, and inequalities using letters, boxes, and other symbols.
Flip Charts Math Grade 5
Vocabulary Terms Evaluate Open Sentences
Quiz, Flash Cards, Worksheet, Game & Study Guide Determine the One Operation Function
Quiz, Flash Cards, Worksheet, Game & Study Guide Evaluate Open Sentences
Quiz, Flash Cards, Worksheet, Game & Study Guide Multi-step Word Problems
Quiz, Flash Cards, Worksheet, Game & Study Guide Open Number Sentences
Quiz, Flash Cards, Worksheet, Game & Study Guide Word Problems

4.4.B. Solve single- and multi-step problems involving familiar unit conversions, including time, within either the U.S. customary or metric system.
Flip Charts Math Grade 4
Quiz, Flash Cards, Worksheet, Game & Study Guide Volume/Capacity

4.4.C. Estimate and determine elapsed time using a calendar, a digital clock, and an analog clock.
Flip Charts Math Grade 5
Vocabulary Terms Time
Quiz, Flash Cards, Worksheet, Game & Study Guide Time
Quiz, Flash Cards, Worksheet, Game & Study Guide Elapsed Time

4.4.D. Graph and identify points in the first quadrant of the coordinate plane using ordered pairs.
Vocabulary Terms Plot Points
Quiz, Flash Cards, Worksheet, Game & Study Guide Coordinates
Quiz, Flash Cards, Worksheet, Game & Study Guide Graphs and Tables
Quiz, Flash Cards, Worksheet, Game & Study Guide Plot Points

4.4.E. Determine the median, mode, and range of a set of data and describe what each measure indicates about the data.
Flip Charts Math Grade 5
Vocabulary Terms Data Analysis
Vocabulary Terms Data Analysis
Quiz, Flash Cards, Worksheet, Game & Study Guide Data Analysis
Quiz, Flash Cards, Worksheet, Game & Study Guide Data Analysis
Quiz, Flash Cards, Worksheet, Game & Study Guide Statistics

4.4.F. Describe and compare the likelihood of events.
Flip Charts Math Grade 5
Vocabulary Terms Probability
Quiz, Flash Cards, Worksheet, Game & Study Guide Probability
Quiz, Flash Cards, Worksheet, Game & Study Guide Probability
Quiz, Flash Cards, Worksheet, Game & Study Guide Probability

## WA.4.5.Core Processes: Reasoning, problem solving, and communication - Students in grade four solve problems that extend their understanding of core mathematical concepts - such as multiplication of multi-digit numbers, area, probability, and the relationships between fractions and decimals - as they make strategic decisions that bring them to reasonable solutions. Students use pictures, symbols, or mathematical language to explain the reasoning behind their decisions and solutions. They further develop their problem-solving skills by making generalizations about the processes used and applying these generalizations to similar problem situations. These critical reasoning, problem-solving, and communication skills represent the kind of mathematical thinking that equips students to use the mathematics they know to solve a growing range of useful and important problems and to make decisions based on quantitative information.

Core Processes: Reasoning, problem solving, and communication - Students in grade four solve problems that extend their understanding of core mathematical concepts - such as multiplication of multi-digit numbers, area, probability, and the relationships between fractions and decimals - as they make strategic decisions that bring them to reasonable solutions. Students use pictures, symbols, or mathematical language to explain the reasoning behind their decisions and solutions. They further develop their problem-solving skills by making generalizations about the processes used and applying these generalizations to similar problem situations. These critical reasoning, problem-solving, and communication skills represent the kind of mathematical thinking that equips students to use the mathematics they know to solve a growing range of useful and important problems and to make decisions based on quantitative information.
4.5.A. Determine the question(s) to be answered given a problem situation.
Flip Charts Math Grade 3

4.5.B. Identify information that is given in a problem and decide whether it is essential or extraneous to the solution of the problem.
Flip Charts Math Grade 3

4.5.C. Identify missing information that is needed to solve a problem.
Flip Charts Math Grade 3

4.5.D. Determine whether a problem to be solved is similar to previously solved problems, and identify possible strategies for solving the problem.
Flip Charts Math Grade 3

4.5.E. Select and use one or more appropriate strategies to solve a problem and explain why that strategy was chosen.
Flip Charts Math Grade 3

4.5.G. Explain why a specific problem-solving strategy or procedure was used to determine a solution.
Flip Charts Math Grade 3

4.5.H. Analyze and evaluate whether a solution is reasonable, is mathematically correct, and answers the question.
Flip Charts Math Grade 3

Science