Fourth Grade Operations and Algebraic Thinking

Essential Skills and Knowledge	Teacher Resources	Student Resources
4.OA.A.1
Student will interpret a multiplication equation as a comparison, e.q., Students will interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Students will represent verbal statements of multiplicative comparisons as multiplication equations.	What Does Multiplication Mean? Prezi modeling for students to show how to interpret a multiplication equation as a comparison. Interpret Equations A teaching tool to show students how to interpret different types of equations. MULTIPLICATION EQUATION In these LearnZillion video lessons, students will interpret a multiplication equation as a comparison, e.q., Interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplication comparisons as multiplication equations. *LOGIN TO LEARNZILLION'S FREE ACCOUNT BEFORE SELECTING LINK* Commutative Property Bar Models *Multiplication is a Comparison	Multiplication Statements Self checking activity (35 is five times as many as ?) Mixed Matching Equations Students will match pairs of equivalent equations to score points. Balloon Pop Mixed Operators Students will solve equations to pop balloons from the smallest to the largest value. Mixed Matching Students will solve to match pairs of equivalent equations. Cool Math Arithmetic Game Students will solve equations quickly by placing the correct numbers into a problem that has the operators, but the numbers missing; however the total on the other side is given. Space Racer Students will solve equations to move your spaceship to avoid asteroids. Khan Academy Students will be quizzed on their knowledge interpreting a multiplication equation as a comparison, e.q., Interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplication comparisons as multiplication equations.
4.OA.A.2	Teacher Resources	Student Resources
Students will multiply or divide to solve word problems involving multiplicative comparisons, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.	Equations A teaching tool to show students how to write, solve, and apply equations and inequalities. Solving Expressions A teaching tool to model how work backwards to solve problems. Expression Song: No Equal Sign An audio about expressions; teachers can print out lyrics. Problem Solving A teaching tool teaching tool to show students how to use pictures and equations to solve multiplication problems. Multiplication Word Problems A LearnZillion video to show students how to multiply or divide to solve word problems involving multiplicative comparisons by using drawings and equations with a symbol for the unknown number to represent the problem. Thinking Blocks-Word Problems A interactive tool to model how to solve word problems by modeling. Can use built in ones or type in your own. Write an Equation to Solve Problems A teaching tool to show students how to write equations to solve word problems using multiplication and division. *SOLVING WORD PROBLEMS* In these LearnZillion videos, students will learn different ways to compare numbers by determining how many more or how many times more using visual models. *LOGIN TO LEARNZILLION'S FREE ACCOUNT BEFORE SELECTING LINK* Represent the Unknown with Symbols or Letters Using Bar Models to Show Multiplication Using a Number Sentence Using Bar Models to Show Division *Using the Inverse Operation	Thinking Blocks - Solving Word Problems Students will solve word problems using thinking blocks to model. Click on the "Start" button, then the "Problems" button. Once a problem appears, click the green button in the top righthand corner and choose "Multiply/Divide" and "Compare A" or "Compare B". Number Expressions and Word Phrases Students will determine the operation needed to solve a word problem. Algernon's Algebra Explorer Students will explore two-step algebraic equations. This also includes and assessment activity. Algebraic Reasoning Students will find the value of a given object based on information from two scales Algebra Puzzles Students will find the value of each object in puzzle using what they know about the missing number in an equation. Mission: Algebra Challenge (Go to Algebra Challenge) Students will solve two-step algebra problems using their understanding of algebraic expressions. (15 multiple choice questions with built in answer checking.) Operator Arithmetic Game Students will use four operators to solve multi-step problems. Calculator Chaos Students will use four operators to solve multi-step problems using a calculator. Khan Academy Students will be quizzed on their knowledge multiplying or dividing to solve word problems involving multiplicative comparisons, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
4.OA.A.3	Teacher Resources	Student Resources
Students will solve multistep word problems posed with whole numbers and having whole-number answers using four operations, including problems in which remainders must be interpreted. Students will represent these problems using equations with a letter standing for the unknown quantity. Students will assess the reasonableness of answers using mental computation and estimation strategies using rounding.	Expressions A teaching tool to show students how to write and identify expressions. Working Backwards A teaching tool to show students how to solve problems by working backwards. Problem Solving A teaching tool to show students how to use pictures and equations to solve word problems. Problem Solving 2 A teaching tool to show students how to act out or use manipulatives as a strategy to solve word problems. Division as Sharing A teaching tool to show students how division is sharing equally.	Thinking Blocks - Solve Word Problems Students will solve word problems using thinking blocks to model. Click on the "Start" button, then the "Problems" button. Once a problem appears, click the green button in the top righthand corner and choose the type of problem you or your teacher would like you to solve. Math Playground - Multistep Word Problem Sets Students will solve multistep problems with the help of video tutorials. Word Problems Students will apply different strategies to solve word problems. Word Problem Database Students will pick and then solve problems using different problem solving strategies. Khan Academy Students will be quizzed on their knowledge to multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
4.OA.B.4	Teacher Resources	Student Resources
Students will find all factor pairs for a whole number in the range 1-100. Students will recognize that a whole number is a multiple of each of its factors. Students will determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Students will determine whether a given whole number in the range of 1-100 is prime or composite.	Patterns and Facts A teaching tool to show students how to use a patterns 2, 5, and 9 to find products. Name That Number (M Cubed Lessons) A teaching tool to show students how to sort, compare, contrast, and classify numbers according to their attributes. That's Odd (M Cubed Lessons) A teaching tool to show students how to construct a geometric understanding of the meaning of multiplication using an area of model. Factors and Composite Numbers In this example, groups of seats at Fenway Park model factors of 24. Note: Login to Discovery Streaming Education before selecting links. Prime and Composite Numbers A prime number is divisible only by itself and one. A composite number has more than two factors. Note: Login to Discovery Streaming Education before selecting links. Multiples of Whole Numbers Boxed baseball gear illustrates the idea of multiples. Note: Login to Discovery Streaming Education before selecting links. Multiples, Factors, Primes, and Composites A Math-Live video covers multiples, factors, prime, and composite numbers. (Includes activity sheets and assessments.) FACTOR PAIRS In these LearnZillion videos, students will learn all factor pairs for a whole number in the range 1-100 and will recognize that a whole number is a multiple of each of its factors. *LOGIN TO LEARNZILLION'S FREE ACCOUNT BEFORE SELECTING LINK* Find all the Factor Pairs of the Number using Area Models Determine Multiples of a Number using Area Models Find Factors of a Pair using a Rainbow Number Line Determine Factors of a Pair using Number Bonds Use Divisibility Rules for Multiples 2, 5, or 10 Find all Factor Pairs of a Number Using a T-Chart Determine if a Number is Prime or Composite Use Divisibility Rules for Multiples of 4 and 7 Determine Multiples of a Number using Number Bonds Find Multiples by Using a Number Line	Factors Game Students will find the factors different numbers. Crazy Taxi Multiples Students will play an Interactive game where they "crash" into cars that are multiples of a given number. Catch the Stars Students will play an interactive game to catch the stars for multiples of the number the student picks. Math Lines: X Factor Students will find the factors for different numbers by shooting the ball the factor that pairs to the selected multiple. Khan Academy Students will be quizzed on their knowledge to find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range of 1-100 is prime or composite. Bike Racing Math Factors Race your motorcycle to the finish line. Race against some tough competitors and try and beat them all by determining factors of numbers. Factor Bones Help the puppies get the right factor bone that they need by changing the arrows to alter the paths. Factor Dogs The Factor Dogs have joined the circus and have a disappearing act. Help them with their act by using your factoring skills to get them to the right platform. Three skill levels to choose from. Math Balloons The factors version of Math Balloons. Remove balloons to make groups of same colored balloons by determining if numbers are factors or not. Make matches over all of the colored squares to complete a level. Math Balloons Prime The prime numbers version of Math Balloons. Remove balloons to make groups of same colored balloons by determining if a balloon's statement about prime numbers is true or false. Make matches over all of the colored squares to complete a level. Math Gate Slide the math gate back and forth to allow the correct number balls to cross while preventing the wrong ones from crossing. Choose to practice one of four skills: counting, multiples, even/odd numbers or number comparison. Math Helicopter Prime Numbers See how long you can survive flying the helicopter. Fly only through prime numbers as the composite numbers are rock solid. Fun and easy to play but hard to survive for long. Math Puppies Prime and Composite Numbers Prime Pup only eats Prime Bones and Composite only eats Composite Bones. Fill them up with the right bones to complete the levels.
4.OA.C.5	Teacher Resources	Student Resources
Students will generate a number or shape pattern that follows a given rule. Students will identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Students will explain informally why the numbers will continue to alternate in this way.	Function Tables A teaching tool for students to identify the expression and solve for the unknown number. Numeric Patterns A teaching tool for students to analyze and generate a rule for a growing numeric pattern. Patterns: Find a Rule A teaching tool that models how to use an input and output table using an addition rule and an equation. Note: Login to Discovery Streaming Education before selecting links. Finding and Writing a Rule A teaching tool that models how to find and write a rule as an equation. Note: Login to Discovery Streaming Education before selecting links. The following are videos from Discovery that incorporates the standard 4.OA.C.5. Extending a Pattern: Terms One, Two, and Three Extending a Pattern: Terms Four, Five, and Six Mental Math: Multiplication Patterns Find a Pattern in Numbers Mental Math: Division Patterns Grade 4: Multiplication Patterns Patterns: Find a Rule Note: Login to Discovery Streaming Education before selecting links.* NUMBER OR SHAPE PATTERNS In these LearnZillion videos, students will generate a number or shape pattern that follows a given rule. *LOGIN TO LEARNZILLION'S FREE ACCOUNT BEFORE SELECTING LINK* Find a Rules using a Vertical Table Understand Repeating Patterns Find Missing Elements in Growing Patterns Find the Pattern Using a Table Determine the Rules in a Decreasing Pattern Using a Table to Find the Rule to a Geometric Pattern Extend a Fraction Pattern using a Number Line Generate a Pattern Sequence using a T-Chart *Find the Missing Inputs of a Function Table	Find Missing Numbers in a Pattern Students will analyze and generate a rule for a numeric pattern using an Excel spreadsheet. Function Machine Students will generate a rule for a numeric pattern using an Interactive function table. Stop that Creature! Students will generate a rule for a numeric pattern using an interactive game to stop an alien creature. Number Patterns Students solve a number pattern to be able to crack the safe code. Number Patterns Students solve number pattern know-how to crack the Mission 2110 codes. UEN: Pattern Games Students may choose from different games to show their understanding of how numbers and shapes following given rules to form a pattern. Pictorial Patterns Students will determine what shape goes next to continue a pattern by playing an interactive game. Bridge Patterns Help MathPup get safely across the bridge by filling in the missing piece of the pattern on the bridge. Sequenz Figure out the rule for the given number patterns. Quickly find the missing number in each pattern before time is up!
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Teacher Notes

Operations and Algebraic Thinking Activities	Website/Activity	Content Standards/Technology Standards
What Does Multiplication Mean? Prezi modeling for students to show how to interpret a multiplication equation as a comparison. Interpret Equations A teaching tool to show students how to interpret different types of equations. Multiplication Statements Self checking activity (35 is five times as many as ?)		Common Core: 4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
		Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration.
Equations A teaching tool to show students how to write, solve, and apply equations and inqualities. Solving Expressions A teaching tool to model how work backwards to solve problems. Expression Song: No Equal Sign An audio about expressions; teacher can print out lyrics Problem Solving A teaching tool to show students how to use pictures and equations to solve multiplication problems. Multiplication Word Problems A LearnZillion video to show students how to multiply or divide to solve word problems involving multiplicative comparisons by using drawings and equations with a symbol for the unknown number to represent the problem. Thinking Blocks-Word Problems A interactive tool to model how to solve word problems by modeling. Can use built in ones or type in your own. Number Expressions and Word Phrases Students will determine the operation needed to solve a word problem. Alginon's Algebra Explorer Students will explore two-step algebraic equations. This also includes and assessment activitiy. Algebraic Reasoning Students will find the value of a given object based on information from two scales Algebra Puzzles Students will find the value of each object in puzzle using what they know about the missing number in an equation. Mission: Algebra Challenge (Go to Algebra Challenge) Students will solve two-step algebra problems using their understanding of algebraic expressions. (15 multiple choice questions with built in answer checking.)		Common Core: 4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
		Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration.
Expressions A teaching tool to show students how to write and identify expressions. Working Backwards A teaching tool to show students how to solve problems by working backwards. Problem Solving A teaching tool to show students how to use pictures and equations to solve word problems. Problem Solving 2 A teaching tool to show students how to act out or use manipulatives as a strategy to solve word problems. Word Problems Students will apply different strategies to solve word problems. Word Problem Database Students will pick and then solve problems using different problem solving strategies.		Common Core: 4.OA.3- Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
		Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration.
Patterns and Facts A teaching tool to show students how to use a patterns 2, 5, and 9 to find products. Name That Number (M Cubed Lessons) A teaching tool to show students how to sort, compare, contrast, and classify numbers according to their attributes. That's Odd (M Cubed Lessons) A teaching tool to show students how to construct a geometric understanding of the meaning of multiplicatiion using an area of model. Factors and Composite Numbers *Please note that the videos must be downloaded prior to viewing as per AACPS guidelines.* Prime and Composite Numbers Please note that the videos must be downloaded prior to viewing as per AACPS guidelines. Multiples of Whole Numbers *Please note that the video must be downloaded prior to viewing as per AACPS guidelines.* Multiples, Factors, Primes, and Composites A Math-Live video covers multiples, factors, prime, and composite numbers. (Includes activity sheets and assessments.) Factors Game Students will find the factors different numbers. Multiples After reading about the Least Common Multiple, students will solve 5 interactive practice problems to find the least common multiple. Crazy Taxi Multiples Students will play an Interactive game where they "crash" into cars that are multiples of a given number.		Common Core: 4.OA.4 Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1- 100 is a multiple of a given one-digit number. Determine whether a given whole number in the range of 1-100 is prime or composite.
		Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration.
Function Tables A teaching tool for students to identify the expression and solve for the unknown number. Numeric Patterns A teaching tool for students to analyze and generate a rule for a growing numeric pattern. Patterns: Find a Rule Please note that the video must be downloaded prior to viewing as per AACPS guidelines. A teaching tool that models how to use an input and output table using an addition rule and an equation. Finding and Writing a Rule Please note that the video must be downloaded prior to viewing as per AACPS guidelines. A teaching tool that models how to find and write a rule as an equation. Find Missing Numbers in a Pattern Students will analyze and generate a rule for a numeric pattern using an Excel spreadsheet. Function Machine Students will generate a rule for a numeric pattern using an Interactive function table. Stop that Creature! Students will generate a rule for a numeric pattern using an interactive game to stop an alien creature. Number Patterns Students solve a number pattern to be able to crack the safe code. UEN: Pattern Games Students may choose from different games to show their understanding of how numbers and shapes following given rules to form a pattern.		Common Core: 4.OA.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.
		Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration.
		Common Core:
		Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration.
		Common Core:
		Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration.
		Common Core:
		Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration.
		Common Core:
		Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration.
		Common Core:
		Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration.
		Common Core:
		Technology Standard:3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration.
		Common Core:
		Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration.
		Common Core:
		Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration.
		Common Core:
		Technology Standard: 3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration.
		Common Core:
		Technology Standard:3.0-Technology for Learning and Collaboration: Students will use a variety of technologies for learning and collaboration.

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