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Grade 6 UNIT 4: Expressions and Equations Suggested Number of Days for Entire UNIT: 45

|Essential Question |Key Concepts |Cross Curricular Connections |

|How is solving an equation or inequality a process of |Relationships of Operations |Art: Students will create their own color by mixing primary colors. |

|answering a question? |Special Notations of Operations |Students will record how much of each color was used in the mixture. Once |

| |Replacing Letters and Numbers |the color is created, figure out how much of each individual color is |

|Unit Vocabulary |Expanding, Factoring, and Distributing Expressions |needed to mix a half-gallon. Extend: Create stained glass with geometric |

|Simple |Expressing Operations in Algebraic Form |patterns. Have students share color creations and color code the patterns |

|Linear Expression |Writing and Evaluating Expressions and Formulas |on their stained glass. |

|Equivalent |Solving Equations | |

|Equation |Applications of Equations |Religion: Create a timeline of events of the Bible showing order and time |

|Truth Values of a Number Sentence | |differences. Set up inequalities based on less or greater than zero, with |

|Exponential Notation for Whole Number Exponents Sum | |zero representing the birth of Christ. Create problems and use an |

|Familiar Terms & Symbols |*Assessments |algebraic equation to solve. |

|Product |Mid-Module Assessment: After Section E | |

|Factor |(5 days -1 day for assessment, 1 day for assessment return, & 3 days for |Science: In the study of formulas (e.g., velocity, Fahrenheit, Celsius, |

|Quotient |remediation) |volume, area, scientific notion), provide problems for students to solve. |

|Expand |End-of-Module Assessment: after Section H (6 days- 1, day for assessment,|For example, if you were to create your own remote control vehicle, given |

|Term |1 day for assessment return, & 4 days for remediation). |the speed of the vehicle, 10 mph, determine the time it would take to |

|Distribute | |travel 400 feet. Use the formula Speed (V) = Total Distance Traveled |

|Variable or Unknown Number | |(D)/Total Time Taken (T). Have students create their own equations and use|

|Number Sentence | |algebraic expression to solve. |

|True or False Number Sentence | | |

|Properties of operations (distributive, commutative, | |Social Studies: Students will research the finances necessary for their |

|associative) | |school to operate. The school’s budget has a deficit of “x.” The school |

| | |requires “y” to run. What is the least amount of money needed to meet the |

| | |school’s budget plan? Write an inequality for the situation and solve. |

|Unit Outcome (Focus) |

|Students understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given situations, evaluate expressions, and use expressions and formulas to |

|solve problems. Students understand that expressions in different forms can be equivalent, and they use the properties of operations to rewrite expressions in equivalent forms. Students know that the |

|solutions of an equation are the values of the variables that make the equation true. Students use properties of operations and the idea of maintaining the equality of both sides of an equation to solve |

|simple one-step equations. |

UNIT 4 SECTION A: Relationships of the Operations Suggested Number of Days for SECTION: 4

|Essential Question |Key Concept |Standards for Mathematical Practice |

| | |1. Make sense of problems and persevere in solving them |

|How is solving an equation or inequality a |The Relationship of Addition and Subtraction |2. Reason abstractly and quantitatively |

|process of answering a question? |The Relationship of Multiplication and Division |3. Construct viable arguments and critique the reasoning of others |

| |The Relationship of Multiplication and Addition |6. Attend to precision |

| |The Relationship of Division and Subtraction |7. Look for and make use of structure |

| |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard | |

| | |( Standard ends at this grade ( Fluency Standard | |

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| | |Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 | |

| |6.EE.3 |(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the |( |

| |(DOK 1) |equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. | |

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|Comments | | | |

|Students understand the relationships of | | | |

|operations and use them to generate equivalent | | | |

|expressions (6.EE.A.3). The topic opens with | | | |

|the opportunity to clarify relationships and | | | |

|provide students with the knowledge to build and| | | |

|evaluate identities that are important for | | | |

|solving equations. In this section, students | | | |

|discover and work with the following identities:| | | |

|[pic], [pic], [pic], [pic] (when [pic]), and | | | |

|[pic]. Students will also discover that if | | | |

|[pic], then [pic]. | | | |

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UNIT 4 SECTION B: Special Notations of Operations Suggested Number of Days for SECTION: 2

|Essential Question |Key Concept |Standards for Mathematical Practice |

| | |1. Make sense of problems and persevere in solving them |

|How is solving an equation or inequality a |Exponents |2. Reason abstractly and quantitatively |

|process of answering a question? |The Order of Operations |3. Construct viable arguments and critique the reasoning of others |

| | |6. Attend to precision |

| | |7. Look for and make use of structure |

|Comments |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard | |

| | |( Standard ends at this grade ( Fluency Standard | |

|Teachers should use caution when introducing |6.EE.1 |Write and evaluate numeric expressions involving whole-number exponents. |( |

|mnemonic devices for remembering Order of |(DOK 2) | | |

|Operation (6.EE.2).Students focus on the device,| | | |

|rather than on the underlying mathematical |6.EE.2 |Write, read, and evaluate expressions in which letters stand for numbers. |( |

|meaning of an expression. This can lead to |(DOK 2) |c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems.| |

|serious misconceptions in future study. | |Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses| |

|In this section, students experience special | |to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface | |

|notations of operations. They determine that | |area of a cube with sides of length s = 1/2. | |

|[pic] is not the same as [pic], which is [pic]. | |. | |

|Applying their prior knowledge from Grade 5, | | | |

|where whole number exponents were used to | | | |

|express powers of ten (5.NBT.A.2), students | | | |

|examine exponents and carry out the order of | | | |

|operations, including exponents. Students | | | |

|demonstrate the meaning of exponents to write | | | |

|and evaluate numerical expressions with whole | | | |

|number exponents (6.EE.A.1). | | | |

UNIT 4 SECTION C: Replacing Letters and Numbers Suggested Number of Days for SECTION: 2

|Essential Question |Key Concept |Standards for Mathematical Practice |

| | |1. Make sense of problems and persevere in solving them |

|How is solving an equation or inequality a |Replacing Letters with Numbers |2. Reason abstractly and quantitatively |

|process of answering a question? |Replacing Numbers with Letters |3. Construct viable arguments and critique the reasoning of others |

| | |6. Attend to precision |

| | |7. Look for and make use of structure |

|Comments |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard | |

| | |( Standard ends at this grade ( Fluency Standard | |

|Students represent letters with numbers and | | |( |

|numbers with letters in Section C. Now, they |6.EE.2 |Write, read, and evaluate expressions in which letters stand for numbers. | |

|use letters to represent numbers in order to |(DOK 2) |c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems.| |

|write the properties precisely. Students | |Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses| |

|realize that nothing has changed because the | |to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface | |

|properties still remain statements about | |area of a cube with sides of length s = 1/2. | |

|numbers. They are not properties of letters, | | | |

|nor are they new rules introduced for the first | | | |

|time. Now, students can extend arithmetic | |Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is | |

|properties from manipulating numbers to | |substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of | |

|manipulating expressions. Students understand |6.EE.4 |which number y stands for. |( |

|that a letter in an expression represents a |(DOK 1) | | |

|number. When that number replaces that letter, | | | |

|the expression can be evaluated to one number. | | | |

|Similarly, they understand that a letter in an | | | |

|expression can represent a number. When that | | | |

|number is replaced by a letter, an expression is| | | |

|stated (6.EE.A.2).. | | | |

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UNIT 4 SECTION D: Expanding, Factoring and Distributing Expressions Suggested Number of Days for SECTION: 6

|Essential Question |Key Concept |Standards for Mathematical Practice |

| | |1. Make sense of problems and persevere in solving them |

|How is solving an equation or inequality a |Writing Addition and Subtraction Expression |2. Reason abstractly and quantitatively |

|process of answering a question? |Writing and Expanding Multiplication Expressions |3. Construct viable arguments and critique the reasoning of others |

| |Factoring Expressions |6. Attend to precision |

| |Distributing Expressions |7. Look for and make use of structure |

| |Writing Division Expressions Lessons 13–14: Writing Division Expressions | |

|Comments |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard | |

| | |( Standard ends at this grade ( Fluency Standard | |

|In Section D, students become comfortable with | | | |

|new notations of multiplication and division and|6.EE.2 |Write, read, and evaluate expressions in which letters stand for numbers. |( |

|recognize their equivalence to the familiar |(DOK 2) |a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation | |

|notation of the prior grades | |“Subtract y from 5” as 5 – y. | |

| | |b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts | |

| | |of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a | |

| | |single entity and a sum of two terms | |

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| | |Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 | |

| | |(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the | |

| |6.EE.3 |equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. | |

| |(DOK 1) | | |

| | | |( |

| | |Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is | |

| | |substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of | |

| | |which number y stands for. | |

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| |6.EE.4 | | |

| |(DOK 1) | |( |

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UNIT 4 SECTION E: Expressing Operations in Algebraic Form Suggested Number of Days for SECTION: 2

|Essential Question |Key Concept |Standards for Mathematical Practice |

| | |1. Make sense of problems and persevere in solving them |

|How is solving an equation or inequality a |Read Expressions in Which Letters Stand for Numbers |2. Reason abstractly and quantitatively |

|process of answering a question? |Write Expressions in Which Letters Stand for Numbers Lessons 13–14: Writing Division |3. Construct viable arguments and critique the reasoning of others |

| |Expressions |6. Attend to precision |

| | |7. Look for and make use of structure |

|Comments |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard | |

| | |( Standard ends at this grade ( Fluency Standard | |

|In Section E, students express operations in | | |( |

|algebraic form. They read and write expressions|6.EE.2 |Write, read, and evaluate expressions in which letters stand for numbers. | |

|in which letters stand for and represent numbers|(DOK 2) |b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts | |

|(6.EE.A.2). They also learn to use the correct | |of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a | |

|terminology for operation symbols when reading | |single entity and a sum of two terms. | |

|expressions. Students write algebraic | | | |

|expressions that record operations with numbers | | | |

|and letters that stand for numbers. Students | | | |

|determine that [pic] can represent the story | | | |

|“Martina tripled her money and added it to her | | | |

|sister’s money” (6.EE.A.2b). | | | |

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UNIT 4 SECTION F: Writing and Evaluating Expressions and Formulas Suggested Number of Days for SECTION: 5

|Essential Question |Key Concept |Standards for Mathematical Practice |

| | |1. Make sense of problems and persevere in solving them |

|How is solving an equation or inequality a |Writing and Evaluating Expressions—Addition and Subtraction |2. Reason abstractly and quantitatively |

|process of answering a question? |Substituting to Evaluate Addition and Subtraction Expressions |3. Construct viable arguments and critique the reasoning of others |

| |Writing and Evaluating Expressions—Multiplication and Division |6. Attend to precision |

| |Writing and Evaluating Expressions—Multiplication and Addition |7. Look for and make use of structure |

| |Writing and Evaluating Expressions—Exponents | |

|Comments |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard | |

| | |( Standard ends at this grade ( Fluency Standard | |

|Students write and evaluate expressions and | | |( |

|formulas. They use variables to write |6.EE.2 |Write, read, and evaluate expressions in which letters stand for numbers. | |

|expressions and evaluate those expressions when |(DOK 2) |a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation | |

|given the value of the variable (6.EE.A.2). | |“Subtract y from 5” as 5 – y. | |

|Students create formulas by setting expressions | |b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts | |

|equal to another variable. | |of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a | |

| | |single entity and a sum of two terms | |

| | |c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems.| |

| | |Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses| |

| | |to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface | |

| | |area of a cube with sides of length s = 1/2. | |

| | | | |

| | |Understand solving an equation or inequality as a process of answering a question; which values from a specified set, if any, make the | |

| | |equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality | |

| | |true. | |

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| |6.EE.5 | |( |

| |(DOK 2) | | |

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UNIT 4 SECTION G: Solving Equations Suggested Number of Days for SECTION: 7

|Essential Question |Key Concept |Standards for Mathematical Practice |

| | |1. Make sense of problems and persevere in solving them |

|How is solving an equation or inequality a |True and False Number Sentences |2. Reason abstractly and quantitatively |

|process of answering a question? |Finding Solutions to Make Equations True |3. Construct viable arguments and critique the reasoning of others |

| |One-Step Equations- Addition and Subtraction |6. Attend to precision |

| |One-Step Equations – Multiplication and Division |7. Look for and make use of structure |

| |Two-Step Problems – All Operations | |

| |Multi-Step Problems – All Operations | |

|Comments |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard | |

| | |( Standard ends at this grade ( Fluency Standard | |

|Students use identities and properties of | | | |

|equality that were introduced earlier in the |6.EE.5 |Understand solving an equation or inequality as a process of answering a question; which values from a specified set, if any, make the |( |

|unit to solve one-step, two-step, and multistep |(DOK 2 |equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality | |

|equations. Students solve problems finding the | |true. | |

|measurements of missing angles represented by | | | |

|letters (4.MD.C.7) using what they learned in | |Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable | |

|Grade 4 about the four operations and what they |6.EE.6 |can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | |

|now know about equations. |(DOK 2) | |( |

| | |Solve real-world and mathematical problems by writing and solving equations in the form [pic] and [pic] for cases in which [pic], [pic] | |

| | |and [pic] are all nonnegative rational numbers. | |

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| |6.EE.7 | | |

| |(DOK 1) | |( |

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UNIT 4 SECTION H: Applications of Equations Suggested Number of Days for SECTION: 5

|Essential Question |Key Concept |Standards for Mathematical Practice |

| | |1. Make sense of problems and persevere in solving them |

|How is solving an equation or inequality a |One-Step Problems in the Real World |2. Reason abstractly and quantitatively |

|process of answering a question? |Problems in Mathematical Terms |3. Construct viable arguments and critique the reasoning of others |

| |Multi-Step Problems in the Real World |6. Attend to precision |

| |From Equations to Inequalities |7. Look for and make use of structure |

| |Writing and Graphing Inequalities in Real-World Problems | |

|Comments |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard | |

| | |( Standard ends at this grade ( Fluency Standard | |

|In Section H, students use their prior knowledge|6.EE.5 |Understand solving an equation or inequality as a process of answering a question; which values from a specified set, if any, make the | |

|from unit 1 to contruct tables of independent |(DOK 2) |equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality |( |

|and dependent values in order to analyze | |true. | |

|equations with two variables from real-life | | | |

|contexts. They represent equations by plotting | |Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable | |

|the values from the table on a coordinate grid |6.EE.6 |can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | |

|(5.G.A.1, 5.G.A.2, 6.RP.A.3a, 6.RP.A.3b, |(DOK 2) | |( |

|6.EE.C.9). The unit concludes with students | |Solve real-world and mathematical problems by writing and solving equations in the form [pic] and [pic] for cases in which [pic], [pic] | |

|referring to true and false number sentences in | |and [pic] are all nonnegative rational numbers. | |

|order to move from solving equations to writing | | | |

|inequalities that represent a constraint or |6.EE.7 |Write an inequality of the form x > c or x  c or x < c have infinitely many solutions; represent solutions of such inequalities on number line |( |

|(6.EE.B.5, 6.EE.B.8). Students understand that | |diagrams. | |

|inequalities have infinitely many solutions and | | | |

|represent those solutions on number line |6.EE.8 |Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to | |

|diagrams. |(DOK 2) |express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. |( |

| | |Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For | |

| | |example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d | |

| | |= 65t to represent the relationship between distance and time. | |

| |6.EE.9 | | |

| |(DOK 2) | |( |

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|Possible Activities |

|WORDS TO EXPRESSIONS GAME: Give three word forms of an expression verbally or on the board. Students write down and solve the expression using terms. Students with the correct answers receive points. The |

|student with the highest points after a certain time period wins the game. Ex: Three more than the product of seven and ten. (Answer: 7(10)+3; 73) Algebraic Expression Millionaire can also be played online |

|(similar to Who Wants to be a Millionaire?). Go to math-. Select Elementary Games on the left side. Select 5th Grade. Scroll down to find Algebraic Expressions Millionaire Game |

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|GUESS THE NUMBER: (whole class or in small groups) Have student guess the mystery number given clues, Ex: Guess the number that when you add 1 and then add -8 the sum is -16. (Answer -9). Students can play |

|online Students can play Guess the Number at . Click on Math Arcade and select Number Games, then Find Your Game then All Number Games. Scroll down to find Guess the Number Plus. |

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|ORDER OF OPERATIONS MILLIONAIRE (similar to Who Wants to be a Millionaire?): Great online game for one or two players. It can also be used as a whole class game with the class divided into teams. Find the |

|link at math- Select Middle School Games on the left side. Select 6th |

|Grade Math Games. Scroll down to Order of Operations Game. |

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|EVERYTHING BALANCES OUT IN THE END: In this unit of three lessons, from Illuminations, students use a pan balance to study equality, order of operations, numerical and variable expressions and other key |

|algebraic concepts. They use a pan balance applet to explore these concepts in varying complexity. |

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|Resources |

|ARMSTRONG ITERATION SPREADSHEET: This reproducible spreadsheet, from an Illuminations lesson, parses its numbers into digits and shows the sums of the cubes of the digits. |

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|SPEED OF ASCENT: In this video segment from Cyberchase , Hacker and the CyberSquad race to reach the Good Vibration on staircases that grow at different rates and have steps of varying sizes. |

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|WRITE NUMERICAL EXPRESSIONS INVOLVING WHOLE-NUMBER EXPONENTS |

|In this lesson you will learn how to write a numerical expression by using whole-number exponents: |

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|Engage NY Grade 6 Module 4 Link: |

|Possible Activities |

|TARGET: Draw a bull’s eye with a target number in the center and five various numbers around the outer circles. Students are challenged to try to use all the numbers in the outer rings to get the target |

|number. If they use all the numbers – they get a bull’s eye and receive 10 points. If the students use only four numbers they get 4 points, three numbers 3 points, etc. They may use any operation and |

|parentheses, and can keep track of their points over the course of multiple days. |

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|ONE, TWO, THREE, FOUR….. Use any combination of the symbols: +, -, x, ÷ and () to make the following sentences true 1 __ 2___ 3 ___ 4 = 0 and |

|1 __ 2 ___ 3 ___ 4 = 1 Extend: Challenge students to also get the sums 2, 4, 5, 6, 10, 13, 14, 20, 21, 24. |

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|I HAVE, WHO HAS? An activity for the entire class to practice solving equations. The students are each given a card or two. Each card contains a number on the top and an equation to solve on the bottom. The|

|answer to the equation leads to the next card; if cards are created they need to be completed all at once. This is a great game to reinforce mental math in solving one step equations or inequalities. Game |

|cards can also be downloaded online (see right). Ex: “I have ____, who has 27 –x = 39? The student with -12 on their card responds: I have -12, who has ….?” The student with that answer reads his or her |

|question and the game continues until all cards are called. |

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|REAL LIFE EXPRESSIONS/EQUATIONS: Pass out an equation or expression to each pair of students. Challenge them to create a real life situation that the equation could represent. Ask them to write the |

|situation in their math journal and solve the equation, and then have them present and defend their |

|answers to the class. |

|REAL LIFE INEQUALITIES: Pass out inequalities to each pair of students. Challenge them to create a real life situation that the inequality could represent. Ask them to write the situation in their math |

|journal and solve the inequality modeling the solution on a number line. Have students present and defend their answers to the class. |

|MIX AND MATCH: Practice simplifying expressions/creating equivalent expressions: Create index cards with algebraic expressions/equations on them and another set of index cards with the simplified versions |

|of the expressions. Have students match the expression with its simplified form. This same activity can be used for solving one step equations or inequalities. Extend: Students can lay cards face down and |

|play the game. Additional practices simplifying and solving algebraic expressions and equations can be found online: math-. Click on Algebra at top then click any of the worksheets. |

|Resources |

|FROM PATTERNS OF INPUT AND OUTPUT TO ALGEBRAIC EQUATIONS: Students explore the relationship between input and output values and learn to use algebraic expressions and equations. |

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|APPS: |

|DRAGON BOX – THE REVOLUTIONARY ALGEBRA APP. Instead of starting with solving equations and problems, the game first teaches the user how to discriminate between two characters and to separate them. It |

|affords the opportunity to practice the same steps that are involved in Algebra. |

|ELEVATED MATH breaks down Algebra into small, easy to understand parts. It pauses frequently to allow students to write notes and complete problems on a provided whiteboard feature. |

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|Possible Activities |

|REAL LIFE INEQUALITIES: Pass out inequalities to each pair of students. Challenge them to create a real life situation that the inequality could represent. Ask them to write the situation in their math |

|journal and solve the inequality modeling the solution on a number line. Have students present and defend their answers to the class. |

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|MIX AND MATCH: Practice simplifying expressions/creating equivalent expressions: Create index cards with algebraic expressions/equations on them and another set of index cards with the simplified versions |

|of the expressions. Have students match the expression with its simplified form. This same activity can be used for solving one step equations or inequalities. Extend: Students can lay cards face down and |

|play the game. Additional practice simplifying and solving algebraic expressions and equations can be found online: math-. Click on Algebra at top then click any of the worksheets. |

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|BOUNCING TENNIS BALLS: In this lesson, from Illuminations, students develop their skills in collecting and recording data using the real-world situation of a bouncing tennis ball. They use the data |

|collected to formulate the relationship between the dependent and independent variable in their experiment. |

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|LINKING NUMBER PATTERNS AND ALGEBRAIC EQUATIONS: Students practice using algebraic expressions by recording data from a video segment in which two staircases ascend at different rates. They record the |

|patterns in two-column tables, draw line graphs and write simple algebraic relations. |

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|SQUARE PROOF ACTIVITY: Have students choose any number. This is going will be their particular number for the proof. Have them square their number. Subtract the starting number. Ask: Is the number you're |

|left with odd or even? Have students create a model or a picture of their calculation, using the chosen number, and examine the model carefully. Ask: Can you use this one model to prove that your result is |

|always true and not just true for the particular number that you chose to start with? Similar activities are available online: more riddles at nrich. . Select For Students in the menu at right|

|and click on Secondary Activities. |

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|Resources |

|CHOCOLATE BAR SALES: In this task students use different representations to analyze the relationship between two quantities and to solve a real world problem. The situation presented provides a good |

|opportunity to make connections between the information provided by tables, graphs and equations: |

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|IDENTIFY VARIABLES AND THEIR RELATIONSHIP IN A REAL-WORLD SITUATION : In this lesson you will learn to identify the variables and their relationship given a real-world scenario |

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|Engage NY Grade 6 Module 4 Link: |

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