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Expressions and Equations The Relationships of the Operations Common Core: Engage New York 6.EE.1, 6.EE.2, 6.EE.3 and 6.EE.4
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Lesson 4: The Relationship of Division & Subtraction Focus Standard: 6.EE.A.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2+) to produce the equivalent expression 6+3; apply the distributive property to the expression 24+18 to produce the equivalent expression 6(4+3); apply properties of operations to ++ to produce the equivalent expression 3.
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What does 6.EE.A.1 cover? Write and evaluate numeric expressions involving whole-number exponents.
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What does 6.EE.A.2 cover? Write, read, and evaluate expressions in which letters stand for numbers a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract from 5” as 5−. 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. 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 =3 and =62 to find the volume and surface area of a cube with sides of length =1/2.
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What does 6.EE.A.3 cover? Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2+) to produce the equivalent expression 6+3; apply the distributive property to the expression 24+18 to produce the equivalent expression 6(4+3); apply properties of operations to ++ to produce the equivalent expression 3.
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What does 6.EE.A.4 cover? 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 ++ and 3 are equivalent because they name the same number regardless of which number stands for.
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Table of Contents DateTitlePage 2/6/14NEW Focus 8- Algebraic Expression Scale and ChartFresh Left 2/6/14F8 Engage NY Lesson 1 – Add and subtract Relationship Fresh Left 2/7/14F8 Engage NY Lesson 2 – Multiplication and Division Relationship Fresh Left 2/10/14F8 Engage NY Lesson 3- Multiplication and Addition Relationship Fresh Left 2/11/14 F8 Engage NY Lesson 4- Division and Subtraction Relationship Fresh Left
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Focus 8 Algebraic Expression Learning Goal I am able to work with numerical expressions and use letters to represent unknowns in problem solving situations, investigate and apply properties of operation in numerical contexts, such as the associative, distributive, and commutative properties. I can build on my understanding of inverse operations to solve algebraic expressions.
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Today, my learning target is to… Build and clarify the relationship of division and subtraction by determining that 12÷=4 means 12−−−−=0
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MY PROGRESS CHART Before we start the Learning Target Lesson, think about the Learning Target for today…. How much prior knowledge do you have regarding that goal? Chart your prior knowledge using your pre-target score icon.
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Lesson Preparation NEEDED! Lesson Notes Students will continue to use the squares from Lessons 1 and 3 to create tape diagrams. Each pair of students will need 30 squares to complete the activities.
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Actual Size- print and cut 2 sets per pair of students
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Activity & Discussion
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Activity & Discussion- Discuss the process step by step to determine that the number of times the divisor was subtracted from the dividend is the same number as the quotient.
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Proving the Relationship- Model the following set of tape diagrams with leading questions for discussion.
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Student Practice- Record your answer in your math workbook.
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Answers
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Student Practice- Record your answers in your math workbook.
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Answers
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Student Practice- Record your answers in your math workbook.
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Answers
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Student Problem Set- Record your answer in your math workbook
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Student Problem Set Answers
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Closing (4 min) Display the graphic organizer provided at the end of the lesson. Copies of the organizer can be made for students to follow along and record. In each of the circles, we can place an operation to satisfy the organizer. In the last four lessons, we have discovered that each operation has a relationship with other operations, whether they are inverse operations or they are repeats of another. Place the addition symbol in the upper left hand circle. Let’s start with addition. What is the inverse operation of addition? Subtraction.
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Closing (4 min) Place the subtraction symbol in the upper right hand circle. After our discussion today, repeated subtraction can be represented by which operation? Division. Place the division symbol in the lower right hand circle. Which operation is the inverse of division? Multiplication. Place the multiplication symbol in the lower left hand circle. Let’s see if this is correct. Is multiplication the repeat operation of addition? Yes. Understanding the relationships of operations is going to be instrumental when solving equations later in this unit.
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Student Exit Ticket for Lesson 4 The Relationship of Division & Subtraction
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Exit Ticket - Lesson 4 Solutions
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Today, I achieved my learning target by… Building and clarifying the relationship of division and subtraction by determining that 12÷=4 means 12−−−−=0
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MY PROGRESS CHART Before we start the Learning Target Lesson, think about the Learning Target for today…. How much prior knowledge do you have regarding that goal? Chart your prior knowledge using your pre-target score icon.
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The End of Lesson 4 The Relationship of Division & Subtraction
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