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

Lesson 1: The Relationship of Addition and 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 to produce the equivalent expression 6(4+3); apply properties of operations to ++ to produce the equivalent expression 3.

What does 6.EE.A.1 cover? Write and evaluate numeric expressions involving whole-number exponents.

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.

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

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.

Table of Contents DateTitlePage 2/6/14NEW Focus 7- Algebraic Expression Scale and ChartFresh Left 2/6/14F7 Engage NY Lesson 1 – Add and subtract relationshipFresh Left

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.

Today, my learning target is to… Build and clarify the relationship of addition and subtraction by evaluating identities such as −+= and +−=.

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.

Lesson Preparation NEEDED! Lesson Notes Teachers need to create square pieces of paper in order for students to build tape diagrams. Each pair of students will need ten squares to complete the activities. If the teacher has square tiles, these can be used in place of paper squares. The template for the squares and other shapes used in the lesson are provided at the end of the lesson. Teachers will need to cut out the shapes.

Actual Size- print and cut 2 sets per pair of students

Math Modeling Strategy- TAPE DIAGRAMS

Opening Exercises (3 minutes)-

Activity & Discussion- Part 1 Provide each pair of students with a collection of 10 squares so they can use these squares to create tape diagrams.

Activity & Discussion- Part 2

Final Discussion- Part 3

Tape diagram of the Identity

Student Practice Exercises- Students will use their knowledge gained in the discussion to create another number sentence using identities. Allow students to continue to work with their partners and the squares. Record your answers in your math notebook. 1.Predict what will happen when a tape diagram has a large number of squares, some squares are removed, but then the same amount of squares are added back on. 1.Possible answer: When some squares are removed from a tape diagram, but then the same amount of squares are added back on, the tape diagram will end up with the same amount of squares that it started with. 2.Build a tape diagram with 10 squares. a)Remove 6 of them. Write an expression to represent the tape diagram. b)Add 6 squares onto the tape diagram. Alter the original expression to represent the current tape diagram. c)Evaluate the expression.

Student Practice Exercises- Students will use their knowledge gained in the discussion to create another number sentence using identities. Allow students to continue to work with their partners and the squares.

Student Problem Set

Student Problem Set Answers

Closing (3 min) In every problem we did today, why did the final value of the expression equal the initial expression? Initially, we added an amount and then subtracted the same amount. Later in the lesson, we subtracted an amount and then added the same amount. Did this alter the outcome? Why were we able to evaluate the final expression even when we did not know the amount we were adding and subtracting?

Student Exit Ticket for Lesson 1 (5 minutes) The Relationship of Addition and Subtraction

Exit Ticket - Lesson 1 Solutions

Today, I achieved my learning target by… Building and clarifying the relationship of addition and subtraction by evaluating identities such as −+= and +−=.

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.

The End of Lesson 1 The Relationship of Addition and Subtraction