1. 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

2. Lesson 2: The Relationship of Multiplication & Division 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.

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

4. 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.

5. 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.

6. 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.

7. 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 2/7/14F7 Engage NY Lesson 2 – Multiplication and Division relationship Fresh Left

8. 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.

10. Today, my learning target is to…

11. 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.

12. 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.

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

14. Opening Exercises (3 minutes)-

15. 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.

17. Final Discussion- Part 3

18. Tape diagram of the Identity

19. Exploratory Challenge - Students will work in pairs or small groups to determine number sentences to show the relationship between multiplication and division. They will use tape diagrams to provide support for their findings. Record your answers in your math notebook. 1.Create two number sentences to show the relationship between multiplication and division. These number sentences should be identities and include variables. Use the squares to develop these number sentences. 2.Write your number sentences on large paper. Show a series of tape diagrams to defend each of your number sentences.

20. Exploratory Challenge Possible Answers

21. Student Problem Set

22. Student Problem Set Answers

23. Closing (3 min) What did you determine about the relationship of multiplication and division? What number sentences can be used to show the relationship of multiplication and division?

24. Student Exit Ticket for Lesson 2 (5 minutes) The Relationship of Multiplication & Division

25. Exit Ticket - Lesson 2 Solutions

26. Today, I achieved my learning target by…

27. 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.

28. The End of Lesson 2 The Relationship of Multiplication and Division