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 3: The Relationship of Multiplication and Addition
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+𝑥) to produce the equivalent expression 6+3𝑥; apply the distributive property to the expression 24𝑥+18𝑦 to produce the equivalent expression 6(4𝑥+3𝑦); apply properties of operations to 𝑦+𝑦+𝑦 to produce the equivalent expression 3𝑦.

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 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.
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=6𝑠2 to find the volume and surface area of a cube with sides of length 𝑠=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+𝑥) to produce the equivalent expression 6+3𝑥; apply the distributive property to the expression 24𝑥+18𝑦 to produce the equivalent expression 6(4𝑥+3𝑦); apply properties of operations to 𝑦+𝑦+𝑦 to produce the equivalent expression 3𝑦.

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 𝑦+𝑦+𝑦 and 3𝑦 are equivalent because they name the same number regardless of which number 𝑦 stands for.

7. Table of Contents Date Title Page F8 Engage NY Lesson 3-
2/6/14
NEW Focus 8- Algebraic Expression Scale and Chart
Fresh Left
F8 Engage NY Lesson 1 –
Add and subtract Relationship
2/7/14
F8 Engage NY Lesson 2 –
Multiplication and Division Relationship
2/10/14
F8 Engage NY Lesson 3-
Multiplication and Addition Relationship

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…
Build and clarify the relationship of multiplication and addition by evaluating identities such as
3∙𝑔𝑔=𝑔𝑔+𝑔𝑔+𝑔𝑔

11. How much prior knowledge do you have regarding that goal?
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
Students will continue to use the squares from Lessons 1 and 2 to create tape diagrams. Each pair of students will need 30 squares to complete the activities.

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

14. Opening Exercises (5 minutes)-

15. Opening Answers

16. Activity & Discussion Provide each pair of students with a collection of 30 squares so they can use these squares to create tape diagrams.

17. Activity & Discussion

18. Activity & Discussion

19. Student Practice- Record your answer in your math workbook.

20. Answers

21. Student Practice- Record your answers in your math workbook
Student Practice- Record your answers in your math workbook. Write an equivalent expression to demonstrate the relationship to multiplication and addition.

22. Answers

23. Student Practice- Record your answers in your math workbook.
Roberto is not familiar with tape diagrams and believes that he can show the relationship of multiplication and addition on a number line. Help Roberto demonstrate that the expression 3x2 is equivalent to on a number line.

24. Answers

25. 2nd Period- Start Here

26. Student Practice- Record your answers in your math workbook.

27. Answers

28. 1st Period & 5th Period
Start 1st & 5th period- Here on Tuesday

29. Student Practice- Record your answers in your math workbook.

30. Answers

31. Student Problem Set- Record your answer in your math workbook
Write an equivalent expression to show the relationship of multiplication and addition.
3. 8×2
4. 3×9
5. 6𝑚
6. 𝑑+𝑑+𝑑+𝑑+𝑑

32. Student Problem Set Answers

33. Closing (4 min) Create a diagram that models 3 groups of size 𝑏.
Write two equivalent expressions that represent this model.
Possible answers: 3𝑏, 𝑏+𝑏+𝑏
Peter says that since the addition expression yields the same value as the multiplication expression, he will always choose to use the addition expression when solving these types of problems. Convince Peter that he may want to reconsider his position.
Answers will vary, but should include the idea that when the group size is large, it is more advantageous to multiply instead of add.

34. Student Exit Ticket for Lesson 3 The Relationship of Multiplication & Addition
Write an equivalent expression to show the relationship of multiplication& addition.

35. Exit Ticket - Lesson 3 Solutions

36. Today, I achieved my learning target by…
Building and clarifying the relationship of multiplication and addition by evaluating identities such as
3∙𝑔𝑔=𝑔𝑔+𝑔𝑔+𝑔𝑔

37. How much prior knowledge do you have regarding that goal?
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.

38. The End of Lesson 3 The Relationship of Multiplication and Addition 