Lesson 12 NYS COMMON CORE MATHEMATICS CURRICULUM 6β’4 Lesson 12: Distributing Expressions Student Outcomes ο§ Students model and write equivalent expressions using the distributive property. They move from the factored form to the expanded form of an expression. Classwork Opening Exercise (3 minutes) Opening Exercise a. Create a model to show π × π. π b. π Create a model to show π × π, or ππ. π π Example 1 (8 minutes) Example 1 Write an expression that is equivalent to π(π + π). ο§ In this example, we have been given the factored form of the expression. ο§ To answer this question, we can create a model to represent 2(π + π). ο§ Letβs start by creating a model to represent (π + π). Create a model to represent (π + π). π + π MP.7 π π The expression π(π + π) tells us that we have π of the (π + π)βs. Create a model that shows π groups of (π + π). π + π π Lesson 12: π + π π Distributing Expressions This work is derived from Eureka Math β’ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from G6-M4-TE-1.3.0-09.2015 π π 132 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 12 NYS COMMON CORE MATHEMATICS CURRICULUM 6β’4 How many πβs and how many πβs do you see in the diagram? There are π πβs and π πβs. How would the model look if we grouped together the πβs and then grouped together the πβs? ππ π ππ π π π What expression could we write to represent the new diagram? ππ + ππ ο§ This expression is written in expanded form. What conclusion can we draw from the models about equivalent expressions? π(π + π) = ππ + ππ ο§ To prove that these two forms are equivalent, letβs substitute some values for π and π and see what happens. Let π = π and π = π. MP.7 ο§ π(π + π) ππ + ππ π(π + π) π(π) + π(π) π(π) π+π ππ ππ Note: If students do not believe yet that the two are equal, continue substituting more values for π and π until they are convinced. What happens when we double (π + π)? We double π, and we double π. Example 2 (5 minutes) Example 2 Write an expression that is equivalent to double (ππ + ππ). How can we rewrite double (ππ + ππ)? Double is the same as multiplying by two. π(ππ + ππ) or ππ + ππ Lesson 12: Distributing Expressions This work is derived from Eureka Math β’ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from G6-M4-TE-1.3.0-09.2015 133 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 12 NYS COMMON CORE MATHEMATICS CURRICULUM 6β’4 Is this expression in factored form, expanded form, or neither? The first expression is in factored form, and the second expression is in expanded form. Letβs start this problem the same way that we started the first example. What should we do? We can make a model of ππ + ππ. ππ ππ How can we change the model to show π(ππ + ππ)? We can make two copies of the model. ππ + ππ ππ + ππ ππ ππ ππ ππ Are there terms that we can combine in this example? ππ ππ ππ MP.7 ππ ππ ππ Yes. There are π π's and π π's. So, the model is showing ππ + ππ. What is an equivalent expression that we can use to represent π(ππ + ππ)? π(ππ + ππ) = ππ + ππ This is the same as π(ππ) + π(ππ). Summarize how you would solve this question without the model. When there is a number outside the parentheses, I would multiply it by all the terms on the inside of the parentheses. Example 3 (3 minutes) Example 3 ππ Write an expression in expanded form that is equivalent to the model below. + π π What factored expression is represented in the model? π(ππ + π) Lesson 12: Distributing Expressions This work is derived from Eureka Math β’ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from G6-M4-TE-1.3.0-09.2015 134 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 12 NYS COMMON CORE MATHEMATICS CURRICULUM 6β’4 How can we rewrite this expression in expanded form? π(ππ) + π(π) πππ + ππ Example 4 (3 minutes) MP.7 ο§ How can we use our work in the previous examples to write the following expression? Example 4 Write an expression in expanded form that is equivalent to π(ππ + ππ). We will multiply π × ππ and π × ππ. We would get πππ + πππ. So, π(ππ + ππ) = πππ + πππ. Exercises (15 minutes) Exercises Create a model for each expression below. Then, write another equivalent expression using the distributive property. 1. π(π + π) π+π π+π π π π π+π π π ππ ππ π π π π π π π ππ + ππ 2. π(ππ + π) ππ + π ππ π ππ + π ππ + π ππ + π ππ π ππ π ππ ππ ππ ππ ππ π ππ ππ π π π π ππ + ππ Lesson 12: Distributing Expressions This work is derived from Eureka Math β’ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from G6-M4-TE-1.3.0-09.2015 135 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 12 6β’4 Apply the distributive property to write equivalent expressions in expanded form. π(π + π) 3. ππ + ππ π(ππ + π) 4. ππ + ππ π(ππ + ππ) 5. πππ + πππ π(πππ + ππ) 6. πππ + πππ 7. ππ πππ π πππ + ππππ π(ππ + ππ) 8. πππ + πππ Closing (3 minutes) ο§ State what the expression π(π + π) represents. οΊ ο§ ο§ π groups of the quantity π plus π Explain in your own words how to write an equivalent expression in expanded form when given an expression in the form of π(π + π). Then, create your own example to show off what you know. οΊ To write an equivalent expression, I would multiply π times π and π times π. Then, I would add the two products together. οΊ Examples will vary. State what the equivalent expression in expanded form represents. οΊ ππ + ππ means π groups of size π plus π groups of size π. Exit Ticket (5 minutes) Lesson 12: Distributing Expressions This work is derived from Eureka Math β’ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from G6-M4-TE-1.3.0-09.2015 136 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 12 NYS COMMON CORE MATHEMATICS CURRICULUM Name 6β’4 Date Lesson 12: Distributing Expressions Exit Ticket Use the distributive property to write the following expressions in expanded form. 1. 2(π + π) 2. 5(7β + 3π) 3. π(π + π) Lesson 12: Distributing Expressions This work is derived from Eureka Math β’ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from G6-M4-TE-1.3.0-09.2015 137 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 12 6β’4 Exit Ticket Sample Solutions Use the distributive property to write the following expressions in expanded form. 1. π(π + π) ππ + ππ 2. π(ππ + ππ) πππ + πππ 3. π(π + π) ππ + ππ Problem Set Sample Solutions 1. Use the distributive property to write the following expressions in expanded form. a. π(π + π) ππ + ππ b. π(π + ππ) ππ + πππ c. π(ππ + πππ) ππ + πππ d. π(ππ + ππ) πππ + πππ e. π(ππ + π) πππ + ππ f. π(ππ + πππ) πππ + ππππ Lesson 12: Distributing Expressions This work is derived from Eureka Math β’ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from G6-M4-TE-1.3.0-09.2015 138 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 12 NYS COMMON CORE MATHEMATICS CURRICULUM 2. 6β’4 Create a model to show that π(ππ + ππ) = ππ + ππ. ππ + ππ ππ ππ + ππ ππ ππ ππ ππ Lesson 12: ππ ππ ππ ππ Distributing Expressions This work is derived from Eureka Math β’ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from G6-M4-TE-1.3.0-09.2015 ππ 139 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
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