Expand and factor expressions using the distributive property and the greatest common factor.
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In Lessons 3 and 4, students expand and factor expressions with rational numbers. Students have prior experience with using the distributive property to generate equivalent expressions from 6th grade (6.EE.3). In Lesson 3, students see negative numbers inside a parentheses group written as subtraction, however, they will not distribute with a negative number outside a parentheses group until Lesson 4.
If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problems 1 and 2 (benefit from worked examples) and Anchor Problem 3 (can be done independently). Find more guidance on adapting our math curriculum for remote learning here.
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Write two equivalent expressions to represent the total area of the rectangle shown. Justify that your two expressions are equivalent.
Expand the expression below by using a rectangular array.
$${\frac{1}{3}(9x-12y-18)}$$
Grade 7 Mathematics > Module 3 > Topic A > Lesson 3 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Modified by Fishtank Learning, Inc.What could be the missing dimensions of the rectangular array? Which set of dimensions uses the greatest common factor of the two terms?
Factor the expression below by using a rectangular array. Use the greatest common factor as the representation of the width.
$${24d-8e+6}$$
Grade 7 Mathematics > Module 3 > Topic A > Lesson 4 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Modified by Fishtank Learning, Inc.The table below includes expressions that are written in expanded form and in factored form. Complete the table. Use rectangular arrays as needed.
Factored Form | Expanded Form |
$$3(x-14y)$$ | |
$$2x+3x$$ | |
$$\frac{3}{4}(8a+16b)$$ | |
$$24m+8n-12p$$ | |
$$\frac{1}{2}\left(\frac{1}{3}x-8y+\frac{2}{3}z\right)$$ | |
$$5xy+15y$$ | |
$$2x(-3+y)$$ |
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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If we multiply $${\frac{x}{2}+\frac{3}{4}}$$ by $$4$$, we get $${{2x+3}}$$.
Is $${{2x+3}}$$ an equivalent expression to $${\frac{x}{2}+\frac{3}{4}}$$? Explain your answer.
Equivalent Expressions?, accessed on Oct. 9, 2017, 9:10 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.