Curriculum / Math / 6th Grade / Unit 5: Numerical and Algebraic Expressions / Lesson 9
Math
Unit 5
6th Grade
Lesson 9 of 12
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Lesson Notes
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Write equivalent expressions using the distributive property (Part 1).
The core standards covered in this lesson
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.
6.EE.A.4 — 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.
The foundational standards covered in this lesson
4.NBT.B.5 — Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Two rectangles were combined to create a larger rectangle, as shown below.
Write as many expressions as you can to represent the area of the larger, outer rectangle.
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Four rectangles are shown in the table below. Some include measurements for length and width, others include measurements for the areas of the smaller rectangles. Fill in the table with expressions to represent length and width, and two ways to show the area of each of the larger rectangles.
The students in Mr. Nolan's class are writing expressions for the perimeter of a rectangle of side length $$l$$ and width $$w$$. After they share their answers, the following expressions are on the board:
Sam: $$2(l+w)$$
Joanna: $$ l+w+l+w$$
Kiyo: $$2l+w$$
Erica: $$ 2w+2l$$
Which of the expressions are correct and how might the students have been thinking about finding the perimeter of the rectangle?
Rectangle Perimeter 2, accessed on Dec. 19, 2017, 11:10 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.
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
For each problem, draw a diagram to represent the expression. Then use the diagram to write an equivalent expression.
a. $${4(2m+n)}$$
b. $${5x+15}$$
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Next
Write equivalent expressions using the distributive property (Part 2).
Topic A: Numerical Expressions with Exponents
Understand the meaning of exponents.
Standards
6.EE.A.1
Evaluate numerical expressions involving whole-number exponents.
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Topic B: Introduction to Algebraic Expressions
Use variables to write algebraic expressions.
6.EE.A.26.EE.A.2.C6.EE.B.6
Evaluate algebraic expressions.
6.EE.A.26.EE.A.2.C
Write expressions for verbal statements and vice versa (Part 1).
6.EE.A.2.A6.EE.A.2.B
Write expressions for verbal statements and vice versa (Part 2).
Topic C: Equivalent Expressions & Applications
Identify equivalent expressions (Part 1).
6.EE.A.36.EE.A.4
Identify equivalent expressions (Part 2).
Write algebraic expressions for application situations (Part 1).
6.EE.B.6
Write algebraic expressions for application situations (Part 2).
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