Curriculum / Math / 7th Grade / Unit 3: Numerical and Algebraic Expressions / Lesson 9
Math
Unit 3
7th Grade
Lesson 9 of 11
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Lesson Notes
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Write and interpret expressions in different ways to shed new meaning on a context.
The core standards covered in this lesson
7.EE.A.2 — Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05."
The foundational 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.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
This lesson touches upon standard 7.EE.2; this standard will be revisited in Unit 5 with percentages and other related contexts.
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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
Malia is at an amusement park. She bought 14 tickets, and each ride requires 2 tickets.
a. Write an expression that gives the number of tickets Malia has left in terms of $$x$$, the number of rides she has already gone on. Find at least one other expression that is equivalent to it.
b. The expression $${14}{-2}x $$ represents the number of tickets Malia has left after she has gone on $$x$$ rides. How can each of the following numbers and expressions be interpreted in terms of tickets and rides?
i. $$14$$
ii. $$-2$$
iii. $$2x$$
c. The expression $$2(7-x)$$ also represents the number of tickets Malia has left after she has gone on $$x$$ rides. How can each of the following numbers and expressions be interpreted in terms of tickets and rides?
i. $$7$$
ii. $$(7-x)$$
iii. $$2$$
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Ticket to Ride, accessed on Oct. 9, 2017, 11:15 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 square fountain area with side length $$s$$ feet is bordered by a single row of square tiles as shown.
What are three different ways to represent the number of tiles needed for the border? Show each representation using the diagram.
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..
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
A picture with dimensions $$x$$ by $$y$$ inches, is framed by a rectangular border. The border is 1 inch wide, as shown in the figure below. Write 2 different expressions to represent the area of the border around the picture.
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.
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Solve multi-step real-world problems with rational numbers.
Topic A: Evaluating Numerical and Algebraic Expressions
Evaluate numerical expressions with rational numbers using the order of operations.
Standards
7.EE.A.17.NS.A.3
Write and evaluate expressions for mathematical and contextual situations.
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Topic B: Generating Equivalent Expressions
Expand and factor expressions using the distributive property and the greatest common factor.
7.EE.A.1
Expand and factor expressions with negative rational numbers.
Add and simplify expressions by combining like terms.
Subtract and simplify expressions.
Simplify expressions by combining like terms and using the distributive property and properties of operations (Part 1).
Simplify expressions by combining like terms and using the distributive property and properties of operations (Part 2).
7.EE.A.2
Topic C: Solving Multi-Step Problems using Expressions
7.EE.B.37.NS.A.3
Model real-world problems involving rational numbers using reasoned estimates.
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