Curriculum / Math / 6th Grade / Unit 6: Equations and Inequalities / Lesson 7
Math
Unit 6
6th Grade
Lesson 7 of 14
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Solve multi-part equations leading to the form $${x+p=q }$$ and $${px=q}$$.
The core standards covered in this lesson
6.EE.B.6 — Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
6.EE.B.7 — Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
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
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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
The Jonas family had a really busy day. After leaving their home, Ms. Jonas dropped her son Cody at his tennis practice. She then drove her daughter Kristin to her soccer game and stayed to watch. After the game, mother and daughter picked up Cody on the way home. Once home, Ms. Jonas saw that they had driven 20 miles that day.
The map below shows the locations of where the Jonas family traveled. The car can only travel along the main streets (gridlines), and all distances between cross streets are the same distance. Assume Ms. Jonas took the most direct routes to and from her destinations.
How far are the tennis courts from home? Set up and solve an equation in one variable to find the distance between the tennis courts and home.
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Busy Day, accessed on Feb. 28, 2018, 2:32 p.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.
Sierra walks her dog Pepper twice a day. Her evening walk is two-and-a-half times as far as her morning walk. At the end of the week she tells her mom, “I walked Pepper for 30 miles this week!”
How long is her morning walk? Write and solve an equation.
Morning Walk, accessed on Feb. 28, 2018, 2:33 p.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.
The school librarian, Mr. Marker, knows the library has 1,400 books, but he wants to reorganize how the books are displayed on the shelves. Mr. Marker needs to know how many fiction, nonfiction, and resource books are in the library. He knows that:
If these are the only types of books in the library, how many of each type of book are in the library? Draw a tape diagram to represent the books in the library, and then write and solve an equation to determine how many of each type of book there are in the library.
Grade 6 Mathematics > Module 4 > Topic G > Lesson 29 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..
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5-10 minutes
A town's total allocation for firefighters’ wages and benefits in a new budget is $600,000. If wages are calculated at $40,000 per firefighter and benefits at $20,000 per firefighter, write an equation whose solution is the number of firefighters the town can employ if they spend their whole budget. Solve the equation.
Firefighter Allocation, accessed on Nov. 6, 2017, 9:04 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.
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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Define and identify solutions to inequalities.
Topic A: Reasoning About and Solving Equations
Represent equations in the form $${ x+p=q }$$ and $${px=q}$$ using tape diagrams and balances.
Standards
6.EE.B.66.EE.B.7
Define and identify solutions to equations.
6.EE.B.5
Write equations for real-world situations.
Solve one-step equations with addition and subtraction.
Solve one-step equations with multiplication and division.
Solve percent problems using equations.
6.EE.B.76.RP.A.3.C
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Topic B: Reasoning About and Solving Inequalities
6.EE.B.56.EE.B.8
Write and graph inequalities for real-world conditions. (Part 1)
6.EE.B.8
Write and graph inequalities for real-world conditions. (Part 2)
Solve one-step inequalities.
6.EE.B.66.EE.B.8
Topic C: Representing and Analyzing Quantitative Relationships
Write equations for and graph ratio situations. Define independent and dependent variables.
6.EE.C.96.RP.A.3.A
Represent the relationship between two quantities in graphs, equations, and tables. (Part 1)
Represent the relationship between two quantities in graphs, equations, and tables. (Part 2)
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