Curriculum / Math / 6th Grade / Unit 6: Equations and Inequalities / Lesson 3
Math
Unit 6
6th Grade
Lesson 3 of 14
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Lesson Notes
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Write equations for real-world situations.
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.2 — Write, read, and evaluate expressions in which letters stand for numbers.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
In this lesson, students encounter real-world problems and either identify or write equations to represent the situations. This requires students to abstract the situations and use symbols in place of verbal descriptions (MP.2). In future lessons, students will also re-contextualize these equations and symbols to understand what they mean in the situation.
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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
Decide which of the following equations best represents each situation. Explain your reasoning.
a. After Lou poured 2 liters of water into a large bucket, the bucket contained 10 liters of water. How many liters were in the bucket to start?
b. Clara ran 10 miles, which was twice as far as Nina ran. How far did Nina run?
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Which goes with Which?, accessed on Feb. 27, 2018, 1:33 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.
At a market, a farmer sells apples for $1.33 per pound. At the end of a weekend, the farmer made $74.48 from selling apples.
Which equation can be used to determine $$x$$, the number of pounds of apples the farmer sold over the weekend?
On Saturday, Brad ran $${1{3\over4}}$$ miles in the morning and then later went for a run in the evening. He determined that he ran a total of $${4{1\over4}}$$ miles on Saturday.
Olivia usually runs the same distance every morning. On Sunday, Olivia went for a longer run and ran 4.6 km. This was twice her normal running distance.
a. Let $$x$$ represent the distance Brad ran on Saturday evening. Write an equation to represent Brad’s total running distance on Saturday.
b. Let $$y$$ represent Olivia’s normal running distance. Write an equation to represent Olivia’s running distance on Sunday.
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
Hodan is planting flowers around her apartment building. The total distance around her building is 120 feet, and she wants to plant a flower every $${4{1\over2}}$$ feet.
Let $$x$$ represent the number of flowers Hodan plants around her apartment building. Write an equation she can use to determine how many flowers she’ll need.
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
Solve one-step equations with addition and subtraction.
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
Solve one-step equations with multiplication and division.
Solve percent problems using equations.
6.EE.B.76.RP.A.3.C
Solve multi-part equations leading to the form $${x+p=q }$$ and $${px=q}$$.
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Topic B: Reasoning About and Solving Inequalities
Define and identify solutions to 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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