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# Equations and Inequalities

## Objective

Write equations for real-world situations.

## Common Core Standards

### Core Standards

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• 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.

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• 6.EE.A.2

## Criteria for Success

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1. Identify which equation matches a real-world context from a list of equations.
2. Write equations to represent real-world situations in the forms ${x+p=q}$ and ${px=q.}$

## Tips for Teachers

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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.

#### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 3 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

## Anchor Problems

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### Problem 1

Decide which of the following equations best represents each situation.

 $x+2=10$ $x=10+2$ $2\cdot 10=x$ $x+10=2$ $10x=2$ $2x=10$
1. 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?
2. Clara ran 10 miles, which was twice as far as Nina ran. How far did Nina run?

#### References

Illustrative Mathematics Which goes with Which?

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.

### Problem 2

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?

1.   $1.33x=74.48$
2.   $1.33+x=74.48$
3.   $74.48-1.33=x$
4.   $74.48 × 1.33=x$

### Problem 3

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.

1. Let $x$ represent the distance Brad ran on Saturday evening. Write an equation to represent Brad’s total running distance on Saturday.
2. Let $y$ represent Olivia’s normal running distance. Write an equation to represent Olivia’s running distance on Sunday.

## Problem Set

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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.

• Smarter Balanced Assessment Consortium: Sample Items Item MAT.06.TE.1.000EE.F.177 C1 TF
• MARS Formative Assessment Lessons for Grade 6 Interpreting EquationsIncludes a great matching activity of equations to situations
• Illustrative Mathematics Make Use of StructureThis task is similar to Anchor Problem #3 in Lesson 2; however, there is no list of values included, so students make use of the structure in the equation in order to determine the solution.

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.