I am using the “Lucy” task for Coordinate Algebra from the Georgia standards for this quest.

**Task: Lucy’s Linear Equations and Inequalities**

**Name_________________________________ Date__________________**

** ****Mathematical Goals**

- Create one-variable linear equations and inequalities from contextual situations.
- Solve and interpret the solution to multi-step linear equations and inequalities in context.

**Essential Questions**

- How do I interpret parts of an expression in terms of context?
- How do I create equations and inequalities in one variable and use them to solve problems arising from linear functions?
- How can I write, interpret and manipulate algebraic expressions, equations and inequalities?

**Common Core Georgia Performance Standards**

**MCC9-12.A.CED.1** Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and exponential functions.

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**MCC9-12.A.SSE.1** Interpret expressions that represent a quantity in terms of its context.

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**MCC9-12.A.SSE.1a **Interpret parts of an expression, such as terms, factors, and coefficients.

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**MCC9-12.A.SSE.1b **Interpret complicated expressions by viewing one or more of their parts as a single entity.

**Standards for Mathematical Practice**

**1 **Reason abstractly and quantitatively.

2. Model with mathematics.

3. Look for and make use of structure.

Lucy has been assigned the following linear equations and inequality word problems. Help her solve each problem below by using a five step plan.

- Drawing a Sketch (if necessary)
- Defining a Variable
- Setting up an equation or inequality
- Solve the equation or inequality
- Make sure you answer the question

- The sum of 38 and twice a number is 124. Find the number.
- The sum of two consecutive integers is less than 83. Find the pair of integers with the greatest sum.
- A rectangle is 12m longer than it is wide. Its perimeter is 68m. Find its length and width.
- The length of a rectangle is 4 cm more than the width and the perimeter is at least 48 cm. What are the smallest possible dimensions for the rectangle?
- Find three consecutive integers whose sum is 171.
- Find four consecutive even integers whose sum is 244.
- Alex has twice as much money as Jennifer. Jennifer has $6 less than Shannon. Together they have $54. How much money does each have?
- There are three exams in a marking period. A student received grades of 75 and 81 on the first two exams. What grade must the student earn on the last exam to get an average of no less than 80 for the marking period?

You Tube link for Lucy’s Equations:

Other useful links:

**http://www.realworldmath.org/project-based-learning.html**

Rubric using irubric:

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