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# 10. Using irrational numbers as distances (A)

teaches Common Core State Standards CCSS.Math.Content.8.NS.A.2 http://corestandards.org/Math/Content/8/NS/A/2
teaches Common Core State Standards CCSS.Math.Practice.MP3 http://corestandards.org/Math/Practice/MP3

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Lesson objective: Apply understanding of irrational numbers as actual distances to solve a real-world problem.

This lesson provides an opportunity for students to apply their knowledge and understanding of irrational numbers to a real-life situation. Students are asked to decide which jet engine compartment a compressor fan will fit into, and make a case for why they agree with the mechanic who chose the same engine they did.

Key Concept students will use:

• Irrational numbers are measures of lengths, and therefore can be located a distance from 0 on the number line.

Skills students will use:

• Perform operations using irrational numbers
• Solve equations of the form $$x^2 = p$$
• Solve a two-step equation (Grade 7, Unit 7)
• Find radius or diameter of a circle given the area (Grade 7, Unit 11)

Students engage in Mathematical Practice 3 (construct viable arguments and critique the reasoning of others) as they defend their process and decisions to round or truncate irrational numbers to solve the problem.

Key vocabulary:

• Area
• Diameter
• Irrational number
• Pi
• Radius

Special Materials:

• Calculators (optional)
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