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Square Dancing (Updated!)

What secrets are hidden in squares?

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Square Dancing (Updated!)

What secrets are hidden in squares?

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Square Dancing - Student Handout.pdf
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Square Dancing - Teacher Guide.pdf
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2023-2024 Versions

In the fall of 2024, Citizen Math released updated versions of every lesson in our library, plus a few new ones! We know you may have already prepped an earlier version or planned a repeat of last year, so we're continuing to make these earlier versions available through Thursday December 5, 2024.

You can find the new lessons through the regular search, and we hope you love them as much as we do. You can read more about these updates in Our Community.

What secrets are hidden in squares? While the Pythagoreans are best known for their triangle theorem, they were in fact religious cult who believed in the god of mathematics. Pythagoras and his followers believed that everything in the universe could be described as a ratio of two numbers...and tenet that was quickly challenged.

In this lesson, students use concrete models to explore square numbers and square roots and confront the philosophical and moral questions posed by the existence of irrational numbers.

REAL WORLD TAKEAWAYS

  • For the Pythagoreans, numbers were a religion and they expected them to reveal the truth of the universe. The Pythagoreans also persecuted Hippasus – one of their own – when he went against their wishes and shared his discovery of irrational numbers, because that “truth” was inconveniently in conflict with their understanding at the time
  • Sometimes humans are persecuted for proclaiming their truths because it threatens a status quo.

MATH OBJECTIVES

  • Develop a geometric understanding of square root; reason about and find square roots of rational numbers
  • Given a square’s width, calculate its area by multiplying the width by itself.
  • Given a square’s area, calculating its width by finding the number that, when multiplied by itself, yields the area
  • Identify the square root of 2 as irrational
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.
Grade 8
Squares, Roots, Irrationals
Grade 8
Squares, Roots, Irrationals
Content Standards 8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. 8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., &pi;<sup>2</sup>). For example, by truncating the decimal expansion of &radic;2, show that &radic;2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
Mathematical Practices MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.6 Attend to precision. MP.7 Look for and make use of structure.

Other Grade 8 Lessons

Domino Effect (Updated!)

How much does Domino’s charge for pizza?

Grade 8
Writing Linear Equations
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.

You're So Fined (Updated!)

How do municipal fines affect people with different incomes?

Grade 8
Solving Linear Systems
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.

Sweet Tooth (Updated!)

How much Halloween candy should you eat?

Grade 8
Functions
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.

Timber (Updated!)

What size tree should we use for lumber?

Grade 8
Cones, Cylinders, Spheres
Appropriate most times as students are developing conceptual understanding.

Fuel Economy (Updated!)

Are hybrid vehicles worth the extra cost?

Grade 8
Solving Linear Equations
Appropriate most times as students are developing conceptual understanding.

Domino Effect (Updated!)

How much does Domino’s charge for pizza?

Grade 8
Writing Linear Equations
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.

You're So Fined (Updated!)

How do municipal fines affect people with different incomes?

Grade 8
Solving Linear Systems
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.

Sweet Tooth (Updated!)

How much Halloween candy should you eat?

Grade 8
Functions
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.

Timber (Updated!)

What size tree should we use for lumber?

Grade 8
Cones, Cylinders, Spheres
Appropriate most times as students are developing conceptual understanding.

Fuel Economy (Updated!)

Are hybrid vehicles worth the extra cost?

Grade 8
Solving Linear Equations
Appropriate most times as students are developing conceptual understanding.