Stacking squares

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This lesson prompts students to explore ways of arranging squares to represent equivalences involving square- and cube-roots. Students’ explanations and representations (with their various ways of finding these roots) form the basis for further work with radicals. Activities in this lesson explore the meaning of square roots and introduce students to radicals.

Students will:

• Investigate ways of finding equivalences that involve square- and cube-roots.
Make and test conjectures about connections between geometric and numeric representations of squares and between whole numbers and their square-roots.
• Communicate their reasoning.

NCTM Standards and Expectations covered in this lesson include:

• Comparing and contrasting the properties of numbers and number systems, including the rational and real numbers, and understand complex numbers as solutions to quadratic equations that do not have real solutions.
• Judging the effects of such operations as multiplication, division, and computing powers and roots on the magnitudes of quantities.

North Carolina Curriculum Alignment