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Honors Algebra 1 Lesson

Radical Operations & Rational Exponents: From Simplifying to Synthesizing

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9th/10th GradeBTC Style / Thinking ClassroomsA1.NR.1.1 Rewrite numerical and algebraic expressions of irrational and rational numbers involving radicals, including addition, subtraction, multiplication, and division. Limit to square and cube roots. A1.NR.2. Represent exponents and radical expressions in different ways. Indicator # Indicator A1.NR.2.1 Translate between rational exponents and radical expressions of irrational and rational numbers. Use properties of addition, subtraction, multiplication, and division to simplify radical and rational expressions. Limit to square and cube roots.90 min
Learning Objective

Students will simplify, add, subtract, multiply, and divide radical expressions involving square and cube roots, and translate fluently between radical notation and rational exponent form using properties of exponents.

Lesson Overview

Students progress from simplifying single square and cube roots through adding, subtracting, multiplying, and dividing radical expressions, then connect radical notation to rational exponent form. Each task changes exactly one variable of complexity.

Materials

  • Vertical whiteboards or chart paper
  • Dry-erase markers (multiple colors)
  • Pencils and notebook paper

Scaffolded Task Progression

1Task 1
Simplify each expression. No calculators.
a) b) c) d)
2Task 2
Simplify by factoring out the largest perfect square.
a) b) c)
3Task 3
Simplify. These involve cube roots with non-perfect radicands.
a) b) c)

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