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Changing the Subject: Requires Factorization WORKSHEET
Suitable for Grades: Algebra I, IM 1
CCSS: HSA.APR.D.6, HSA.SSE.B.3
CCSS Description: Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★ a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★ a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%
Changing the Subject: Requires Factorization WORKSHEET DESCRIPTION
Students will be challenged yet supported while completing this worksheet, which will change the subject of complex formulas and equations.
In Section A, students will fill the gaps in multi-stage rearrangement processes. This is aimed to guide learners through the process and focus on using the correct inverse operations in the correct order.
Section B consists of 6 increasingly difficult but minimally different formulas which students will rearrange on their own using the steps from section A.
Then, Section C presents multiple-choice challenges, requiring learners to select the correct rearrangement from three possible answers.
Lastly, Section D will see learners rearranging increasingly sophisticated equations with up to three variables.
