Intentional Thinking Map for PLC Planning (Questions 1 & 2) Title of Unit: Rational Expressions Standard(s) being addressed? MACC.912.A-­‐APR.4.6: (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. Circle the Verbs and underline the key concepts (important nouns and noun phrases). PLC question #1: What do we expect all students to learn? ! PLC question #2: How will we know if and when they have learned it? Know Declarative knowledge: Facts, vocabulary, information Understand “Essential understandings,” or generalizations, and represent ideas that are transferable to other contexts. Understand that complex rational expressions can be rewritten as a polynomial, which may be added to one simple rational expression. Do Procedural knowledge: Skills, strategies and processes that are transferrable to other contexts. Rational expressions are in the form a(x)/b(x). Comprehension Rewrite simple rational expressions in different forms. Analysis 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, [synthetic division], or for more complicated examples, a computer algebra system. Prerequisite skills: What prior knowledge (skills from previous grade levels) do students need to have mastered to be successful with this standard(s)? Simplifying Rational Expressions, Long Division Learning Goal(s)/Objective(s): (Based on standards above) DSBPC-­‐OTL Intentional Thinking Map for PLC Planning (Questions 1 & 2) Standard MACC.912.A-­‐APR.4.6: 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. Sample Task(s) Aligned to the Cognitive Complexity of the Learning Progression Score Learning Progression (Ways to check for Understanding) 4.0 I can… • Divide complicated polynomials. 3.5 I can do everything at a 3.0, and I can demonstrate partial success at score 4.0. I can… • Write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), 3.0 q(x), and r(x) are polynomials with the degree of r(x) less Target than the degree of b(x) using inspection, long division or (Standard) synthetic division. • Rewrite rational expressions in different forms. 2.5 1. Divide: (2x4 – 5x3 + 5x + 22) ÷ (2x2 + 3). Write the answer as the sum of a polynomial and a simple rational expression. 1. Divide: (x4 – 3x3 – 8x2 + 4) ÷ (x + 5). Write the answer as the sum of a polynomial and a simple rational expression. 2. Simplify x 2 − 4 x − 21
x+3
I can do everything at a 2.0, and I can demonstrate partial success at score 3.0. 2.0 I can… • simplify simple rational expressions. 1.5 I can do some things at a 2.0 with some success 1.0 I need prompting and/or support to complete 2.0 tasks. (2x + 3)(x − 2)
(2x + 3)
25x 3 −10x 2
2. Divide: 5x
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DSBPC-­‐OTL