Inquiry Questions How are the models of rational and radical equations related? (Engaging- Can the graphs of rational and radical functions be transformed in the same way as quadratic and linear functions? Debatable): Unit Strands Number and Quantity: The Real Number System Algebra: Reasoning with Equations and Inequalities Algebra: Arithmetic and Polynomials and Rational Expressions Concepts properties of operations, rational expressions, rational equations, radical equations, properties of integer exponents, properties of rational exponents Generalizations Guiding Questions Factual Conceptual Understand My students will that… Properties of operations transform rational expressions How can inspection, long division and computer algebra Why do we rewrite rational expressions in different with the intention of creating more efficient forms of the systems be used to rewrite rational expressions? forms? expression. (MA10-GR.HS-S.2-GLE.3-EO.g) How do you use factoring to rewrite a rational Why can computers solve problems that humans expression? cannot? (MA10-GR.HS-S.2-GLE.4-IQ.3) Solving rational and radical equations can result in How do you check for extraneous solutions? Why do extraneous solutions occur? extraneous solutions. (MA10-GR.HS-S.2-GLE.4-EO.b.ii) When do extraneous solutions arise? How can you determine if a solution is not viable? The properties of integer exponents extend to rational What are the properties of exponents? Why do we need both radicals and rational exponents? exponents. MA10-GR.HS-S.1-GLE.1-EO.a) What is the relationship between rational exponents and radicals? How can properties of exponents be used to transform rational expressions into radical expressions or vice versa? How are radical expressions simplified? What students will know and be able to do are so closely linked in the concept-based discipline of mathematics. Therefore, in the mathematics samples what students should know and do are combined. Key Knowledge and Skills: My students will…
Inquiry Questions (Engaging- Debatable): How are the models of rational and radical equations related? Can the graphs of rational and radical functions be transformed in the same way as quadratic and linear functions? Unit Strands Number and Quantity: The Real Number System Algebra: Reasoning with Equations and Inequalities Algebra: Arithmetic and Polynomials and Rational Expressions Concepts properties of operations, rational expressions, rational equations, radical equations, properties of integer exponents, properties of rational exponents Generalizations My students will Understand that… Guiding Questions Factual Conceptual Properties of operations transform rational expressions with the intention of creating more efficient forms of the expression. (MA10-GR.HS-S.2-GLE.3-EO.g) How can inspection, long division and computer algebra systems be used to rewrite rational expressions? How do you use factoring to rewrite a rational expression? Why do we rewrite rational expressions in different forms? Why can computers solve problems that humans cannot? (MA10-GR.HS-S.2-GLE.4-IQ.3) Solving rational and radical equations can result in extraneous solutions. (MA10-GR.HS-S.2-GLE.4-EO.b.ii) How do you check for extraneous solutions? When do extraneous solutions arise? How can you determine if a solution is not viable? Why do extraneous solutions occur? The properties of integer exponents extend to rational exponents. MA10-GR.HS-S.1-GLE.1-EO.a) What are the properties of exponents? What is the relationship between rational exponents and radicals? How can properties of exponents be used to transform rational expressions into radical expressions or vice versa? How are radical expressions simplified? Why do we need both radicals and rational exponents? Key Knowledge and Skills: My students will… What students will know and be able to do are so closely linked in the concept-based discipline of mathematics. Therefore, in the mathematics samples what students should know and do are combined.