Factoring and expanding linear expressions with rational coefficients Generally, all SMPs can be applied in every standard. The following SMPs can be (7.EE.1) highlighted for this standard. Understand that rewriting expressions into equivalent can reveal other 4 Model with mathematics – relationships between quantities (7.EE.2) Connections Disciplinary Literacy Interpreting the factors in context (NC.M1.A-SSE.1b) As stated in SMP 6, the precise use of mathematical vocabulary is the expectation Understanding the relationship between factors, solutions, and zeros in all oral and written communication. (NC.M1.A-APR.3) Students should be able to compare and contrast the zeros of a function and the Solving quadratic equations (NC.M1.A-REI.4) solutions of a function. Rewriting quadratic functions into different forms to show key features of New Vocabulary: quadratic expression the function (NC.M1.F-IF.8a) Mastering the Standard Comprehending the Standard Assessing for Understanding Students factor a quadratic in the form where Students should understand that the reasoning behind rewriting quadratic expressions into factored form is to is an integer in order to reveal the zeroes of the reveal different key features of a quadratic function, namely the zeros/x-intercepts. quadratic function. Example: The expression represents the height of a coconut thrown from a person in a tree to a basket on the ground where is the number of seconds. x Students use the linear factors of a quadratic Rewrite the expression to reveal the linear factors. function to explain the meaning of the zeros of Identify the zeroes and intercepts of the expression and interpret what they mean in regards to the context. quadratic functions and the solutions to How long is the ball in the air? quadratic equations in a real world problem. Part A: Three equivalent equations for are shown. Select the form that reveals the zeros of without Example: changing the form of the equation. Part B: Select all values of for which . (from the Smarter Balanced Assessment Consortium) Students should understand that the reasoning behind rewriting quadratic expressions into factored form is to reveal the solutions to quadratic equations. Example: A vacant rectangular lot is being turned into a community vegetable garden with a uniform path around it. The area of the lot is represented by where is the width of the path in meters. Find the width of the path surrounding the garden. Instructional Resources Tasks Additional Resources Back to:
Factoring and expanding linear expressions with rational coefficients (7.EE.1) Understand that rewriting expressions into equivalent can reveal other relationships between quantities (7.EE.2) Generally, all SMPs can be applied in every standard. The following SMPs can be highlighted for this standard. 4 – Model with mathematics Connections Disciplinary Literacy Interpreting the factors in context (NC.M1.A-SSE.1b) Understanding the relationship between factors, solutions, and zeros (NC.M1.A-APR.3) Solving quadratic equations (NC.M1.A-REI.4) Rewriting quadratic functions into different forms to show key features of the function (NC.M1.F-IF.8a) As stated in SMP 6, the precise use of mathematical vocabulary is the expectation in all oral and written communication. Students should be able to compare and contrast the zeros of a function and the solutions of a function. New Vocabulary: quadratic expression Mastering the Standard Comprehending the Standard Assessing for Understanding Students factor a quadratic in the form where is an integer in order to reveal the zeroes of the quadratic function. Students use the linear factors of a quadratic function to explain the meaning of the zeros of quadratic functions and the solutions to quadratic equations in a real world problem. Students should understand that the reasoning behind rewriting quadratic expressions into factored form is to reveal different key features of a quadratic function, namely the zeros/x-intercepts. Example: The expression represents the height of a coconut thrown from a person in a tree to a basket on the ground where x is the number of seconds. Rewrite the expression to reveal the linear factors. Identify the zeroes and intercepts of the expression and interpret what they mean in regards to the context. How long is the ball in the air? Example: Part A: Three equivalent equations for are shown. Select the form that reveals the zeros of without changing the form of the equation. Part B: Select all values of for which . (from the Smarter Balanced Assessment Consortium) Students should understand that the reasoning behind rewriting quadratic expressions into factored form is to reveal the solutions to quadratic equations. Example: A vacant rectangular lot is being turned into a community vegetable garden with a uniform path around it. The area of the lot is represented by where is the width of the path in meters. Find the width of the path surrounding the garden. Instructional Resources Tasks Additional Resources Back to:
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