| Code |
Description |
| MA.912.AR.3.1: | Given a mathematical or real-world context, write and solve one-variable quadratic equations over the real number system.Clarifications:
Clarification 1: Within the Algebra 1 course, instruction includes the concept of non-real answers, without determining non-real solutions.
Clarification 2: Within this benchmark, the expectation is to solve by factoring techniques, taking square roots, the quadratic formula and completing the square.
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| MA.912.AR.3.2: | Given a mathematical or real-world context, write and solve one-variable quadratic equations over the real and complex number systems.Clarifications:
Clarification 1: Within this benchmark, the expectation is to solve by factoring techniques, taking square roots, the quadratic formula and completing the square. |
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| MA.912.AR.3.3: | Given a mathematical or real-world context, write and solve one-variable quadratic inequalities over the real number system. Represent solutions algebraically or graphically. |
| MA.912.AR.3.4: | Write a quadratic function to represent the relationship between two quantities from a graph, a written description or a table of values within a mathematical or real-world context.Clarifications:
Clarification 1: Within the Algebra 1 course, a graph, written description or table of values must include the vertex and two points that are equidistant from the vertex.Clarification 2: Instruction includes the use of standard form, factored form and vertex form. Clarification 3: Within the Algebra 2 course, one of the given points must be the vertex or an x-intercept.
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| MA.912.AR.3.5: | Given the x-intercepts and another point on the graph of a quadratic function, write the equation for the function. |
| MA.912.AR.3.6: | Given an expression or equation representing a quadratic function, determine the vertex and zeros and interpret them in terms of a real-world context. |
| MA.912.AR.3.7: | Given a table, equation or written description of a quadratic function, graph that function, and determine and interpret its key features.Clarifications:
Clarification 1: Key features are limited to domain; range; intercepts; intervals where the function is increasing, decreasing, positive or negative; end behavior; vertex; and symmetry.Clarification 2: Instruction includes the use of standard form, factored form and vertex form, and sketching a graph using the zeros and vertex. Clarification 3: Instruction includes representing the domain and range with inequality notation, interval notation or set-builder notation. Clarification 4: Within the Algebra 1 course, notations for domain and range are limited to inequality and set-builder.
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| MA.912.AR.3.8: | Solve and graph mathematical and real-world problems that are modeled with quadratic functions. Interpret key features and determine constraints in terms of the context.Clarifications:
Clarification 1: Key features are limited to domain; range; intercepts; intervals where the function is increasing, decreasing, positive or negative; end behavior; vertex; and symmetry.Clarification 2: Instruction includes the use of standard form, factored form and vertex form. Clarification 3: Instruction includes representing the domain, range and constraints with inequality notation, interval notation or set-builder notation. Clarification 4: Within the Algebra 1 course, notations for domain, range and constraints are limited to inequality and set-builder.
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| MA.912.AR.3.9: | Given a mathematical or real-world context, write two-variable quadratic inequalities to represent relationships between quantities from a graph or a written description.Clarifications:
Clarification 1: Instruction includes the use of standard form, factored form and vertex form where any inequality symbol can be represented. |
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| MA.912.AR.3.10: | Given a mathematical or real-world context, graph the solution set to a two-variable quadratic inequality.Clarifications:
Clarification 1: Instruction includes the use of standard form, factored form and vertex form where any inequality symbol can be represented. |
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This cluster includes the following access points.
| Access Point Number |
Access Point Title |
| MA.912.AR.3.AP.1: | Given a one-variable quadratic equation from a mathematical or real-world context, select the solution to the equation over the real number system. |
| MA.912.AR.3.AP.2: | Solve mathematical one-variable quadratic equations with integer coefficients over the real and complex number systems. |
| MA.912.AR.3.AP.3: | Given a mathematical or real-world context, select a one-variable quadratic inequality over the real number system that represents the solution algebraically or graphically. |
| MA.912.AR.3.AP.4: | Select a quadratic function to represent the relationship between two quantities from a graph. |
| MA.912.AR.3.AP.5: | Given the x-intercepts and another point on the graph of a quadratic function, select the equation for the function. |
| MA.912.AR.3.AP.6: | Given an expression or equation representing a quadratic function in vertex form, determine the vertex and zeros. |
| MA.912.AR.3.AP.7: | Given a table, equation or written description of a quadratic function, select the graph that represents the function. |
| MA.912.AR.3.AP.8: | Given a mathematical and/or real-world problem that is modeled with quadratic functions, solve the mathematical problem, or select the graph using key features (in terms of context) that represents this model. |
| MA.912.AR.3.AP.9: | Select two-variable quadratic inequalities to represent relationships between quantities from a graph or a written description. |
| MA.912.AR.3.AP.10: | Select the graph of the solution set to a two-variable quadratic inequality. |
Vetted resources educators can use to teach the concepts and skills in this topic.
| Name |
Description |
| Quadratic Function Part 2: Launches: | Learn about different formats of quadratic equations and their graphs with experiments involving launching and shooting of balls in this interactive tutorial.
This is part 2 of a two-part series: Click HERE to open part 1. |
| Quadratic Functions Part 1: Ball Games: | Join us as we watch ball games and explore how the height of a ball bounce over time is represented by quadratic functions, which provides opportunities to interpret key features of the function in this interactive tutorial.
This is part 1 of a two-part series: Click HERE to open part 2. |
| Highs and Lows Part 2: Completing the Square: | Learn the process of completing the square of a quadratic function to find the maximum or minimum to discover how high a dolphin jumped in this interactive tutorial.
This is part 2 of a 2 part series. Click HERE to open part 1. |
| Highs and Lows Part 1: Completing the Square: | Learn the process of completing the square of a quadratic function to find the maximum or minimum to discover how high a dolphin jumped in this interactive tutorial.
This is part 1 of a 2 part series. Click HERE to open Part 2. |
| Solving Rational Equations: Cross Multiplying: | Learn how to solve rational linear and quadratic equations using cross multiplication in this interactive tutorial. |
| Finding the Zeros of Quadratic Functions: | Learn to find the zeros of a quadratic function and interpret their meaning in real-world contexts with this interactive tutorial. |
| Finding the Maximum or Minimum of a Quadratic Function: | Learn to complete the square of a quadratic expression and identify the maximum or minimum value of the quadratic function it defines. In this interactive tutorial, you'll also interpret the meaning of the maximum and minimum of a quadratic function in a real world context. |
| Graphing Quadratic Functions: | Follow as we discover key features of a quadratic equation written in vertex form in this interactive tutorial. |
| Name |
Description |
| Comparing Quadratics: | Students are asked to compare two quadratic functions, one given by a table and the other by a function. |
| Quilts: | Students are asked to write and solve an equation that models a given problem. |
| Graphing a Quadratic Function: | Students are asked to graph a quadratic function and answer questions about the intercepts, maximum, and minimum. |
| Zeros of a Quadratic: | Students are asked to identify the zeros of polynomials, without the use of technology, and then describe what the zeros of a polynomial indicate about its graph. |
| Model Rocket: | Students are asked to graph a function in two variables given in context. |
| Hotel Swimming Pool: | Students are asked to write an equation in two variables given a verbal description of the relationship among the variables. |
| Rocket Town: | Students are asked to rewrite a quadratic expression in vertex form to find maximum and minimum values. |
| Jumping Dolphin: | Students are asked to find the zeros of a quadratic function in the context of a modeling problem. |
| Complete the Square - 1: | Students are asked to solve a quadratic equation by completing the square. |
| A Home for Fido: | Students are asked to rewrite a quadratic function in an equivalent form by completing the square and to use this form to identify the vertex of the graph and explain its meaning in context. |
| Launch From a Hill: | Students are asked to factor and find the zeros of a polynomial function given in context. |
| Complete the Square - 2: | Students are asked to solve a quadratic equation by completing the square. |
| Complete the Square - 3: | Students are asked to solve a quadratic equation by completing the square. |
| Complex Solutions?: | Students are asked to explain how to recognize when the quadratic formula results in complex solutions. |
| Which Strategy?: | Students are shown four quadratic equations and asked to choose the best method for solving each equation. |
| Name |
Description |
| Solving Quadratic Equations by Completing the square: | Students will model the process of completing the square (leading coefficient of 1) with algebra tiles, and then practice solving equations using the completing the square method. This lesson provides a discovery opportunity to conceptually see why the process of squaring half of the b value is considered completing the square. |
| Solving Quadratics - Exploring Different Methods: | Students will explore how different methods find the solutions (roots) to quadratic equations including, factoring, graphing, and the quadratic formula. |
| Discovering Properties of Parabolas by Comparing and Contrasting Parabolic Equations: |
- Teachers can use this resource to teach students how to derive the equation of a parabola in vertex form y = a(x – h)2 + k, when given the (x, y) coordinates of the focus and the linear equation of the directrix.
- An additional interactive graphing spreadsheet can be used as a resource to aid teachers in providing examples.
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| Acting Out A Parabola: the importance of a vertex and directrix: | Students will learn the significance of a parabola's vertex and directrix. They will learn the meaning of what exactly a parabola is by physically representing a parabola, vertex, and directrix. Students will be able to write an equation of a parabola given only a vertex and directrix. |
| How High Can I Go?: | Students will graph quadratic equations, and identify the axis of symmetry, the maximum/minimum point, the vertex, and the roots. Students will work in pairs and will move around the room matching equations with given graphs. |
| Ranking Sports Players (Quadratic Equations Practice): | In this Model Eliciting Activity, MEA, students will rank sports players by designing methods, using different indicators, and working with quadratic equations.
Model-Eliciting-Activities, MEAs, allow students to critically analyze data sets, compare information, and require students to explain their thinking and reasoning. While there is no one correct answer in an MEA, students should work to explain their thinking clearly and rationally. Therefore, teachers should ask probing questions and provide feedback to help students develop a coherent, data-as-evidence-based approach within this learning experience. |
| Radical Mathematical: | In this lesson students will solve radical equations, showing how extraneous solutions may arise. Students will solve radical equations that model real-world relationships. |
| Hip to be (completing the) Square: | This lesson is an introduction to completing the square. Students will learn what it means to "complete the square" with a quadratic trinomial expression. They will practice both with manipulatives and mathematically, and will then use that information to find the maximum or minimum value of an expression using the vertex form of a quadratic. This lesson moves through all levels of Concrete, Representational, Abstract instruction. |
| Where did the answers go? Oh, they're imaginary!: | In this lesson, students will solve quadratic equations with imaginary (complex) solutions and be facilitated in the discovery of the Fundamental Theorem of Algebra. |
| Parts and more Parts-- Parabola Fun: | This is an entry lesson into quadratic functions and their shapes. Students see some real-life representations of parabolas. This lesson provides important vocabulary associated with quadratic functions and their graphs in an interactive manner. Students create a foldable and complete a worksheet using their foldable notes. |
| Graphing Quadratics Made Easy: Vertex Form of the Equation: | This lesson covers quadratic translations as they relate to vertex form of a quadratic equation. Students will predict what will happen to the graph of a quadratic function when more than one constant is in a quadratic equation. Then, the students will graph quadratic equations in vertex form using their knowledge of the translations of a quadratic function, as well as describe the translations that occur. Students will also identify the parent function of any quadratic function as  . |
| The Quadratic Quandary: | Students will sort various quadratic equations by the method they would use for solving (ie. factoring, quadratic formula). Then as a class they justify their placements and eventually discover that there are many ways to solve and that some make sense in different situations, however there is no real "correct" method for each equation type. |
Vetted resources students can use to learn the concepts and skills in this topic.
| Title |
Description |
| Quadratic Function Part 2: Launches: | Learn about different formats of quadratic equations and their graphs with experiments involving launching and shooting of balls in this interactive tutorial.
This is part 2 of a two-part series: Click HERE to open part 1. |
| Quadratic Functions Part 1: Ball Games: | Join us as we watch ball games and explore how the height of a ball bounce over time is represented by quadratic functions, which provides opportunities to interpret key features of the function in this interactive tutorial.
This is part 1 of a two-part series: Click HERE to open part 2. |
| Highs and Lows Part 2: Completing the Square: | Learn the process of completing the square of a quadratic function to find the maximum or minimum to discover how high a dolphin jumped in this interactive tutorial.
This is part 2 of a 2 part series. Click HERE to open part 1. |
| Highs and Lows Part 1: Completing the Square: | Learn the process of completing the square of a quadratic function to find the maximum or minimum to discover how high a dolphin jumped in this interactive tutorial.
This is part 1 of a 2 part series. Click HERE to open Part 2. |
| Solving Rational Equations: Cross Multiplying: | Learn how to solve rational linear and quadratic equations using cross multiplication in this interactive tutorial. |
| Finding the Zeros of Quadratic Functions: | Learn to find the zeros of a quadratic function and interpret their meaning in real-world contexts with this interactive tutorial. |
| Finding the Maximum or Minimum of a Quadratic Function: | Learn to complete the square of a quadratic expression and identify the maximum or minimum value of the quadratic function it defines. In this interactive tutorial, you'll also interpret the meaning of the maximum and minimum of a quadratic function in a real world context. |
| Graphing Quadratic Functions: | Follow as we discover key features of a quadratic equation written in vertex form in this interactive tutorial. |
Vetted resources caregivers can use to help students learn the concepts and skills in this topic.
