Algebra 1 for Accelerated Learners: Introductions to Quadratic Equations
In this rigorous math course, learners will interpret, write, and solve quadratic equations and answer questions about quadratic functions using reasoning,the zero product property, the quadratic formula, and completing the square.
Malikai Bass M.A
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5.0
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What's included
30 live meetings
25 in-class hoursHomework
Students will complete one mathematical modeling project.Assessment
Students will receive regular written feedback.Class Experience
US Grade 7 - 10
Intermediate Level
This is the seventh and last course in a year-long sequence which covers standards and ideas in Algebra 1 intended for learners in middle school ready to begin Algebra 1 or high school learners who need additional support. These courses are taught in small-groups to provide individual instruction and social-learning opportunities aligned with a social constructionist or situated cognition view of learning. The curriculum is problem-based this means instead of lectures or videos students work together as a small group to solve problems to discover principles and strategies with teacher guidance, as necessary. Therefore, we will spend approximately 90% of each class period working on problems and discussing them as a group. The use of discussion and problem-solving leads to generalized mathematics or proofs and students will construct their own models or proofs of real-world scenarios in project based assignments. This process prepares students well who may seek advanced mathematics in high-school or beyond. In this unit, students delve into the world of quadratic equations, learning to interpret, write, and solve them. They discover the power of algebraic solutions in determining input values for desired output values, exemplified by finding the ticket price that yields a $10,000 revenue for a theater. The journey starts with reasoning through quadratic equations, exploring the possibility of 2, 1, or 0 solutions. The zero product property becomes a valuable tool, aiding in the solution of equations in factored form. Perfect squares provide another avenue for straightforward solutions, but completing the square introduces a more universal method, laying the groundwork for the quadratic formula. Students grapple with its application, exploring its derivation and strategic use. The unit unfolds with an exploration of irrational solutions and culminates in the synthesis of knowledge, guiding students to employ diverse methods in solving both applied and mathematical problems, demonstrating a comprehensive understanding of quadratic equations. Week 1: - Readiness Check - Finding Unknown Inputs for Quadratic Expressions - Writing Quadratic Equations - Solving Quadratic Equations with Reasoning - Zero Product Property Week 2: - Identifying Number of Solutions for Quadratic Equations - Recognizing Factored Form - Rewriting into Factored Form - Factored Form without Linear Terms - Solving Using Factored Forms Week 3: - Factored Form with non-1 Coefficients - Mid-Unit Assessment - Perfect Squares -Modeling Project Week 4: -Completing the Square - Irrational Solutions -Quadratic Formula Week 5 - Applying the Quadratic Formula - Deriving the Quadratic Formula - Rational and Irrational Solutions - Sums and Products of Rational and Irrational Numbers Week 6 - Vertex Form -Using Vertex Form to Solve Problems - Using Vertex Form to Model Situations - End of Unit Assessment
Learning Goals
HSA-CED.A
Create equations that describe numbers or relationships.
HSA-CED.A.1
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
HSA-CED.A.2
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
HSA-CED.A.3
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
HSA-CED.A.4
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
HSA-REI.B.4
Solve quadratic equations in one variable.
HSA-REI.B.4.a
Use the method of completing the square to transform any quadratic equation in into an equation of the form that has the same solutions. Derive the quadratic formula from this form.
HSA-REI.B.4.b
Solve quadratic equations by inspection (e.g., for ), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as for real numbers and .
HSA-SSE.B
Write expressions in equivalent forms to solve problems.
HSA-SSE.B.3
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
HSA-SSE.B.3.a
Factor a quadratic expression to reveal the zeros of the function it defines.
HSA-SSE.B.3.b
Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.HSF-IF.B
Interpret functions that arise in applications in terms of the context.
HSF-IF.B.4
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
HSF-IF.B.5
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function gives the number of person-hours it takes to assemble engines in a factory, then the positive integers would be an appropriate domain for the function.
HSF-IF.B.6
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
HSF-IF.C
Analyze functions using different representations.
HSF-IF.C.7
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
HSF-IF.C.7.a
Graph linear and quadratic functions and show intercepts, maxima, and minima.
Other Details
Parental Guidance
Students will need to use Nearpod. They will need to click a link and enter their first name or initial. No other identifying information will be collected.
Supply List
Learners will need standard notetaking supplies. A teacher provided printable guided note-taking workbook will be provided.
External Resources
In addition to the Outschool classroom, this class uses:
Joined April, 2021
5.0
316reviews
Popular
Teacher expertise and credentials
Professional Experience:
I have been a math tutor for over 12 years and have worked with students from ages 5-25 in small group and academic settings including serving as a primary teacher for home educated learners. I have received training and tutoring certification/awards from nationally recognized organizations. I was a group supplemental instruction leader for math at the collegiate level for four years at ETSU including working with dual enrolled and accelerated learners. I have taught and tutored math up to a graduate level in algebra, geometry, probability, and quantitative reasoning.
Academic Experience:
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Reviews
Live Group Class
$450
for 30 classes5x per week, 6 weeks
50 min
Completed by 5 learners
Live video meetings
Ages: 12-15
3-6 learners per class
