![]() Students will return to their groups, go through the list and sort the conjectures into ones they agree with and ones they disagree with. After 10 minutes each group will share at least one conjecture which I will record on the screen. ![]() ![]() Once students have completed their charts, they will work with their group to form 3 conjectures about the relationships between the structure of the equations and the structure of the graphs. In groups of two to three, students will move around the classroom and complete the Polynomials Investigation chart in Google Slides for each polynomial. Ten different polynomial equations will be posted around the classroom. Slide 4 re-emphasizes that point and reveals that we need more information in order to sketch an accurate graph. Students will see that there are several possibilities for the sketch. Then on slide 3 students will attempt to sketch the polynomial based upon the x-intercepts. Slide 2 asks students to factor and solve the polynomial. Slide 1 is a visual of a roller coaster and asks students to determine and interpret several key features of polynomials in the context of the roller coaster. In the first 5 minutes of class students will complete slides 1 - 2 of the Intro to Polynomials Desmos. HSF.IF.C.7.c – Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. HSF.IF.B.4 – Sketch graphs showing key features including intercepts, intervals where the function is increasing, decreasing, positive, or negative relative maximums and minimums symmetries end behavior and periodicity. Polynomials Investigation Google Slides.It occurs directly after students learn about the degree, leading coefficient, continuity, roots, turning points, and end behavior of polynomials. Students learned how to determine key features such as the vertex, the x-intercept(s), the y-intercept, and the axis of symmetry from the equation and then how to plot the key features in order to sketch the graph of the quadratic function.This is the first time students will ever work with polynomial functions, so prior to this investigation activity students learned about the degree, leading coefficient, continuity, roots, turning points, and end behavior of polynomials.This is the second lesson in the unit. Students learned how to factor and solve quadratic equations to reveal the x-intercepts. Prior to this lesson: Prior to this unit students learned about quadratic functions, which are 2nd-degree polynomials. Social Learning: Students will work with others to compare conjectures and provide counterexamples.Students then identify the key features in relation to the diagram of the roller coaster. Use of Visuals: In the warm-up, the graph of a polynomial equation is compared to the shape of a roller coaster.Chunking: Each component of the lesson will last about 15 minutes.Active Learning (Movement): Students will be moving around the classroom during the first part of the lesson.Grade: 10 - 12th grade (Honors Algebra 2)īrain-based Strategies Used in the Lesson: Based on identified relationships and their knowledge of key features, students will be able to construct a possible polynomial equation to represent a given graph.Įssential Question: How can we use structure to interpret polynomials and to construct a sketch of the graph?.Based on identified relationships, students will be able to sketch a graph of any polynomial function using key features and the equation’s structure.The students will be able to make connections between the algebraic representation of a polynomial and its graph features.The students will identify key features from the graphs of several polynomial functions and then use repeated reasoning and structure to make conjectures about possible relationships between polynomial characteristics.This graph has two \(x\)-intercepts.Polynomials Investigation Lesson Lesson Objectives: \): Illustration of the end behaviour of the polynomial.
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