Students play and record the “Mary Had a Little Lamb” song using musical instruments and analyze the intensity of the sound using free audio editing and recording software. Then they use hollow Styrofoam half-spheres as acoustic mirrors (devices that reflect and focus sound), determine the radius of curvature of the mirror and calculate its focal length. Students place a microphone at the acoustic mirror focal point, re-record their songs, and compare the sound intensity on plot spectrums generated from their recordings both with and without the acoustic mirrors. A worksheet and KWL chart are provided.

3-minute video about "Symbol Imagery" (taking a picture with your mind) and practice applying that to remember that the x-coordinate of the vertex of a parabola is -b/2a .

Grade Level: Students taking Algebra 2Content: The curriculum being discussed is creating the vertex equation for a parabola from the parent equation.Previous Knowledge: Students should know how to transform a linear equation. That knowledge will aid when they are manipulating the quadratic equation.Students should know the basic quadratic equation information and how it affects the graph i.e. x-intercepts, vertex, axis of symmetry.Students should know that a basic (parent) quadratic equation is y = x².Objective: Be able to write an equation for a parabola in vertex form given multiple parameters. Will also use technology to aid in this discovery.IntroductionAfter reviewing the objectives for the day’s lesson, I have students open their notebooks. Then, I let students know that I want them to take notes as they watch a 2-minute video over quadratic functions and parabolas in the real world.After the video is complete, I ask students to complete the following Think-Pair-Share protocol:Think – 2 minutes to write down your thoughts and update your notes from watching the videosPair – 3-5 minutes to compare and contrast your ideas with a partnerShare – 5-10 minute class discussion of ideas answering the prompt “Describe different characteristics of quadratic functions and their graphs”VocabularyParabolaQuadratic EquationVertexAxis of SymmetryMinimumMaximumBody of LessonThe students will get into pairs to log in to the desmos website. They will be given approximately ten different scenarios of how to move their parabola. For instance, they will be given the parent equation of y = x² and told to move it five units to the left. The student will have to guess where to represent the five in the equation to make the entire graph move five units. The different scenarios could include moving the graph right or left, up or down, and stretching or compressing the parabola.After they have worked out the different scenarios, the students will work with their partners to create the formula for vertex form for a quadratic equation.Next, the students will then use the equation they just created to help them in graphing more parabolas.As part of the closure, we will discuss as a class how the actual vertex (h, k) relates to the equation.Accommodations/ ModificationsGo around the classroom and make sure all students understand what to doPair students with a compatible partner so they can teach each otherProvide extra time for students to finish assignment or assessmentsReduce independent practice to half of the problemsAllow students to use the textbook in their first language or use a Dictionary to help them translate words so that they understand what is being asked of them​​​​​​​AssessmentThe the students will be given a quiz over the concept of parabolas the next day.The students will be assessed over this concept at the end of the chapter on the chapter test.​​​​​​​MaterialsTextbookComputer with Internet ConnectionNotebookPencil​​​​​​​StandardsA-CED 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.F-IF 7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.F-BF 3. Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.MA 11.2.1.g Analyze and graph quadratic functions (standard form, vertex form, finding zeros, symmetry, transformations, determine intercepts, and minimums or maximums)​​​​​​​

Video lecture on quadratic equations and their graphs. The video connects the equation, the graph, the roots, and the minimum or maximum of the quadratic function.

In this activity, students explore how trebuchets were used during the Middle Ages to launch projectiles over or through castle walls as well as how they are used today in events such as Punkin’ Chunkin’. Students work as teams of engineers and research how to design and build their own trebuchets from scratch while following a select number of constraints. They test their trebuchets, evaluate their results through several quantitative analyses, and present their results and design process to the class.