   • 03/07/14   |   Adjusted: 03/08/16   |   1 file # What Goes Up, Days 1–3

• Description
• Files

Mathematically:

• Addresses standards F-IF.B.4, F-IF.B.6, F-BF.B.3, A-CED.A.2, MP.4
• Connects a quadratic function with its graph, table, and matching verbal description
• Develops students' understanding of key features of a quadratic function in a real-world context (F-IF.B.4)
• Includes several stages of the basic modeling cycle (computing, interpreting, and validating) (MP.4)
• Provides opportunities for students to make use of the structure of a quadratic function (MP.7)
• Requires students to use precision in describing the path of an object, both qualitatively and quantitatively (MP.6)

In the classroom:

• Allows for student collaboration and discussion
• Uses technology to help make the mathematics explicit
• Gives formal and informal opportunities for teachers to check for understanding
• Provides extensive time for students to engage deeply with the mathematics

• Making the Shifts

How does this lesson exemplify the instructional Shifts required by CCSSM?

 Focus Belongs to the Widely Applicable Prerequisites for College and Careers Coherence Builds on many key understandings of functions from grade 8 and Algebra 1, expanding from linear to quadratic functions Rigor Conceptual Understanding: primary in this lesson Procedural Skill and Fluency: not addressed in this lesson Application: primary in this lesson
Within this lesson, students apply key understandings of functions and equations from previous grades or courses. Students graph the function $h(t)=-16t^2+50t+5$, showing how the height, $h(t)$, of a stone changes with relation to time, $t$. To create the graph, students evaluate the function for several input values of $t$. To find the specific time at which the stone will return to launch height (or similarly when it will hit the ground), students will need to find inputs that correspond to a specific output. For example, requiring that $h(t)=5$ gives an equation in one variable, $-16t^2+50t+5=5$, solvable by factoring. The distinction between function and equation is an important one as the two terms are often conflated by students and teachers. Equations answer a question: “For what values of the variable(s) is the equation true?” Functions, on the other hand, describe a rule for turning an input number into an output number and are neither true nor false. Confusion may arise when graphing: the graph of the solutions to an equation in two variables (an infinitude of $(u, v)$ pairs that satisfy the equation) can often look the same as the graph of a function (a picture of the output changes as the input changes). For more information, read pages 2 and 3 of the progression document, High School, Algebra.