Students will be able to interpret word problems to create equations in one variable and solve them (i.e., determine the solution set) using factoring and the zero product property

Adapted from mathematicsvisionproject.com’s Material Overview:
The Mathematics Vision Project (MVP) was created as a resource for teachers to implement the Common Core State Standards (CCSS) using a task-based approach that leads to skill and efficiency in mathematics by first developing understanding. The MVP approach develops the Standards of Mathematical Practice through experiential learning. Students engage in mathematical problem solving, guided by skilled teachers, in order to achieve mathematical proficiency: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. The MVP authors created a curriculum where students do not learn solely by either “internalizing what a teacher or book says or, on the other hand, solely by inventing mathematics on their own.”
The MVP classroom experience begins by confronting students with an engaging problem and allows them to grapple with solving it. As students’ ideas emerge, take form, and are shared, the teacher deliberately orchestrates the student discussions and explorations toward a focused math goal. Students justify their own thinking while clarifying, describing, comparing, and questioning the thinking of others leading to refined thinking and mathematical fluency. What begin as ideas become concepts that lead to formal, traditional math definitions and properties. Strategies become algorithms that lead to procedures supporting efficiency and consistency. Representations become tools of communication which are formalized as mathematical models. Students learn by doing mathematics.

Image of parabola on coordinate plane, with hot spots indicating focus and directrix, along with an example of deriving the equation for a parabola given the focus and directrix.

In this task students use their techniques for changing the forms of quadratic expressions (i.e., factoring, completing the square to put the quadratic in vertex form, or using the quadratic formula to find the x-intercepts) as strategies for solving quadratic equations.

This video models a context that concerns a candy vending machine. The model turns out to be a quadratic inequality.

The purpose of this task is to develop a strategy for solving quadratic inequalities and extend this strategy to higher-degree polynomials when the factors are known. The context of the task gives students an opportunity to engage in mathematical modeling: students will use mathematical models, in this case quadratic and cubic inequalities, to model various contextualized situations. The solutions to the inequalities then have to be interpreted in terms of what they mean in the situations. That is, the solutions for x in the inequalities are not the answers to the questions being asked in the situations—rather they provide information from which those questions can be answered. Students will have to keep track of the meaning of the variables as they work through these problems.

Course presentation showing relationship of sine and cosine of angles in a right triangle

Description of sine function with image, calculation of length of hypotenuse with known angle and opposite side, calculation of angle with known opposite and hypotenuse sides. Explanation of inverse sine. Interactive fill in the blank of main points.

Description of tangent function with image, calculation of length of opposite side with known angle and adjacent side, calculation of angle with known opposite and adjacent sides. Explanation of inverse tangent Interactive fill in the blank of main points.

The purpose of this task is to solidify student understanding of quadratic functions by giving another opportunity to create a quadratic model for a context. This task introduces the idea that quadratic functions are models for the sum of a linear function, which obviously creates a linear rate of change. Again, students have the opportunity to use algebraic, numeric, and graphical representations to model a story context with a visual model.

This is a PBL project originally done in a Math 2 class at the beginning of the year. It was a relatively low stakes project that allowed students to get a feel for the PBL process and identify gaps of fundamental math knowledge so they could develop a personalized plan to close those gaps - ideally while relating it to their academic and career goals. It can also be adapted to other math courses.