Playing the role of engineers in collaborations with the marketing and production …
Playing the role of engineers in collaborations with the marketing and production teams in a chocolate factory, students design a container for a jumbo chocolate bar. The projects constraints mean the container has to be a regular trapezoidal prism. The design has to optimize the material used to construct the container; that is, students have to find the dimensions of the container with the maximum volume possible. After students come up with their design, teams present a final version of the product that includes creative branding and presentation. The problem-solving portion of this project requires students to find a mathematical process to express the multiple variables in the prism’s volume formula as a single variable cubic polynomial function. Students then use technology to determine the value for which this function has a maximum and, with this value, find the prism’s optimal dimensions.
Roller coasters projects are frequently used in middle and high school physics …
Roller coasters projects are frequently used in middle and high school physics classes to illustrate the principle of conservation of mechanical energy. Potential energy transforms to kinetic energy and vice versa, with gravity being the driving force during the entire process. Even though friction force is mentioned, it is rarely considered in the velocity calculations along the coasters’ paths. In this high school lesson, the friction force is considered in the process. Using basic calculus and the work-energy theorem for non-conservative forces, the friction along a curved path is quantified, and the cart’s velocity along this path is predicted. This activity and its associated lesson are designed for AP Calculus. Practice problems/answers, a PowerPoint® presentation and student notes are provided.
Although this task is quite straightforward, it has a couple of aspects …
Although this task is quite straightforward, it has a couple of aspects designed to encourage students to attend to the structure of the equation and the meaning of the variables in it. It fosters flexibility in seeing the same equation in two different ways, and it requires students to attend to the meaning of the variables in the preamble and extract the values from the descriptions.
In this activity, students explore how trebuchets were used during the Middle …
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.
The purpose of this task is to emphasize the adjective "geometric" in …
The purpose of this task is to emphasize the adjective "geometric" in the "geometric" series, namely, that the algebraic notion of a common ratio between terms corresponds to the geometric notion of a repeated similarity transformation.
In this task students must investigate this conjecture to discover that it …
In this task students must investigate this conjecture to discover that it does not work in all cases: Pick any two integers. Look at the sum of their squares, the difference of their squares, and twice the product of the two integers you chose. Those three numbers are the sides of a right triangle.
Using manipulatives, students figure out patterns in problems involving seating arrangements. They …
Using manipulatives, students figure out patterns in problems involving seating arrangements. They write algebraic equations to describe the relationships.
Students are introduced to algebraic expressions that use more than one variable …
Students are introduced to algebraic expressions that use more than one variable and have multiple solutions. They figure out combinations of two items at different costs, with each combination adding up to 100.
Prepared with pre-algebra or algebra 1 classes in mind, this module leads …
Prepared with pre-algebra or algebra 1 classes in mind, this module leads students through the process of graphing data and finding a line of best fit while exploring the characteristics of linear equations in algebraic and graphic formats. Then, these topics are connected to real-world experiences in which people use linear functions. During the module, students use these scientific concepts to solve the following hypothetical challenge: You are a new researcher in a lab, and your boss has just given you your first task to analyze a set of data. It being your first assignment, you ask an undergraduate student working in your lab to help you figure it out. She responds that you must determine what the data represents and then find an equation that models the data. You believe that you will be able to determine what the data represents on your own, but you ask for further help modeling the data. In response, she says she is not completely sure how to do it, but gives a list of equations that may fit the data. This module is built around the legacy cycle, a format that incorporates educational research feindings on how people best learn.
This set of problems for Linear Algebra in the open-source WeBWorK mathematics …
This set of problems for Linear Algebra in the open-source WeBWorK mathematics platform was created under a Round Eleven Mini-Grant for Ancillary Materials Creation. The problems were created for an implementation of the CC-BY Lyrix open textbook A First Course in Linear Algebra. Also included as an additional file are the selected and modified Lyryx Class Notes for the textbook.
Topics covered include:
Linear Independence Linear Transformations Matrix of a Transformation Isomorphisms Eigenvalues and Eigenvectors Diagonalization Orthogonality
The principal purpose of the task is to explore a real-world application …
The principal purpose of the task is to explore a real-world application problem with algebra, working with units and maintaining reasonable levels of accuracy throughout.
Students act as food science engineers as they explore and apply their …
Students act as food science engineers as they explore and apply their understanding of cooling rate and specific heat capacity by completing two separate, but interconnected, tasks. In Part 1, student groups conduct an experiment to explore the cooling rate of a cup of hot chocolate. They collect and graph data to create a mathematical model that represents the cooling rate, and use an exponential decay regression to determine how long a person should wait to drink the cup of hot chocolate at an optimal temperature. In Part 2, students investigate the specific heat capacity of the hot chocolate. They determine how much energy is needed to heat the hot chocolate to an optimal temperature after it has cooled to room temperature. Two activity-guiding worksheets are included.
The purpose of this task is to give students practice writing a …
The purpose of this task is to give students practice writing a constraint equation for a given context. Instruction accompanying this task should introduce the notion of a constraint equation as an equation governing the possible values of the variables in question.
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