Modeling Our World with Mathematics Unit 4: Finances for Life Topic 1 - Introduction to Finance 

 Modeling Our World with Mathematics Unit 4: Finances for Life Topic 3 - Business

Modeling Our World with Mathematics Unit 5: Digital World Topic 1 - Digital Presence

This engineering design challenge is a great hands-on activity that utilizes the engineering design process, 3D modeling, and 3D printing technology. The challenge can be completed individually or in groups of 2 to 3. Students will work to complete the following challenge: Using the design process, design, document, model, and produce a toy car with interchangeable parts.

The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards.  Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.

This resource was created by the Washington Office of Superintendent of Public Instruction. 

This resource was created by the Washington Office of Superintendent of Public Instruction. 

This lesson unit is intended to help teachers assess how well students are able to: interpret a situation and represent the constraints and variables mathematically; select appropriate mathematical methods to use; explore the effects of systematically varying the constraints; interpret and evaluate the data generated and identify the optimum case, checking it for confirmation; and communicate their reasoning clearly.

This course is designed to cover topics in Algebra ranging from polynomial, rational, and exponential functions to conic sections. Trigonometry concepts such as Law of Sines and Cosines will be introduced. Students will then begin analytic geometry and calculus concepts such as limits, derivatives, and integrals. This class is important for any student planning to take a college algebra or college pre-calculus class.

The PhET Activities Database is a collection of resources for using PhET sims. It includes hundreds of lesson plans, homework assignments, labs, clicker questions, and more. Some activities have been created by the PhET team and some have been created by teachers.

Students groups act as NASA/GM engineers challenged to design, build and test robotic hands, which are tactile feedback systems made from cloth gloves and force sensor circuits. Student groups construct force sensor circuits using electric components and FlexiForce sensors to which resistance changes based on the applied force. They conduct experiments to find the mathematical relationship between the force applied to the sensor and the output voltages of the circuit. They take several measurements force vs. resistance, force vs. voltage and use the data to find the best fit curve models for the sensor. Different weights applied to the sensor are used as a scalable force. Students use traditional methods and current technology (calculators) to plot the collected data and define the curve equations. Students test their gloves and use a line of best fit to determine the minimum force required to crack an egg held between the index finger and thumb. A PowerPoint(TM) file and many student handouts are included.

Student teams are challenged to evaluate the design of several liquid soaps to answer the question, “Which soap is the best?” Through two simple teacher class demonstrations and the activity investigation, students learn about surface tension and how it is measured, the properties of surfactants (soaps), and how surfactants change the surface properties of liquids. As they evaluate the engineering design of real-world products (different liquid dish washing soap brands), students see the range of design constraints such as cost, reliability, effectiveness and environmental impact. By investigating the critical micelle concentration of various soaps, students determine which requires less volume to be an effective cleaning agent, factors related to both the cost and environmental impact of the surfactant. By investigating the minimum surface tension of the soap, students determine which dissolves dirt and oil most effectively and thus cleans with the least effort. Students evaluate these competing criteria and make their own determination as to which of five liquid soaps make the “best” soap, giving their own evidence and scientific reasoning. They make the connection between gathered data and the real-world experience in using these liquid soaps.

Algebra students need practice determining equations of lines given a pair of points, or the line parallel or perpendicular to a given line through a given point. This Demonstration, along with guiding worksheets or a teacher presentation, gives students a chance to see the relationships between these lines and points.

This lesson unit is intended to help teachers assess how well students are able to formulate and solve problems using algebra and, in particular, to identify and help students who have the following difficulties: solving a problem using two linear equations with two variables; and interpreting the meaning of algebraic expressions.

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.

This resource is geared for teacher use. It is loosely linked to the Secondary Math II, Mathematics Vision Project curriculum.