This is a simple exercise in creating equations from a situation with many variables. By giving three different scenarios, the problem requires students to keep going back to the definitions of the variables, thus emphasizing the importance of defining variables when you write an equation. In order to reinforce this aspect of the problem, the variables have not been given names that remind the student of what they stand for. The emphasis here is on setting up equations, not solving them.

This lesson looks at how to determine the multiplicity of a zero/root of a polynomial function.

Precalculus (was College Algebra) is an introductory text. The material is presented at a level intended to prepare students for Calculus while also giving them relevant mathematical skills that can be used in other classes. The authors describe their approach as "Functions First," believing introducing functions first will help students understand new concepts more completely. Each section includes homework exercises, and the answers to most computational questions are included in the text (discussion questions are open-ended). Graphing calculators are used sparingly and only as a tool to enhance the Mathematics, not to replace it. Note: this book was updated on the BC Open textbook Project site on February, 17, 2015 to include the version of the textbook with chapters on Trigonometry.

This task compares the usefulness of different forms of a quadratic expression. Students have to choose which form most easily provides information about the maximum value, the zeros and the vertical intercept of a quadratic expression in the context of a real world situation. Rather than just manipulating one form into the other, students can make sense out of the structure of the expressions.

This Flexbook is community contributed through ck12.org. It covers three lessons on the Pythagorean Theorem. 1) Introduction and Determining if the Triangle is a Right Triangle, 2) Finding the Hypotenuse, and 3) Finding a leg. It includes step by step instructions, application problems, and answers (at the end of each lesson). Ck12.org material is downloadable, editable, and accessible offline and online.

This lesson focuses on students making decisions about what tools to apply to solve different problems related to quadratic expressions and equations. It is also intended to build awareness of the form an answer will take in order to help students make sense of the kind of problem they are solving. (9th/10th/11th Grade Math)

This question provides students with an opportunity to see expressions as constructed out of a sequence of operations: first taking the square root of n, then dividing the result of that operation into s. Students studying statistics encounter the expression in this question as the standard deviation of a sampling distribution with samples of size n when the distribution from which the sample is taken has standard deviation s.

This task has some aspects of a mathematical modeling problem (SMP 4) and it also illustrates SMP 1 (Making sense of a problem). Students are given all the relevant information on the nutritional labels, but they have to figure out how to use this information. They have to come up with the idea that they can set up two equations in two unknowns to solve the problem.

This tasks is an example of a mathematical modeling problem (SMP 4) and it also illustrates SMP 1 (Making sense of a problem). Students are only told that there are two ingredients in the pasta and they have a picture of the box. It might even be better to just show the picture of the box, or to bring in the box and ask the students to pose the question themselves.

The purpose of the task is to show students a situation where squaring both sides of an equation can result in an equation with more solutions than the original one. The reason for this is that it is possible to have two unequal numbers whose squares are equal.

This reading goes over steps to calculate rate of reactions. Calculating rate of reactions can seem a little bit confusing, but hopefully going over this reading you’ll be more confident.

During the early days of the coronavirus pandemic, we all made sacrifices to slow the spread of the virus and to flatten the curve of infections.The curve itself appears in the susceptible-infected-recovered (SIR) model – a simple epidemiological model that explains some of the basic dynamics of infectious disease. Curve-flattening effects of mitigation measures such as social distancing, mask wearing, and hand washing can be seen in the dynamics of the SIR model as can the phenomenon of herd-immunity.In this activity, students are encouraged to derive the SIR model from scratch and to explore dynamical features of the model such as curve flattening and herd immunity.These resources were created by Dr. Robert Kipka of Lake Superior State University. They are intended for high school students and teachers. Calculus or familiarity with families of functions such as logarithms is not required. However, in spite of the relatively modest mathematical background called for, this activity may be challenging.It may help to complete the Three Weeks in March activity before beginning.

The purpose of this task is to provide an opportunity for students to reason about equivalence of equations. The instruction to give reasons that do not depend on solving the equation is intended to focus attention on the transformation of equations as a deductive step.

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.

The purpose of this task is to identify the structure in the two algebraic expressions by interpreting them in terms of a geometric context. Students will have likely seen this type of process before, so the principal source of challenge in this task is to encourage a multitude and variety of approaches, both in terms of the geometric argument and in terms of the algebraic manipulation.

Explore your own straight-line motion using a motion sensor to generate distance versus time graphs of your own motion. Learn how changes in speed and direction affect the graph, and gain an understanding of how motion can be represented on a graph.

In this undergraduate level seminar series topics vary from year to year. Students present and discuss the subject matter, and are provided with instruction and practice in written and oral communication. Some experience with proofs required. The topic for fall 2008: Computational algebra and algebraic geometry.

Seminar for mathematics majors. Students present and discuss the subject matter and write up exercises. Topic for Fall 2002: Classical geometry, beginning with Euclid's Elements and continuing to applications of Galois theory that solve the geometry problems of antiquity. No prior knowledge of Galois theory required. Instruction and practice in oral communication provided.

This is an Algebra 2 Unit that explores sequences and series.  This includes arithmetic, geometric, and other sequences, as well as recursive and explicit formulas that generate these sequences.  Arithmetic, finite geometric, and infinite geometric series are also covered in this unit.  This unit is designed as a flipped instructional unit.  Worksheets and video links are provided.

This word problem is based estimating the height of a person over time. Note that there is a significant amount of rounding in the final answer. This is because people almost never report their heights more precisely than the closest half-inch. If we assume that the heights reported in the task stem are rounded to the nearest half-inch, then we should report the heights given in the solution at the same level of precision.