See how the equation form of Ohm's law relates to a simple …
See how the equation form of Ohm's law relates to a simple circuit. Adjust the voltage and resistance, and see the current change according to Ohm's law. The sizes of the symbols in the equation change to match the circuit diagram.
"Open textbooks are textbooks that have been funded, published, and licensed to …
"Open textbooks are textbooks that have been funded, published, and licensed to be freely used, adapted, and distributed. These books have been reviewed by faculty from a variety of colleges and universities to assess their quality. These books can be downloaded for no cost, or printed at low cost."
Student groups work with manipulatives—pencils and trays—to maximize various quantities of a …
Student groups work with manipulatives—pencils and trays—to maximize various quantities of a system. They work through three linear optimization problems, each with different constraints. After arriving at a solution, they construct mathematical arguments for why their solutions are the best ones before attempting to maximize a different quantity. To conclude, students think of real-world and engineering space optimization examples—a frequently encountered situation in which the limitation is the amount of space available. It is suggested that students conduct this activity before the associated lesson, Linear Programming, although either order is acceptable.
In this video lesson, students will learn about linear programming (LP) and …
In this video lesson, students will learn about linear programming (LP) and will solve an LP problem using the graphical method. Its focus is on the famous "Stigler's diet" problem posed by the 1982 Nobel Laureate in economics, George Stigler. Based on his problem, students will formulate their own diet problem and solve it using the graphical method. The prerequisites to this lesson are basic algebra and geometry. The materials needed for the in-class activities include graphing paper and pencil. This lesson can be completed in one class of approximately one hour. If the teacher would like to cover the simplex algorithm by George Dantzig as an alternative solution method, an additional whole class period is suggested.
This is a simple exercise in creating equations from a situation with …
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.
To plot an inequality, such as x>3, on a number line, first …
To plot an inequality, such as x>3, on a number line, first draw a circle over the number (e.g., 3). Then if the sign includes equal to (≥ or ≤), fill in the circle. If the sign does not include equal to (> or <), leave the circle unfilled in. Finally, draw a line going from the circle in the direction of the numbers that make the inequality true.
Prealgebra is designed to meet scope and sequence requirements for a one-semester …
Prealgebra is designed to meet scope and sequence requirements for a one-semester prealgebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text introduces the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.
This task compares the usefulness of different forms of a quadratic expression. …
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 lesson is about properties of quadrilaterals and learning to investigate, formulate, …
This lesson is about properties of quadrilaterals and learning to investigate, formulate, conjecture, justify, and ultimately prove mathematical theorems. Students will: Analyze characteristics and properties of two- and three-dimensional geometric shapes; develop mathematical arguments about geometric relationships; and apply appropriate techniques, tools, and formulas to determine measurements.Explore relationships among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them. Employ forms of mathematical reasoning and proof appropriate to the solution of the problem at hand, including deductive and inductive reasoning, making and testing conjectures, and using counter examples and indirect proof. Identify, formulate and confirm conjectures. Establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others. (9th/10th Grade Math)
This Flexbook is community contributed through ck12.org. It covers three lessons on …
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 …
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 …
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) …
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) …
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 …
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 lesson unit is intended to help teachers assess how well students …
This lesson unit is intended to help teachers assess how well students are able to: translate between decimal and fraction notation, particularly when the decimals are repeating; create and solve simple linear equations to find the fractional equivalent of a repeating decimal; and understand the effect of multiplying a decimal by a power of 10.
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