This college technical math textbook has been edited to cover the topics …
This college technical math textbook has been edited to cover the topics of operations with real numbers, working with and converting measurements, solving equations, using percents, using proportions and variation, graphing linear equations, geometry basics, trigonometry basics, and vectors.
This college mathematics textbook has bee edited to cover the law of …
This college mathematics textbook has bee edited to cover the law of sines and cosines, polynomials, factoring, quadratic equations, rational expressions, and systems of equations.
The purpose of this task is to help students understand the connection …
The purpose of this task is to help students understand the connection between counting and cardinality. Thus, oral counting and recording the number in digit form are the most important aspects of this activity. However, teachers can extend this by making a bar graph about how many students are wearing the color each day.
This 2-lesson unit focuses on combinations, a subject related to probability. Students …
This 2-lesson unit focuses on combinations, a subject related to probability. Students develop strategies for discovering all the possible combinations in two given situations. They learn to collect and organize data and then use the results to generalize methods for determining possible combinations. They discuss how the number of possible outcomes is affected by decisions about the order of choices, or whether choices may be repeated. The unit includes student activity sheets, questions and extensions for students, and a link to an interactive applet.
This course analyzes combinatorial problems and methods for their solution. Topics include: …
This course analyzes combinatorial problems and methods for their solution. Topics include: enumeration, generating functions, recurrence relations, construction of bijections, introduction to graph theory, network algorithms, and extremal combinatorics.
Thorough treatment of linear programming and combinatorial optimization. Topics include network flow, …
Thorough treatment of linear programming and combinatorial optimization. Topics include network flow, matching theory, matroid optimization, and approximation algorithms for NP-hard problems. 18.310 helpful but not required.
Content varies from year to year. An introduction to some of the …
Content varies from year to year. An introduction to some of the major topics of present day combinatorics, in particular enumeration, partially ordered sets, and generating functions. This is a graduate-level course in combinatorial theory. The content varies year to year, according to the interests of the instructor and the students. The topic of this course is hyperplane arrangements, including background material from the theory of posets and matroids.
Content varies from year to year. An introduction to some of the …
Content varies from year to year. An introduction to some of the major topics of present day combinatorics, in particular enumeration, partially ordered sets, and generating functions. This course serves as an introduction to major topics of modern enumerative and algebraic combinatorics with emphasis on partition identities, young tableaux bijections, spanning trees in graphs, and random generation of combinatorial objects. There is some discussion of various applications and connections to other fields.
The primary purpose of this problem is to rewrite simple rational expressions …
The primary purpose of this problem is to rewrite simple rational expressions in different forms to exhibit different aspects of the expression, in the context of a relevant real-world context (the fuel efficiency of of a car). Indeed, the given form of the combined fuel economy computation is useful for direct calculation, but if asked for an approximation, is not particularly helpful.
As a class, students use a low-cost air quality monitor (a rentable …
As a class, students use a low-cost air quality monitor (a rentable “Pod”) to measure the emissions from different vehicles. By applying the knowledge about combustion chemistry that they gain during the pre-activity reading (or lecture presentation, alternatively), students predict how the emissions from various vehicles will differ in terms of pollutants (CO2, VOCs and NO2), and explain why. After data collection, students examine the time series plots as a class—a chance to interpret the results and compare them to their predictions. Short online videos and a current event article help to highlight the real-world necessity of understanding and improving vehicle emissions. Numerous student handouts are provided. The activity content may be presented independently of its unit and without using an air quality monitor by analyzing provided sample data.
Introduces students to the basic tools in using data to make informed …
Introduces students to the basic tools in using data to make informed management decisions. Covers introductory probability, decision analysis, basic statistics, regression, simulation, and linear and nonlinear optimization. Computer spreadsheet exercises and examples drawn from marketing, finance, operations management, and other management functions. Restricted to Sloan Fellows.
Students groups create scientific research posters to professionally present the results of …
Students groups create scientific research posters to professionally present the results of their AQ-IQ research projects, which serves as a conclusion to the unit. (This activity is also suitable to be conducted independently from its unit—for students to make posters for any type of project they have completed.) First, students critically examine example posters to gain an understanding of what they contain and how they can be made most effective for viewers. Then they are prompted to analyze and interpret their data, including what statistics and plots to use in their posters. Finally, groups are given a guide that aids them in making their posters by suggesting all the key components one would find in any research paper or presentation. This activity is suitable for presenting final project posters to classmates or to a wider audience in a symposium or expo environment. In addition to the poster-making guide, three worksheets, six example posters, a rubric and a post-unit survey are provided.
In this course students will learn about Noetherian rings and modules, Hilbert …
In this course students will learn about Noetherian rings and modules, Hilbert basis theorem, Cayley-Hamilton theorem, integral dependence, Noether normalization, the Nullstellensatz, localization, primary decomposition, DVRs, filtrations, length, Artin rings, Hilbert polynomials, tensor products, and dimension theory.
Lesson objective: Compare lengths of objects both directly and indirectly. Understand that …
Lesson objective: Compare lengths of objects both directly and indirectly. Understand that if object A is longer than object B and object B is longer than object C, then object A is longer than object C. This lesson helps to build fluency with comparing lengths of objects indirectly. Images and clues are used here because they allow students to build the relationships between direct and indirect comparison. Students engage in Mathematical Practice 7 (Look for and make use of structure) as they use transitivity, indirect comparison to compare length measurement.
This resource provides repeated practice of measurement to the nearest inch. Practice …
This resource provides repeated practice of measurement to the nearest inch. Practice includes measurement of different real life objects, and then asks students to compare lengths of given objects in an interactive format.
Lesson objective: Extend prior knowledge about comparing two objects and develop the …
Lesson objective: Extend prior knowledge about comparing two objects and develop the understanding that comparing lengths of objects requires taking both endpoints into account. This lesson helps to build understanding that comparing lengths of objects requires taking both endpoints into account. Images are used here because they support the procedural skills of comparing lengths of objects. This work develops students' understanding that both endpoints must be taken into account when comparing lengths of objects. Students bring prior knowledge of comparing two objects describing measureable attributes of objects, such as length or weight (Grade K, Unit 8, K.MD.1D), and directly compare two objects with a measureable attribute in common, to see which object has "more of"/"less of" the attribute, and describe the difference (Grade K, Unit 8, K.MD.1D). This prior knowledge is extended to taking both endpoints into account as students must determine which pieces of licorice are longer. A conceptual challenge students may encounter is considering only one pair of endpoints when comparing objects. The concept is developed through work with linear models such as ribbons, pieces of paper, or string which allow students to physically match up and align objects at the same endpoints and compare the other endpoints. This work helps students deepen their understanding of numbers because when students compare length they can extend this to number comparisons. It also extends understanding of equivalence and non-equivalence. Students engage in Mathematical Practice 2 (Students reason quantitatively and abstractly as they use measurements of others to compare their results), Mathematical Practice 3 (Construct viable arguments and critique the reasoning of others as students compare the measurements of others and construct a viable argument as to why the process produced correct or incorrect responses), and Mathematical Practice 6 (Attend to precision). Students will use mathematics vocabulary properly when discussing problems. Carefully showing the steps in solving comparison problems. Key vocabulary: lengthlongshortmeasureendpoint
In this lesson plan students learn to create bar graphs using unifix …
In this lesson plan students learn to create bar graphs using unifix cubes, translate this representation to graph paper, and then compare the data that has been collected and displayed. Students are encouraged to make up their own questions about the data (favorite juice) and to practice with multiple sets of data. Sample questions for students and extension ideas are included. The lesson contains links to a PDF of graph paper and the Bar Grapher tool which is cataloged separately in this database.
In this 6-lesson unit, students explore 5 models of subtraction (counting, sets, …
In this 6-lesson unit, students explore 5 models of subtraction (counting, sets, number line, balanced equations, and inverse of addition) using connecting cubes. The lesson activities focus on the comparative mode of subtraction as children investigate the relationship between addition and subtraction, write story problems in which comparison is required, and practice the subtraction facts. The lessons include printable student activity sheets, a bibliography of children's counting books, questions for student discussion and teacher reflection, assessment options, extensions, and links to online applets (cataloged separately).
This task gives students an opportunity to work with exponential functions in …
This task gives students an opportunity to work with exponential functions in a real world context involving continuously compounded interest. They will study how the base of the exponential function impacts its growth rate and use logarithms to solve exponential equations.
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