CK-12 Foundation's Basic Algebra FlexBook is an introduction to the algebraic topics of functions, equations, and graphs for middle-school and high-school students.
This module contains the an algebraic expressions and equations from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.
This lesson unit is intended to help teachers assess how well students are able to: work with concepts of congruency and similarity, including identifying corresponding sides and corresponding angles within and between triangles; Identify and understand the significance of a counter-example; Prove, and evaluate proofs in a geometric context.
A statistics lesson on describing and making claims from data representations, specifically linearly increasing data. Applies ideas of rate-of-change to develop writing a linear equation to fit the data, using the equation to interpolate and extrapolate additional information, and integrating the mathematical interpretation appropriately into a social sciences argument.
Find out how angles and symmetry come into play in the game of pool in this video adapted from Annenberg Learner’s Learning Math: Measurement.
This lesson unit is intended to help you assess how well students are able to use geometric properties to solve problems. In particular, it will support you in identifying and helping students who have the following difficulties: Solving problems relating to using the measures of the interior angles of polygons; and solving problems relating to using the measures of the exterior angles of polygons.
The main objective of this lesson is to illustrate an important application of mathematics in practical life -- namely in art. Most of the pictures selected for this lesson are visible on the walls of Al-Hambra – Granada (Spain), which is one of the most important landmarks in the Islamic civilization. There are three educational goals for this lesson: (1) establishing the concept of isometries; (2) giving real-life examples of groups; (3) demonstrating the importance of matrices and their applications. As background for this lesson, students just need some familiarity with the concept of a group and a limited knowledge about matrices and the inverse of a non-singular matrix.
Students are introduced to Pascal's law, Archimedes' principle and Bernoulli's principle. Fundamental definitions, equations, practice problems and engineering applications are supplied. A PowerPoint® presentation, practice problems and grading rubric are provided.
Students explore the interface between architecture and engineering. In the associated hands-on activity, students act as both architects and engineers by designing and building a small parking garage.
The purpose of this learning video is to show students how to think more freely about math and science problems. Sometimes getting an approximate answer in a much shorter period of time is well worth the time saved. This video explores techniques for making quick, back-of-the-envelope approximations that are not only surprisingly accurate, but are also illuminating for building intuition in understanding science. This video touches upon 10th-grade level Algebra I and first-year high school physics, but the concepts covered (velocity, distance, mass, etc) are basic enough that science-oriented younger students would understand. If desired, teachers may bring in pendula of various lengths, weights to hang, and a stopwatch to measure period. Examples of in- class exercises for between the video segments include: asking students to estimate 29 x 31 without a calculator or paper and pencil; and asking students how close they can get to a black hole without getting sucked in.
In this lesson, the students will discover the relationship between an object's mass and the amount of space it takes up (its volume). The students will also learn about the concepts of displacement and density.
This Freshman Advising Seminar surveys the many applications of magnets and magnetism. To the Chinese and Greeks of ancient times, the attractive and repulsive forces between magnets must have seemed magical indeed. Through the ages, miraculous curative powers have been attributed to magnets, and magnets have been used by illusionists to produce "magical" effects. Magnets guided ships in the Age of Exploration and generated the electrical industry in the 19th century. Today they store information and entertainment on disks and tapes, and produce sound in speakers, images on TV screens, rotation in motors, and levitation in high-speed trains. Students visit various MIT projects related to magnets (including superconducting electromagnets) and read about and discuss the history, legends, pseudoscience, science, and technology of types of magnets, including applications in medicine. Several short written reports and at least one oral presentation will be required of each participant.
Students are introduced to the concept of engineering biological organisms and studying their growth to be able to identify periods of fast and slow growth. They learn that bacteria are found everywhere, including on the surfaces of our hands. Student groups study three different conditions under which bacteria are found and compare the growth of the individual bacteria from each source. In addition to monitoring the quantity of bacteria from differ conditions, they record the growth of bacteria over time, which is an excellent tool to study binary fission and the reproduction of unicellular organisms.
Students explore combinations in this open-ended Nrich task. Students are asked to discuss and document their work pictorially and numerically.
The PFACS game engages students in playing the role of a music producer who must use data and computational thinking to promote their artist’s careers. “Data and Analysis” is one of five strands in the CS K-12 Framework — and it is a strand that readily bridges to mathematics and science content that you already teach. By giving students time to play the game and then having related classroom discussions, you can gain insight into your students’ progress in understanding these concepts.
This game does NOT require any coding skills nor knowledge of any programming language. It is about making choices using computational thinking concepts, not about writing code.
Beats Empire was designed for teachers:
In middle schools classrooms
That integrate data science, computational thinking and related concepts
For about an hour of use spread over 2-3 class periods
Where students have access to any computer, laptop or desktop, with Chrome or Firefox browser (not recommended for tablets or phones).
The key goals of Beats Empire are:
Students explore how their data skills addresses a real world challenge
Students gain career awareness of attractive data science jobs
Teachers increase their understanding of what students know and can do
In this optics activity, learners discover that when they rotate a special black and white pattern called a Benham's Disk, it produces the illusion of colored rings. Learners experiment with the speed of rotation and direction of rotation to observe varying patterns. Use this activity to explain to learners how our eyes detect color and how different color receptors in the eye respond at different rates.
Students are introduced to the challenge question, which revolves around proving that a cabinet x-ray system can produce bone mineral density images. Students work independently to generate ideas from the questions provided, then share with partners and then with the class as part of the Multiple Perspectives phase of this unit. Then, as part of the associated activity, students explore multiple websites to gather information about bone mineral density and answer worksheet questions, followed by a quiz on the material covered in the articles.
Students revisit the mathematics required to find bone mineral density, to which they were introduced in lesson 2 of this unit. They learn the equation to find intensity, Beer's law, and how to use it. Then they complete a sheet of practice problems that use the equation.
Students examine an image produced by a cabinet x-ray system to determine if it is a quality bone mineral density image. They write in their journals about what they need to know to be able to make this judgment. Students learn about what bone mineral density is, how a BMD image can be obtained, and how it is related to the x-ray field. Students examine the process used to obtain a BMD image and how this process is related to mathematics, primarily through logarithmic functions. They study the relationship between logarithms and exponents, the properties of logarithms, common and natural logarithms, solving exponential equations and Beer's law.
Experiment with rocket designs and a PVC launcher to discover how high—and how far—you can make your rockets go.