This short video and interactive assessment activity is designed to give fifth graders an overview of metric capacity operations.
This short video and interactive assessment activity is designed to teach fifth graders about multiplying and dividing decimals - word problems.
This short video and interactive assessment activity is designed to teach fourth graders about mixed operations with compound units using multiplication and division - word problems.
This short video and interactive assessment activity is designed to teach fifth graders about mixed problems in fractions.
This short video and interactive assessment activity is designed to teach third graders about mixed review (numbers up to 100,000).
This short video and interactive assessment activity is designed to teach fifth graders about different unit length comparisons.
This task assumes students are familiar with mixing problems. This approach brings out different issues than simply asking students to solve a mixing problem, which they can often set up using patterns rather than thinking about the meaning of each part of the equations.
In order to solve this problem, students must assume that if you mix a cubic foot of sand with a cubic foot of cement, you will have 2 cubic feet of mix.
The problem deals with a rational expression which is built up from operations arising naturally in a context: adding the volumes of the fertilizer and the water, and dividing the volume of the fertilizer by the resulting sum. Thus it encourages students to see the expression as having meaning in terms of numbers and operations, rather than as an abstract arrangement of symbols.
Students learn about life-cycle assessment and how engineers use this technique to determine the environmental impact of everyday products and processes. As they examine what’s involved in making and consuming cupcakes, a snack enjoyed by millions of people every year, students learn about the production, use and disposal phases of an object’s life cycle. With the class organized into six teams, students calculate data for each phase of a cupcake’s life cycle—wet ingredients, dry ingredients, baking materials, oven baking, frosting, liner disposal—and calculate energy usage and greenhouse gases emitted from making one cupcake. They use ratios and fractions, and compare options for some of the life-cycle stages, such as different paper wrapper endings (disposal to landfills or composting) in order to make a life-cycle plan with a lower environmental impact. This activity opens students’ eyes to see the energy use in the cradle-to-grave lives of everyday products. Pre/post-quizzes, worksheets, activity cards, Excel® workbook and visual aids are provided.
First of two-term sequence on modeling, analysis and control of dynamic systems. Mechanical translation, uniaxial rotation, electrical circuits and their coupling via levers, gears and electro-mechanical devices. Analytical and computational solution of linear differential equations and state-determined systems. Laplace transforms, transfer functions. Frequency response, Bode plots. Vibrations, modal analysis. Open- and closed-loop control, instability. Time-domain controller design, introduction to frequency-domain control design techniques. Case studies of engineering applications.
Mathematics, as we all know, is the language of science, and fluency in algebraic skills has always been necessary for anyone aspiring to disciplines based on calculus. But in the information age, increasingly sophisticated mathematical methods are used in all fields of knowledge, from archaeology to zoology. Consequently, there is a new focus on the courses before calculus. The availability of calculators and computers allows students to tackle complex problems involving real data, but requires more attention to analysis and interpretation of results. All students, not just those headed for science and engineering, should develop a mathematical viewpoint, including critical thinking, problem-solving strategies, and estimation, in addition to computational skills. Modeling, Functions and Graphs employs a variety of applications to motivate mathematical thinking.
The primary purpose of this task is to elicit common misconceptions that arise when students try to model situations with linear functions. This task, being multiple choice, could also serve as a quick assessment to gauge a class' understanding of modeling with linear functions.
In this class, students use data and systems knowledge to build models of complex socio-technical systems for improved system design and decision-making. Students will enhance their model-building skills, through review and extension of functions of random variables, Poisson processes, and Markov processes; move from applied probability to statistics via Chi-squared t and f tests, derived as functions of random variables; and review classical statistics, hypothesis tests, regression, correlation and causation, simple data mining techniques, and Bayesian vs. classical statistics. A class project is required.
This undergraduate course focuses on traditional algebra topics that have found greatest application in science and engineering as well as in mathematics.
Students will breed fruit flies through several generations and record their data using mathematical models in order to demonstrate the inheritance of trait variations.
This task asks students to solve a problem in a context involving constant speed. This task provides a transition from working with ratios involving whole numbers to ratios involving fractions.
This task is designed to help students focus on the whole that a fraction refers to. It helps students to realize that two different fractions can describe the same situation depending on what you choose to be the whole.
Students learn the physical properties of sound, how it travels and how noise impacts human health—including the quality of student learning. They learn different techniques that engineers use in industry to monitor noise level exposure and then put their knowledge to work by using a smart phone noise meter app to measure the noise level at an area of interest, such as busy roadways near the school. They devise an experimental procedure to measure sound levels in their classroom, at the source of loud noise (such as a busy road or construction site), and in between. Teams collect data using smart phones/tablets, microphones and noise apps. They calculate wave properties, including frequency, wavelength and amplitude. A PowerPoint® presentation, three worksheets and a quiz are provided.
This lesson teaches students how to make decisions in the face of uncertainty by using decision trees. It is aimed for high school kids with a minimal background in probability; the students only need to know how to calculate the probability of two uncorrelated events both occurring (ie flipping 2 heads in a row). Over the course of this lesson, students will learn about the role of uncertainty in decision making, how to make and use a decision tree, how to use limiting cases to develop an intuition, and how this applies to everyday life. The video portion is about fifteen minutes, and the whole lesson, including activities, should be completed in about forty-five minutes. Some of the activities call for students to work in pairs, but a larger group is also okay, especially for the discussion centered activities. The required materials for this lesson are envelopes, small prizes, and some things similar in size and shape to the prize.