This is a 3-Act-Task in which students will solve the problem 58 …
This is a 3-Act-Task in which students will solve the problem 58 x 14. No guidance is given as to how to solve the task, so student can invent a strategy that works for them. Solutions may include arrays, repeated addition, traditional multiplication algorithm, area models, etc. Discussion should be centered around student strategies and efficiency. For information on how to implement 3-Act-Task lessons, visit: http://blog.mrmeyer.com/2013/teaching-with-three-act-tasks-act-one/
The purpose of this learning video is to show students how to …
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.
The subject of enumerative combinatorics deals with counting the number of elements …
The subject of enumerative combinatorics deals with counting the number of elements of a finite set. For instance, the number of ways to write a positive integer n as a sum of positive integers, taking order into account, is 2n-1. We will be concerned primarily with bijective proofs, i.e., showing that two sets have the same number of elements by exhibiting a bijection (one-to-one correspondence) between them. This is a subject which requires little mathematical background to reach the frontiers of current research. Students will therefore have the opportunity to do original research. It might be necessary to limit enrollment.
The Art of the Probable" addresses the history of scientific ideas, in …
The Art of the Probable" addresses the history of scientific ideas, in particular the emergence and development of mathematical probability. But it is neither meant to be a history of the exact sciences per se nor an annex to, say, the Course 6 curriculum in probability and statistics. Rather, our objective is to focus on the formal, thematic, and rhetorical features that imaginative literature shares with texts in the history of probability. These shared issues include (but are not limited to): the attempt to quantify or otherwise explain the presence of chance, risk, and contingency in everyday life; the deduction of causes for phenomena that are knowable only in their effects; and, above all, the question of what it means to think and act rationally in an uncertain world. Our course therefore aims to broaden students’ appreciation for and understanding of how literature interacts with--both reflecting upon and contributing to--the scientific understanding of the world. We are just as centrally committed to encouraging students to regard imaginative literature as a unique contribution to knowledge in its own right, and to see literary works of art as objects that demand and richly repay close critical analysis. It is our hope that the course will serve students well if they elect to pursue further work in Literature or other discipline in SHASS, and also enrich or complement their understanding of probability and statistics in other scientific and engineering subjects they elect to take.
This two-lesson unit from Illuminations, exposes students to algebra, measurement, and data …
This two-lesson unit from Illuminations, exposes students to algebra, measurement, and data analysis concepts and the major theme of analyzing change. In the first lesson, students measure the heights of classmates and older students and construct a table of height and age data to compare them. The second lesson's instructional goal is to understand how change in one variable, age, can relate to change in a second variable, height. Instructional plan, questions for the students, assessment options, extensions, and teacher reflections are given.
In this assessment in a one-to-one setting, a student is shown the …
In this assessment in a one-to-one setting, a student is shown the numbers from 1Đ10, one number at a time, in random order. The teacher asks, Ňwhat number is this?"
This assessment may be used in a small group or whole group …
This assessment may be used in a small group or whole group setting, give each student a piece of paper. Students who have trouble writing certain numbers can then get targeted practice.
Students design and develop a useful assistive device for people challenged by …
Students design and develop a useful assistive device for people challenged by fine motor skill development who cannot grasp and control objects. In the process of designing prototype devices, they learn about the engineering design process and how to use it to solve problems. After an introduction about the effects of disabilities and the importance of hand and finger dexterity, student pairs research, brainstorm, plan, budget, compare, select, prototype, test, evaluate and modify their design ideas to create devices that enable a student to hold and use a small paintbrush or crayon. The design challenge includes clearly identified criteria and constraints, to which teams rate their competing design solutions. Prototype testing includes independent evaluations by three classmates, after which students redesign to make improvements. To conclude, teams make one-slide presentations to the class to recap their design projects. This activity incorporates a 3D modeling and 3D printing component as students generate prototypes of their designs. However, if no 3D printer is available, the project can be modified to use traditional and/or simpler fabrication processes and basic materials.
Inquiry-Based Bioengineering Research and Design Experiences for Middle-School Teachers RET Program, Department of Biomedical Engineering, Worcester Polytechnic Institute
Students explore area as an attribute of two-dimensional figures and relate it …
Students explore area as an attribute of two-dimensional figures and relate it to their prior understandings of multiplication. Students conceptualize area as the amount of two-dimensional surface that is contained within a plane figure.
Lesson Time Estimate: 90 Minutes Students will be able to: -Utilize knowledge …
Lesson Time Estimate: 90 Minutes
Students will be able to: -Utilize knowledge and strategies to get the best possible financing terms (that meet their individual needs and budget) for a new or used car -Explain the difference between a car loan and a lease as well as the advantages and disadvantages of each -Have a backup plan if they find themselves unable to afford their car payments
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