- Course type: Self-paced
- Available Lessons: 104
- Average Lesson Length: 8 min
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Watch a preview:chapter 1 / lesson 1Critical Thinking and Logic in Mathematics
Course SummaryUtilize the videos, quizzes and transcripts in this helpful lesson plan course to teach contemporary math concepts to your students. Our short video lessons help capture your students' attention, and the quizzes can be easily modified into your own assessment materials.
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Course Practice TestCheck your knowledge of this course with a 50-question practice test.
- Comprehensive test covering all topics
- Detailed video explanations for wrong answers
How It Works
You can use this contemporary math course as a template for designing and implementing your course. Here are the key components of the course and how you can use them:
- Chapters - Each chapter covers a unit of contemporary math, from an in-depth look at logic and critical thinking to methods of ranking candidates in an election and interpreting statistical findings. Use these chapters as mile markers as you map out your course. We recommend planning to spend a week on each chapter, but you can always allocate the chapters according to the length of your specific contemporary math course.
- Lessons - Within each chapter are video lessons that further break down topics into bite-sized chunks. These lessons cover single topics like the standard deviation or simple conditional probabilities. Each one is often appropriate for a single class.
- Key Terms - Within each lesson are key terms. These are emphasized on screen and in the transcript. As you develop your syllabus, these key terms help you focus on the most important learning objectives. For example, the lesson on mathematical sets includes key terms like set, union and intersection.
As you work on your contemporary math lesson plans, save time by incorporating video lessons from this resource. Here's how:
- Introduce Topics - Your students will be in the right mindset for understanding topics like how to calculate a permutation if you begin class with a short video. It can be a jumping-off point for a lecture, group activity or class discussion.
- Break Up Lectures - The video format, which often includes animation, helps students visualize topics like solving multiple-step word problems and finding Z-scores.
- Assign For Homework - Each lesson in the course, from the 3-Way Principle of Mathematics to the quota rule of political apportionment, can be assigned to your students as homework.
Each video lesson includes a complete transcript. You can utilize these transcripts in several ways:
- Lecture Notes - Do you need a guide as you plan a lecture, such as one on Euler paths and circuits or logic and critical thinking in solving math problems? The transcripts cover each topic in depth, with key terms highlighted for quick reference.
- Student Reading - Perhaps you'd like your students to learn about the probabilities in games of chance, such as poker or lotteries, but you don't have class time available. Assign the transcripts as extra reading.
- Study Tools - When it's time for a unit exam on the mathematics of voting, you can point your students to the transcripts on preference ballots, the plurality method, the pairwise comparison method and the recursive and extended methods of ranking candidates.
Each video lesson has a corresponding quiz. Here's how to use the quizzes:
- Homework - Assign a quiz to your students as homework. You'll receive an email with the results, which enables you to verify they've completed the assignment and that they've understood the material. Questions cover everything from practice word problems to key facts, like the two categories of statistics.
- Tests - You can meld the material in the quizzes into your own student assessments, saving you valuable time. Need a few questions on statistics? There are plenty!
- Discussions - Jump-start a discussion with questions like: What are some problems that might arise in apportioning political districts?
Below is a sketch of the contemporary math syllabus modeled on a 9-week course. This sample can be adapted based on your course schedule. Navigate the chapters and lessons for more detail.
|Week||Unit||Sample of Topics Covered|
|Week 1||Mathematical Reasoning and Problem-Solving||Critical thinking, logical fallacies, principles and processes for problem-solving|
|Week 2||Solving Math Word Problems||Steps in solving word problems, how to use diagrams to help figure out a word problem, how to personalize a word problem|
|Week 3||Statistics Overview||Descriptive and inferential statistics, ways to determine median, mode, mean and range, the standard deviation, histograms|
|Week 4||Probability Overview||Basic set theory, various types of events and their probability, calculations involving combinations and permutations, relative frequency|
|Week 5||Discrete Probability Distributions||Definition of a random variable, expected values of games of chance, including dice and blackjack, how to find binomial probabilities using tables and formulas|
|Week 6||The Normal Curve and Continuous Probability Distributions||How to graph probability distributions, how to estimate percentages, normal distribution|
|Week 7||The Mathematics of Voting||Types of ballots, methods of determining winners, Arrow's Impossibility Theorem|
|Week 8||The Mathematics of Apportionment||Problems with apportionment in politics, the quota rule, various methods of apportionment and their benefits and drawbacks|
|Week 9||Graph Theory||Mathematical graphs, Euler Paths and Circuits, traveling salesmen problems, how to find the most efficient circuit|
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