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Homework

Lecture Examples |
• | Textbook |
• | Website Bank |
• | Random Problems |
• | To Turn In |

Homework is the foundation of civilization.

- Tom Foster

This class has five types of homework.

Five types of homework!

The process moves you slowly from problems that are the most like what you saw during class (lecture example problems) to slightly different problems (textbook example problems), then to lots of practice (textbook section probems and the website problem bank), then to randomly made test-like problems, and finally as the "icing on the cake" a few problems to turn in.

At first this system might seem new or complicated. But it is how to help your brain best learn math.

Example problems are the first step.

Soon after class, look at the notes you took during class. Do your notes make sense? How well do they refresh your memory of learning?

Then go to the math topics portion of the website and actively read the online notes a second time. Each time you get to an example problem, try to solve the problem yourself before looking at the solution. If you get stuck, only look at the solution one line at a time. Either scroll down very carefully or hold a piece of paper over the screen to block the lower text. If you are still stuck, contact the instructor or bring questions to class!

If you use the green *Basic Mathematics* textbook, look at its example problems. Try to only look at the solution one line at a time. Hold a piece of paper over the page to block the lower text. If you are still stuck, contact the instructor or bring questions to class!

If you use the e-book *Prealgebra* textbook, look at its example problems. Try those, only looking at the solution one line at a time if needed, by holding a paper over your screen. How about the "practice example" problems next to the example problems in the textbook that pop up with the orange symbol?

Click a book cover below to go to a new page that highlights the best homework problems, organized by our math topics.

Prealgebra Best HW Problems |
Basic Mathematics Best HW Problems |

These lists are designed for a hypothetical student with a "typical" math background. If your math foundation is weak, do even more odd-numbered problems. If your math foundation is strong, do fewer.

Build the habit of asking yourself if each answer you get is reasonable. Check your answers so you do not practice bad habits.

As you do homework, make your notes more complete. Check that changes of topic and subtopic have a very visible header. Check that definitions stand out. Update your narrative explanations of how a process or algorithm works. Include your favorite homework problems as extra example problems.

Your notes should make homework the *end point* of a chain that links the group learning during class to your personal practice. During class your instructor provided the energy and momentum. Use your notes to carry some of that into your personal practice.

Your notes should make homework the *beginning* of a chain that links your personal practice to your final exam preparation. Your notes should become a customized resource with everything you need to get ready for the final exam.

If possible, do homework with others. Students who participate in study groups almost always pass the class. You can ask your instructor to help students find study groups.

If you love the online textbook, the publisher has granted us temporary access through April 17th to try their homework tracking and personalized homework routine. Your instructor will

notsee this. It would only be for your own benefit, if you wish.If this interests you, click here. Then click on the "Redeem a Student Access Code" button and enter Lane. Then click the "Create Account" button on the lower left.

Our website problem bank has a bunch of problems. All of them have three images to click on. You can see only the answer, a written step-by-step answer, or a video step-by-step answer.

It is up to you to use the problem bank wisely. Use some of the problems for step-by-step guidance as you learn to mimic an algorithm. Use other problems as practice with frequent hints as needed. Use other problems to test yourself to make sure you are not falling behind as the term progresses.

(The website problem bank is under contruction. It takes a lot of time to find videos online, and then add written step-by-step answers too.)

Random problems are third step.

**This page** has random problems for each math topic. Each time you reload the page the numbers change.

These problems also have an answer key. Get as much practice as you need.

These are the problems that will appear on our tests!

At the very end, the problems to turn in are the last type of homework.

These problems are the icing on the cake. They have no answer key. You turn them in to demonstrate you have mastered the topic.

**This page** has problems to turn in for each math topic. Do this work on scratch paper and get answers you are happy with *before* you use the website to turn in the homework.

If you score 80% or more you are done with that homework assignment. If you score less, you will need to try again.

As with all other homework, please use the homework to notice where your notes need improvement, and work in study groups when you can.

There are **Three Levels of Math Understanding**. (Thanks go to Cathy Miner for this insight.)

- At the first, you can follow what the instructor does on the board and be helped by lecture.
- At the second, you can do "open book" work and so most of your homework problems are correct.
- At the third, you can do "closed book" work and succeed on a test without notes and with the pressure of a time limit.

It is completely normal to have different levels of math understanding for different math topics and subtopics. And it is completely normal to *not know* what level you are at for a topic until you try "open book" and "closed book" problems.

So part of the purpose of math homework is to determine your Level of Understanding for each new subtopic. This is the purpose of the above recommendation to actively read the online notes a second time. They are **prompt homework problems** that should be done as soon after class as possible.

Prompt Homework Problems

After class attempt a few problems "open book". If you get stuck on any problem, skip it while making a note that you are at the first level of understanding for that problem. If you can answer it, try a similar problem "closed book". Then you will know whether you are at the second or third level of understanding.

When you are done, plan how much time you will need for studying, and how to pace yourself.

Later you can do what we call **enough homework problems**. This is not as urgent. Waiting a day or two after the lecture can be okay. But it is usually best to structure **every day** to include some homework time. Really doing the homework problems might take more time than you can afford to dedicate to a single study session.

Enough Homework Problems

Do all the assigned homework problems, and even more problems if you need extra practice. Now you are working to master each topic and reach the third level of understanding.

Use all your resources for help. Join a study group if you can. Work forward from the concepts, not backwards from the answer key.

Please do not worry if a topic is difficult. It is normal to have different levels of understanding. It is normal to have trouble with some topics for a few days. A day or two of struggle is not a danger sign. But if a math topic remains difficult after a three days then make sure to get help promptly, so you do not fall behind. Visit office hours, the MRC, or get help from a friend.

Notice how the four types of homework slowly transition you from the first to second levels of math understanding. Doing review of what happened in class with the online notes (and your own notes) is the thing most like actual class time. A textbook chapter that provides additional explanation and example problems is a less like actual class time but still somewhat like class. Random problems with answers provided are quite different from actual class time. Finally, problems to turn in are the farthest from actual class time.