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Math OER

Welcome

Welcome to a fun website stuffed full of resources to help you enjoy math.

The very top menu organizes the resources I use when teaching math classes or leading high school math club explorations. Besides this welcome, it has links to a Zoom room, online whiteboard, free online textbook, lecture archives, and an online calculator.

Next are five pages containing vast amounts of wisdom. You can ponder what it means to be a mather, read about a dumpload study skills, browse the classroom library, entertain yourself in playgrounds, and familiarize yourself with LCC resources.

The final menu has our math topics, arranged in six topics. The first three topics involve foundational math skills:

shapeshifting We start with the art of shapeshifting: everything we can do that changes a single number.

mad science Then we look at mad science: everything we can do that involves combining numbers together.

justice Finally we consider justice: doing the same thing to both sides of an equation.

These foundational skills grant fluency with fractions, decimals, percentages, and measurement. But it is much easier to learn (or review) these skills in those three categories with silly names.

Next come three categories of applications:

health decisions First comes health decisions and looking closely at calories, metabolism, and recipes.

personal finance decisions Then we consider personal finance decisions with a focus on mortgages and saving for retirement.

business decisions We conclude with business decisions that involve pricing and likelihood.

Have fun exploring the website! Try clicking on things. Use Ctrl-F to search for text.

Math 105 at LCC link to here

Everything should be made as simple as possible, but not simpler.

- Albert Einstein

Our class meets Monday and Wednesday, 2:00 pm to 3:50 pm. Office hours are still to be determined.

Weekly homework is due weekly Monday at midnight of the following week. This allows students who do their homework on the weekend a chance to ask questions at the Monday study session before turning it in. (If a weekly quiz is take-home instead of in-class, it will also be due Monday at midnight.)

Our class uses Moodle for discussion forums, homework, and quizzes. Instead of a "news and announcements forum" I will send an e-mail after every class. Please monitor your LCC e-mail account!

instructor photo You may call me David. I have taught Math 20 and Math 25 at LCC for over a decade. This is my first time teaching Math 105.

Math 105 is very similar to Math 25 but requiring a prerequisite familiarity with algebra allows us to go deeper into every topic. For example, Math 25 only studies annual annuities, but Math 105 includes annuities compounded with other time periods. Math 25 briefly mentions standard deviation, but Math 105 explores it more and calculates it. Math 25 discusses only basic probability, but Math 105 includes contingent, complementary, and conditional events. I am excited about leading students more deeply into the practical math I enjoy.

After you give me your code name, the following drop-down menu will personalize this page with your achievements.

Select your code name:

Math 105 Class Information

Class times:
Mon/Wed 2:00 pm to 3:50 pm

Study Session times:
Mon/Wed 1:30 pm to 2:00 pm
Saturdys 9:00 pm to 10:00 pm

Office Hours by appointment

4 credits, 4 lecture hours per week

about 8 hours homework per week

CRN 35386

 

Instructor Information

LCC home

David Van Slyke

website: http://mathoer.net

Zoom room: https://lanecc.zoom.us/my/vanslyked

work email: vanslyked@lanecc.edu

work cell phone: (541) 357-7551

office: Building 16 Room 261

(Please communicate with me using the above cell phone or LCC email. Please do not use my LCC office phone or moodle's messages.)

Course Summary

Course Description

syllabus humor

Math 105 includes a review of basic Math 20 topics and greatly expands their real-life usefulness in problem solving, using data, and applications involving finance and probability.

You will be required to learn and use specific techniques and processes that may be different from what you have used in the past, and develop your ability to communicate mathematically by showing all work in a neat and organized manner.

Students are encouraged to use study groups for all types of homework. A study group can be classmates, or working with friends or family members. Studying in-person is best. Doing homework together on speaker-phone or computer voice chat is also usuallly better than working alone.

Official Course Description: MTH 105 is survey of mathematical topics and applications of those topics for non-science majors including probability, statistics, finance and exponential modeling problem solving. Math 105, 106, and 107 are a three course sequence but may be taken in any order, with a prerequisite of Math 095, Math 098, or equivalent course completed with a grade of C− or better within the past two years, or placement by the College's Math Placement Process.

Other Issues Regarding Stuff in Class

You are welcome to use a cell phone calculator, except on the final exam (when cell phone use is not allowed).

Class times are informal discussions, not formal lectures. You may leave and return quietly without permission. When you have something to contribute, raising your hand might help me guide the flow of conversation and ensure all students have a chance to talk—or it might not be important to do. When speaking without raising your hand, please be polite and socially aware.

Although it has never been an issue in my many years of math teaching, please know that LCC instructors are Mandatory Reporters who cannot extend confidentiality to threats of imminent harm or death to one's self or others.

Grading

You must be present each week so I can see your face. If you cannot attend at least one of the week's classes or study sessions, then submit a link to a video of you doing homework or something like that. This expectation is for politeness and friendliness as a student to your classmates, as well as my attempt to prevent anyone from falling behind.

Our class uses a combination of numeric and achievement based grading. We do not use the unreliable Moodle gradebook.

The numeric part of grading requires earning your letter grade with thresholds to meet or exceed with your weekly quiz completion, final exam score, twice-weekly homeworks completed on time, and weekly discussion forums completed on time.

The weekly quiz has three problems, and happens at the end of Wednesday's class. You must get two of the three problems right (with small leniency for careless errors) for that quiz to be considered "complete".

Letter GradeComplete QuizzesFinal ExamHomeworks CompletedDiscussions Completed
A985%2010
B875%189
C770%168
D665%147
Fbelow 6below 65%below 14below 7

The achievement part of grading lowers the requirement for complete quizzes by one-eigth per achievement. For example, a student earning 24 of the 54 achievements would only need an 6 complete quizzes to earn an A. This allows you to compensate for missing class by participating more outside of class.

The seven colors of achievements correspond to the seven aspects of being a mather: participation in discussions is red, devouring math is orange, exploring math is yellow, analyzing real-life issues is green, using resources is blue, taking a test is purple, and time management is brown. The requirement for weekly homeworks completed on time is decreased by two, and the requirement for and discussion forums completed on time is decreased by one, for each color in which you earn three or more achievements.

Achievements also use class participation to determine if your letter grade receives a + or −. You earn a − if you do not complete at least 14 achievements. You get a + if you complete 30 or more achievements.

Students who checking items off a list might enjoy a page that simply lists all of the achievements.

A grade of Incomplete is only for a student who has successfully completed 75% of the work before the end of the term, and can reasonably be expected to finish the work. Incompletes are used only in cases when serious illness or other emergency prevents a student from completing the course. See LCC's incomplete policy.

Time and Materials Needed

Our class has a lot of homework. Expect to spend 6 to 10 hours each week doing homework if you have an average math foundation from the previous class.

Please schedule different blocks of time for appetizer and real homework, as explained in the study skills page.

calculator

Please bring to class paper, a pencil, a highlighter, and a notebook.

You will need a scientific calculator that can do exponents, parenthesis, and a π key. The official class guidelines recommend a Sharp D.A.L. 500 calculator. This model is most popular. Some students instead use a Casio that is also inexpensive and also gets good reviews.

Our textbook is the PDF book Math in Society by David Lippman of Pierce College. The author has put many accompanying videos on YouTube.

You will, of course, need a computer and internet to use this website, the textbook, and other online resources, as well as to turn in assignments online.

Together our class times, study sessions, this class website, textbook, and other resources linked from the class website provide many different ways of understanding each math topic. Find the resources that work best for you!

One of your key tasks is to condense your class notes, thoughts, homework, and favorite example problems into an improved set of notes that you are useful when studying for the final exam. Preparing these notes carefully is invaluable!

Key Resources

LaneCC Student Resources

LaneCC provides dumploads of resources to help students succeed. You can click on the image to the right to see my own compilation of student resources. Also see the tutoring section in the study skills page.

It is often valuable to visit an Early Outreach Specialist who is trained to connect students to whatever resources can help. The one who normally works most closely with Math 20 students is Katherine Kaylegian (e-mail).

Study Sessions

Instead of quiet office hours we have chatty study sessions!

These can serve several different purposes.

You do not need to bring questions to study sessions. It can be nice to simply study quietly while knowing that help is available from the instructor or classmates. That help can look like a few things:

MRC

The free tutoring provided by the Math Resource Center currently happens remotely.

First, make a reservation for a 30-minute appointment using the website WC Online. This is quicker if you use the pull-down menu to select the topic in which you want tutoring.

Second, five minutes early before your appointment go to a Zoom meeting room named Study Annex Tutoring, where a front desk person will greet you and assign you to a "breakout room" in Zoom. The front desk person can also help you get Zoom working with text chat, audio, and/or video to best suit your needs and what tools you have available at home.

Third, your tutor joins you in the breakout room. Enjoy your live tutoring!

Math Resource Center online hours are Monday through Friday 9:00am to 4:30pm, and also 5:00pm to 8:00pm on Tuesday through Thursday. The Math Resource Center is considering offering some weekend hours. Please let them know if that would help your schedule.

CAR

CAR

Lane Community College is dedicated to providing inclusive learning environments. The Center for Accessible Resources coordinates all academic accomodations for students. If you anticipate or experience academic barriers due to a disability, to request assistance or accommodations, contact CAR at 541-463-5150 or accessibleresources@lanecc.edu.

SHeD

The LCC Student Help Desk (nicknamed the SHeD) provides technology loans and support to students. It can be reached at 541-463-3333.

Emergency Phone Numbers

Procedures for Bad Weather

Sign up for LaneAlert

Distance learning is more immune to weather issues, but we should still know the routines...

Sign up for LaneAlert to receive e-mails or texts about weather closures! Log into mylane. In the Home tab, locate the box labeled Personal Information. Select the Lane Alert Emergency Notification link. Select which notifications you would like to receive. Scroll down to the very bottom of the page and click Save Changes.

You can also listen to KLCC (FM 89.7) or KUGN (AM 590 or FM 97.9) for campus closure information. You can also check the websites of LCC and FlashAlert.

If class is canceled or you are absent, please read ahead using the class website to familiarize yourself with the upcoming topics and assignments. Then we can more quickly cover the missed material.

LCC's website has more about its weather closure policies.

warning - objects in syllabus are closer than they appear By LCC policy, missing all classes and assignments during the first week causes you to be dropped from the class.

The deadline for a tuition refund is 11:59 pm on the Sunday at the end of the first week of the class.

The deadline for schedule changes, dropping classes, grading option changes, etc. is February 26th.

The Winter term holidays are Martin Luther King Jr. Day (Week 3, Monday, January 18th) and Presidents Day (Week 7, Monday, February 15th).

Our final exam has a scheduled time Monday during finals' week, starting at 2pm (our normal class start time) and lasting for 110 minutes. This may or many not be useful to us.

You can add this calendar to your own calendar app using this ICAL address.

Please note that LCC policy allows students with three or more finals on the same day to reschedule one of them. Sometimes final exams may be taken early because of medical or other concerns.

Whenever you get stuck use a good first way to get help is with our class Get Help Forum.

But LCC has a lot of other resources, including lots of free tutoring!

During Winter term the Math Resource Center will be offering online tutoring using Zoom.

This is part of the Lane Support Hub and uses that hub's Zoom room.

links for Lane Support Hub

The Math 105 tutors with whom you can reserve a half-hour appointment using MyWCOnline are named Kristen, Paula, Carrie, Cullen, Greg D., Mike H., and Zachary.

Contacting TRiO is another great source of tutoring if you qualify.

You can also visit an Early Outreach Specialist to quickly learn about college resources. You will be amazed how many resources there are, and how many people are ready to say "I got your back".

Since 2016 LCC has also paid to collaborate with eTutoringOnline.org. In theory, going to this websiteshould be a free way to get tutoring during the hours when the Math Resource Center is closed. However, the current shift nationwide to distance learning has made eTutoring Online really busy. The wait times for an appointment might be unworkable. So feel free to try eTutoring Online, but be warned.


This week, in addition to getting introduced to each other and to the course, we review some topics like percents, rates, and geometry, and use them to practice solving problems. We will also talk about appreciation, depreciation, and simple interest.

In this chapter, we begin to use math as a tool. This will be a recurring theme in the course.

Whenever you get stuck use the Get Help Forum.

To Do List for Week One

1. Attend the Zoom sessions. The last 15 minutes of each Wednesday class has our weekly quiz. If you are ever absent, watch the archived videos of the lessons, ask questions, and check in by attending a study session or submitting a video of you doing math work.

2. Skim the textbook chapter about Problem Solving. Be ready to use it as a resource when doing this week's work.

3. Complete this week's activity. Work on your own as much as you can. Then review the answer key. This item will not be collected. It is just for you to make sure that you can use the math topics we are learning.

4. This week's discussion forum is for introducting ourselves. The requirement is what will usually be true: make a contribution soon, then come back and reply to two other students' posts. (Moodle should show a completion checkmark when you have done that.)

5. Complete the homework, part A and part B, before the end of the week. Keep trying each homework assignment until you get 8 out of 10 or more.

6. Perhaps go over Paula's weekly worksheet. If it is helpful, write out solutions for yourself to make sure you understand. You do not turn this in, but may contact me with specific questions if there are parts you don't get. Unfortunately, this worksheet does not have an answer key.

Week 1, Monday review day Jamboard notes Zoom video YouTube video
Week 1, Wednesday problem solving Jamboard notes Zoom video YouTube video
Study Session on Saturday problem solving Jamboard notes not recorded not recorded

Elaine's Note Pages external link

U. S. Census Data Spreadsheet external link which you only care about if exploring Paula's weekly worksheet

Tips for using online math videos:

1. Be selective! Watch the videos that you want to know more about. If you're already familiar with a topic, you may not need to watch the video.

2. Reuse! If you find a video that is helpful, you may want to watch it more than once. Make a note and review the video at a later time.

3. Go further! If you don't understand something from a video, or would like to see more examples, post in the weekly Get Help Forum.

Introduction to Percent external link
Ex 1: Relating Fractions, Decimals, and Percents external link
Ex 2: Relating Fractions, Decimals, and Percents external link

The Percent Equation external link
Ex 1: Solve a Percent Problem Using a Percent Proportion external link
Ex 2: Solve a Percent Problem Using the Percent Equation external link
Ex 3: Determine What Percent One Number is of Another external link

Percent of Change external link
Ex 1: Determine a Percent Change (Decrease) external link
Ex 2: Determine a Percent Change (Increase) external link

Rates and Unit Rates external link

American Unit Conversions external link

Metric Unit Conversions external link
Ex: Convert km/hr to meters per second external link

Perimeter and Area Formulas external link

Achievements can be earned at any time during the term. They have no due date.

By the end of this week it is possible you have earned the following achievements:

Voting Present

ask a question during class

Anyone? Anyone?

do a problem on the board during class

Happy Hour

participate in an office hour study session

Math Flix

watch a math video with a classmate, then talk about it together

Really Useful Engine

work with a classmate who asks for help with a homework problem

Brazil Thinks You're Cute

teach a friend about one of our math topics

To Battle!

for one weekly activity explain a problem during class

Handwriting Analysis

for one weekly homework show all 16 characteristics of well-written problems

Spelunker

find a new online video explaining our math topics

Onward and Upward

work with a tutor (perhaps at the MRC)

Not in Kansas Any More

turn in the start of term reflection

Scholarly

share something you learned from the Dr. Chew study skills videos

We start a new chapter this week: finance. We use our review of simple interest as a foundation for studying compound interest. This sets the stage for more advanced work in finance, such as saving for retirement and installment loans.

Whenever you get stuck use the Get Help Forum.

To Do List for Week Two

1. Attend the Zoom sessions. The last 15 minutes of each Wednesday class has our weekly quiz. If you are ever absent, watch the archived videos of the lessons, ask questions, and check in by attending a study session or submitting a video of you doing math work.

2. Skim the textbook chapter about Finance. Be ready to use it as a resource when doing this week's work.

3. Complete this week's activity. Work on your own as much as you can. Then review the answer key. This item will not be collected. It is just for you to make sure that you can use the math topics we are learning.

4. This week's discussion forum is for investing anecdotes and savings account research. The requirement is what will usually be true: make a contribution soon, then come back and reply to two other students' posts. (Moodle should show a completion checkmark when you have done that.)

5. Complete the homework, part A and part B, before the end of the week. Keep trying each homework assignment until you get 8 out of 10 or more.

5b. This week we had a take-home take-home quiz

6. Perhaps go over Paula's weekly worksheet. If it is helpful, write out solutions for yourself to make sure you understand. You do not turn this in, but may contact me with specific questions if there are parts you don't get. Unfortunately, this worksheet does not have an answer key.

Week 2, Monday simple and compound interest Jamboard notes Zoom video YouTube video
Week 2, Wednesday mortgages and annuities Jamboard notes Zoom video YouTube video
Study Session on Thursday problems from HW 2A Jamboard notes not recorded not recorded
Study Session on Saturday problems from HW 2B and quiz
(It starts on page 13 of the Wed class Jamboard,
the link goes right there)
Jamboard notes not recorded not recorded
Study Session on Monday 1/18 problems from HW 2A and 2B and quiz Jamboard notes Zoom video YouTube video

When studying finance formulas it is very important to learn which formula to use. All the formulas involve an initial amount (principal), an interest rate, and one or more payments. So the formulas look similar. Be sure to really understand what makes financial situations similar and different, and which formula to use for each situation. This week has this extra accordion section to focus on this issue!

Here are some hints on deciding which equation to use based on the wording of the problem.

The easiest types of problem to identify are loans. Loan problems almost always include words like: "loan", "amortize" (the fancy word for loans), "finance (a car)", or "mortgage" (a home loan). Look for these words. If they are there, you are probably looking at a loan problem. To make sure, see if you are given what your monthly (or annual) payment is, or if you are trying to find a monthly payment.

If the problem is not a loan, the next question you want to ask is: "Am I putting money in an account and letting it sit, or am I making regular payments or withdrawals every month/quarter/year ?" If you are letting the money sit in the account with nothing but interest changing the balance, then you are looking at a compound interest problem. The exception would be bonds and other investments where the interest is not reinvested—in those cases you are looking at simple interest.

If you are making regular payments or withdrawals, the next question is: "Am I putting money into the account, or am I pulling money out?" If you are putting money into the account on a regular basis then you are looking at a basic annuity problem, which is sometimes called a savings annuity. Basic annuities are when you are saving money. Usually in these problems your account starts empty, and has money in the future.

If you are pulling money out of the account on a regular basis, then you are looking at a payout annuity problem. Payout annuities are used for things like retirement income. You start with money in your account, pull money out on a regular basis, and your account ends up empty in the future.

Remember, the most important part of answering any kind of question, money or otherwise, is first to correctly identify what the question is really asking. Then determine what approach will best allow you to solve the problem.

For more practice, look at these slides external link and their answer key external link

Elaine's Note Pages - Annotated Finance Formulas Version external link

My version of Elaine's Finance Formulas external link

Tips for using online math videos:

1. Be selective! Watch the videos that you want to know more about. If you're already familiar with a topic, you may not need to watch the video.

2. Reuse! If you find a video that is helpful, you may want to watch it more than once. Make a note and review the video at a later time.

3. Go further! If you don't understand something from a video, or would like to see more examples, post in the weekly Get Help Forum.

Simple Interest Formula external link
Ex 1: Determine an Account Balance Using Simple Interest external link

Compound Interest external link
Ex 1: Compounded Interest Formula - Quarterly external link
Ex 2: Compound Interest Formula - Determine Deposit Needed external link

Determine the Value of an Annuity external link
Payout Annuity Formula, Part 1 external link
Payout Annuity Formula, Part 2 external link

Installment Loan Formula external link
Determine the Remaining Balance external link

By the end of this week it is possible you have earned the following achievements:

Problem Solving Machine

do a second problem on the board during class

Field Photographer

turn in photos of two study groups or study sessions that you attended

And That's The Way It Is

find an example of our math topics in online news

More Details Just Arrived

find an example of our math topics in a print magazine or journal

Second Down

for another weekly activity explain one problem during class

Side by Side

for another weekly homework show all 16 characteristics of well-written problems

Mathsplaining

teach a friend about non-class math topics

Road Not Taken

work with a stranger on a math problem

Got Your Hens in a Row

teach another student some study skills

Unstuck

report on becoming more capable at getting help when it is needed

Ludicrous Speed

finish the multiplication speed quiz in time

Fluency

finish the representational fluency quiz quickly

Note that Monday is the Martin Luther King Jr. Day holiday. There is no class.

This week we continue our study of finance by moving to more advanced topics: annuities, payout annuities, and loans. (We'll omit remaining loan balance.) These topics are useful in a variety of applications, such as retirement savings, car loans, mortgages, and refinancing a loan.

Whenever you get stuck use the Get Help Forum.

To Do List for Week Three

1. Attend the Zoom sessions. The last 15 minutes of each Wednesday class has our weekly quiz. If you are ever absent, watch the archived videos of the lessons, ask questions, and check in by attending a study session or submitting a video of you doing math work.

2. Skim the textbook chapter about Finance. Be ready to use it as a resource when doing this week's work.

3. Complete this week's activity. Work on your own as much as you can. Then review the answer key. This item will not be collected. It is just for you to make sure that you can use the math topics we are learning.

4. This week's discussion forum is for for reflecting on your study skills and test preparation. The requirement is what will usually be true: make a contribution soon, then come back and reply to two other students' posts. (Moodle should show a completion checkmark when you have done that.)

5. This week does not have the usual homework. Instead, complete two practice tests and after grading your answers submit photos of your work (preferably using a shared folder in Google Drive, instructions here).

5b. During class we talked about an Example Savings Plan Spreadsheet. You can make your own copy and experiment with it as a make-up quiz (if you missed a quiz during the firs two weeks).

6. Perhaps go over Paula's weekly worksheet. If it is helpful, write out solutions for yourself to make sure you understand. You do not turn this in, but may contact me with specific questions if there are parts you don't get. Unfortunately, this worksheet does not have an answer key.

Next week we will have our first test. Begin preparing for it now! Test One covers everything we have done so far, plus "Which Equation to Use" which we will discuss next week. You will take this test during Week 4.

To Do List for Test One

Review your notes. Rewrite the most important things you have learned, helpful terms, and examples from each concept. Organize what we learned each class. Make useful notes to use on the test. The process of reviewing and rewriting is very helpful to get your brain organized and confident. Having carefully prepared notes will allow you to work efficiently during the test.

Review the activities and their answer keys, and your homework and quizzes.

Use Paula's review sheet.

Take lots of practice tests.

Share questions you have in the Get Help Forum.

Use other resources! Remember to look at the "Getting Help" section above.

Study Session on Monday 1/18 problems from HW 2A and 2B and quiz Jamboard notes Zoom video YouTube video
Study Session on Monday 1/18 When is it wise to pay off a mortgage? Jamboard notes Zoom video YouTube video
Wednesday - Review Day with Practice Test When is it wise to pay off a mortgage? Jamboard notes Zoom video YouTube video

Resources for Formulas

Merriam-Webster's history of why biweekly and bimonthly are ambiguous external link

Bankrate has an payout annutity calculator external link

Bankrate also has an installment loan calculator external link to find the monthly payment when you know the loan total

CalculatorSoup has an installment loan calculator external link to find the loan total when you know the monthly payment (set the Sales Tax, Down Payment, and Trade In Value to zero)

Resources for Understanding Account Types

The Motley Fool page on account types external link

Wikipedia's page for IRAs external link

OCCU's page for Traditional vs. Roth IRAs external link (requires scrolling down a lot)

Investopedia's page about 529 Plans external link

The Oregon 529 Plan Website external link

Resources for Understanding Retirement Investment Options

Vanguard's pages for Get Smart on Investing external link

The current cost of TurboTax Premier external link as a warning not to foolishly leap into investing.

For steady withdrawls and low risk (but not low fees) use an annuity fund.

Investopedia's page on payout annuity funds external link

The Balance page on the fees in payout annuity funds external link

For steady withdrawls and low risk (but not low effort) use a "ladder" made of bonds or bank certificates of depoist.

The Motley Fool page on understanding Treasury bonds external link

Treasury Direct page about Treasury bonds external link

Treasury Direct page about Treasury bonds external link

Fidelity's page about bond ladders external link

For low fees and low risk (but not steady withdrawls) use a whole-market exchange traded stock fund for a long-term investment.

ETF Report for IVV (for S&P500 Index) external link

ETF Report for MGC (for Entire U. S. Market) external link

For low fees and low risk (but not steady withdrawls) use a whole-market exchange traded bond fund for a medium-term investment.

ETF Report for AGG (for Aggregate Bond Index) external link

ETF Report for VTEB (for Government Bond Index) external link

For low fees and moderate withdrawl flexibility (but not low risk) use a broad collection of boring and reliable dividend stocks.

The Motley Fool page on Dividend Aristocrats external link

Kiplinger's Picks for 2021 Dividend Stocks external link

By the end of this week it is possible you have earned the following achievements:

This One Goes to Eleven

ask eleven questions during classes

Dynamic Duo

study for a math test with someone else

Someone's Got My Back

work with CAR or TRiO

Habit Builder

work with an Early Outreach Specialist to develop a success strategy plan

Friend Indeed

teach another student some hidden curriculum

Swiss Army Knife

for two math quizzes turn in a page of notes with all 8 characteristics of well-written notes

Three Shall be the Number

for a third weekly activity explain one problem during class

Well Lit

for a third weekly homework show all 16 characteristics of well-written problems

This week we take our first test to conclude the problem solving and finance chapters.

Then we start a new chapter, Describing Data. This branch of statistics is known as "descriptive" because we use it to describe what we see in the world around us. This week we will look at categorical data. Next week we will look at quantitative data. For both types of data we will learn how to analyze and create tables and graphs.

Whenever you get stuck use the Get Help Forum.

To Do List for Week Four

1. Attend the Zoom sessions. The last 15 minutes of each Wednesday class has our weekly quiz. If you are ever absent, watch the archived videos of the lessons, ask questions, and check in by attending a study session or submitting a video of you doing math work.

2. Skim the textbook chapter about Describing Data. Be ready to use it as a resource when doing this week's work.

3. Complete this week's activity. Work on your own as much as you can. Then review the answer key. This item will not be collected. It is just for you to make sure that you can use the math topics we are learning.

4. This week's discussion forum is for for reflecting on your study skills and test preparation. The requirement is what will usually be true: make a contribution soon, then come back and reply to two other students' posts. (Moodle should show a completion checkmark when you have done that.)

5. Complete the homework, part A and part B, before the end of the week. Keep trying each homework assignment until you get 8 out of 10 or more.

Students vs. Mystery Group Dataexternal link

Animation of Age Distributions in China and Indiaexternal link

Animation of Age Distributions in the United Statesexternal link

Tips for using online math videos:

1. Be selective! Watch the videos that you want to know more about. If you're already familiar with a topic, you may not need to watch the video.

2. Reuse! If you find a video that is helpful, you may want to watch it more than once. Make a note and review the video at a later time.

3. Go further! If you don't understand something from a video, or would like to see more examples, post in the weekly Get Help Forum.

Categorical and Quantitative Data external link

Overview of Categorical Displays external link

Bar Graphs for Categorical Data external link

Pareto Chart external link

Creating a Pie Chart external link

Reading a Pie Chart external link

Bad Graphical Represenations of Data external link

By the end of this week it is possible you have earned the following achievements:

I am so smart! S-M-R-T!

earn 70% or more on either midterm

Perfect Ten

earn a perfect score on any test

Connect Four

for a fourth weekly activity explain one problem during class

The Write Stuff

for a fourth weekly homework show all 16 characteristics of well-written problems

This week we continue the Describing Data chapter by looking at quantitative data. Again we focus on analyzing and creating tables and graphs.

Whenever you get stuck use the Week Five Get Help Forum.

To Do List for Week Five

0. Pick a math playground to do this week or weekend.

1. Attend the Zoom sessions. If you cannot, watch the archived videos of the lessons and check in by attending a study session or submitting a video of your math work.

2. Go over Paula's weekly worksheet. Write out the solutions for yourself, and make sure you understand. Contact me with specific questions if there are parts you don't get.

3. Skim the textbook chapter about Describing Data. Be ready to use it as a resource when doing this week's work.

4. Complete this week's activity (below). Work on your own as much as you can. Then review the answer key. This item will not be collected. It is just for you to make sure you can do the work we are learning. The activity is similar to questions you will see on the quizzes and tests.

5. This week's discussion forum is for critiquing a David Ramsey video named How to Drive Free Cars for LIFE!. Pay attention to how he presents and analyzes data. He is obviously a salesman promoting his book. What can you learn about salesmanship and describing data? (Don't get distracted by the validity of his financial advice, which we can discuss during class time.) Your contribution is due by Saturday night (preferably sooner). Then come back and reply to two other students' posts. (Your Moodle won't show completion until you have done the two reply posts).

6a. Complete the first homework by Saturday night (9 problems, no time limit, plan on 1-2 hours)

6b. Complete the second homework by Saturday night (7 problems, no time limit, plan on 1-2 hours)

7. The weekly quiz opens Thursday after class and is due Sunday night 11:59pm. (8 problems, 90 minute time limit)

Week 5, Monday Jamboard notes Zoom video YouTube video
Week 5, Wednesday Jamboard notes Zoom video YouTube video

Paula's Lecture Notesexternal link

Practice with Quantitative Data

Show your work or explain your thinking. There may be a few different methods that work.

1a. This table shows the data generated in a past term from counting how many times students could snap their fingers in 15 seconds. Each student recorded two attempts. Complete the table with your own attempt.

PersonFinger Snaps in 15 Sec
Annette Azzlemahm40 and 46
Bronson Boldstock54 and 57
Clarabelle Crinkmack47 and 48
Dexter Dazzlespout48 and 45
Eliza Ebbletack40 and 45
Frederick Fiddlefeather52 and 46
Ginger Gupperworth52 and 60
Heathcliff Hablingford57 and 20
Your Attempts

1b. Since there are so many different results possible, it makes sense to group the data into bins. Start by finding the highest and lowest values, and subtract to find the range of the data. Then divide your range by how many bins you want to use (between 5 and 9) to obtain the width of each bin.

2. Create a frequency distribution table. Your table might have fewer or more rows, if you chose to use fewer or more bins. Your starting and ending values might be different if your own attempt yielded especially low or high numbers.

BinFrequency
(raw count)
Relative Frequency
(as decimals)
Relative Frequency
(as percentages)
20 to ?
? to ?
? to ?
? to ?
? to ?
? to 60
Total

3. Create a histogram to display the data you organized above. Start by marking the boundaries of your bins on the horizontal axis. Label the vertical axis with Frequency and label the horizontal axis with Number of Snaps in 15 sec. Indicate the scale you are using for each axis. Draw the rectangles above each bin with heights representing the frequency for that bin.

blank charts

4. What percent of students in your group had fewer than 50 finger snaps in 15 seconds?

5. What percent of students had greater than 60 finger snaps in 15 seconds?

6. What percent of students had between 50 and 60 finger snaps in 15 seconds?

7a. Find the mean of this finger-snapping data set.

7b. Write a sentence that tells what the mean is and the significance in this particular context.

8a. Find the median of this finger-snapping data set.

8b. Write a sentence that tells what the median is and the significance in this particular context.

9a. Find the mode of this finger-snapping data set.

9b. Write a sentence that tells what the mode is and the significance in this particular context.

9c. Is it easier to see the mode from the original table of data or the ordered list you created when finding the median?

David Ramsey's video How to Drive Free Cars for LIFE!external link

LCC Career Community Survey Data with Graphsexternal link

Census 2014 Income Distributionexternal link

CBO's 2017 Wealth Transferexternal link

One example projectexternal link

Another example projectexternal link

Answer Key to This Week's Activity external link

Tips for using online math videos:

1. Be selective! Watch the videos that you want to know more about. If you're already familiar with a topic, you may not need to watch the video.

2. Reuse! If you find a video that is helpful, you may want to watch it more than once. Make a note and review the video at a later time.

3. Go further! If you don't understand something from a video, or would like to see more examples, post in the weekly Get Help Forum.

Creating a Histogram external link

Defining Class Intervals for Quantitative Data external link

Mean of a Data Set external link

Mean from a Frequency Table external link

Median from a Data List external link

Median from a Frequency Table external link

Mode for Categorical Data external link

By the end of this week it is possible you have earned the following achievements:

Backyard Retreat

share what you did with one playground

Play Together

work on a playground with someone else

Kept Going

share what you did with a second playground

Cocktail Party

share personal learning about some geometry, algebra, number theory, topology, or business math

Law of Fives

for a fifth weekly activity explain one problem during class

The Fifth Element

for a fifth weekly homework show all 16 characteristics of well-written problems

This week we finish the Describing Data chapter by looking at measures of variation. Then we start our next chapter, Probability, by discussing likelihood and expected value.

Whenever you get stuck use the Week Six Get Help Forum.

To Do List for Week Six

0. Share during class about your math playground if you have not yet done so.

1. Attend the Zoom sessions. If you cannot, watch the archived videos of the lessons and check in by attending a study session or submitting a video of your math work.

2a. Go over Paula's weekly worksheet. Write out the solutions for yourself, and make sure you understand. Contact me with specific questions if there are parts you don't get.

2b. Go over Paula's expected value worksheet. Write out the solutions for yourself, and make sure you understand. Contact me with specific questions if there are parts you don't get.

3a. Skim the textbook chapter about Describing Data. Be ready to use it as a resource when doing this week's work.

3b. Skim the textbook chapter about Probability. Be ready to use it as a resource when doing this week's work.

4. Complete this week's activity (below). Work on your own as much as you can. Then review the answer key. This item will not be collected. It is just for you to make sure you can do the work we are learning. The activity is similar to questions you will see on the quizzes and tests.

5. This week's discussion forum is about the Pareto Principle, which is a problem solving tool to helps you prioritize. After visiting the links in the references below, explain the basic idea in your own words. Then pick an example that stands out to you: do you agree? have you noticed this phenomenon? Your contribution is due by Saturday night (preferably sooner). Then come back and reply to two other students' posts. (Your Moodle won't show completion until you have done the two reply posts).

6a. Complete the homework #1 by Saturday night (6 problems, no time limit, plan on 1-2 hours)

6b. Complete the homework #2 by Saturday night (7 problems, no time limit, plan on 1-2 hours)

7a. The weekly quiz #1 opens Thursday after class and is due Sunday night 11:59pm. (7 problems, 90 minute time limit)

7b. The weekly quiz #2 opens Thursday after class and is due Sunday night 11:59pm. (4 problems, 90 minute time limit)

Next week we will have our second test. Begin preparing for it now! Test Two covers everything we have done so far. You will take this test during Week 7.

To Do List for Test Two

Review your notes, rewrite the most important things you have learned, helpful terms, and examples from each concept. Organize what we learned each class. Make a notes sheet for yourself to use on the test.

You are allowed to use your class notes on the test, but the process of reviewing and rewriting is very helpful to get your brain organized and confident.

Review the activities and their answer keys, and your homework and quizzes.

Work as many problems as possible on the review sheet.

Share questions you have in the Studying for Tests Get Help Forum.

For the test it will be important to write out your solutions while explaining your process. State your answer in a complete sentence. You will only get half-credit (or less) for the correct answer alone.

Use the Math Resource Center! The link gives you a place to set up an appointment. Also see the "Getting Help" section at the top of our Moodle page.

Week 6, Monday Jamboard notes Zoom video YouTube video
Week 6, Wednesday Jamboard notes Zoom video YouTube video

 

Practice with Standard Deviation

Show your work or explain your thinking. There may be a few different methods that work.

1. Suppose a class was split into two teams of fourteen students for a finger-snapping contest. (Note: the two teams are considered two populations.) Find the mean for each team.

Red Team Blue Team
Data ValueDeviationDeviation2 Data ValueDeviationDeviation2
50 50
42 54
30 50
43 50
41 43
40 44
44 59
36 53
45 49
40 40
42 10
35 28
41 45
38 48

2. Find the standard deviation for each team.

3. Which group had the higher mean?

4. Which group was more consistent at finger-snapping?

5. What conclusions can you arrive at if the standard deviation for the number of finger snaps for an entire group is zero?

6. One student answered that the only way that can happen is if everyone in the group had zero finger snaps. Is that student correct? Explain why or why not.

Practice with Likelihood and Expected Value

1. A charity is holding a raffle, selling 300 tickets. The ticket costs $5. The one winning ticket holder gets $500. What is the expected value for a person buying one ticket?

OutcomeNumeric ValueProbabilityProduct
Win
Lose
Expected Value:

2. If there were three winning tickets for $500 each, what would be the expected value for a person buying one ticket?

OutcomeNumeric ValueProbabilityProduct
Win
Lose
Expected Value:

For the following questions, write your answer as (a) a fraction, (b) a decimal with 2 decimal places, and finally (c) a percentage rounded to the nearest whole percent.

3a. The table below shows the number of credit cards owned by a group of individuals. If one person was chosen at random, find the probability that the person was female.

ZeroOneTwo or MoreTotal
Male951933
Female18102048
Total27153981

3b. If one person was chosen at random, find the probability that the person was male and had two or more credit cards.

3c. If one person was chosen at random, find the probability that the person was male or had two or more credit cards.

3d. If one person with zero credit cards was chosen at random, find the probability that the person was female.

3e. If one person who is female was chosen at random, find the probability that the person was had zero credit cards.

Presenting Data slideshowexternal link

Variation among weights of apples and onionsexternal link

Spreadsheet about retirement projectionsexternal link

Annuity Payout Calculator websiteexternal link

Paula's sample surveyexternal link

Paula's video about how to create a surveyexternal link

To go with the optional videos below, skip to page two for Paula's notes about expected valueexternal link

To go with the optional videos below, the answer key for Paula's notes about expected valueexternal link

Answer Key #1 to This Week's Activity external link

Answer Key #2 to This Week's Activity external link

Answer Key to Test Two Review Sheet external link

Tips for using online math videos:

1. Be selective! Watch the videos that you want to know more about. If you're already familiar with a topic, you may not need to watch the video.

2. Reuse! If you find a video that is helpful, you may want to watch it more than once. Make a note and review the video at a later time.

3. Go further! If you don't understand something from a video, or would like to see more examples, post in the weekly Get Help Forum.

Overview: Range and Standard Deviation external link
Examples: Range external link
Examples: Standard Deviation, Part 1 external link
Examples: Standard Deviation, Part 2 external link

Introduction to Probability external link

Basic Probabilities external link

Paula's first video on Expected Value external link
Paula's first video on Expected Value external link

By the end of this week it is possible you have earned the following achievements:

Goldboss

schedule when you will take three practice tests

I Love It When a Plan Comes Together

after a practice test turn in a study schedule and plan

This week is a holiday and our second test.

Whenever you get stuck use the Week Seven Get Help Forum.

To Do List for Week Seven

0. Attend the Wednesday Zoom session. This is our test!

1. If you wish, explore our class library and maybe earn easy achievements.

2. Say or send a thank you to a classmate who has helped you this term.

3. Relax. You have earned a break!

By the end of this week it is possible you have earned the following achievements:

Fact Full

summarize the first chapter of Factfulness

There's an App for That

share what you learned about an app or podcast from the classroom library

Safety Dance

earn 70% or more on both midterms

Now I Am the Master

earn 90% or more on both midterms

This week we deepen our exploration of probability by looking at contingent, complementary, independent, and conditional events. We also use tree diagrams.

Whenever you get stuck use the Week Eight Get Help Forum.

To Do List for Week Eight

1. Attend the Zoom sessions. If you cannot, watch the archived videos of the lessons and check in by attending a study session or submitting a video of your math work.

2. Go over Paula's weekly worksheet. Write out the solutions for yourself, and make sure you understand. Contact me with specific questions if there are parts you don't get.

3. Skim the textbook chapter about Probability. Be ready to use it as a resource when doing this week's work.

4. Complete this week's activity (below). Work on your own as much as you can. Then review the answer key. This item will not be collected. It is just for you to make sure you can do the work we are learning. The activity is similar to questions you will see on the quizzes and tests.

5. This week's discussion forum is about the difference between independent events and mutually exclusive events. Students sometimes mix the two ideas up. First, explain in your own words what independent events are, and what mutually exclusive events are. Then give four examples (two of each kind) from your life. (Avoid things like rolling dice and drawing cards!) Explain why you think your first two examples are independent, and your second two examples are mutually exclusive events? Your contribution is due by Saturday night (preferably sooner). Then come back and reply to two other students' posts. (Your Moodle won't show completion until you have done the two reply posts).

6. Complete the homework by Saturday night (6 problems, no time limit, plan on 1-2 hours)

7. The weekly quiz opens Thursday after class and is due Sunday night 11:59pm. (6 problems, 90 minute time limit)

Week 8, Monday Jamboard notes Zoom video YouTube video
Week 8, Wednesday Jamboard notes Zoom video YouTube video

 

Practice with Independent or Mutually Exclusive Events

1. Would the amount of time a customer spends browsing online have an impact on the amount of money they spend? To put it another way, is "Shopping Time" independent of "Money Spent"? Complete the table by finding the totals.

Shopping Time$0 to $50 Spent$51 to $100 Spent$101 or More SpentTotal
0 to 10 Minutes303518
11 to 20 Minutes224220
21 or More Minutes51315
Total200

2. Can you make any conclusions from these numbers? Does shopping longer make you spend more?

For the follwing problems, write probabilities as decimals rounded to 2 decimal places.

3. What is the probability that a shopper spends 0 to 10 minutes shopping?

4. What is the probability that a shopper spends over 21 minutes shopping? (Name this event A.)

5. What is the probability that a shopper spends more than $100? (Name this event B.)

6. What is the probability that a shopper 0 to 10 minutes shopping and spends more than $100?

7. What is P(A and B)?

8. What is P(A) × P(B)?

9. Based on this information, do you think that shopping time and money spent are independent?

10. What is P(A or B)?

11. Find the probability that a shopper either spends 11-20 minutes shopping, or over 21 minutes shopping.

Practice with Contingency Tables and Conditional Probability

Show your work or explain your thinking. There may be a few different methods that work.

1. According to the 2019 U.S. Census, the country's total population was 328,239,523 people. The Census only uses male and female genders: 50.8% of the population was female, and the rest male. The census does not ask about handedness, but other studies estimate 11.8% of males are left-handed, and 9.6% of females are left-handed. Use this information to fill out the table below.

FemaleMaleTotal
Right Handed
Left Handed
Total

For the follwing problems, use the following labels for situations: L = left handed, R = right handed, M = male, and F = female.

2. The statement "11.8% of males are left-handed" can be rephrased as the probability a person is left-handed, given that the person is male, is 11.8%. The notation for this conditional probability is P(L|M) and we could write the equation P(L|M) = 0.118. Write a similar equation for the statement "9.6% of females are left-handed".

3. Would you say that gender and handedness are independent? That is, does one’s gender affect one’s likelihood of being left handed or right handed?

4. Recall that for independent events A and B, P(A and B) = P(A) × P(B). Can we say that P(M and L) = P(M) × P(L)?

5. n general, if events A and B are not independent, then we write P(A and B) = P(A) × P(B|A). Knowing L and M are not independent, write P(M and L) as a product.

6. Knowing L and F are not independent, write P(F and L) as a product.

7. The DSM-5 estimates that 0.005% to 0.014% of male newborns will experience gender dysphoria at some time in their life. Studies have linked high levels of maternal first-trimester intrauterine testosterone to both left-handedness and gender dysphoria. Furthermore, a 2001 study found 19.5% of its boys with gender dysphoria were left-handed. Use this information to fill out the table below for Oregon's population of 700,000 boys of age 14 years or younger.

Boys without Gender DysphoriaBoys without Gender DysphoriaTotal
Right Handed
Left Handed
Total

For the follwing problems, use the following labels for situations: L = left handed, R = right handed, N = boy without Gender Dysphoria, and Y = boy with Gender Dysphoria.

8. Find low and high estimates of P(L|N).

9. Find low and high estimates of P(N|L).

10. Find low and high estimates of P(L|Y).

11. Find low and high estimates of P(Y|L).

12. Remind yourself about the probability "or" formula, and then find low and high estimates of P(Y or L).

U.S. Census Bureau Quick Factsexternal link

Answer Key to This Week's Activity external link

Tips for using online math videos:

1. Be selective! Watch the videos that you want to know more about. If you're already familiar with a topic, you may not need to watch the video.

2. Reuse! If you find a video that is helpful, you may want to watch it more than once. Make a note and review the video at a later time.

3. Go further! If you don't understand something from a video, or would like to see more examples, post in the weekly Get Help Forum.

Probability of Complements external link

Probabilities of Independent Events: P(A and B) external link

Probability of Two Events: P(A or B) external link

Probabilities from a Table: AND and OR external link

Basic Conditional Probability external link

Conditional Probability with Cards external link

Conditional Probability from a Table external link

Review of Probability Concepts external link

By the end of this week it is possible you have earned the following achievements:

The Danger Zone

turn in eight homework assignments on time

Actively Healthy

attend 14 or more classes

This week we finish our exploration of probability by looking at permutations and combinations, and conditional probability.

Whenever you get stuck use the Week Nine Get Help Forum.

To Do List for Week Nine

1. Attend the Zoom sessions. If you cannot, watch the archived videos of the lessons and check in by attending a study session or submitting a video of your math work.

2. Go over Paula's weekly worksheet. Write out the solutions for yourself, and make sure you understand. Contact me with specific questions if there are parts you don't get.

3. Skim the textbook chapter about Probability. Be ready to use it as a resource when doing this week's work.

4. Complete this week's activity (below). Work on your own as much as you can. Then review the answer key. This item will not be collected. It is just for you to make sure you can do the work we are learning. The activity is similar to questions you will see on the quizzes and tests.

5. This week's discussion forum is about comparing the currend pandemic with the 1918 Spanish Flu. Consider the world population in 1918 and 2019. Consider how many people caught each disease, and died from each disease. What percentage of the world population died from each disease? What else do you wonder about these or other pandemics—what would you like to know or research to gain a better perspective on the scope or magnitude of these pandemics? Your contribution is due by Saturday night (preferably sooner). Then come back and reply to two other students' posts. (Your Moodle won't show completion until you have done the two reply posts).

6a. Complete the homework #1 by Saturday night (11 problems, no time limit, plan on 1-2 hours)

6b. Complete the homework #2 by Saturday night (11 problems, no time limit, plan on 1-2 hours)

7. The weekly quiz opens Thursday after class and is due Sunday night 11:59pm. (10 problems, 90 minute time limit)

Week 9, Monday Jamboard notes Zoom video YouTube video
Week 9, Wednesday Jamboard notes Zoom video YouTube video

 

Practice with Counting Permutations and Combinations

For each question, first decide if you are dealing with a permutation or a combination. Then answer the question and show your work.

1. The local pizzeria offers a choice of 2 pizzas (supreme or vegetarian), 3 sides (chips, salad, or coleslaw), and 4 drinks (juice, coke, ginger beer, or water). For dinner I decide to have 1 pizza, 1 side, and 1 drink. How many possible meals do I have to choose from?

2. How many different car plates could be made if each will display 4 letters followed by 2 numbers? Assume repetition is allowed.

3. How many different car plates could be made if each will display 4 letters followed by 2 numbers? Assume repetition is not allowed.

4. Your friend wants to perform a magic trick and asks you to draw 2 cards from a standard deck of 52. The first card you draw must be placed face down, and the second card placed face up on the table. How many ways are there of drawing the two cards?

5a. In an 18 team league, how many ways can the 8 teams for the finals be decided?

5b. In an 18 team league, how many ways can the first 4 positions be decided?

6. A child wants to draw a picture using only three different colours from a set containing twelve different colour pencils. In how many ways can the colours be chosen?

7. In the front of a building there are three doors each to be painted a different colour from twelve different available colours. How many colour arrangements for the doors are there?

Information Is Beautiful presents Infectious Diseasesexternal link

Our World in Data describes the Spanish Fluexternal link

CDC page on the 1918 Pandemicexternal link

CDC page on the COVID-19 Pandemicexternal link

WHO page on the COVID-19 Pandemicexternal link

Probability Summary Study Sheetexternal link

Final Exam Reviewexternal link

Final Exam Review Answersexternal link

Answer Key to This Week's Activity external link

Tips for using online math videos:

1. Be selective! Watch the videos that you want to know more about. If you're already familiar with a topic, you may not need to watch the video.

2. Reuse! If you find a video that is helpful, you may want to watch it more than once. Make a note and review the video at a later time.

3. Go further! If you don't understand something from a video, or would like to see more examples, post in the weekly Get Help Forum.

Tree Diagrams external link

Counting Using the Factorial external link

Permutations external link

Combinations external link

Combinations - Two Categories external link

Probability Using Combinations external link

Probabilities Using Combinations: Cards external link

By the end of this week it is possible you have earned the following achievements:

Five Minutes of Fame

do a practice final problem on the board during class

Jack of All Trades

earn a passing score on every homework assignment

Travel My Way

earn 66% or more on a practice final

I Can't Hear You Over the Sound of How Awesome I Am

earn a perfect score on a practice final

Week 10 is a review week. We will do many practice finals.


OER Details

The acronym OER stands for Open Educational Resources. Different OER materials have different rules for how they may be shared, copied, or modified.

Copyright Logo I am slightly protective of my explanations of math concepts. These explanations are written for a specific audience. It is easy for a paraphrase to unknowingly explain math concepts badly. In some places my written explanations unexplicitly take into consideration my accompanying lecture style. For those reasons, I ask that other educators please contact me before modifying my math concept explanations. However, you may share or copy my math concept explanations verbatim as much as you wish if you provide attribution with a mention of this website.

This website uses some public domain images. For example, the this page has images of a heart-shaped library shelf, girls in a library, and Bob Ross.

Creative Commons License Logo Everything else (all my diagrams, math problems, study tips, etc.) uses the Creative Commons Attribution-NonCommercial-ShareAlike license. This means you cannot use my work to earn money, but otherwise you may share, copy, or modify that stuff without asking permission if you provide attribution with a mention of this website.

I am always excited to hear by e-mail how my work is helping other educators!