Warm-up

 

If a three ounces of French fries is equal to 13 fries, how many fries will you have in 6.25 pounds of fries?

Math + Minimum Payments

 

Most everyone has at least one credit card in today's society.  You need a credit card to rent a car, book a stay at a hotel, or even pay when overseas.  I've found I can use my card to buy currency from the place I'll be traveling to.  

Most savvy people know that one should always pay more than the minimum payment for the month but young people have not always learned that yet.  I've often wondered how credit cards determine the minimum amount listed on the monthly bill.

Many credit card companies use the interest plus one percent formula to calculate the minimum payment.  This means they take one percent of the current balance and add it to the amount of interest accrued for the month to get the minimum payment unless the balance is $25.00 or less in which case, the minimum will be $25.00.  The other way used by some credit card companies is to calculate the minimum payment as two percent of the current balance.  

If the card has an interest rate of 15.5% which was the average rate in 2018, it will take 226 months to pay off a balance of $5500 with no additional charges using the first calculation for the minimum payment.  Imagine taking almost 19 years to pay off this amount.  On the other hand, using the second method to calculate the minimum payment, it would take a person about 290 months or about 24 years to pay it down.  In addition, the first method means a person saves just over $2,300 of interest and about 5 years of payments.

If a person has a smaller balance of say $1,000, it will take a person about 57 months using either method because they work out about the same on smaller balances.  It is with the larger balances that the differences become more apparent.  Although most of the largest credit card companies use the interest plus one percent, many of the smaller ones including Discover use the two percent method.  Note that the lower the interest rate, the faster the balances are paid off but it can still take a long time to do it using only minimum balances.  Sometimes, any late fees are included in the minimum payment while other times they are added to the balance which again depends on the company.

When a person applies for a credit card, the method of calculation should be located in the pamphlet that arrives with the card, otherwise it should be found online in the person's card account.  When in doubt call the credit card company and ask a representative how the company calculates the minimum payment.

This website has some nice activities to show students some basics on balances and the minimum payment. The video showing how to calculate things only looks at a minimum payment of $25.00 rather than either of the above methods but it would be easy to extend the activity to have them calculate the minimum payment using both methods.  The second video discusses how much interest is saved when more than the minimum payment is made. The videos are in Edpuzzle so they are interactive and require the student to participate.  

In addition, there are additional worksheets so students get to practice calculating interest and balances for other situations. Furthermore, students are required to graph the total interest paid over 5 months and the remaining balance after 5 months for three different people. At the very end, are suggestions for teachers to simplify the work or extend it.  

Now, as a teacher you know how they calculate the minimum payment.  Let me know what you think, I'd love to hear.  Have a great day.

PhET Interactive Simulations

 

It is always nice to find a real interactive activity for students to explore rather than relying on worksheets of any sort.  PhET is run by the University of Colorado in Boulder and is free.  It has 806 simulations for math, physics, chemistry, earth science, and biology currently.  What makes this site different is that the majority of stimulations are written in HTML5 rather than Flash so they can be used on the iPad or Mac.

When you click on Math, there are 44 total simulations but only 39 of them are done in HTML5. They cover topics like ratios, proportions, algebraic concepts, number lines, fractions, equivalents, quadratics, vectors, graphing, and more.  

Each simulation comes with a basic version to explore and play with and at least one more complex version to use what you learned with the introduction.  I did not find instructions for the student to read but it was quite easy to play with the simulation to figure out how to use it.  Fortunately, the site has extensive materials for the teacher.  

Furthermore, each simulation can be assigned via google classroom.  You also have the option of downloading the simulation or embedding it in something else.  At the bottom there is a description of the activity, the topics it covers, sample learning goals, and standards alignment.  Under the teachers section for the simulation, there are suggestions and teacher created lessons but you need to join the site to access them.  If you are working with students who are not proficient in English, there is an option to translate the activity into another language. 

In addition, they let you know about related simulations. For the curve fitting activity, there is a least square regression, and a calculus grapher.  The last two parts cover software requirements, which digital devices it can be used on, and who wrote it.  Lots of great information.  

There is a short about section which provides general information on the site if you look under teaching. In addition, there is a huge section of tips for using these simulations in the lecture, with clickers, designing and facilitating their use, and videos on facilitating the simulations.  There is also a professional development workshop available for this site.

Then there is a browse section which is actually a search engine so you can click on the type of simulation you'd like such as area model or function machine, choose the type of simulation such as remote, homework, lab, guided, or other choices, choose the subject, grade level, and/or language.  I tried the search engine by clicking on build a fraction, homework, and English.  The engine came back with 18 suggestions that I could choose from

The 18 were all listed under one title and if the title is clicked, there is information on who wrote it, when, language, and a downloadable document to go with everything but you do have to set up an account to do this.  It doesn't take long to sign up.

Overall, this site offers quite a lot of activities and support so it is something to think about using when you need an exploration or homework for class.  Let me know what you think, I'd love to hear.  Have a great day.

Get The Math!

 

I love it when I stumble across interesting websites.  I came across one titled "Get the math" which is a lovely site geared for middle and high school students by showing them real life applications of algebra and other levels of math.  

Each lesson has an introduction where someone shares basic information on the topic.  This is followed by a challenge which requires students to use material from the introduction to help solve the problem.  

The challenge is set up so it introduces the issue and provides enough help to work on it but not enough to fully give the answer. It even allows students to try again if they don't get it right. Once the challenge is done, students are given the opportunity to view a video on how others solved the challenge.  The section has one more challenge so students can practice what they've learned in the previous challenge.  

This site covers math in music, the fashion industry, video games, restaurants, basketball, and the use of math in special effects.  The math challenges are not the standard problems one associates with textbooks. Instead, they are the things that people face within that line of work.  For instance, in the math in music section, students learn about beats per minute and how to mix two different tracts into one so they are moving at the same speed and matched beautifully.

In restaurants, students learn how the prices they see on the menu are set by the chef.  Students are giving the job of calculating the price for guacamole next year based on previous costs.  This activity has students making predictions based on previous prices to come up with the future price.  In fashion, they get to change a design so it is able to be sold at a specific price point after learning how math is used by fashion designers.  For special effects, they learn about distance and light to get just the right exposure for the look they want.

The site lets you look at only the challenges, or the videos if you want but it also includes lesson plans for each situation.  The lesson plans include an overview, learning objectives, list of resources and materials needed for the lesson.  It also includes a list of things to be done before the lesson, the lesson itself with two activities and the culmination along with end of course questions that cover the same algebraic concepts as covered in this lesson.  There is also a long list of common core standards the lesson touches on.  

Finally the site allows you to download the lesson plans, all handouts, and end of course questions for each section so you have the material on your computer.  In addition, if you or your students have issues with the internet, it is possible to download all the material including the videos and challenges so it can be done locally.  

I love this last part because not all schools have great internet and if this is something you want your students to do as a flipped activity, it can be easily done by sending the videos home on thumb drives.  I am impressed by the way the math is introduced to students.  It is done in a friendly way without all the mathematical equations we see in textbooks.  I think students might find it easier to understand the concept.  Let me know what you think, I'd love to hear.  Have a great day.

Happy July 4th

 

Warm-up

 

In 2018, Washington DC spent 6.5 million on fireworks.  In 2019, they spent 13 million.  What percent increase was that?

Thinking In 3D = Better Math Results

Every so often I check out Mathematical news to see what is happening in the field.  In the process, I found several studies which indicate the children who have better spatial reasoning, do better in mathematics later on.  For instance, a study done by the University of Chicago found that children who could see how shapes fit together did better with number lines and performing computations.

Although the world is three dimensional, we teach everything as if it were flat. When we teach numbers and letters to students we don't take time to talk about them in terms of how rounded or pointy they are, or how their heights compare, or even how close or far they are.  This helps children develop their spatial reasoning which has long term benefits.

Two ways to help young children develop their spatial skills is to let them play with puzzles and blocks.  The study discovered that when parents play with their children using blocks, they are more likely to use spatial vocabulary such as "above", "over", or "through". Another study indicates that parents who use words like "curvy", "edge", or "face", their children are more likely to use that terminology later on in school.  In fact, the more terms the parents use, the better their children do in mathematics.

This is important because spacial skills are used in the STEM fields such as engineering, science, technology, and mathematics. Furthermore, a different study found that students who score well in spatial reasoning on tests in high school were more likely to go into STEM subjects in college.  Students who do well, usually come from homes where parents used the terms when they were young and introduced them to spacial reasoning as children.

Another study, this one from Switzerland, found that a students success in Primary school can be determined by their spatial ability at the age of three.  They also found that students who had a lower spatial relationship ability at three, did improve but they never caught up to the ones who did well at three.    They also found out that at the age of three, there is little difference in the abilities of boys and girls but over the coming years, girls tend to develop slower than boys. 

It is suspected this happens because the toys designed for boys tend to encourage the use of spatial reasoning and appropriate use of language while toys for girls focus more on social skills.  It is also possible that there is a bit of gender bias in regard to the perceived roles of men vs women.  

Fortunately, there are things we can do as parents and as teachers to help improve spatial reasoning from childhood on.  First, it is important to use the appropriate vocabulary in everyday situations.  Rather than using words such as this or that, be specific with language such as "the ball on the second shelf on the left hand side." This serves two purposes.  First, it helps children with developing their spatial ability and second, the person has to visual position to describe it.

Next,  try taking up chess because it requires the players to visual multiple moves ahead of the current ones.  Each time a move is made, the board changes and by looking at things ahead, one visualizes all the changes that happen each move.  You are also aware of all the possible moves your opponent has after each move.

Go back to playing with Legos.  This is a perfect activity to work on spatial exploration when putting the modular pieces together in creative ways.  How do you use Legos to make a building, a spacecraft, or even a tree? Another way to improve spatial reasoning is to picture places like your apartment, your favorite coffee shop, or other building in your mind.  Picture everything you can in it's proper location in your head.  This is called creating a memory palace and can be used to remember telephone numbers and anything else.

Or you could play video games because you use spatial intelligence as your character moves through the game.  Have fun creating place in minecraft because it helps develop spatial reasoning as you put things together.  Want something a bit more fun, buy yourself a drone and fly it.  Again, you use spatial intelligence as you determine where the drone has to fly, changes one has to make to avoid things, and plan ahead to where it is going.

As a parent, do any of the above with your child.  As a teacher, spend a bit of time using these in class.  When it is fun, people are more likely to do it.  Go ahead and do this regardless of age.  Let me know what you think, I'd love to hear.  Have a great day.