100% Fake Snow

In the past, most places hosting the Winter Olympics, snow was not an issue because it was a normal thing in the area or fairly close but China chose a location where snow is not a regular part of winter. If the area gets snow, they don't get more than about 7 inches which is not enough for all the events. Since they needed snow,  China had to make 185 metric liters of snow because they didn't have any. 

Although it is labeled fake, the headlines are referring to the fact they are using artificial snow rather than relying on the natural stuff.  There are cases in the past where artificial snow was used to supplement the supply but this is the first time, a country has had to make all the snow required for the events. The Chinese government hired a single company to provide snow for all four venues. 

Normally, when people create artificial snow, they use water under high pressure, compressed air, and a special nozzle to blow extremely small droplets of water that freeze in the cold air.  Unfortunately, pure water doesn't really freeze until the temperature gets low, usually around -40 degrees F. However, if the water is in tiny droplets, it can freeze at 32 degrees F but humans usually use something like sodium iodide to start the process of creating snow while nature relies upon a tiny ice crystal.

When humans use tiny droplets of water, the snow is actually a small spherical ball of ice that looks like snow to the naked eye but isn't.  This is why artificial snow feels so hard and icy. Most recreational skiers want a nice fresh powder but the competitive skiers want snow that will help them go faster, turn sharper, etc. 

Another issue with making snow for China, is that the outdoor temperatures have to be down at freezing and the area around Beijing has not gotten that cold in the last 30 years. On the other hand, the venues in the higher elevations will not have this problem. The company hired used a bunch of snow cannons, fan driven snow generators, and cooling towers to produce the snow. 

Due to the demands of needing to produce around 1.2 million cubic meters of snow over an area of 800,000 square meters, the demand for water is extremely high. It has been estimated the company is using around 49 million gallons of water which is the same amount needed to fill 3,600 average sized swimming pools or provide drinking water to around 100 million people for the day.  The cost is estimated to be over $60 million dollars just for the machines that has to be calculated as part of the expense of hosting the olympics. 

The use of artificial snow changes the way competitors react and sometimes it is more dangerous because the snow is too icy and too fast.  This is the way China met the challenge of no snow so it could host the demands of the Winter Olympics.  Let me know what you think, I'd love to hear. 

Comparing Methods Of Solving Problems

 

When we teach students the steps needed to solve certain types of problems, students end up memorizing the steps rather than taking time to understand the mathematical principles behind each step.  It's also hard to "tell" students those principles because it often goes in one ear and out the other but researchers at Vanderbilt University has found a way to help students with this. 

They discovered if you ask students to compare different ways of solving the same problem, it encourages higher level thinking while demonstrating a deeper understanding of the concepts.  It has been found that comparison is a more natural way of learning for humans. People use comparison so much in real life such as when they shop, they look to see which deal is a better one, or they compare routes from point A to point B.  

These researchers even took time to determine which problems are the best to use comparison with.  As mentioned earlier, one type of problem is to compare the different ways to solve problems. Another type of problem to compare are those problems which are confessable and finally, comparing correct with incorrect strategies. They discovered when students compared these three types of problems, they acquired greater conceptual knowledge and were more flexible when solving problems.

Furthermore, the researchers looked at the best time during the learning process to use this comparison technique. One thing they discovered was that students could compare methods if they understood at least one method.  After some practice, students showed they were able to compare the similarities and differences between two or more unknown methods but this needed more support from teachers.

When introducing comparison to students, teachers need to provide clear and visible examples to students while showing the solutions at the same time. In addition, students did better at figuring out the similarities and differences between mentors when teachers used well defined vocabulary, terms, gestures and visual clues.  Furthermore, teachers should provide questions to prompt clear explanation of key points and summarization of the major points brought up during the comparison. 

These same researchers are getting ready to explore how using the comparison method impacts student attitude towards mathematics, or for teachers to use it to decide if students need additional support. Fortunately Vanderbilt University has a site with the materials in a downloadable form to show you how to implement this method.  They have activities for linear equations, functions and linear equations, solving systems of linear equations, polynomials and factoring, and solving quadratics.  

I downloaded the first topic on linear equations.  The 27 page module has several activities from "Which is correct" to "Why does it work?" to "How does it work?" to "Which is better?" for multiple scenarios.  Each scenario shows two students doing the same problem and students are asked specific questions they discuss during a think, pair, share activity with a big idea at the end.  It provides the worksheets students need to do the activities.

Furthermore, there is a teachers guide which provides suggestions on when each activity should be done during the lesson, at the beginning, the middle, or the end. There are also questions provided to help guide the discussion students are asked to do.  I like they've provided the materials needed to try this method in class.  Let me know what you think after you've checked it out because I'd love to know.  Have a great day.

Storyboard That for Comic Strips

In January, I wrote a piece on turning word problems into comic strips.  I mentioned a couple of websites but since then I found one that works so much better and is easier for me because it has so many more objects to use.  Today, I'll be doing a step by step visual instruction on doing the comic strip so you can see how it's done.

Storyboard that is the website I discovered and like so much.  It is the program I used to create the comic strips you've seen the past couple weekends for warm-ups.

When you open the program, you are shown to this screen.  It automatically comes with three separate frames but you can add in more frames if you need them.  There is a button that says add/delete. 

I chose this problem because it has a comparison and is fairly easy but the process is the same no matter what grade level you are doing.  

"Aaron’s candy container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. Bruce’s container is 25 centimetres tall, 9 centimetres long and 9 centimetres wide. Find the volume of each container. Based on volume, whose container can hold more candy?"

I have to sit down and figure out what I need to do this.  I think I'll do it in 6 frames so that the information is given in smaller chunks but I could do it in three.

1.  Aaron alone with his box.

2. Bruce alone with his box.

3. Aaron with box measurements

4. Bruce with box measurements

5. Aaron and Bruce bragging they can have more candy

6.  Question.

Now that I have my plan, I'll set my storyboard for 6 frames and select a background.

After I click and drag the background into the frame, I go through the characters tab looking for a tab.  I don't have to use the names in the original problem, I can change the names to reflect the ethnicity makeup of my class.  I chose teens to reflect the age of my students.

Next step is to find boxes for the characters so go to the search bar and type in box or boxes to see which has the most for the best choice.  

Then I put in all the speech boxes and filled them out. I put all the information in and changed all the text from 10 to 14 so it was big enough to read.

So now you have a full strip.  I usually just take a screen shot of the strip itself and print it off to use in class.  I included the headings and such so you can see what it does.  If you want, you can log in using Microsoft, Google, or a variety of other programs and if you do, you are allowed to make two comic strips a month.  If you don't sign in, there does not seem to be a limit if you do the screen shot method.

This is a step by step guide using the Storyboard That program online.  Let me know what you think, I'd love to hear. Have a great day.

Warm-up

 

Warm-up

 

Ways To Help Students Understand Math Better

 

I know we all have that point in teacher where we know we've taught the material, thought they understood it and then nothing. It's like you have to completely reteach everything and it seems like no matter how you choose to teach the material, it ends up the same.  There are some things you can do to increase the likelihood of having students remember and understand the material better.

We want them to understand what is taught, to apply the skills they learn, and remember the material in the future when referred to.  It does no good for students to only remember it for the space of a few days.

First, create a good class opener, bell ringer, or warm-up to start the class with. The first five minutes of class set the tone for the rest of the lesson. It is suggested teachers post the agenda telling students what material will be covered that day. In addition, there should be information on the learning objective or essential question for students.  It is best to form the learning objective as an I can statement rather than saying "Students will learn......." This allows the teacher to have students reflect on how well they met the learning objective by asking them at the end of the time. There should also be a short active warm-up to review or assess prior knowledge or show a short video to expose students to upcoming materials.

Second, when introducing new material to students it is best to provide multiple representations because the more representations offered, the better the chance students have of understanding it. One should show the concept with manipulative, pictures, breaking down the problem, or a symbolic representation.  Depending on the concept, it might involve showing the equation, on a number line, a picture, or words.  This is so you find a way to communicate the material to the students.

Next, think about solving the problems in multiple ways to students see there is more than one way to solve a problem and it encourages students to come up with their own creative way to solve the same problem.  The more ways students are shown to solve a problem, the deeper the conceptual understanding of the material students develop. In addition, once students solve the problem using one method, encourage them to solve it again using a different method. 

Furthermore, it is important to take time to show students how the concept is used in the real world.  When we can show how the equation or concept is applied in the real world, it increases student understanding of the math. If we can't find a real world application, we should look for how its applied within math or another subject or show how it was developed over time by looking at the history of it. 

Then one should take time to have students communicate their reasoning behind solving the problem.  They should communicate using both written and verbal forms and teachers can use this to help assess how well students understand the concept.  It is easy to incorporate 10 minutes during class for students to explain to each other their reasoning. 

Finally, set aside the last seven to ten minutes of the class to have students do a self assessment of how well they understood the concept using a rating scale of 1 to 5 with one meaning I'm still lost and 5 meaning I've got it and can teach others the concept.  This is the perfect opportunity to give students a preview of the object for the next day's class.  The teacher can take time to discuss where the lesson is going the next time.  The final thing to do during this time is to preview the homework assignment to eliminate any misunderstanding.

If you make sure you do all of these things during each lesson, you will increase the chances of your students understanding and retaining the concept.  Let me know what you think, I'd love to hear.  Have a great day.

The Math Of The Mollusk Shell

 

I love finding articles that help support the point of view that math explains the world around us.  I came across on where scientists looked at an extinct mollusk to figure out mathematically how it got its shell shape. The cephalopods include octopus, squid, cuttlefish or nautilus. Historically, the number of extinct species outnumber the current populations with the highest number during the Paleozoic and Mesozoic ages.

Quite a few of the 10,000 species of the extinct cephalopods had tightly coiled shells.  One of those, the Nipponites mirabilis had a shell that twisted so it looked like something M. C. Escher might draw.  The convoluted shell twisted itself so it seemed to have to beginning or ending.

At first, it looks like nothing more than a tangled mass but if you examine it more carefully, you begin to notice there is a pattern to all that twisting.  Several scientists created a mathematical mannequin for this and other shells that did not display the standard pattern.

The mathematical mannequin shows how mechanical forces twist the shell so that it is uneven. In addition, the mannequin also shows how some snails develop their spiraling form.  This mannequin is able to show how three different shells were formed, specifically the spiral shell, the helical shell, and the meandering swerves of the Nipponites mirabilis. In fact, this came out of a desire to understand the physics behind the formation of seashells. 

Mullosks actually create their own shells using the outer mantle which is a fleshy organ.  The mantle actually secrets calcium carbonate in layers that harden into the shell. The scientists designed the mannequin to capture the interactions between the mantle and the outer shell. Although the ancient ammonite the mannequin is based upon died out around 68 million years ago, they had bilateral symmetry similar to their squid cousins. 

The mannequin was to help answer the question of how could a bilateral secretion cause an uneven finished product. One possibility is if the actual body grows faster than the shell, then it can become too big for the shell and cause enough physical stresses to twist the body and cause a twisted shell.  If the conditions are right, it twists unevenly to make the weird shell of the Nippoinits mirabilis. 

This is a cool way to use mathematical modeling. The scientists used currently knowledge and mathematics to create a mathematical model (mannequin) so they could figure out why an ancient mullosk ended up looking like a tangled mess. Let me know what you think, I'd love to hear.  Have a great day.