Math Contest: Fall 2011

This week we've started an online challenge for Swift Middle School.  8th grade students select games to play from the website, Sumdog.com and earn points for each time they score.  The games not only involve gaming ability, but have some problem solving and math knowledge as well. 
Students can play as much as they like and earn extra credit homework points for their scores or comments on our class blog.  

Please comment below to share some of your favorite games, and tips for this math challenge. 

Stretch your skills at fractions and probability

Check out the online versions of Connect Four and Racing Game!  Click a link below to begin.
Connect Four 
Racing Game

Below are 3 easy steps for finding the sum or difference of fractions include:
1) Find a common denominator-  list the multiples of both denominators and find the lowest one in common. 
example  2/5  +  1/2     5 and 2 both have  a common multiple of 10
2) Make equivalent fractions- Divide the original denominators by 10 (common denominator).  Use the quotient to multiply by the numerator. 
example  10/5=2   2(2)=4  equivalent fraction 2/5 = 4/10;   10/2=5  5(1)=5  equivalent fraction 5/10=1/2
3) Add/Subtract numerators- Keep the denominator the same, and take the sum or difference of the numerator
example   4/10 + 5/10 =     4 + 5    =  9
                                          ------      ---
                                            10         10

Real life use of Fractions involves beats in music, cooking recipes, clothing design, city buildings, and sports statistics.  What are some ways you see fractions used in real life?  How does your science fair experiment involve the use of fractions, data, or math displays?       

Equations and Surface Area of a Figure

Equations are a way we represent a problem by using numbers and symbols.  After we develop an equation it becomes easy to apply it to many similar problems. 
Pythagoras, a famous mathematician developed a famous equation to find the side lengths of any right triangle.  His equation is called the Pythagorean Theorem. A theorem is a math rule that is developed from tests over time.  It is kind of like a science experiment in that it has to be proven through repeated tests. 
The equation shows that the square of the sides of right triangles forms a pattern.  It says that a right triangle has a side across from the right angle which is equal to the sum of the other two sides squared.  In equation form:  a^2 + b^2 = c^2  This equation is shown in picture form at this web link- Pythagorean theorem
We can use the Pythagorean theorem to solve real life problems that involve finding the sides of triangles.  I think it's interesting how the web link above has problems about finding the distance on a baseball diamond, and finding the length of a ladder needed to reach a window.  Careers in medicine, construction, engineering, and architecture use equations to solve problems.
One example is how 3D figures like square pyramids use the Pythagorean theorem. For example, how do I find the surface area of a square pyramid?  Surface area is found when we want to know the amount of material needed to cover a 3D shape.

A square pyramid has four triangles and one square as shown in the net of the 3D shape above. The 3D shape becomes folded out in a "net" or "net drawing". The website Interactives 3-D Shapes shows a video clip of how to make a net.
The Pythagorean theorem can help us find the side lengths of the triangles if we know the side lengths but need to find the height.  The base of a yellow triangle needs to be bisected, or divided in half with a perpendicular line, to form a right angle.  If the base is 6 cm and we bisect it, then the side of the right triangle formed will be 3 cm.  If the hypotenuse, or side across from the right angle is 5 cm then we can find the height with the Pythagorean theorem.
We use the equation 3^2 + b^2 = 5^2 to find the height of the triangle.  When the equation is used to solve for the missing side we can find the exact length quickly!
Can you find the missing side using the equation above?  Which city buildings or designs use the square pyramid shape? 

Attack Integer Computation with Success

Integers are made up of natural numbers 0, 1, 2, 3... and negative whole numbers  -1, -2, -3...
The number line is a familiar way to recall the rules of computing integers.   In the example pictured above we see the numeral two as our starting point which is symbolized with a dot.  This is followed by a subtraction sign, which leads us to move to the left three spaces as shown with curved line and arrow.
Helpful hints are another way that we can remember how to add and subtract integers.
We learned the first hint: Two like signs become a positive sign.
Example  2 - (-3) = ?   This can be rewritten as 2 + 3 = ? since there are 2 like signs in the original problem. 
Another example  -3 - (-4) = ?   Rewritten as - 3 + 4 =? Again like signs - and - turn into a positive sign.

And conversely the second hint: Two unlike signs become a negative sign.
Example 2 + (-2) = ?  This is rewritten as 2 - 2 = ? because there are unlike + and - signs in the problem. 
Another example  -4 + (-2) = ?  Rewritten as -4 - 2 ?  We start at -4 on a number line, and move to the left (away from zero) 2 spaces.  This leads us to -6 as the difference. 

Now, we find the product or quotient of two integers to be:
Positive only when both integers are positive, or both are negative.
Examples:  -4(-4) =  -4 * -4 = 16     -24/-2 =  12
Negative when one integer is positive and the other is negative.
Examples  30/(-5)= -6  or   -5(7) =  -5 * 7 = -35

Which type of integer calculation do you find easiest to solve?   
Try your skill with the interactive version of Integer Battleship found at the link below.  After you make a locate a Battleship you'll be challenged with an integer problem to see if you can hit the target.
Integer Battleship   


What are some other tips that you have for ways to calculate integers?  Share a website, strategy you've learned from a teacher, or a way that helps you keep integer computation clear.   What other games or activities have you done with Integers?  Work at it and Integer computation will become automatic.

Student Math Projects- Amazing Facts and Feats: Data Displays

Have you ever wondered, Is that even possible? Or, was that statement really true? Amazing facts can sound too incredible to believe.
Our projects will show some of these amazing facts and feats. Take for instance the fact that "Humans breathe about 23,000 times a day!" If you measured a person breathing for one minute you may find that they breathe about 20 times. That same person would breathe about 1200 times in an hour, and 28,800 times in a day. The Math and Data Displays behind the fact helps us to judge whether this sounds believable or not.
We will be able to find information to support the amazing facts and feats from books, computers sources, or teachers/librarians/adults that we know. For example, a website called, Interesting Facts lists some Science related facts:

• Each person sheds 40lbs of skin in his or her lifetime.
• Koalas sleep an average of 22 hours a day, two hours more than the sloth.
• Light would take .13 seconds to travel around the Earth.
• The largest desert in the world, the Sahara, is 3,500,000 square miles.

21facts.com also has some interesting facts about the Civil War that you may or may not believe?

• The total deaths in the United States Civil War was over 1,000,000 people
• During the Battle of Cold Harbor in the Civil War there were 7,000 people that died within 20 min.
• There were over 550 generals who served during the Civil War.
• A Confederate prison camp called Andersonville had 12,000 people die.

Books like the World Almanac, Atlases, as well as Encyclopedias could be used to find out more about these amazing facts. There is often a lot of background information and facts that can help to make the amazing facts more believable. On the other had the research often helps us point out errors or misconceptions. Either way our projects will have fun with the investigations.

Extra Support from Loyola Teacher Candidates

Swift 7th and 8th graders advance their math skills with the help of Loyola's tutoring support and team teaching.
Our Loyola teacher candidates include:
8th- 313 Jessica & Elizabeth
8th- 312 Jessica
8th- 315 Hana
7th- 314 Haley & Christina
Emphasis for these lessons is on building mathematical vocabulary, developing math concepts, strengthening math fluency, and supporting math problem solving.
Loyola University has a library of math videos. Click on this link for- Countdown Videos
These videos include review of math content and support students'
development in mathematical thinking.
What are some of your favorite activities that you've done in math?
Do you find videos helpful in reviewing and learning math? Why or Why not?

Best Fit Lines on a Scatter Plot

Best Fit Lines show the general direction of points on a data display. The best fit line doesn't connect the points, but instead is shown to be close to as many points as possible within the constraints of a straight line.

This week students measured their heights and jumping heights using meter sticks. These two variables were compared to see if one of them had any effect on the other. For example, does the height of a person affect how high the can jump? The Scatter Plot display of our data should help us see whether the answer to this question is true, or false.

Here is a website that has information and questions about scatter plots. I like the fun graphics and the way the questions give feedback about your answer. Click here to find an interactive Scatter Plots Website

Another website called The Challenge Club shows the steps to create a scatter plot.
Besides comparing the example above about whether tall people have larger hands or not, you can make scatter plots about things you're into. For example whether your favorite band's new album sales relate with the amount of attention that they're getting on the radio or Internet.
Does one thing affect another? When we make a scatter plot and draw a best fit line, we can see the relationship more clearly.

Amazing facts and music

The variety of musical interests' of Swift students is shown through the graphs and charts outside Ms. Gamble's room. The data that shows what kinds of music we prefer fits in well with the circle graph and bar graph displays. Other types of music facts such as specific information about favorite albums, songs, the number of awards, or how long a song remains popular can be interesting to check out too. Some of these facts can best be shown on graphs with types of averages- box and whisker plots, changes over time- line graphs, and relationships between data- scatter plots.

One website where music data from all genres is shown is called All Music. This website gives a plethora of updated facts on musicians. The link above shows the band "Sugar Ray" from the 90's and early 2000's. In addition to some amazing numbers the website gives the bands history and links to other bands that are similar.

What links to musicians have you found on the Internet? A band's website, Face book page, or a music station like All Music that has lots of different bands?

Data Displays

How to make your favorite data display?

Circle Graphs-

Start with a table for Categories, Frequency, Percentages, and Angle Measures.
Use a compass to draw the circle and form sectors using a protractor and the angle measures.
Label the circle graph with categories, percentages and colors for each sector.

Example- What is your favorite color?

Category- Blue; Frequency- 4


Percentage- 4/10 = 40%


Angle Measure- .40*360= 144 degrees


Interactive Website: Making a Histogram. Online resource to use- Illuminations Webpage

Find the range of your data and determine your intervals. Make a data table with Intervals and Frequency (number of data points in those intervals). Label your vertical (y-axis) with frequency and the horizontal (x-axis) with the intervals in your table. The bars on your histogram should touch each other and run continuously along the x-axis. Label your histogram with a title and label for your horizontal axis to represent the meaning of the data.

Example: Weekly Hours of Practice: Data 12, 21, 16, 18, 31, 25, 8, 22
Intervals 0-9, 10-19, 20-29, 30-39
Frequency 0-9 =1, 10-19 =3, 20-29=3, 30-39=1

The circle graph and histograms are both interesting visual graphs that show comparisons.
One key difference is the histogram can show the frequency of an event or how many times it falls within a certain interval. What other situations or data sets could you use for circle graphs or histograms? What tips can you offer to display data in a clear and entertaining way?

Quotes about Life

When we want a little inspiration, or to reflect on why we are here Quotations can help us open up a discussion or think about something more deeply. Below are some quotes that I found inspiring as we begin a new school year. What thoughts do these quotes bring to mind for you? What are some of your favorite life lessons or quotes?

"The best way to cheer yourself up is to try to cheer somebody else up" Mark Twain

I like this quote because when I am helping and encouraging others I feel uplifted. What are some things in your life make you feel joy?

"Talent is like electricity--we don't understand electricity we use it" Maya Angelou

Each person brings unique talents that they can offer to share with others. We don't understand why we have these talents but it is these things that make us special. What is a special talent or interest that you have?

"So you see! There's no end To the things you might know, Depending how far beyond Zebra you go" Dr. Seuss

We can stretch ourselves far beyond where we once thought possible. The zest in our imagination will bring us new knowledge and stretch our potential as humans on a rich planet. What are some things that you've learned or wished to learn which help you grow?

"Home is where one starts from" TS Elliot

The foundation that we've learned from our families carries with us. Who are those people in your life you call family?

"No one can make you feel inferior without your consent" Eleanor Roosevelt

We are in charge of our lives. The power to change our mood, move past misfortune, and overcome obstacles makes us stronger. What challenges have you overcome in life?

"If a person doesn't keep pace with their companions, perhaps it is because he hears a different drummer. Let him step to the music which he hears, however measured or far away" Henry David Thoreau

"Nothing can be loved or hated unless it is first understood" Leonardo da Vinci

"The injury we do and the one we suffer are not weighed in the the same scale" Aesop

"We may all have come on different ships, but we're all in the same boat now" Martin Luther King Jr.

"We must be authors of our own age" Madeline Albright

"No individual has any right to come into the world and go out of it without leaving behind him/her distinct and legitimate reasons for having passed through it" George Washington Carver

"Genius is 1 percent inspiration, 99 percent perspiration" Thomas Edison

"A book is like a garden carried in a pocket" Chinese proverb

It's a Small World

The chance to travel to a new place can be a fun way to learn about other cultures around the world. If you're limited by time or money reading a book, website, or listening to music may be a great way to experience another place.
Here are some websites that are fun to check out when exploring life in other places.

A website that shows different parts of the world is found at A Kid's Life in...
Teens and kids who live all over the world show us about their country. I like how you can get a first hand account about different places. The web site's graphics also help you to get a sense for interesting aspects of their culture.

Another handy resource when looking at different countries is a metric/customary conversion chart which can be found at Kid's corner: Metric Weights and Measures
When have you needed to convert between metric units, or from customary to metric units? Last year, I was training for a 10K run and wanted to know how many miles I'd need to train for. The conversion, 1.6093 kilometers = 1 mile would have been useful. Before running I thought it was around 5 miles, but after checking the math I realized a had run more.

Another question that's worth asking is: How much is your money worth? Money Exchange is done on a daily trade market which can be found at XE World Currency Converter.
This converter tool has a calculator type feature that will show you exactly how much your money is worth on any one day. For example, upon checking we can see that one US dollar is worth 12.5150 Mexican pesos. Which other types of currency do you know about? What other travel resources have you used that could also be helpful?

Sizzling Sounds of Summer

The sounds of music add sizzle to the summer. In outdoor venues the sounds of music fill the air. Some of my favorite venues in the summertime are Millenium Park and Ravinia.

Millenium Park area has an incredible Jazz Festival. One jazz musician is two time Grammy Award winner, Roy Hargrove. Hargrove plays jazz that is infused with hip hop, funk, gospel, and soul music. The Video link here shows Hargrove playing the trumpet along with lots of rhyme and soul. I like how jazz music blends different styles together. Concerts at Millennium Park are free of charge and bring lots of talented musicians to Chicago.

Ravinia is a 30 minute Metra train ride north of Chicago. Like Millenium Park, Ravinia is a summer time festival that has famous musicians and young stars. Ravinia has tunes from lots of different bands including Rock, R&B, Blues, Country, Gospel, and Classical. The Chicago Symphony Orchestra (CSO) plays at Ravinia on many nights. Trumpet player, Tage Larsen from the CSO has a video link here. Larsen says, "I was amazed by the balance and unity (of the CSO). I could hear how they matched each other and was blown away by that 'Chicago Sound'"

It's fun to kick back and listen to the rich sounds of these star trumpet players. The music that fills the evening sky is like an ocean that carries many different sounds and memories with it.

Persuasive Writing: Are You Convinced?

School or Sleep. Why must we choose?

This Teensink author includes some research about the effects of oversleeping and undersleeping. There's an easy to follow list of reasons that supports her claim that students should petition their schools for a later start time. Use of vocabulary and depth in explanation provides convincing support for the author's argument.

Nature Comes Alive on a Summer Hike

A hike over the swamp
on an elevated trail.


A carnivorous, Pitcher Plant
eats insects that live in the bog.

In the book Walden, Thoreau says, "You only need sit still long enough in some attractive spot in the woods that all its inhabitants may exhibit themselves to you by turns." Nature holds many treasures in its forests, parks, and beaches.

I recently went to a forest preserve in Western Michigan. This forest had an interesting ecosystem called a bog. The pictures show the way we were able to walk above the water of the bog and observe some of the carnivorous plants that lived there.

The sounds of snakes, frogs, birds, and insects were all around us as we hiked along the path. At one point along the trail I was taking pictures and was startled by the rustling of an animal in the reeds. I heard loud croaking as the animal moved closer towards me. This animal showed itself to me in a way that caught me by surprise. Afterward, I couldn't help but think that this may have been a bear, moose, or other large animal letting me know that I had crept a little to close to its home.

It was interesting how this forest preserve was so untouched by human influence. As my family drove into the forest we noticed just a few other cars. The gravel roads that winded through the forest were surrounded by trees and didn't any have houses or businesses. The isolation allowed plants and animals to flourish without competing with people for space. In looking at the images on this webpage about Western Michigan there are some similarities between this area and how Chicago was a swamp before it was developed into a city.

Math Connections at Chicago Museums

Chicago offers visitors and residents some world class museums. Recently, I got the chance to savor some of the new, interactive exhibits these museums have on display.

Shedd Aquarium's Jellies exhibit has the slogan, 95% water, 100% amazing. One interesting fact that I learned while visiting this exhibit was how jellyfish are such resilent creatures. Jellyfish survive in areas where other fish are dying off because of pollution. As a result jellyfish are growing exponentially as pollution creates deadzones in the world's oceans. Jellyfish by the Numbers includes statistics about how Jellyfish are affecting our world's ocean water.

Exponential growth is illustrated on the King's chessboard story where every square is double the one before it. When a species grows in this way it quickly becomes overwhelming to its ecosystem.

How Do You Use Internet Resources?

What are some of your favorite Internet tools? The Internet has learning tools for practice, research, connecting with others, and creating projects.

Math Practice- Review skills while playing online games. There's a basketball game that challenges your skill in solving equations.

http://www.math-play.com/Middle-School-Math-Games.html

Research- Find information about topics of interest. Bookmark your favorite sites to find the latest updates or write down the website address to share with others.

http://www.chicagoparkdistrict.com/ Find out about many free summertime activities
http://discovermagazine.com/ Breaking news on science, technology, and more

Connecting online- Share information with others and keep connected with your friends online. Find a book blog like the ones Swift students' created and chat about your favorite characters or scenes in the story.

Projects-Refresh your skills on making videos, or even setting up a presentation.

http://www.prezi.com/ build a flashy online presentation, increased options for a student and teacher account
http://www.animoto.com/ create animated video slideshows

http://docs.google.com/ online PowerPoint presentations, online sharing of group word documents, sharing information and discussion comments

Summer Plans, Yet?

Summer vacation has finally arrived! There are many things to do over the summer that make vacations truly memorable. I think the neighborhoods in Chicago have lots of fun things to do if you're looking for something to do. The lakefront is one of my favorite parts about living in Chicago, and the diverse cultures and types of people are another that's right up there on top.


Both, fun by the lake and different cultures can be found right in Edgewater!


As I sit inside the library on this gorgeous day, I am looking at the sparkling, blue water and rippling waves of The Lake. Even though I can't be at the beach today, I know that the summer has much in store for beach lovers like me :)


What's your favorite summertime festival? Just north in Rodger's Park they have an arts festival in July and lots of cool events throughout the weeks. News for Rodger's Park highlights new happenings and shows on their monthly web page.


I'm looking forward to checking out my favorite baseball team a few times too. What's summer without baseball and barbeques? The Chicago White Sox boast Fireworks on Friday nights and Half Price tickets on Mondays.


Or, better yet doing instead of watching is fun too! Outside I am looking forward to playing Frisbee, soccer, or catch. Prefer inside? Grab a book, or notebook and imagine yourself in the place you've always wanted to go. Start a book club with a few friends. Teenreads.com has some great ideas for books and how to get started. Beginner's Luck by Laura Pederson looks like a great read.


I hope to keep posting summer happenings you can check back for updates. Hope you're having a safe and fun summer.

Congratulations Class of 2011!

The end of the school year is upon us, and it's a time to celebrate all the achievements that we've had as a team. The Class of 2011 has shared lots of special memories that will definitely not be forgotten. I am very excited for you as you transition to your new high schools.

Over the summer, I hope you have a safe and fun break. You developed many strong friendships during the past year. I'm sure you will certainly stay connected with each other. Keep up the awesome writing, reading, and thinking this summer. Take advantage of one of the great summer programs in Chicago or keep reading and writing on your own. I am very proud of the growth you've shown over the past year. You are going to do awesome as you take your next step into high school.

Your enthusiasm and hard work have made your teachers very proud of you.

Share some of your thoughts or memories.

Congratulations on a fantastic year!

More 8th Grade Blogs!

Here are some of the blogs from the 8th Grade Class of 2011. Check out the bloggers' latest posts. You will find a variety of creative topics and thoughtful questions. Here's a short summary of what you'll find on the blogs.

A book review of "Hoot" by, Carl Hiaasen. The blog shares ideas about funny and mysterious parts of the book. http://www.sghoot.blogspot.com/

This blog shows interesting parts of "Hoot" the book and movie. It includes pictures of the movie and explanation about the books' ideas. http://www.bohalterman.blogspot.com/

A review of the young adult book called Black and White. This blog gives updates about interesting parts of the novel. http://www.brandonblackandwhite.blogspot.com/

A book blog highlights scenes from the novel, "Hoot" and has video links as well. Videos show glimpses of the movie. The blog includes a response to the different scenes from each of the books' chapters. Check out this book blog at: http://jp-hootreview.blogspot.com/

The blog, Broken Hearted includes poems and ideas about love. Poetry from teen authors show the mixed emotions that come with love. http://www.loveislonely12.blogspot.com/

A blog dedicated to entertainer, Will Smith. Reviews from his movies, tv shows, and hit songs are showcased through pictures and creative descriptions. http://sheriannsarah.blogspot.com/

What books do you recommend? Which of the 8th Grade Blogs do you like, and why?

Hoot and Environmental Effects

The story Hoot (the book) tells about a boy who discovers a conflict between a business and nature. Roy finds out that a group of burrowing owls lives on the site where the business wants to build their store. (BTW check out the link above for a short and interesting book review of Hoot)

On the author's webpage Carl Hiaasen answers questions about Hoot.
Carl Hiaasen says,
"The world can be nasty place, and there's nothing wrong with going after the bad guys in a novel...Funny stuff happens, weird stuff happens, but the soul of the plot is Roy's quest to stop something very bad from happening. And that's serious"

The environment damage that businesses can cause is a serious issue that affects our future. Watch this YouTube video about the BP oil spill. The G4 News Crew finds out how corporations have negatively affected pelicans of the Gulf Coast. (A Big Thanks goes to Mr. Cornfield for finding this video)

As they mention in the G4 News story there are ways people can work to help restore the environment on the Gulf Coast. One simple way is by sharing ideas about this disaster so it is not forgotten. The BP oil spill devastated peoples' lives and continues to affect the area today.

• Do you remember when you first heard about the BP Oil Spill?





• What are your thoughts about how human activity can affect our environment?





• How does the BP Oil Spill relate with destruction of the owls' habitat in Hoot?