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Finding Symmetry

Recently students flipped through magazines looking for images that included lines of symmetry. Once an image was selected they cut along the line of symmetry and drew the missinng half. Not all of the images they selected are true defintions of symmetry but I believe that came away with a better understanding of how to identify symmetry.

Merriam Webster defines SYMMETRY as:
 the property of being symmetrical; especially : correspondence in size, shape, and relative position of parts on opposite sides of a dividing line or median plane or about a center or axis

Giving Students Choice: Planning and making decisions together.

All year long students have sat together in groups. Each group is named after a college in Washington (UW, WSU, Seattle U, Seattle Pacific U, WWU, and Gonzaga). Groups are important for communication, collaboration, and provide a sense of belonging. Together, students become a part of a whole. Students for the most part have the opporutnity to move their desks where they see fit. Some have chosen to steer away from the group and sit alone. At the beginning of the year, they chose to use a draft system when it was time to change desks. Every month or so, a student would communicate using the "Parking Lot" to let the class know that they thought it was time for groups to change.

For the last three weeks I decided to let the students choose how they'd like the desks to be set up. Any student who had an idea came up with a blueprint plan and presented it to the class. Students then had a chance to preview the plans and anonymously drop their vote in a hat.

Here was the result:
  
It's too often that decisions are made for students without asking them what they want. If someone (teacher) is always making the decisions, as a student, it's easy to always comply or wait for something to happen. As you can see, these students do not shy from generating ideas and making decisions.  I truly believe that if we give students opportunities to make decisions, eventually they will become better decision makers.

Tessellations

   

According to Merriam Webster Dictionary, a tessellation is:  a covering of an infinite geometric plane without gaps or overlaps by congruent plane figures of one type or a few types.

Here are some examples of tesslations that students created.

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Taking a Closer look at Paper and Plastic Bags

We've spent the last two days breaking down the differences and similarities between paper and plastic. Using the informational visual to the right, we read about consumption, production, pollution, recycling, and whether either is biodegradable.

Throughout this experience I've thought about my consumption for both paper and plastic. When I go to the grocery store, I generally ask for plastic. I reuse the plastic bags for garbage can liners, a bag to take my lunch in, as well as bags to have in the classroom in case students need to bring things home. I'm personally going to make an effort to try and reduce the amount of plastic bags I use by purchasing a reuseable bag for groceries. I'm not ready to quit using plastic but if I can limit my use, I know I'll be making somewhat of a difference.

What do you do with paper or plastic bags at home?

Do you use a reusable bag? If so, how often do you use paper or plastic?

What unconscious behavior (things you do that you don't notice yourself doing) do you catch yourself doing that you'd like to change (with paper or plastic)?

http://www.washingtonpost.com/wp-dyn/content/graphic/2007/10/03/GR2007100301385.html

Paper, Plastic, or Neither?

 
Imagine going to the grocery store and NOT hearing the question, "Would you like paper or plastic?" The longstanding debate over whether to use plastic or paper or neither is an issue we will be tackling over the next several weeks.  Students will be learning how to do the following:

• Write persuasively.
• Research and gather information to support ideas.
• Form opinions.
• Make decisions.
• Plan
• Inspire
• Debate

Edmonds Beach Walk

Last Tuesday we went to the beach to observe and explore. Here are some pictures of some of the fascinating things we discovered. Enjoy!

Prime and Composite Numbers

Prime Numbers- Any whole number that has only two factors, one and itself.

    ex. 7 - 1 x 7 & 7 x 1 (1 and 7 are the only factors for the number 7)

Composite Numbers- Any whole number that has more than 2 factors.

    ex. 12 - 1 x 12, 2 x 6, 3 x 4 (1, 2, 3, 4, 6, and 12)

Knowing the difference between prime and composite numbers will help to deepen your understanding of multiplication!

Purpose Statement

Why am I here? Why do I have to learn this? Good questions to ask when you devote almost seven hours a day to something.

At the beginning of the year I had students work in teams to construct a purpose statement. Five groups created their own statements and together they combined them into one.
I wanted this year to be an experience that they've never had before. When they walk through the classroom door, they know why they're here and what they're here to do. Like the "Pledge of Allegiance," we've used our purpose statement as a common start to the day (thanks BM). Collectively reading the statement is a solid reminder. Learnig doesn't start and stop at school. My students want more!
 

"Our purpose is to get an education and to have better future job and life. We should have fun when we learn. We want to improve in everything we do. Our hope is to reach wisdom with our learning."

Our experiences are important and I hope that I'm providing a positive learning environment every time the kids walk into the classroom. Where they go, is completely up to them!
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Chapter 9 Factors and Multiples

The last two weeks have been packed with new math concepts and vocabulary . Each lesson has been a building block for the next lesson. Here's an overview of what students have been learning:

Common Factors - When comparing two or more numbers, list the factors for each number from smallest to greatest. Circle or select any factors that the numbers (in comparison) have in common.
    ex. 9 - 1, 3, 9
         24- 1, 2, 3, 4, 6, 8, 12, 24
Common factors are: 1 and 3

Greatest Common Factor (G.C.F.) - Use the same idea for common factors. Instead, only one factor will be selected. This is the greatest factor the two numbers have in common.
When comparing 18 and 24:
    ex. 18 - 1, 2, 3, 6, 9, 18
         24 -  1, 2, 3, 4, 6, 8, 12, 24

In this case, 6 is the G.C.F.

Using the G.C.F. we can simplify fractions! Check out the picture for the step by step process. When we simplify a fraction we are making an equivalent fraction. The fraction is being broken down into smaller parts. Simplified fractions are easier to work with. Have you ever used these fractions? 1/2 , 1/4, 1/3, 1/5, etc.


MULTIPLES- Count up by the number you start with. If we're looking for multiples of 3, this is how you might list them:
3- 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Multiples can often times be mistaken for listing factors. Remember that factors are numbers that are multiplied by other numbers to get a product or numbers that can be divided evenly into a whole number. 


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Sunset Off the Coast of California

This was a picture I took from a cruise ship along the coast of California over Spring Break. I was fascinated by how quickly the sun disappeared. I knew I was facing west (sun rises in the east, sets in the west) but I was curious about the following questions:
-What is the average time for the sun to start and finish its descent?
-Do all sunsets appear the same no matter where you go on the planet?
-How do our sunsets compare to those of other plantets?
-Are the colors in a sunrise and a sunset different?

Can you answer any of these questions?
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Investigating the capacity of lifeboats.

  

Before we began our investigation, students discussed what they knew about lifeboats. The most common response was that they were used on the Titanic and aided people to safety. Lets all thank James Cameron for the prior knowledge!
The investigation started with a "BIG Question." What variables might affect how many passengers a boat can hold? For our investigation we used a paper cup and pennies to serve as boats and people. Each boat measured 3cm. The students ran two sets of three trials. Pennies were placed in the cup (boat) until it sunk. Each group then shared their results. We had anywhere from 6 pennies to 28 pennies. Why were the results so different if all boats were the same? This question brought us back to our BIG Question. Students listed the following as possible variables for boat capacity:
-Loading procedure (how the pennies were placed in the cup)
-Size of boats
-Water conditions
-Type of coin
In the second set of trials, we changed one variable. All boats needed to have a standard loading procedure. The pennies were placed carefully, one at a time, and balanced. The results seemed to be more consistent but differences still existed. Were the capacities for each boat really the same? To determine the capacity for each boat we used a graduated cylinder (ml) and a syringe. Three out of the two boats had different capacities. The students decided there might have been complications in the building process (boat was smaller or bigger than 3cm). How does this investigation relate to deciding the construction and capacity of a real boat?

What connections can you make with our investigation?
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What's your vertical?

 

In an effort to understand how to use a line plot,  students measured their vertical jumping ability. Each student tested their "vertical" and collected data using a t-chart. After the data was graphed, they found the mean (average), mode, median, outliers, and the range. This was a fun way to learn while being active. I even tested my vertical too!



Mean- The average of numbers. Add all the numbers in a set of data and divide by how many pieces of data there are.
Mode- I teach the students to think "most." The number that occurs the most in a set of data.
Median- Think "middle." The number that falls in the middle of the data when it is organized from least to greatest.
Outlier-The piece of data that is isolated. It is furthest away from the other numbers.
Range- Take the biggest and smallest number in a set of data and find the difference (subtract).
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I WONDER who, what, where, when, why, how???



      Finding and learning new information can be an exciting journey, especially when it is something you are interested in. Like scientists, it usually begins with making an observation and then asking a question. When people want answers to the question(s), they seek the information. Knowing where to find resources is also very important. Recently, I gave the students an opportunity to investigate a topic of their choice. It needed to be something they didn't know much information about. Using their resources, they needed to collect the new information and decide how they wanted to present it in written form. They needed to consider their purpose for writing. Think about who the audience will be. What would make someone want to read your writing? After prewriting, writing, editing, revising, and receiving feedback, they would finally post their research and ideas on the classroom blog.

Stay tuned to see what the students come up with...

Building a road

We don't see many roads like this anymore. This is a picture I took recently in Seattle. Why do you think roads were created like this? What type of math was needed to build this road? When was this built? How do these types of roads differ than the ones we commonly see today?

This is a picture of Beacon Hill in Boston which was built in the 1820s. What similarities or differences do you notice about the picture above? Why do you think they are not used as much today?

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Investigating Swingers (pendulums)

                                            

   Last week we began our first investigation (swingers) in our new science kit "Variables." I thought of two ways to approach this investigation: 1. Tell the students exactly what to investigate and show them how to do it step by step. OR 2. Challenge them to think and act like scientists. Scientists make and share observations. They generate questions that can be investigated. I decided on the second approach and we took off!

   Before we began the investigation, I shared the materials with the students. "What could we investigate with these materials?" Silence began to overwhelm the room. I began thinking the first approach may have been easier. I reminded myself that real learning takes time and doesn't always happen right away. I wasn't quite ready to gift wrap the investigation to the students so I asked for a volunteer to help me explore what we could make with the given materials. Little by little the students then began thinking like scientists. "Maybe we could swing string around in the air and see how many we can make in a certain time." "We could count the number of laps (ah ha! You mean CYCLES?)." The students were on a roll.

   The students investigated the following question: How many cycles will the swinger make in 15 seconds? The next step was to agree on the variables. Students shared some of the things that could affect the number of cycles: length of string, time, weight, release point, definition of a cycle and force. The controlled variables were agreed upon and the students continued to investigate!

Thanks to M. O-B

  One of the important elements of thinking and acting like a scientist is organization of recorded information. Anyone should be able to pick up your science journal and be able to either duplicate the investigation (not necessarily the same results) or understand what's being investigated.

   Finally, the students shared the data they collected and analyzed the results. In there conclusion I asked them to revisit the question as well as their prediction. I overheard one student say, "I'm changing my prediction!" I reminded the students the investigation is not about being right or wrong. It's about thinking, questioning, exploring, and understanding. If you prediction was correct, what led you to it? If you were wrong, why do you think you were wrong?

What are some other investigations we could explore using the swingers? What could we add or subtract from the swingers that might increase/decrease the number of cycles? Do you notice any variables that affect certain outcomes at school or at home?

Alcatraz...so close but so far away

 

During Winter Break, I had the opportunity to visit San Francisco for the first time. Touring Alcatraz was at the top of my list for things I wanted to do; unfortunately tours must be booked months in advance. I never did get to see Alcatraz up close and personal. Instead it would remain a mysterious island that I only knew general information about. As I looked at Alcatraz from Pier 39, I wondered more and more about the island. I began to come up with many questions: When was it first established? How many people could it hold? Why is it no longer in use? How often did people escape? Did many people survive after they escaped? Do islands serve as a good place to have prisons? 

What do you know about Alcatraz? What questions do you have? If you are unfamilar with Alcatraz, I challenge you to do some investigating and report back any information you've learned.