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...