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Monthly Archives: September 2011

Multiplication Easy?

Not can addition be confusing but so can multiplication; multiplication is another one of the those things that we do because we were told to. multiplication can also be confusing in different base just like in addition.

one way to do multiplication in a different base or just general multiplication is to create pictures. You can think of multiplication as an array of number or a rectangle. Below are two pictures of the rectangle method.

The rectangle method is easy to understand, but when we switch base it can be confusing. We can use the cookie method to help with multiplication of different bases. The pictures below show multiplication of base 5 and base 6.

We can also use other methods besides the rectangle and the cookie method. We can use the Statndard Multiplaction (pictured below).

Or we can use the Partial Products (pictured below).

In Partial Products we can see why we carry and how we arrive at an answer to the problem.

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Posted by on September 30, 2011 in Uncategorized

 

Base 5, Click!

In Math many of the things that we do can make absolutely no sence at all, we just do them because we were told to do them and that is the way they told us to do them. My classmates and I can be examples of this; many of us had epiphany in class.

When our instructor explained to us; using the same method but in a different way and it clicked for us; all of our faces lit up and we were excited about it! The picture below is how excited we were.

(From Flickr by Rachel Allysson)

She gave us a better understanding of why we carry and borrow in addition and subtraction. We learned not only how to  carry and borrow from base 10 numbers but also from other bases!

When in base 5 there are five digits; these digits are 0,1,2,3, and 4. Shown below are four problems two of them are addition and the other two are subtraction of base 5.

When in base 5 you can count till 4 and then you have to go to a different place value.

____    ____    ____

25’s      5’s      1’s

 
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Posted by on September 29, 2011 in Uncategorized

 

Numbers, Numbers Oh My!

Numbers are a huge part of what we do. there is not a day that goes by where we do not use numbers. number systems are all a big thing. before we have the Decimal system these where other systems!

The Egyptains had a system of pictures that had meaning to a number value. this is a non-postional system (no ordern how the number/symbols are written). there is also no zero in the egyptian number system. we can use the symbols to write numbers.

1= 10= 100= 1000=

(From Number System)

another system is the Babylonian. this is also a system of signs, however the Babylonian system is positional (has order to how the number/symbols are written). this is also a system that does not have zero.

The Babylonian system is a bit more conplex, this system only has 2 symbols, this is where the position of the symbols becomes important. This system is based off the powers of “60.”

______       _____    ___      ____

216000’s    3600’s     60’s      ones

Our number system is the Decimal system. the Decimal system is a positional system and has a zero.

these are only three of the number systems but there are many more!

 
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Posted by on September 23, 2011 in Uncategorized

 

Puzzle

Logic puzzle are a great way to enhance learning. Some of the logic puzzles that you can do are Sudoku; these can be found for all ages and different levels! Some other puzzles are Strikmo puzzles, Paint by number, and Logic puzzles.

 (Sudoku Puzzle KS07)

Sudoku puzzles can be used for many things; you can use them as warm ups, homework assignments, or even just for fun.

Another good brain exercise is brain logic puzzles. These are good to do in as the warm up and to do them in a group. We did one is class it was titled Best Subject. Then I went home an did another one this one called
Balloons.
 

 
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Posted by on September 18, 2011 in Uncategorized

 

Function Function

Meijer Scanner ~

Ramen               .10

Milk                    3.59

Eggs                  3.59

Lucky Charms   2.99

The food list is the domain and the price list is the range.  You need to have both to have a function. In a
function you also need to have a rule or a relation between the sets. Each element of the first be assigned to exactly one element of the second set.

We can write the domain and range in different ways.

Domain {ramen, Milk, Eggs, Lucky Charms}

Range {.10, 3.59, 3.59, 2.99}

 
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Posted by on September 18, 2011 in Uncategorized

 

Pac-man or Not?

Remember in elementary school when the teacher was teaching less than, greater than; I do. I remember the teacher telling me that the Pac-man eats the bigger number; well today I found out that this is not the
case. For instance what if you have a -3 and a -6 which number is larger? You could also have a 4 and 8 which number is larger?

These are examples where students can become confused because you are working with negative numbers and numbers of different written sizes. One way to think about it is that the less than sign when opened up makes an “L” where the greater than sign doesn’t.

When working with inequalities you want to make it simple but not confusing. Confusing the students can only cause problems later in math when you the properties of inequalities. These properties include the Addition (or subtraction) Property of Inequality; which states that you can add or subtract a number, as long as you do it to both sides. The other property is Multiplication (or Division) Property of Inequality; which states you can multiply or divide but any positive number, as long as you do it to both sides. If multiplying or dividing by a negative number you have to flip the inequality sign.

 
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Posted by on September 12, 2011 in Uncategorized

 

Venn Diagrams

Venn Diagrams can be used to compare and contracts stores, objects and many other things. They can also be used in math. When using Venn Diagrams for math it normally has to do with shapes, sizes and color.

When exploring Venn Diagrams I found some extra practice problems that I did to help; this page was very helpful at give me some extra problems to do the problem below is an example of a problem where all the
information that was given was needed.

After applying basic Venn Diagram functions then we moved to shading them;  I understood it in the classroom when it was being done, but when I went home to do the homework and went to do the problems
I was lost. I used the tools that we got in class, but I also went online. I found a website called purplemath that was helpful.

Some of the problems that we did where:

  • A’
  • AUB
  • (AUB)’

When writing a set we use { } at the beginning and end of each. For example if I said that A={2, 4, 6, 8, 10} and set B={3, 5, 7, 9, 11}. We use the brackets to start and to end a set. You can write set using Venn Diagrams or by having them giving to you and combining them; for example AUB (A union B)={2, 3, 4, 5, 6, 7, 8, 9, 10, 11}.

 
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Posted by on September 9, 2011 in Uncategorized