Elementary School Mathematics

Week 2: Converting Bases
*Using base 10 blocks

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The normal base used in the United States is base 10. When converting to base ten, it is important to note that there are units, that then turn to longs, that then turn into a flat, then to a cube. After this cycle, it becomes a bigger unit, bigger long, etc...*Numbers can NEVER be = to the base you are in Ex. 45 base 5 does not work so 44 base 5 would be a better option*

Week 3: Adding & Subtracting (in bases) & converting using algorithms

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When converting bases using algorithms, it is important to know the value of the numbers you are using.For example, going left to right, the values of the numbers 162085 would go as follows:5 4 3 2 1 01 6 2 0 8 5These values become important when using algorithms to convert others bases into base 10.When converting other bases into base 10, backwards division is used (LLLLLLLeave). For example, turning 37 base 10 into base 8 would look like8|37 |__*It is important to remember that the numbers you get from dividing should never be bigger than the base you are converting to. So in the previous example, the biggest number can only be 7. Also, your remainder will go on the outside of the L. 8|37 |__ 4|58 So the answer will be 45 base 8.

Week 4: Alternative algorithms for add/sub

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The alternative algorithms work similar for both adding and subtracting bases. It is important to note an important part:When adding/subtracting in different bases, it is important to look for when units, longs, flats, etc... turn into the next bigger thing. Such as if you are adding 2 base 3 and 1 base 3, the answer will be 1o base 3 because the units turn into a long and zero units. Likewise if you are subtracting.

Week 5: Alternative algorithms for adding and subtracting & alternative algorithms for multiplication

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Similar to add/sub, these algorithms are useful in visually seeing what is being multiplied. Remembering place value is important to make sure the correct value, such as hundreds or ones, is being multiplied correctly. Place value is important!

Alternative Algorithms for adding/subtracting

Equal add ins

Lattice

Multiplication

Base 10 blocks

Using this helps students visually see what
is being multiplied. It also makes it easy to
see longs, flats, and cubs, be made.

Expanded form

Like addition and subtraction,
only this time you will be multiplying
the values

Area Model

Area model creates a box, almost like expanded form
making it easier to multiply. After multiplying, simply add across then down.

Lattice

Lattice works the same as in add/sub. Set up is similar, just multiply

Groups

Grouping helps to visually see what is being done
ex. 4(3) = 4 groups of 3, usually in a circle

Array

Once again, this helps visually see what is being multiplied
ex. 4(3) would look like:
. . .
. . .
. . .
. . .

Week 6: Integers

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Integers help with the idea of negatives. The idea of zero banks then is more apparent because in some situations you do not have enough of a given positive or negative. Also, when adding you get introduced to the idea of KCC (Keep Change Change).

Week 8: Multiplication

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Multiplication is easy to learn if the two rules are remembered. The way problems are read is also important when solving these types of problems.

Week 9: Fractions

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The reason we need common denominators when adding and subtracting and not when multiplying or dividing is because in the adding or subtracting case, we need equal sizes of the pieces. When multiplying or dividing isn't combining. It is more a group times what is inside the group.