av Angelique Vasquez Quintero 5 år siden
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Mer som dette
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.
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.
6:40
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).
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!
Once again, this helps visually see what is being multiplied ex. 4(3) would look like: . . . . . . . . . . . .
Grouping helps to visually see what is being done ex. 4(3) = 4 groups of 3, usually in a circle
Lattice works the same as in add/sub. Set up is similar, just multiply
Area model creates a box, almost like expanded form making it easier to multiply. After multiplying, simply add across then down.
Like addition and subtraction, only this time you will be multiplying the values
Using this helps students visually see what is being multiplied. It also makes it easy to see longs, flats, and cubs, be made.
This helps to keep number in order and it makes it easier to have students write down numbers in the way they normally would. Draw the box under the addition or subtraction problem then add lines between the gaps of the numbers to create squares. Then connect diagonal lines from coroner to corner.
This allows for the number to be put into simpler form making it easier to add/subtract 47-16 : add 3 to both 50-19 =31
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.
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 0
1 6 2 0 8 5
These 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 like
8|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.
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*
