Elementary Mathematics

When teaching elementary kids addition, you want to teach them by going left to right. For example, 55+62. You start in the tens position and add 50 plus 60 together to get 110 and then 5 and 2 together to get 7. Finally, you add 110 and 7 together to get 117. There is also another way to teach them which is the one we are more familiar with which is starting from the ones column and moving towards the left as you add while carrying numbers over in order to get an answer.

There are many different bases. The one that is most commonly used is base ten which is the normal counting system. However, there are other bases like base five. Unlike base ten where 9 is the highest single number, 4 is the highest in base base. When representing base five with blocks, 23 can be created by using 2 longs and 3 units. This is equal to 13 due to the longs in base five being 5 units each plus the other 3 units equaling to be 13 units.

When converting bases, you must first consider whether you are converting from base ten or to base ten. If converting to base ten, then you must follow these steps. Ex. 123 base five to base ten. First, label the places based on the block terms. There is 1 flat, 2 longs, and 3 units. Then multiply using exponents. (5^2 x 1)+(5^1 x 2)+(5^0 x 3). Finally, add up the results. In this case the answer is 38. On the other hand, if you are converting from base ten, then you must use the hockey stick method, a.k.a. upside down division.

One way to add in different bases is to "scratch out" the numbers that add up to the base number in order to indicate creating a bigger piece with these numbers. For example, adding numbers in base five would mean looking for "happy numbers" like 2 and 3 that easily add up to 5 and crossing them out.

This is a little tricky as it doesn't work the same way as addition, however, you can do subtraction in other bases by borrowing and remembering what base you are in. In base five, each long is five, so if you borrow from a long, you add 5 units to the units that are already there in order to subtract the other number from the first one.

Instead of PEMDAS use:G- GroupingE- ExponentsMD- Multiplication/Divison left to rightAS- Addition/Subtraction left to rightL->R Inside Group

The "Colby Error" is when a student that is adding writes a number how they normally write it (i.e. 17- 1 and then 7) when trying to carry over a 10,100,etc. Because of this, their answer is wrong. In order to avoid things like this, it is suggested to teach another method like the lattice algorithm which would allow the student to write the normal like they normally do.

Alternative Subtraction Algorithms include using base blocks in order to show subtraction and the Equal Addition Algorithm. Example of using the equal addition algorithm: 56+3 59-27+3 30 29Add 3 to both numbers in order to keep it equal and make it easier to subtract without borrowing.