Integers

This week in class we learned how to solve addition, subtraction, multiplication, and division problems with negatives added to the mix. We learned how to solve these problems using the number line method and counters.


Addition: For addition we solved the problems by starting at the first number and depending on the sign in front of the second number we would count left or right on the number line, left for negative and right for positive.

Subtraction:
I will be using the problem -8-7 for this example. When we started we were asked to try and solve -8-7 how we thought and then we were shown how the book says to do it, which confused everyone. Then we were shown how to do it by showing the difference.

Multiplication: 

For multiplication i will be using the problems 2x5, 5x2, -5x2, 5x-2, and -5x-2. multiplication was the most difficult so far because sometimes, the way we were doing it at first, we were drawing 2x5 and 5x2 the same way when they should have looked different while coming up with the same answer. 5x2 is 5 groups of 2, while 2x5 is 2 groups of 5.

Models for Division

This week in class we learned how to solve division problems in 3 different ways. For all three of the methods I will be using the problem 3445 divided by 14.

The first way is by use of the Area Model. This model uses a box that you separate into smaller pieces to figure out how many times you can put the original number into it until you pass the number you are trying to divide.

The next way to solve a division problem is through the use of Partial Quotients. In this method you take bits of the larger number that you are trying to divide away piece by piece, kind of like the Area model method.

The third method for division that we were shown was the Table Method which involves a small amount of guessing and checking, and when dividing larger numbers can get a bit long. In this method you make an input output table. This shows how much you get from putting in a specific number.

There was a fourth method that we learned about that is taught to school children in Singapore  This method is called the Number Bonds Method, which I found was actually very easy compared to the other methods. The Number Bonds method is basically the decomposing of a number to make it more friendly to work with.  Instead of 3445 divided by 14 I will be using 4816 divided by 4.

Multiplication

This week in class we learned about the models for multiplication and division. First we were asked to try and come up with a story problem for 8x7 and 45/9. Then we listed the models for multiplication which are as follows:

Area/Array Model:

Repeated Addition:

Combinations: This model of multiplication is probably the most confusing as it is the most difficult to draw      out.

I will go over the division models in next weeks blog.