Week Three: Number lines and chip models!

This week, we focused on using number line models and chip models/activities to understand negative and positive numbers. We started off with an activity out of our booklets that involved chips to show positive and negative numbers. In this activity, red chips represented negative and yellow represented positive. 


One example we were given was (-3)+(-4)= -7. By using chips, we were taught to show 3 red chips and 4 red chips and total it up to be 7 red chips (or negative).
At first, for me and my group members, this was a bit confusing for us but after awhile we got used to the patterns. 


Here is another example: In the example to the right, we started with two groups, one of 5 positive chips and one of 4 negative chips. In step two, we combined these two groups into one. In step three, we had to match up the amount of negative chips with the equal amount of positive chips (4 and 4). This meant those groups of four cancelled out each other, leaving us with an answer of positive one.

 

These activities got harder as we did subtraction problems instead of addition. For example, we did a problem similar to (-6)-3=-9. For this problem you would do a circle with 6 red chips and a circle with 3 yellow chips. In this problem, since there are no positive numbers to be taken away, you have to add 3 negative chips and 3 positive chips to get to zero. Now that 3 positive chips were removed, you can easily find your answer of -9 by removing yellow chips and leaving you with 9 red chips. 

I found this difficult at first but slowly got the hang of it with more practice! :)

Week Two: Multiplication & Division

This week, we started off reviewing alot of the concepts we went over on week one. We started off by refreshing our memories with multiplication methods of partial products, area model and ratio table. Eventually we started using these same methods to solve division problems as well.
An example of one of these is:
Partial Products:
 19
x48
 72
280
360
400
=912
This way of solving a multiplication problem involves stacking the two numbers being multiplied together and then breaking it into pieces based on which place value the numbers hold/are in. This is similar to the traditional way of solving it but the steps are a little more clear and organized.


We then moved into the concept of expanded notation. For me, I loved doing this because it was an easy way to break down larger numbers and expand it into steps that are easier to see. Before this I was also familiar with scientific notation and exponents. 
This is an example we did for 12,508:

The exponents you see were represented by this table:

We were then told to solve a problem without using division and with using partial quotients, ratio table and an area model. 
The problem was: After Andrews Middle School is built, it will hold 609 students. Each classroom will have 29 students. How many classrooms does the school have?

I first solved this problem using a very unorganized and messy way by drawing out sets of classrooms with 29 students in it. This way probably would have taken years to find the answer if I would have stuck with it, so I moved on and tried the area model, partial quotients and ratio table. They looked like this:

I got an answer of 21 classrooms in the school.

The second part of class involved doing an activity out of the book based on inverses. We used red and yellow chips with red representing negative and yellow representing positive. 
A way to explain this is if you had two red chips and 4 yellows, the answer would be 2 because 2 reds cancel out two yellows and you are left with two additional yellows. Yellow is positive numbers. 
I learned a lot about inverses and was refreshed with the idea of negatives in this activity.

Till next time! :)

Week One: Multiplication

On our first week of Unit Two in math, we started the week off on Tuesday with learning about different types of story problems including repeated addition, array/area, and tree/combinations. 

Repeated Addition:
Ryann had 4 plates of cookies, with 7 cookies each. How many cookies does Ryann have altogether?

This picture shows repeated addition because a child could add up 7 plus 7 plus 7 plus 7 to get 28 instead of actually multiplying 7 times 4.

Area/Array Model:
In the classroom there are desks lined up in 4 rows with 7 desks in each row. How many total desks are in the classroom? 















This method shows a pattern with the set of objects or numbers.

Tree/Combinations:
Adam has 4 pairs of pants and 7 different shirts. How many different outfits can he make?













This method shows all possibilities using "sets" and "branches".

On Tuesday we also learned the properties of multiplication:
Commutative Property: a*b=b*a
Associative Property: a*(b*c)=(a*b)*c
Identity Property: a*1=a
Distributive Property: a*(b+c)=(a*b)+(a*c)



On Thursday, we used
Strings:
10x3=30
9x3=27
10x5=50
10x8=80
If you do 10x3=30 and 9x3=27 you realize that 27 is 3 less than 3 because the multiple is 3.

We also learned different models of division including repeated subtraction, partition, area model practice, ratio table and partial products.