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:
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! :)
This post was very informative to me, one of the things I liked the most about it was how you put in bold the terms you were referring to this made it very easy to reference back to something quickly. Having the actual pictures of your work was very helpful also since that's how we will show our students someday it was a good real world example.
ReplyDeleteI really liked the way you explained expanded notation. It was also very helpful that you included what each notation is, I enjoyed that because sometimes it is easy to forget what each notation actually stands for. I also like the pictures you included of each method, they were easy to understand and helpful.
ReplyDeleteThe visuals you included were very organized and easy to read. It makes it easier to follow when things aren't all jumbled up everywhere. It was good that you used the same math problem with each example to show that there are many different ways to answer the same division problem, because division can be really hard for a lot of people.
ReplyDeleteI feel like I learned a lot from your blog. For me my two favorite methods are the partial quotients and the ratio tables. You showed all three methods very nicely. Since you had visuals for all of your other problems I think that it would of been nice to add in a picture model for the chips as well.
ReplyDeleteYou did an excellent job explaining all of the concepts in a clear, thorough way. Your drawings of the area table and samples of the partial products and partial quotients were organized, and easy to follow. The boldness of the main terms learned in the daily lesson was a great idea, because it is a key to what may be on an exam in the future. I as well, really like the expanded notation because it is a simple way to break down the numbers into smaller easier pieces. I also agree that a picture of the chips would've been a great visual to understand the concepts of the colored chips when we worked with positive and negative integers. Great job!
ReplyDelete