Saturday, March 2, 2013

Week Two: Area Models, Partial Products, and Ratio Tables

During the second week of the new unit, we continued on with finding easier ways to solve mulitplication and division problems. Three main student-friendly ideas we learned about were area models, partial products, and ratio tables. I will break down each one here.

Area Model: 


The picture above describes how to solve the problem 19x48 with an area model. What to do to solve it in this manner is to draw out the multiplication problem in an area model box. Then, you simplify each entity (19 and 48) in the box to make it easier. In the picture, I broke down 48 into 20, 20, and 8. As well as breaking down 19 into 10 and 9. You then draw lines to divide the box into those numbers. After it's divided, you multiply the "length" and "width" to solve the answer in the smaller box. The answers for the smaller boxes within the large area model were 200, 200, 80, 180, 180, and 72. Once you have all the smaller solutions, you add those to find the final total. The final total of 19x48 was 912. This is a great way to create a simple visual for a difficult multiplication problem.

Partial Products: 

In this photo above, it displays the way of solving the same problem (19x48). It looks like a normal stacking method of solving a multiplication problem...but instead of borrowing you just put the total below. For example, in the picture, you put below the line the total answer of 9x8 which is 72. You do this for each part of the problem, and then add up the total. It is a much easier way than the traditional borrowing method.

Ratio Tables: 

The way to solve the same problem (again...) 19x48 with ratio tables is so so easy!! You make a table of the multiplication tables of one of the parts of the problem with just a few multiples. Such as using 1, 2, 5, and 10 and mulitplying it by 48. So, you have options of 1x48=48, 2x48=96, 5x48-240, and 10x48=480. The problem is 19x48, so you just have to add up the multiples to get to 19...what I did was I chose 10+5+2+2=19. So I added the answers from the ratio table, 480+240+96+96= 912. I got thw same answers using this way as the area model and partial products ways. Again, this is such a simple way to solve a difficult multiplication problem for a young student. It is always a good idea to put visuals (tables, area models, etc.) when solving a difficult problem.

3 comments:

  1. I really like the way of how when you showed the steps you took with the multiplication, you broke it down even further to show how you got each answer for each step. It makes it really easy to follow along with your thought processes

    ReplyDelete
  2. Your blog is great! I really enjoyed how simple you presented the information, even though the steps may not be. I also liked how the visuals you used, matched the problems you were explaining. My suggestion to add to your blog would be to go over the steps to solve division problems as well. Although we focused more on multiplication, those same processes will work to solve division as they somewhat go hand in hand. I enjoyed your blog, thanks!

    ReplyDelete
  3. This was a really informative entry! I loved the way you had your pictures set up alongside each step you were describing, it was a great way to keep your readers on track and really allow them to visualize what you were saying.

    ReplyDelete