Area model for whole numbers will generally be with an open grid:
The area model for fractions is similar, where the top side of the box is one fraction and the left side is another fraction.
This area model represents 1/2 X 3/5. The top fraction, 1/2 in red, was the first cut to be made in the box. Then only 1/2 was shaded because the problem asks for one 1/2 pice . Then on the left side, the box was then cut into 1/5 pieces. The second number asks for three 1/5 pieces, and that is shaded in blue. The mixed-shaded colour, purple, is the answer, 3/10.
The actual computation of 1/2 X 3/5 equals 3/10, and that is done without a visual by multiplying numerators together and denominators, respectively.
Mixed numbers can also be represented in the area model. An open area model is best used for mixed numbers.
The mixed numbers were broken up, much like whole numbers are on a mixed number. When multiplying whole numbers by fractions, simply putting a 1 underneath the whole number turns it into a fraction, so that multiplying across the top and bottom are easy. Then, just like in the whole numbers area model, you add up all of the numbers inside the box.
10 + 4/8 + 5/3 + 2/24 = 12 3/12 (simplified is 12 1/4)
Next, we have division of fractions. The way our elementary teachers explained it to us a little kids (4th grade?) was to flip the second fraction and then multiply across. While I don't know the reason behind flipping the second fraction and multiplying across, it is easy to do. Although, an even easier method of division is to utilize common denominators. For example:
When flipping the second fraction, 167 turn into 1 due to "cross cancelling", and then multiplying across leaves us with 9/3, which is just 3. Knowing number relations is very important for children to learn, as it makes problems such as this much easier.
Danielle,
ReplyDeleteYour blog is very easy to follow and has awesome visual aids. You went into just enough detail to get the point across effectively without the entry being too wordy. I agree, I also really enjoy the area model for fractions. That was my favorite way we learned how to do multiplication, and it is just as easy and straight forward for multiplying fractions. I think it is very useful for a visual learner - we can see exactly the actions we need to do.
I absolutely loved your blog. I did not come to class last Tuesday and I was scared that I would miss valuable material. After reading your blog I completely understand what I missed on Tuesday regarding the area models. How clear your explanations were in your bog made it super easy to follow. I loved the pictures that you included with the area model by showing the double shading! Overall very well done.
ReplyDeleteI really like your explanation for multiplying fractions by using the area model. I found it really confusing at first but after some practice and reading over this blog I understand it a lot better. Your pictures and examples of using the area model for different equations really helped. Overall, good job!
ReplyDeleteI thought your pictures went well to demonstrate the area model of multiplication. I like how you showed how an area model would look with whole numbers before you showed what it would look like with fractions. It was a nice reminder and made the fraction area model easier to understand. I also thought your explanation of dividing fractions was also clear and easy to understand. I really find your blog helpful with refreshing my memory behind multiplying and dividing fractions!
ReplyDeleteI really liked the way you showed the area model and used the different whole numbers, it really helped make the objective clear before you showed area model using the fraction idea. Your work is very easy to follow adn understand, your visual aids help a ton and it is an extra bonus how net and organied they are! Great job!
ReplyDeleteI think your bog this week is really great. I think your area models are really helpful. For me multiplication is the hardest part of fractions for me and the area model makes it seem more simple and easier to grasp. The division of fractions explanation is also good because I have been studying and can't figure out a way to remember exactly what to do to memorize a way to do the division and your way is actually really good. I will definitely be using it in the test! Overall your pictures are helpful and explanations are good.
ReplyDeleteDanielle,
ReplyDeleteI think that the your wrote a good third blog post. You include all the information from lecture and the pictures you included into were very helpful. I liked that your included the topic of cross canceling was an important aspect in this week lesson.
-Alisha