I have observed that many books start Fraction with Pizza example.
I have a suggestion – Let’s replace Pizza with Cadbury, Chikki (Indian sweet) or anything which is rectangular in shape for a better visual understanding.
Let me explain my point with an example.
Comparison of Fraction
Which fraction is bigger 3/4 or 5/6 ?
I suggest my students to draw it and see it themselves. We use rectangle for the same.. My students start with 2 same sized rectangles.
Now, they partition 1st rectangle into 4 parts to see 3/4 and partition 2nd rectangle into 6 parts to see 5/6
So, they need to compare 3 units (boxes) from 1st rectangle and 5 units (boxes) from 2nd rectangle. If they name the units in both rectangles as A & B,
Then they need to compare 3 A vs. 5 B
Generally, how do we compare 2 quantities?
10 dollars vs. 100 cents
30 meter vs. 3 kilometer
We convert them into same units and then comparison is just a visual exercise, right?
1000 cents vs. 100 cents
30 metre vs. 3000 metre
So, we need same units for easier comparison. Let’s get back to our fraction comparison now.
We need to compare 3 A vs. 5 B, where A & B are not same.
I ask my students to think how can they make A & B same. (I don’t ask them to calculate L.C.M at this point, I let them visualize the process behind L.C.M).
Now, sub-partitioning comes into picture and students start to subdivide these rectangles.
Subdividing the first rectangle gives us – 4 , 8, 12…. sub parts
Subdividing the second rectangle gives us – 6, 12,….. sub parts
And, here they go, students have already found out L.C.M unknowingly. Now, picture looks like this
Now,as you see, we have the same unit size in both rectangles and our fractions take the new equivalent forms
3/4 = 9/12
5/6 = 10/12
Eventually, we are comparing 9 U vs. 10 U
and the answer is visually clear that 10 U i.e. 5/6 is bigger.
Now, try to do this same working with standard Pizza introduction and you will know why I am suggesting to use rectangle shape for introducing fraction. Think about this word problem :
A group of people signed up for an excursion. ⅖ of the people were adults and the rest were children. ⅔ of the children were girls. If there were 90 children altogether, how many more adults than boys signed up for the excursion?
I think that rectangular shape model will give a better visual feel to solve this question.
Moral of the story
I don’t see value in introducing fraction using an example of pizza and then train students to use rectangles for solving the word problems. First introduction is the most ever lasting impression on someone’s mind. Let’s make sure that the first impression of any concept is in the most useful form.
For sure, eventually children should be clear with fractions using any shape – triangle, hexagon….But, at the first place, we should surely use rectangles as they provide more crisp & clear visual understanding.
Time for more Rectangles
Attaching few interesting questions here, try to draw them. Once you master the skill of converting Maths into Art (Maths2Art) , You will have a ‘speaking picture’ as an outcome. Speaking picture means the picture will guide you how to solve the question. Wish you all joy of learning !
- 154 people took part in a marathon. 4/7 of them were men. How many women were there?
- There were 63 apples in a crate. 2/7 of them were rotten. How many apples were not rotten?
- John spent 2/9 of his money and donated 4/7 of the remainder to charity. He had $30 left. How much money did he have at first?
- There are 245 workers in a company. 4/7 of them are women and ¼ of the women are married. If all the men are married, find the total number of workers who are married.
- An author wrote ¼ of a book in January and 4/9 of the remaining book in February. She completed the remaining 125 pages of the book in March. Find the total number of pages in the book.
- A baker prepared 270 doughnuts. He sold ⅗ of them and gave away ¼ of the remainder. How many doughnuts did he have left?
Proper introduction of the concept plays a key role in further learning. Introduction should be as intuitive as possible and it should be very close to our students’ lives so that they can grasp the concept just like 1, 2, 3.
Making Maths Simple & Visual !