Making Sense with Fractions Representation : vuja-de
Some basics in maths and science are presented in disconnected pieces without much explanation and that makes it hard for students to grasp the fundamentals. The same can be explained in a refreshing new form that makes the basics very clear. This “vuja-de” series brings out such refreshing new perspectives from nubtrek.com .
Representation of and Arithmetic with Fractions
In arithmetic, students learn first about counting a number of items. In that, students continue into large numbers with face value and place value of numbers.
- In 234, the number 2 has face value “2” and place value “200”
Continuing on the study of numbers, fractions are introduced as part of a whole and given as a number in p/q form.
The fraction arithmetic addition, subtraction, multiplication, and division are all learnt as matter-of-fact knowledge.
references:
Fractions introduction in Khan Academy
Fractions addition in Khan Academy
Thought-Process to Learn Fractions in nubtrek
nubtrek provides a refreshing new view into the Representation and Arithmetic of Fractions.
Given a number of objects, students know to count them.
If an object is cut into pieces, students naturally choose to count the number of pieces. The fractions is not natural for students.
- eg: 2 pieces of pizza. Students are not used to specifying 2/6 of whole pizza.
Now pose this question: How many pieces are there in this figure?
- is it 2 pieces? or 2 unequal pieces?
- If unequal, then how to identify the pieces apart from one other?
- Reference: nubtrek
So, the pieces are shown in reference to the whole and add how many equal pieces are made while cutting it out
- The place value system helps to specify this.
- 1/8 means one piece with place value of one eighth.
- 1/12 means one piece with place value of one twelfth
- the representation is count (numerator) by place value (denominator)
Having explained equivalent fractions, and converting unlike fractions to like fractions, fractional arithmetic is started.
When it comes to arithmetic like comparison or addition, the count (numerator) is not sufficient to perform the arithmetic. The place value (denominator) has to be considered.
Addition 3/8 + 2/8 is performed directly by adding the count, since the place values are equal.
Addition 1/4 + 3/8 requires some process to make the place values equal.
- The fractions are converted to like fractions 2/8 + 3/8
Addition 3/4 + 2/3 requires similar processing to make the place values equal.
In nubtrek, the basics are explained in a refreshing new form that makes the learning something to discover from what one knows already. Later, procedural-simplification is explained. This helps the students to understand and retain.
Thanks for reading.