# 3.2 – Solve this Problem

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• #2332

Put these fractions in order from least to greatest:

2/3,  1/6,  3/5,  2/8

As you solve the problem, think about what conceptual understanding students need to be successful. Share your ideas here.

• #2425

1/6, 2/8, 3/5, 2/3

To be successful in solving this problem, students need to conceptually understand that a fraction is a part of a whole and that the denominator does not necessarily define the size of the whole, but rather how many pieces the whole is partitioned into.

• #2437

1/6; 2/8; 3/5; 2/3

As my colleague says, it is necessary for students to understand that a fraction is part of a whole and that the denominator does not necessarily define the size of the whole, but rather how many parts the whole is divided into.
That is why for them to be able to visualize this concept, I draw a rectangle of the same size and divide it according to the indicated fraction.
In this case, I draw 4 rectangles of the same size and divide each one according to the denominator of the indicated fraction. This is how they can see that 1/6 is less than 2/3, because the 2/3 rectangle is more “painted” than the 1/6 rectangle, even though both are the same size.

• #3172

Understanding that a fraction is part of a whole is essential. Dividing 4 rectangles according to the denominator and shading the numerator shows the solution.

• #3874

I would make pies for each of the fractions. and as williwoodz stated the amount of slices would be the denominator and then I would have them shade the numerator.
This should reinforce the concept that a fraction is part of the whole.

• #3915

1/6, 2/8, 3/5, 2/3

It is important for students to understand that a fraction is part of a whole. They also need to make sure they are aware that the denominator shows how many parts the whole is divided into. What would be helpful for them to understand is that the closer the numerator and denominator are to each other, the larger the fraction and the farther apart the two numbers are…the smaller the fraction.