3.2 – Solve this Problem

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.

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.

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.

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.

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.

To teach fractions, I will use manipulative objects, so that my students can see and understand why the fractions are ordered the way they are. This will allow my students to then talk about how they understand how to solve the problem according to what they know. I can observe their explanations and correct where needed.

White Boards
Quick response, pictorial drawing, etc. Easy for many strategies.
Stop and Jot
Stop learning to write down big ideas.
Colored Cards
Cards are given based on concept understanding. Used to group students.
Exit/Entry Ticket
A quick assessment of specific skills to determine student understanding.
5 Words
What 5 words would you use to describe __? Support with evidence.
Teacher Observation
Blank roster with notes about each student’s learning.
Analogies
Explain the main idea using an analogy.
KWL Chart
Three-column chart of what students know, want to know and learn.