021. Representing Fractions

Learning Intentions

• To know what the numerator and denominator of a fraction represent in different situations
• represent fractions on a number line
• represent a fraction of a shape by dividing it into several regions and shading some of the regions

Pre-requisite Summary

• Understand that a whole can be divided into equal parts
• Know that equal parts must be the same size for a fraction to be valid
• Recognise basic fractions such as
• Understand that the denominator tells how many equal parts the whole is divided into
• Understand that the numerator tells how many of those equal parts are being counted
• Be able to count partitions and shaded parts accurately
• Be able to locate whole numbers on a number line
• Understand that fractions can Describe part of a region, part of a set, or a point on a number line

Worked Examples

Worked Example 1

For each fraction, State what the numerator and denominator represent:

a) of a pizza

b) of a class set of counters

c) of a strip divided into equal parts

Worked Example 2

Represent each fraction on a number line from to :

a)

b)

c)

Worked Example 3

Represent each fraction of a shape by dividing and shading:

a) of a rectangle

b) of a square

c) of a circle

Worked Example 4

A rectangle is divided into equal regions and are shaded.

a) Write the fraction shaded.

b) State what the numerator represents.

c) State what the denominator represents.

Worked Example 5

A number line from to is divided into equal parts.

a) Which point represents ?

b) Which point represents ?

c) Explain how the denominator helps place the points.

Worked Example 6

A hexagon is divided into equal regions.

a) Shade of the shape.

b) Explain how many regions must be shaded.

c) Explain why the regions must be equal.

Problems

Problem 1

For each fraction, state what the numerator and denominator represent:

a) of a cake

b) of a set of marbles

c) of a bar divided into equal parts

Problem 2

Represent each fraction on a number line from to :

a)

b)

c)

Problem 3

Represent each fraction of a shape by dividing and shading:

a) of a rectangle

b) of a strip

c) of a circle

Problem 4

A rectangle is divided into equal regions and are shaded.

a) Write the fraction shaded.

b) State what the numerator represents.

c) State what the denominator represents.

Problem 5

A number line from to is divided into equal parts.

a) Which point represents ?

b) Which point represents ?

c) Explain how the denominator helps place the points.

Problem 6

A pentagon is divided into equal regions.

a) Shade of the shape.

b) Explain how many regions must be shaded.

c) Explain why the regions must be equal.

Exercises

Understanding and Fluency

Exercise 1.

For each fraction, state what the numerator and denominator represent:

a)

b)

c)

Exercise 2.

A whole is divided into equal parts. State what each fraction means:

a)

b)

c)

Exercise 3.

Represent each fraction on a number line from to :

a)

b)

c)

Exercise 4.

Represent each fraction on a number line from to :

a)

b)

c)

Exercise 5.

Divide each shape into equal regions and shade the given fraction:

a) of a rectangle

b) of a strip

c) of a square

Exercise 6.

Divide each shape into equal regions and shade the given fraction:

a) of a circle

b) of a rectangle

c) of a bar

Exercise 7.

A shape is divided into equal parts. Write the fraction shaded:

a) out of parts shaded

b) out of parts shaded

c) out of parts shaded

Exercise 8.

A number line from to is divided into equal parts. State the fraction at the marked point:

a) the nd point out of equal parts

b) the rd point out of equal parts

c) the th point out of equal parts

Reasoning

Exercise 9.

Explain why the parts of a shape must be equal when representing a fraction.

Exercise 10.

A student says in the tells how many equal parts the whole is divided into. Explain the mistake.

Exercise 11.

Explain why on a number line must be closer to than .

Exercise 12.

A student shades parts of a shape divided into unequal regions and says the shaded fraction is . Explain why this may be incorrect.

Problem-solving

Exercise 13.

A chocolate block is divided into equal pieces. Mia eats pieces. What fraction of the block does she eat?

Exercise 14.

A ribbon from to metre is marked into equal parts. At what fraction is the th mark?

Exercise 15.

A rectangle is divided into equal regions. Shade a fraction showing that regions are shaded. What is the fraction?

Exercise 16.

A class uses a strip model divided into equal parts. If parts are coloured, what fraction is coloured?

Exercise 17.

On a number line from to , a point is at the rd division when the line is split into equal parts. What fraction is represented?

Exercise 18.

A circle is divided into equal sectors. If is shaded, how many sectors are shaded?

Potential Misunderstandings

• Students may confuse the numerator and denominator
• Students may think the denominator counts shaded parts rather than total equal parts
• Students may think the numerator tells the total number of parts
• Students may place fractions randomly on a number line instead of partitioning the interval into equal parts
• Students may forget that the number line from to must be divided into the number of equal parts given by the denominator
• Students may divide shapes into unequal regions and still label the result as a fraction
• Students may count boundary lines instead of intervals on a number line
• Students may think fractions only describe shaded regions and not positions on a number line

Next: 022. Equivalent Fractions and Simplifying them