NZ Level 3
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Shaded Figures and Number Lines
Lesson

Remember our discussion on identifying fractions? Well identifying fractions that are not unit fractions works in the same way.

Fractions in an area model

We need to know two things

1) How many equal parts is the whole shape or object divided up into? This goes on the bottom and is called the denominator.

2) How many parts we are interested in, these could be shown separate, shaded or marked on a number line.  This goes on the top and is called the numerator.

 

Example

Evaluate: What fraction is shaded in this picture?

Think: How many parts in total is the shape divided up into? This is the denominator.

           How many parts is shaded in?  This is the numerator.

Do: $\frac{\text{numerator }}{\text{denominator }}=\frac{3}{7}$numerator denominator =37

Fractions in a Linear Model

Identifying fractions on a number line is similar to identifying fractions in an area model.  

We need to know two things

1) How many equal parts is the number line broken up into (we need to count the parts in 1)? This goes on the bottom and is called the denominator.

2) How many parts along the number line the mark is. This goes on the top and is called the numerator. 

Example

What fraction is marked on this number line?

Think: Count how many parts are dividing up each whole  -> $5$5

Count how many parts along the line the X is positioned at  -> $2$2

Do:The fraction is $\frac{2}{5}$25

Worked Examples

Question 1

What fraction of the square is shaded blue?

Leave the answer in unsimplified form.

Question 2

What fraction of the circle is shaded?

Leave your answer in an unsimplified form.

 

Question 3

What is the fraction represented by the point on the number line?

01234

Outcomes

NA3-1

Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.

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