Lesson 28: Fractions of Shapes
Focussing on non-unit fractions such as
Do Now
Task sheet 28a can be utilised at this stage. Students must group the different shaded shapes in
any way that they feel is appropriate.
Students might group by the number of sections shaded, or the proportion of the shape shaded,
or they might be much more creative! Encourage students to explain their rationale for their
grouping. Encourage them also so discuss the properties of all the shapes. Do they have anything
in common? What makes them different?
Coach Input
All of the shapes in the Do Now were divided into equal segments. This means each segment represents equal fractions of the whole shape.
To give the shaded part as a fraction of the whole shape start by counting the number of segments. This gives the value of the denominator.
The circle is divided into four so each segment is a
quarter and the denominator is 4.
The heptagon is divided into seven so each segment is a
seventh and the denominator is 7.
To find the numerator count the number of shaded segments  two in both cases.
The circle is
shaded and the heptagon is
shaded.
It is essential that students appreciate that unless the
segments are equal in size they are not the same
fraction, for example this rectangle is not cut into thirds.
Encourage students to go back and state the fraction that is shaded in each of the other shapes
from the Do Now.
Talk Task
Task sheet 28b can be utilised at this stage.
Start with all the pictures face down and turn over shapes a pair at a time trying to match the fraction and the shape. Students can complete the task in pairs or groups. To reduce the level of challenge you may decide to remove some of the shapes and fractions.
Develop Learning A
Often the number of segments will not be equal to the denominator, for example if asked to shade
in of the shape below:
This shape has 16 segments...
means shade 1 in every 2 segments.
As there are 16 segments you will need to shade 8 of them
It doesn’t matter which 8 segments you shade as they are all the same size.
Further examples:
Shade
of the shape below:
means 1 in every 3 segments
There are 4 sets of 3 segments
4×1=4
So shade 4 of the 12 segments
Shade
of the shape below:
means 3 in every 5 segments
There are 2 sets of 5 segements
2×3=6
So shade 6 of the 10 segments
Note that for the purpose of this lesson the number of segments in the shape should be a multiple
of the denominator of the fraction required.
Independent Learning A
Task sheet 28c can be utilised at this stage.
Whilst this is an independent task, coaches should ask students to explain their answers, perhaps
choosing one question in each section to discuss.
Develop Learning B
Students have seen that each segment must be equal in size to be the same fraction, and learned
how to shade a fraction of a shape when the number of segments is a multiple of the denominator. In the example below both of these properties are explored further:
Discuss each of these statements  which ones are true? How can you tell?
Independent Learning B
Task sheet 28d can be utilised at this stage.
Whilst this is an independent task, coaches should ask students to explain their answers, perhaps
choosing one question in each section to discuss.
Plenary
Coaches can summarise findings or extend the strategies learnt today by exploring more challenging fractions of shapes. They could explore fractions of shapes that are equal in area despite being
a different shape.
Any of the task sheets could be used for interim homework allowing students to practise their
skills and consolidate their learning. Do share any useful resources with members of the Mathematics Mastery community via the online toolkit.
Teacher notes: