Fractions and Decimals 5_Guided and Independent Investigation
(Year 2) ACMNA033, NSW MA1 7NA
Eighth shapes and lengths by eighthing, by halving a quarter and by quartering a half.
GUIDED AND INDEPENDENT INVESTIGATION
These investigations allow children to investigate and explain the concept in new and varied situations, providing formative
assessment data for both the child and the teacher. ‘Doing’ mathematics is not enough and is not a good indicator of
understanding.
Children investigate and explain independently over many lessons at just beyond their current level of understanding, informing
both themselves and the teacher of their current level of understanding. It is during independent investigation that deep understanding and
metalanguage develops.
As they investigate, allow children to experience confusion (problematic knowledge) and to make mistakes to
develop resilience and deep understanding, If children knew what it was they were doing, it would be called learning!
GUIDE children through the INVESTIGATION process until they are ready to investigate INDEPENDENTly.
Investigate
eighths of
shapes.

In pairs, children have paper squares, circles and strips. They divide them into eighths, check for equality by superimposing
and looking for gaps and overlaps, record their eighths and explain how they made their eighths, why they are called eighths,
what fraction of a quarter an eighth is, and what fraction of a half an eighth is.
Show an eighth
in various ways.

In pairs, children are asked to show an eighth in as many different ways as they can. For example, they may divide different
shapes into eighths in different ways.
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
1
Investigate not
eighths.

In pairs, children cut some shapes into 8 parts that are not eighths. They explain why the parts are not eighths because they
are not equal.
Eighths of
different sized
shapes.

In pairs, children have shapes of different sizes and shapes. They divide them in eighths. They compare the areas of the
shapes and the areas of the eighths, explaining that an eighth of a larger shape is larger than an eighth of a smaller shape.
Decorate a ‘cake’
in eighths.

In pairs students have a shape to pretend is a cake. Decorate an eighth of the cake with smarties, 3 eighths of the cake with
sprinkles, 2 eighths of the cake with choc buds and leave 2 eighths of the cake undecorated.
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
2
Investigating Eighths of Shapes
FRACTIONS AND DECIMALS 5 Eighths of shapes
Sit with a friend.
Have some paper squares, circles or strips.
Divide them into eighths.
Check if the parts are equal by superimposing and looking for gaps and overlaps
Record your eighths.
Explain how you made your eighths.
Explain why they are called eighths.
http://www.alearningplace.com.au
Investigating Eighths of Shapes
FRACTIONS AND DECIMALS 5 Eighths of shapes
Sit with a friend.
Cut some shapes into 8 parts that are not eighths.
Explain why the parts are not eighths because they are not equal.
http://www.alearningplace.com.au
Investigating Eighths of Shapes
FRACTIONS AND DECIMALS 5 Eighths of shapes
Sit with a friend.
Show an eighth in as many different ways as you can.
For example, you may have a shape and divide it into eighths in different ways.
http://www.alearningplace.com.au
Investigating Eighths of Shapes
FRACTIONS AND DECIMALS 5 Eighths of shapes
Have a shape to pretend is a cake.
Decorate an eighth of the cake with smarties, 3 eighths of the cake with sprinkles, 2
eighths of the cake with choc buds and leave 2 eighths of the cake undecorated.
http://www.alearningplace.com.au
Investigating Eighths of Shapes
FRACTIONS AND DECIMALS 5 Eighths of shapes
Sit with a friend.
Have shapes of different sizes and shapes.
Divide the shapes in eighths.
Compare the areas of the shapes and the areas of the eighths.
Explaining that a eighth of a larger shape is larger than a a eighth of a smaller shape.
http://www.alearningplace.com.au