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MEASUREMENT AND GEOMETRY 32_INVESTIGATIONS AND REFLECTION
(Year 3) ACMMG063, NSW MA2 15MG
Identify regular and irregular quadrilaterals, name special quadrilaterals, describing sides, angles and symmetry.
GUIDED AND INDEPENDENT INVESTIGATIONS and REFLECTION
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 wouldn’t be called learning!
GUIDE children through the INVESTIGATION process until they are ready to investigate INDEPENDENTly.
Children DISCUSS then RECORD their response to the REFLECTION question.
Teaching Segment and Video 1:
Regular and irregular, special
quadrilaterals.
 Children have quadrilaterals, including squares, rectangles, rhombuses, kites and trapeziums. They
measure the quadrilateral’s sides to determine whether they are the same or different lengths. They
compare the quadrilateral’s vertices testing the angles using a square as a right angle. They draw and
name the quadrilateral, labelling it regular or irregular. Reflection: How can we describe quadrilaterals?
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1
More investigations.
Rectangles from sticks.
 In pairs, children have 4 craft sticks of the same or different lengths. Children make quadrilaterals.
Children name, record and label their quadrilaterals regular or irregular. Children identify that some combinations
of craft sticks cannot be joined to make quadrilaterals, for example, one long craft stick and 3 very short craft sticks
(because the shortest distance between 2 points is a straight line, so the sum of the lengths of the other craft sticks
needs to be longer than the length of the long craft stick.) Reflection: How can we describe quadrilaterals?
Symmetry in faces.
 Take photos of children’s faces, and give each child a digital copy.
Children make 3 copies (copy and paste ‘in front of text’), totalling 4.
Children crop each face in half – 2 with right part remaining, and 2
with left part remaining (double click on picture and select crop.)
Children reflect (flip) one left part and 1 right part (double click on the
part, select rotate, select flip horizontal). Children join the 2 left parts
adding a line down the centre. Children join the 2 right parts, adding a
line down the centre. Children discuss whether their face has symmetry and whether the line is a line of symmetry.
Children could also investigate symmetry in the faces of famous people. Enter ‘face left and right’ into Google and
select images for loads of example! Reflection: What is symmetry?
Symmetry in letters.
 Children investigate lower case and upper case letters, identify which letters have symmetry. Reflection: What is a
line of symmetry?
Symmetry in art.
 Children create symmetrical blob art works by folding a page in the centre, unfolding the page, squeezing small
amounts of differently coloured paint on to one half of the page, then refolding the page. When unfolded a
symmetrical picture will result. Reflection: What is a line of symmetry?
Symmetry in objects.
 Children go on a symmetry hunt, looking for symmetry in objects and shapes in the room or outside. Reflection:
What is a line of symmetry?
Mirror symmetry.
 Children play ‘mirrors’ with a friend. They stand facing each other in identical positions. They take turns to make a
move which the other child mirrors. For example, one child raises their right arm and the other raises their left arm
in unison. Reflection: What is symmetry?
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
2
Art in quadrilaterals.
Geoboard quadrilaterals
 Children create art works using only regular and irregular quadrilaterals. Children could base their art works on
Cubism, examples of which are freely available on the internet. Reflection: What is a quadrilateral?
 Have a real or virtual geoboard (freely available on the internet). Make and describe different kinds of
quadrilaterals, including regular and irregular, and special quadrilaterals. They identify lines of symmetry.
Reflection: What is a quadrilateral? What is symmetry?
 In pairs, children have a quadrilateral in a bag. They feel the quadrilateral, visualising and describing its features,
whether it is regular or irregular, and whether it has any lines of symmetry, and whether it is a special quadrilateral.
Reflection: How can we describe quadrilaterals?
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
3
PROBLEM SOLVING directly linked to explicit teaching, investigations and reflections
Problems allow children to investigate concepts in new and varied situations. Any problem worth solving takes time and effort
– that’s why they’re called problems!
Problems are designed to develop and use higher order thinking. Allowing children to grapple with problems, providing minimal
support by asking strategic questions, is key. Differentiating problems allows children to solve simpler problems, before solving
more complex problems on a concept.
Problems may not always be solved the first time they are presented – or at all. The focus of problem solving is the development
of problem solving understanding and capacity – not mastery! Returning to a problem after further learning, develops both
resilience and increased confidence as children take the necessary time and input the necessary effort.
After solving problems, children also create their own problems.
Create 3 levels of a problem. GUIDE children through the first level using the problem solving steps. Allow children to investigate the second level
with friends, with minimal guidance. Allow children to investigate the third level INDEPENDENTly. Children create their own problem.
Teaching Segment and Video 1:
Regular and irregular
quadrilaterals.


I drew a regular quadrilateral. What might it look like? Does this quadrilateral have a special name? (a
quadrilateral with 4 equal sides and vertices – a square
)
I drew an irregular quadrilateral with 3 equal sides and 1 unequal side. What might it look like? Does this
quadrilateral have a special name? (a quadrilateral with 3 equal sides – a trapezium
)
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
4
Quadrilaterals
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
5
Investigating Quadrilaterals – Special, Regular, Symmetry.
Measurement and Geometry 32 Identify regular and irregular quadrilaterals, name special quadrilaterals, describing sides, angles and
symmetry.
Have a quadrilateral, for example, a square, a rectangle, a rhombus, a kite or a
trapezium.
Measure the
quadrilateral’s sides to
determine whether
they are the same or
different lengths.
Compare the
quadrilateral’s vertices
by testing the angles
using a square as a right
angle, checking to see
if the other vertices are
the same or different
sizes.
Draw and name the quadrilateral, and label it regular or irregular.
Draw on any lines of symmetry.
Reflection: How can we describe quadrilaterals?
Problem Solving
I drew a regular quadrilateral.
What might it look like?
Does this quadrilateral have a special name?
Hint: Change regular to irregular, and allow children to solve again!
Problem Solving
I drew an irregular quadrilateral with 3 equal
sides and 1 unequal side.
What might it look like?
Does this quadrilateral have a special name?
Hint: Change irregular to regular, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Quadrilaterals – Special, Regular, Rigid.
Measurement and Geometry 32 Identify regular and irregular quadrilaterals, name special quadrilaterals, describing sides, angles and
symmetry.
Have 4 craft sticks of the same or different lengths.
Make quadrilaterals, including a square, a rectangle, a rhombus, a kite and a
trapezium.
Record and label your quadrilateral as regular or irregular.
Does your quadrilateral have a special name?
Can you make a quadrilateral with all combinations of craft sticks, for example, 1
long straw and 3 very short craft sticks? Why?
Reflection: How can we describe quadrilaterals?
http://www.alearningplace.com.au
Investigating Quadrilaterals – Special, Regular, Rigid.
Measurement and Geometry 32 Identify regular and irregular quadrilaterals, name special quadrilaterals, describing sides, angles and
symmetry.
Have a digital photo of your face.
Make 3 copies (copy and paste ‘in front of text’), totalling 4.
Crop each face in half – 2 with right part remaining, and 2 with left part remaining
(double click on picture and select crop.)
Reflect (flip) one left part and 1 right part (double click on the part, select rotate,
select flip horizontal).
Join the 2 left parts adding a line down the centre.
Join the 2 right parts, adding a line down the centre.
For example,
Discuss whether your face has symmetry and whether the line is a line of symmetry.
You could also investigate symmetry in the faces of famous people.
Reflection: What is symmetry?
http://www.alearningplace.com.au
Investigating Quadrilaterals – Special, Regular, Rigid.
Measurement and Geometry 32 Identify regular and irregular quadrilaterals, name special quadrilaterals, describing sides, angles and
symmetry.
Write some lower case and upper case letters.
Which letters have symmetry?
Reflection: What is a line of symmetry?
http://www.alearningplace.com.au
Investigating Quadrilaterals – Special, Regular, Rigid.
Measurement and Geometry 32 Identify regular and irregular quadrilaterals, name special quadrilaterals, describing sides, angles and
symmetry.
Create symmetrical blob art works by




folding a page in the centre,
unfolding the page,
squeezing small amounts of differently coloured paint on to one half of the
page,
then refolding the page.
When unfolded a symmetrical picture will result.
Reflection: What is a line of symmetry?
http://www.alearningplace.com.au
Investigating Quadrilaterals – Special, Regular, Rigid.
Measurement and Geometry 32 Identify regular and irregular quadrilaterals, name special quadrilaterals, describing sides, angles and
symmetry.
Go on a symmetry hunt, looking for symmetry in objects and shapes in the room or
outside.
Reflection: What is symmetry?
http://www.alearningplace.com.au
Investigating Quadrilaterals – Special, Regular, Rigid.
Measurement and Geometry 32 Identify regular and irregular quadrilaterals, name special quadrilaterals, describing sides, angles and
symmetry.
Play ‘mirrors’ with a friend.
Stand facing each other in identical positions.
Take turns to make a move which the other child mirrors.
For example, one child raises their right arm and the other raises their left arm in
unison.
Reflection: What is symmetry?
http://www.alearningplace.com.au
Investigating Quadrilaterals – Special, Regular, Rigid.
Measurement and Geometry 32 Identify regular and irregular quadrilaterals, name special quadrilaterals, describing sides, angles and
symmetry.
Create art works using only quadrilaterals.
You could base your art works on Cubism, examples of which are freely available on
the internet.
Reflection: What is a quadrilateral?
http://www.alearningplace.com.au
Investigating Quadrilaterals – Special, Regular, Rigid.
Measurement and Geometry 32 Identify regular and irregular quadrilaterals, name special quadrilaterals, describing sides, angles and
symmetry.
Have a real or virtual geoboard (freely available on the internet).
Make and describe different kinds of quadrilaterals, including regular and irregular,
and special quadrilaterals including a square, a rectangle, a rhombus, a kite and a
trapezium.
Identify lines of symmetry.
Reflection: What is a quadrilateral? What is symmetry?
http://www.alearningplace.com.au