S1 Lesson 1 - Origami House
Description
Students fold paper to make a picture and use the simple technique of folding in. They discuss
the various shapes made as their pictures take shape.
Purpose
Folding paper helps students to visualise 2D to 3D transformations. Some simple folding
techniques are practiced. Students can make attractive craft and art works from folding
activities. This lesson provides opportunities for dynamic imagery for both 2D and 3D space.
Outcomes
SGS1.2 Manipulates, sorts, represents, describes and explores various twodimensional shapes
Knowledge and skills
Students learn about
 using the terms ‘sides’ and corners’ to
describe features of two-dimensional
shapes
 making representations of twodimensional shapes in different
orientations, using drawings and a
variety of materials
Working mathematically
Students learn to
 visualise, make and describe recently
seen shapes (applying strategies,
communicating)
 identify shapes that are embedded in an
arrangement of shapes or in a design
(applying strategies)
SGS1.1 Sorts, describes and represents three-dimensional objects including
cones, cubes, cylinders, spheres and prisms and recognises them in pictures and
the environment
Knowledge and skills
Students learn about
 Using the terms ‘faces’, ‘edges’ and
‘corners’ to describe three-dimensional
objects
Working mathematically
Students learn to
 Explain or demonstrate how a simple
model was made (reasoning,
communicating)
Key ideas
Identify and name triangles and rectangles in pictures and the environment, and when
presented in different orientations
Identify and name parallel, vertical and horizontal lines
Identify corners as angles
Recognise three-dimensional objects in pictures and the environment, and when presented in
different orientations
Expected learning strategies
The student attends to spatial features and is beginning to make comparisons, relying on what
she/he can see or do. The student:
 recognises shapes in different orientations and proportions, checking by physical
manipulation
 describes similarities and differences and processes of change as he/she uses materials
The student is developing mental images associated with concepts. She/he demonstrates an
increasing use of standard language. The student:
 generates images of shapes in a variety of orientations and with different features

discusses shapes, their parts, and actions when the shape is not present
Materials
Two squares of paper per student and another piece for a background. Paste, paints, coloured
pencils or other things for decorating the background for the house.
Fold square in half
Fold square
in half again
Lift top flaps and push in
crease to make triangles.
Glue house onto paper and
decorate.
Fold sides into
middle line
S1 Lesson 1- Origami House
Activities
Teaching Points and Questions
Introduction (individual with whole class)
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Take the square and ask student how they
can fold it to get a rectangle. Fold the top
down so the fold line is at the top
horizontally. Students can do the same.
Now ask how they can fold it into 4 equal
parts in a row. Students can do the same.
Show students how they can fold the corner
of the outer squares down to form the edge
of the roof. Ask what shape has been folded
down. Do the same on the other side and
students can do the same.
Now unfold the triangle and fold the
triangle inside between the outer sheets.
How can we make one fold and get a
rectangle?
This rectangle can be folded into 4 parts.
How many folds do we need and how?
The bottom part of the rectangle is to be the
house and the top will be the roof.
How might we fold it to get the roof?
Activity (individual or pairs)
Give students the other square of paper.
Students can investigate folding another- What other shaped house might we have that
shaped house. Some student might just make is not so symmetrical or that is taller?
the same house.
Students decide how they can prepare a
background for their house. Paste on the How do you want to decorate the
house and decorate the background. background?
Alternatively, students can make a wall
display.
Conclusion (whole class)

Students share what other shapes they
might know how to fold.

Additional: Make a flip-flop (chatter-box)
in which the corners of a square are folded
into the centre, turned over and corners
folded in again. Fingers can be put inside
the flaps. Students might write answers
inside to mathematical questions on shapes.
How can we fold a square to get a square
half its size?
Take ideas and then encourage students to
think about folding in a corner to the centre
carefully.
Now turn the square over. What fraction of
the original square will we get if we fold in
the corners again?
What shapes do we know?
What questions might you ask about shapes
with those answers?
Students enjoy playing flip-flops but need
to be directed to write in appropriate
mathematical questions.
S1/2 Lesson 2 – Geoboard Symmetry
Description
Students work in pairs to make a symmetrical shape on a geoboard.
Students draw the shape on dot paper and cut it out. The shape can be folded to test for
symmetry.
Purpose
Students need to match parts of shapes, in reflected positions. They need to reverse (reflect)
directions of oblique lines. They need to place shapes at an equal distance from the line of
symmetry.
Outcomes
SGS1.2 Manipulates, sorts, represents, describes and explores various twodimensional shapes
Knowledge and skills
Students learn about
 using the terms ‘sides’ and corners’ to
describe features of two-dimensional
shapes
 making representations of twodimensional shapes in different
orientations, using drawings and a
variety of materials
Working mathematically
Students learn to
 visualise, make and describe recently
seen shapes (applying strategies,
communicating)
 identify shapes that are embedded in an
arrangement of shapes or in a design
(applying strategies)
SGS2.2a Manipulates, compares, sketches and names two-dimensional shapes
and describes their features
Knowledge and skills
Students learn about

using measurement to describe features
of two-dimensional shapes e.g. the
opposite sides of a parallelogram are the
same length

finding lines of symmetry for a given
shape
Working mathematically
Students learn to

explain why a particular two-dimensional
shape has symmetry (communicating,
reflecting)
Key ideas
Find all lines of symmetry for a two-dimensional shape
Expected learning strategies
The student is developing mental images associated with concepts. She/he demonstrates an
increasing use of standard language. The student:
 generates images of shapes in a variety of orientations and with different features
 discusses shapes, their parts, and actions when the shape is not present.
The student uses pattern and movement in her/his mental imagery and is developing conceptual
relationships. The student:
 predicts changes mentally modifying shapes and their attributes using motion or pattern analysis
 discusses patterns and movements associated with combinations of shapes and relationships
between shapes.
Materials
Geoboards, rubber bands, pencils, square dot paper (make sure the dots exactly match the
geoboards)
S1/2 Lesson 2 – Geoboard Symmetry
Activities
Teaching Points and Questions
Introduction (whole Class)
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Class discusses how to use a rubber
band on the geoboard to cut the
board in halves (horizontally,
vertically or diagonally)
Teacher demonstrates how to make
half a shape on one side of the line
with one rubber band and the other
half of the shape (with another
rubber band) on the other side of
the line
Discuss how to make sure that the
shapes are exactly the same on both
sides of the line.
What makes the shape symmetrical?
Demonstrate to the students that the pegs on
the geoboard can be used to help make the
shapes symmetrical
What shapes can I make using the
geoboard?
Can I make a triangle that is symmetrical?
How do I know that it is symmetrical?
Activity (pairs)
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Students share one geoboard
One of the students makes a shape
with one rubber band and the other
student completes the shape with
another rubber band
Students then copy the shape onto
dot paper, cut out the shape and
fold the shape to check the shape is
symmetrical
Change roles so that both students
take turns to complete the shape.
How did you make sure that both sides of
the pattern were the same?
Ensure that the students copy the shape
exactly.
Encourage students to count the number of
pegs enclosed by the shape and then match
this to the dot paper when copying.
Conclusion (whole Class)
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What shapes can you make on the
geoboard?
Students report to class on how
they made their shapes symmetrical Why is the shape symmetrical? Not
symmetrical?
A student is chosen to make a
How can we change the non-symmetrical
shape on the geoboard. Students
shape into a symmetrical shape?
discuss whether the shape is
Who would like to ask another student about
symmetrical or non-symmetrical.
the shape on her/his board?
S2/3 Lesson 3 – Investigating Pentominoes
Description
The students can investigate how many pentonimoes they can make and then explore areas,
perimeters and symmetries (two lessons)
Purpose
Students develop tactics for making new shapes, realise again that shapes may not have
symmetry or names. They realise that area and perimeter are distinct attributes, and that
shapes can have both rotational symmetry or line symmetry.
Outcomes
SGS2.2a Manipulates, compares, sketches and names two-dimensional shapes
and describes their features
Knowledge and skills
Students learn about

using measurement to describe features
of two-dimensional shapes e.g. the
opposite sides of a parallelogram are the
same length

finding lines of symmetry for a given
shape
Working mathematically
Students learn to

explain why a particular two-dimensional
shape has symmetry (communicating,
reflecting)
SG3.2a Manipulates, classifies and draws two-dimensional shapes and describes
side and angle properties
Knowledge and skills
Students learn about
 using templates to draw regular and
irregular two-dimensional shapes
 identifying shapes that have line and
rotational symmetry, determining the
order of rotational symmetry
 applying measurement knowledge to
identify features of shapes especially
area and perimeter
Working mathematically
Students learn to
 construct designs with rotational
symmetry (applying strategies)
 [extension: construct a shape using
computer drawing tools, from a
description of its side and angle
properties (applying strategies)]
Key ideas
Identify shapes that have rotational symmetry
Expected learning strategies
The student uses pattern and movement in her/his mental imagery and is developing
conceptual relationships. The student:
 develops and uses a pattern of shapes or relationship between parts of shapes
 discusses patterns and movements associated with combinations of shapes and
relationships between shapes.
The student selects from a range of spatial strategies that are appropriate for a particular
problem or concept. The student efficiently uses imagery, classification, part-whole
relationships, and orientation. The student:

assesses images and plans the effective use of properties of shapes and composite units to
generate shapes
describes effective use of properties of shapes to generate new shapes.

Materials
60 squares per pair. Grid paper. Paper for recording. Computer drawing tools, Tetra game
S2/3 Lesson 3– Investigating Pentominoes
Activities
Teaching Points and Questions
Introduction


Introduce the investigation to make as
many five square shapes as possible.
The sides of the squares must touch
exactly and not by halves or on points.
Tell the students to leave the shapes
they make on the desk and to keep
making different ones. If shapes are
rotated or reflected then they are
regarded as the same.
Activity 1
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Students make shapes. When they
have the full number of shapes in front
of them.
Get them to record their shapes on the
grid paper.
Ask about the perimeters and areas.
Ask about the lines of symmetry.
Discussion
 Discuss if this activity helped students
to decide what was a shape.
Not
Making pentominoes can be done by
students in earlier stages. Students may
start to make only symmetrical or named
shapes and then realise they can make
other shapes. This is good for them to
realise that not all shapes are named or
are symmetrical.
There are 12 different possible shapes.
If students struggle, begin with 4 squares.
There are only 4 different shapes.
This first part of the activity is suitable
for Stage 2.
Do you think you have any shapes that
are the same? Why?
How many do you have now?
Are you following any tactics to make
new shapes?
Where else can you systematically put the
last square?
How did you decide whether you had
repeated shapes? What did you show or
say to your partner if she/he disagreed

Discuss how they made new shapes.
Activity 2
 Students decide what is the largest and
smallest perimeter of the shapes they
have made.
 They also decide what the areas of the
shapes are.
with you about repeated shapes? Why did
that convince you?
How many shapes did you make?
What tactics did you use or could you use
to make new shapes?
Perimeters can vary from 10 to 12.
Areas are always 5.
What is the most common perimeter?
Why?
Which shape has the smallest perimeter?
Why?
What are the areas of the shapes?
Discussion
 Discuss which shape has the smallest
area and why this might be the reason.
 Discuss whether the area and
perimeter are linked.
Which shape has the largest perimeter?
What is the most common perimeter?
Why?
Which shape has the smallest perimeter?
Why?
What are the areas of the shapes?
What can you say about the perimeters of
shapes that have an area of 5 square
units?
What if you made a shape with 6 square
units?
Activity 3 (pairs)
 Find the symmetries for each shape.
 Group them into those with no, one,
two or more lines of symmetry.
 Students decide why shapes have more
lines of symmetry.
 Students decide which shapes have
symmetry that is rotational rather than
line symmetry.
 Students draw other shapes that have
rotational symmetry
How many lines of symmetry does each
shape have?
Where are they?
What is different about each shape’s
symmetry?
Can you draw other shapes with
rotational symmetry?
How many times do you turn the shape to
return it to its original position?
If the tracing of the shape is turned once
so it lies on itself and then again so it is in
the original position, then it is said to
have order 2 symmetry. The number of
turns to reach its original position is its
order. The plus-sign shape has order 4
and the Z shape has order 2.