Download Geometry through Teaching for Mastery

Geometry
Teaching for Mastery
A brief exploration of the progression in geometry
in the Shanghai text books
for Grades 1 – 5 (Yr 2-6)
and reflection on two geometry lessons
regarding parallelograms
taught in Shanghai.
Parallelogram
A
D
B
C
Two pairs of parallel sides makes a
parallelogram。
The parallelogram can be represented by
.The figure can be recorded as ACBD
or ADCB
Is this a parallelogram?
√ × Special parallelogram features
Name
A
B
C
D
Opposite
sides
perpendicular
Opposite the
length is
equal
Adjacent edge
perpendicular
to each other
Adjacent
edge is
equal length
A specific
name
The relationship between special parallelograms
square
rectangle
The relationship between special parallelograms
parallelogram
square
rectangle
The relationship between special parallelograms
parallelogram
square
diamond
The relationship between special parallelograms
parallelogram
rectangle square
diamond
PARALLELOGRAMS IN REAL LIFE
PARALLELOGRAMS IN REAL LIFE
PARALLELOGRAMS IN REAL LIFE
The next lesson
What is this type of shape called?
Is the shape ABCD a parallelogram? Explain.
A
D
B
C
Parallel
Not parallel
What do you think we call the line segment AC?
A
D
B
Line segment AC is called a diagonal line.
C
What do you think we call the line segment BD?
A
B
Line segment BD is called a diagonal line.
D
C
I am interested in this parallelogram.
A
B
D
C
I am interested in this parallelogram.
A
D
I have some parallelograms that I want you to
explore.
What can you discover about the
parallelogram ABCD
when you cut along line AC or BD?
B
C
What have you discovered about the properties
of a parallelogram?
D
A
C
B
What have you discovered about the properties
of a parallelogram?
A
B
D
C
1.The opposite sides of a
parallelogram are parallel and of
equal length.
2.The opposite angles of a
parallelogram are of equal size.
Is this always, sometimes or never
true?
What have we learnt today?
1.The opposite sides of a
parallelogram are of equal length.
2.The opposite angles of a
parallelogram are of equal size
Look in your book at page 61 and
underline the learning.
Can you make different triangles using the three lengths?
Triangles are rigid – they have stability.
Can you make different parallelograms using the four lengths?
What is the same and what is different with these two shapes?
Parallelograms are not fixed – they can be different shapes?
Parallelograms in real life