MEASUREMENT AND GEOMETRY 61 – TEACHING SHAPES WITH SAME AREA/DIFFERENT PERIMETERS, SAME PERIMETER/DIFFERENT AREAS
ESSENTIAL PRIOR, RELATED AND NEXT LEARNING
Identify students’ current levels of understanding using tracking data, and formative embedded or separate assessment for this concept, and for the essential prior learning.
Differentiate learning
by including the
segment of each
Teaching Plan that
children demonstrate
they are ready to
investigate.
Essential Prior Learning
Essential Related Learning
Measurement and Geometry 52
– Area in hectares and square
kilometres.
Measurement and Geometry 59
– Convert between all metric
length units.
Place Value 28, Fractions and Decimals 25 –
Standard, non-standard, and multiplicative
place value of whole numbers and decimals of
any size by multiplying and dividing by 10, 100
and 1000.
Place Value 29, Multiplication and Division 25,
Fractions and Decimals 26 – Multiply and divide
decimals to thousandths by whole numbers
and powers of 10.
Essential Next Learning
Measurement and Geometry 64 –
Relationship between millilitres and
cubic centimetres, convert between
liquid volume and capacity units.
Measurement and Geometry 67 –
Relationship between liquid and mass
units, convert between mass units.
Use assessment data to select the levels of this concept, or essential related concepts, and the segments of each explicit teaching plan, to teach.
TEACHING VIDEOS, EXPLICIT TEACHING PLAN, INVESTIGATION, REFLECTION, PROBLEM SOLVING
The videos and the explicit teaching plan are divided into the same segments of the concept.
TEACHING SEGMENT and VIDEO 1: Identify two-dimensional shapes with same area / different perimeters, same perimeter / different areas.
VIEW the videos before teaching, to develop YOUR understanding and metalanguage, then teach the concept using YOUR understanding
and metalanguage and the Explicit Teaching PowerPoint, and/or SHOW the video to the whole class / groups of children / individual
children, pausing regularly to allow children to ask and answer questions, to develop THEIR understanding and metalanguage.
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
1
MEASUREMENT AND GEOMETRY 61 – TEACHING SHAPES WITH SAME AREA/DIFFERENT PERIMETERS, SAME PERIMETER/DIFFERENT AREAS
MEASUREMENT AND GEOMETRY 61_OVERVIEW OF TEACHING PLAN
(Year 6) NSW MA3-9MG, MA3-10MG
Identify two-dimensional shapes with same area / different perimeters, same perimeter / different areas.
THIS IS A SUMMARY OF THE EXPLICIT TEACHING PLAN, DESCRIBING THE SEQUENCE WHICH WILL OCCUR OVER MULTIPLE LESSONS. THE COMPLETE EXPLICIT TEACHING PLAN STARTS ON PAGE 3.
Construct Children:
 construct shapes with the same area and different
shapes
perimeters, for example,
with the
Area: 16 square centimetres
same area
Perimeter: 16 centimetres
and
Perimeter: 20 centimetres
different
Perimeter: 22 centimetres
perimeters.
Construct
shapes
with the
same
perimeter
and
different
areas.
 construct shapes with the same perimeter and different
areas, for example,
Perimeter: 16 centimetres
Area: 16 square centimetres
Area: 7 square centimetres
Area: 6 square centimetres
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
Children
 ask one another questions about shapes with same area and
different perimeters, and shapes with same perimeter and
different areas, for example:

How could we construct a shape?

What is the area of the shape?

What is the perimeter of the shape?

How could we construct a shape with the same area and
different perimeter?

How could we construct a shape?

What is the perimeter of the shape?

What is the area of the shape?

How could we construct a shape with the same perimeter
and different area?
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
2
MEASUREMENT AND GEOMETRY 61 – TEACHING SHAPES WITH SAME AREA/DIFFERENT PERIMETERS, SAME PERIMETER/DIFFERENT AREAS
MEASUREMENT AND GEOMETRY 61_EXPLICIT TEACHING PLAN
(Year 6) NSW MA3-9MG, MA3-10MG
FULL EXPLICIT TEACHING PLAN, EMBEDDING THE INVESTIGATIONS, REFLECTIONS AND PROBLEMS THAT MAY BE USED TO DEVELOP DEEP UNDERSTANDING OVER MULTIPLE LESSONS.
Resources: square centimetres, pencil, paper
What could we do?
Focuses children’s
thoughts on the
concept, exposing
current
understanding and
any
misconceptions.
Children think about, talk and listen to a friend about, then have the
opportunity to share what they already know.
Reviews
perimeter as the
distance around a
shape.
(Measurement and
Geometry 59)
What language could we use to explain and ask questions?
►
Today brings an investigation about area and perimeter.
►
What do you know about area and perimeter?
►
Talk about area and perimeter with a friend.
►
Is anyone ready to share what they are thinking about
area and perimeter?
►
We’ve investigated perimeter.
►
And we found that perimeter is a measurement of
length.
►
We found that perimeter is the distance around a shape.
►
We could measure the perimeters of the surfaces on
this rectangular prism.
Display an object, for example,
Trace the perimeters of different
surfaces of the object, for example,
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
3
MEASUREMENT AND GEOMETRY 61 – TEACHING SHAPES WITH SAME AREA/DIFFERENT PERIMETERS, SAME PERIMETER/DIFFERENT AREAS
Reviews
►
We’ve investigated area.
►
And we found that area is a measurement of the
amount space a shape or surface takes up in 2
dimensions.
►
It could take up space left to right, and front to back.
►
It could take up space left to right, and up and down.
Point to the surface that takes up space up and down, and front to
back
►
Or it could take up space up and down, and front to
back.
Display 16 square centimetres - either plastic square centimetres or
cubic centimetres, for example,
►
Today we’re going to investigate both the area and the
perimeter of shapes.
Children measure the dimensions of the surface of the
block to describe its area as 1 square centimetre.
►
What is the area of the surface of this block?
►
Is the surface 1 square centimetre?
►
Because the surface is 1 square centimetre, let’s call this
a square centimetre.
►
How many square centimetres do we have?
►
Do we have 16 square centimetres?
►
How could we arrange these square centimetres to form
a quadrilateral?
►
What is the area of this shape?
►
How many rows?
►
Are there 2 rows?
►
How many in each row?
area as the amount Display an object, for example,
of space a shape
or object takes up Point to the surface that takes up space
in 2 dimensions. left to right, and front to back.
(Measurement and Point to the surface that takes up space
Geometry 52)
left to right, and up and down.
Introduces
quadrilaterals with
the same area and
the different
perimeters.
Children arrange the square centimetres into a quadrilateral, for
example,
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
4
MEASUREMENT AND GEOMETRY 61 – TEACHING SHAPES WITH SAME AREA/DIFFERENT PERIMETERS, SAME PERIMETER/DIFFERENT AREAS
►
Are there 8 square centimetres in each row?
►
What is 2 times 8?
Record, for example, Area: 2 x 8 = 16 cm2 or 16 square centimetres
►
Is the area, 8 square centimetres?
Record, for example,
►
How could we record the shape and the area??
►
What is our unit of measurement?
►
Is our unit of measurement a square centimetre?
►
What does the symbol cm2 say?
►
Does the symbol cm2 say square centimetres?
►
What is the perimeter of this shape?
►
Because we've made a rectangle, could we use the
properties of a rectangle to help us to find the
perimeter?
►
Are opposite sides in a rectangle equal?
►
We have two 8 centimetres lengths and two 2
centimetre lengths.
Record, for example,
►
What does 2 times 8 plus 2 times 2 equal?
cm2
►
Is the perimeter, 20 centimetres?
►
So the area is 16 square centimetres and the perimeter
is 20 centimetres.
8cm
2cm
Record, for example, 2 x 8 = 16 cm
Record, for example, 2 x 2 = 4 cm
Record, for example, 16 + 4 = 20 cm
Record, for example, Perimeter: 20 cm
Area: 16
Perimeter: 20 cm
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
5
MEASUREMENT AND GEOMETRY 61 – TEACHING SHAPES WITH SAME AREA/DIFFERENT PERIMETERS, SAME PERIMETER/DIFFERENT AREAS
Children arrange the 16 square centimetres into a different
quadrilateral, for example,
Record, for example, Area: 4 x 4 = 16 cm2
Record, for example,
►
Do you think we could use these square centimetres to
make another quadrilateral with an area of 16 square
centimetres, but with a different perimeter? Let’s
investigate!
►
What shape have we made?
►
Have we made a square?
►
Do we know the area is still 16 square centimetres?
►
Is 4 times 4, 16?
►
Because we've made a square, could we use the
properties of a square to help us to find the perimeter?
►
Are all sides in a square equal?
►
What is the length of this side?
►
Is the length of this side 4 centimetres?
►
What is 4 times 4?
►
What is the perimeter of the shape?
►
How could we record the shape?
►
Do our 2 shapes have the same area?
►
And do our 2 shapes have different perimeters?
►
Have we made 2 shapes with an area of 16 square
centimetres?
►
Did one have a perimeter of 20 centimetres, and the
other have a perimeter of 16 centimetres?
4cm
4cm
Record, for example,
Perimeter: 4 x 4 = 16 cm
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
6
MEASUREMENT AND GEOMETRY 61 – TEACHING SHAPES WITH SAME AREA/DIFFERENT PERIMETERS, SAME PERIMETER/DIFFERENT AREAS
Children arrange the 16 square centimetres into a different
quadrilateral, for example,
Record, for example, Area: 16 cm2
Record, for example, Perimeter: 34 cm
Record, for example,
16 cm
►
Could we arrange the square centimetres to make
another quadrilateral with the same area and different
perimeter?
►
We know the area – it’s still 16 square centimetres.
►
Is 16 times 1, 16?
►
What is the perimeter?
►
We have two 16 centimetre lengths, and two 1
centimetre lengths.
►
That makes 34 centimetres.
►
How could we record the shape?
►
So we’ve made 3 different quadrilaterals with an area of
16 square centimetres.
►
Did all of the quadrilaterals with 16 square centimetre
areas have the same perimeter?
►
Which quadrilateral with 16 square centimetre area had
the shortest perimeter?
►
Did the square have the shortest perimeter?
►
Do you think the square will always have the shortest
perimeter?
1 cm
Introduces
square shapes
have the largest
area for the
smallest
perimeter.
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
7
MEASUREMENT AND GEOMETRY 61 – TEACHING SHAPES WITH SAME AREA/DIFFERENT PERIMETERS, SAME PERIMETER/DIFFERENT AREAS
Introduces non-
quadrilateral
shapes with the
same area and the
different
perimeters.
Display some square centimetres, for example,
►
We’ve investigated quadrilaterals with the same area
and different perimeters.
►
Let’s investigate non-quadrilaterals.
►
Let’s make some non-quadrilateral shapes with an area
of 10 square centimetres.
►
What is the area of the shape?
►
Is the area 10 square centimetres?
►
What is the perimeter of this shape?
Record, for example, Perimeter: 16 cm
►
Is the perimeter 16 centimetres?
Children construct a non-quadrilateral with an
area of 10 square centimetres, for example,
►
Let’s make another shape with an area of 10 square
centimetres.
►
What is the area of the shape?
►
Is the area 10 square centimetres?
►
What is the perimeter of this shape?
►
Is the perimeter 20 centimetres?
Children construct a non-quadrilateral with an area of 10 square
centimetres, for example,
Record, for example, Area: 10 cm2
Record, for example, Area: 10 cm2
Record, for example, Perimeter: 20 cm
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
8
MEASUREMENT AND GEOMETRY 61 – TEACHING SHAPES WITH SAME AREA/DIFFERENT PERIMETERS, SAME PERIMETER/DIFFERENT AREAS
Introduces
quadrilaterals with
the same
perimeter and
different areas.
Display some square centimetres, for example,
►
We’ve investigated shapes with the same area and
different perimeters.
►
Today we’re going to investigate quadrilaterals with the
same perimeter and different areas.
►
Let’s make a quadrilateral with a perimeter of 16
centimetres.
►
The length of each side is 4 centimetres, so does this
square have a perimeter of 16 centimetres?
►
What is the area of the quadrilateral?
►
Is the area 16 square centimetres?
Children construct a quadrilateral with a perimeter of 16 centimetres,
for example,
►
Let’s make a different quadrilateral with a perimeter of
16 centimetres.
Record, for example, Perimeter: 16 cm
►
Does this quadrilateral have a perimeter of 16
centimetres?
►
What is the area of the quadrilateral?
►
Is the area 7 square centimetres?
Children construct a quadrilateral with a perimeter of 16 centimetres,
for example,
Record, for example, Perimeter: 4 x 4 = 16 cm
Record, for example, Area: 16
cm2
Record, for example, Area: 7 cm2
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
9
MEASUREMENT AND GEOMETRY 61 – TEACHING SHAPES WITH SAME AREA/DIFFERENT PERIMETERS, SAME PERIMETER/DIFFERENT AREAS
Introduces nonquadrilateral
shapes with the
same perimeter
and different
areas.
►
So we constructed 2 quadrilaterals with perimeters of
16 centimetres.
►
One had an area of 16 square centimetres and the other
had an area of 7 square centimetres.
►
What shape had the larger area?
►
Did the square have the larger area?
►
Does a square have the largest area for the shortest
perimeter?
►
We’ve investigated quadrilaterals with the same area
and different perimeters, and quadrilaterals with the
same perimeter and different areas.
►
Let’s investigate non-quadrilaterals.
►
Let’s make some shapes with a perimeter of 16
centimetres.
►
What is the perimeter of this shape?
►
Is the perimeter 16 centimetres?
►
What is the area of the shape?
Record, for example, Area: 16 cm2
►
Is the area 10 square centimetres?
Children construct a non-quadrilateral with
a perimeter of 16 centimetres, for example,
►
Let’s make another shape with a perimeter of 16
centimetres.
►
What is the perimeter of this shape?
►
Is the perimeter 16 centimetres?
►
What is the area of the shape?
►
Is the area 6 square centimetres?
Display some square centimetres, for example,
Children construct a non-quadrilateral with
a perimeter of 16 centimetres, for example,
Record, for example, Perimeter: 16 cm
Record, for example, Perimeter: 16 cm
Record, for example, Area: 6 cm2
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
10
MEASUREMENT AND GEOMETRY 61 – TEACHING SHAPES WITH SAME AREA/DIFFERENT PERIMETERS, SAME PERIMETER/DIFFERENT AREAS
Introduces
the investigation,
reflection and
problem solving
related to this
segment of the
concept.
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
11