Gifted and Talented
Research Project
Program
Outline
Students
and their
Work
Teacher’s Diary
and Reflection
Teaching
Project
Program Outline
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How the students were identified
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Mathematics area of the C.S.F.
How the G.L.I.M.
students were identified
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S.I.N.E Clinical Interview and Diagnostic Test
One of the children completed the D.A.R.T. assessment.
Identification and Assessment of Gifted Students (Bright
Futures 1999)
Mathematics Area
of the C.S.F.
Measurement
Measuring and Estimating
Level 4
At this level students focus on the identification of attributes which can be
measured and select and use appropriate units when estimating,
describing, comparing and measuring length, perimeter and area. They
choose appropriate measuring instruments and use them accurately.
Level 5
At this level students become familiar with metric units used to measure a
range of quantities and common rates and choose units appropriate to the
purpose of measurement.
They choose instruments to measure to the required accuracy, devising
ways to extend capabilities of the instruments and using their knowledge
of fractions and decimals to read scales in which not all graduations are
labelled.
They relate metric units to quantities in their everyday experience and use
this knowledge to make reasonable estimates of other quantities as
required.
Using Relationships
Level 4
At this level students understand and use relationships between different
attributes in measurement situations involving the perimeter and area of
polygons.
Level 5
At this level students investigate the relationship between the dimensions
of two-dimensional shapes and three-dimensional solids and their areas
and volumes. They use these relationships to determine perimeters, areas
and volumes of a range of shapes and objects. They use and calculate rates
in their everyday experience.
Mathematical Reasoning
Level 4
At this level students continue to formulate and test conjectures in the
areas of space, number, measurement and chance and data. The emphases
are on providing evidence for conjectures and arguments, systematically
testing these conjectures and arguments for exceptions, completeness and
reasonableness and making modifications as appropriate. As well, students
decide when to use mathematical models appropriate to this level and to
check the reasonableness of the results obtained by using these models.
They discuss and write about mathematical situations, relationships and
models using mathematical terms, symbols and notations.
Level 5
At this level students continue to develop the skills and dispositions
associated with the formulation and testing of conjectures in all areas of
the curriculum. An emphasis is on the development of general statements
in symbolic form. Students also consider the assumptions and constraints
which underpin the mathematical models they use and develop. As well,
they consider the reasonableness of the results obtained by using these
models in relation to the context.
Students And Their Work
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Students
Demographics of the Group
LB
DH
JC
JE
LR
Students
BB
JB
JF
J Cl
L B’s Profile
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Age: 12
Grade: 6
People in family: 5 people in family. Mum and dad older brother and
younger sister.
Pet: Golden Labrador called Jackie.
Favourite subject: Maths
Favourite sport: Football and tennis.
Favourite hobby: surfing.
I like to go to school see my friends and to work hard. On the weekends I
play my two favourite sports tennis and footy. I play for a club. I hope to be
an A.F.L footy player but I also want to go really well in school to be a vet.
L B’s Work
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Amazing Arrays 1
Amazing Arrays 2
Find The Area Of ….
My Area Worksheet
House Plan
My Dream Bedroom
Bedroom Expenditure
Area is 100cm² and Perimeter is 66cm
Evaluation
J Cl’s Profile
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Favourite Hobby: Surfing.
Favourite Subject: Maths.
Favourite Sport: Lifesaving.
Age: 12
What you would like to be when you are older: Pilot in the Air force.
My name is Jack and I am 12 years old I enjoy Maths because I like being
challenged in areas of learning. I wanted to be apart of this maths group
because I thought it would be a great experience and seeing that I want to
be a pilot in the air force it would help me be closer to my dream job as a
pilot. I also enjoy sport and I just competed in the state Cross Country
championships which I came in the place 4th. My other favourite subjects
are English and History.
J Cl’s Work
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Amazing Arrays 1
Find The Area Of ….
My Area Worksheet
House Plan
My Dream Bedroom
Bedroom Expenditure
Area is 100cm² and The Perimeter is 66cms
Evaluation
J F’s Profile
I am 9 years old. I am an only child.
Things that I enjoy doing are maths, reading, playing games and
working on the computer.
The sports I enjoy are cricket, basketball, tennis, swimming and
soccer.
When I grow up I want to be a doctor, specializing in surgery.
J F’s Work
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Amazing Arrays 1
Amazing Arrays 2
Find The Area Of ….
My Area Worksheet
House Plan
My Dream Bedroom
Bedroom Expenditure
Evaluation
Demographics of the Group
The group consisted of nine boys – eight were year six students and one
was a year four student. This student who was a new admission to our
school this year. The boys are being taught in six different grades, but we
met at least once a week for an hour session while working on the project.
Teaching
Project
Teaching Project
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Learning Needs To Be Targeted
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Links to Other Curriculum Areas
Learning Needs To Be
Targeted
My focus for these children was to review and extend their understanding
of the measurement strand of the Mathematics K.L.A; particularly the topic
of area and perimeter. I wanted the boys to see that so many of our daily
activities are influenced in some ways by measurement procedures. I aimed
to provide them with rich mathematical investigation that would generate
meaningful problem solving strategies that they could use in their project.
My plan was to provide explicit teaching on how to find the area and
perimeter of regular and irregular polygons and then lead the children to
investigate ways they could solve the area of parallelograms, quadrilaterals,
triangles and circles. Throughout our sessions together my endeavor was to
provide tasks that challenged and engaged the children. Many of the tasks
were designed to promote discussion and lead to further inquiry and
sorting out of formulas. The children needed to have a solid understanding
of this topic before they could springboard into their individual projects.
The project while having parameters was aimed at providing opportunities
for the children to be creative and put their individual mark on the task. The
project outline was composed in consultation with the children after we
had agreed what were to be basic inclusions. The use of technology was to
be incorporated throughout this project.
Links To Other
Curriculum Areas
This work while essentially a Mathematics unit does have links with the
Technology K.L.A. Throughout the project the use of software, digital
imagining and programming was used to enhance and modify tasks. The
boys were asked to explain and create solutions as well as plan, construct
and modify their designs and report on them using different materials.
The boys were asked to investigate house plans from a variety of sources
and see why houses are built in many different ways. We talked about
materials used and how designs have changed over the years. This area
could have been expanded and the children chosen a dwelling from
another part of the world and investigated size, materials used and why,
age of dwelling, design structure, permanency and if construction relates to
environment, climate or availability of materials. Unfortunately time did
not allow for such investigations.
Teacher’s
Diary
Session One
In this session the children came together and discussed what the project
was about and where it might be leading. We discussed what the words
area and perimeter meant to them as individuals; as well as linking them to
everyday life. We brainstormed various occupations that might use this
form of measurement in their work. Some of the jobs that were proposed
were: builders, landscape gardeners, pool construction, carpet layers,
interior designer, surveyor, picture framer, plumbers, glaciers, surfboard
makers, architects and farmers. Following this discussion the children
created individual mind maps and shared their ideas with the group.
Session Two
This was an explicit teaching session where the children reviewed/discovered how
to work out the perimeter and area of a regular polygon.
The children brainstormed with the teacher their knowledge about how to work
out the perimeter and the area of a shape. They then worked on a sheet that was
designed for them to discover if there was any correlation between the sides of a
regular shape and its area. Squares Following this task we discussed their findings.
Every child in the group had input here. I posed the question “Is there a more
efficient way to calculate the area of a square or rectangle than just counting the
squares in the grid?” Feed back was automatic from all the boys and I was able to
gauge that each of them had a solid understanding of the formulas for finding the
perimeter of a shape and calculating the area of squares and rectangles.
Session Three
As a review of the work from the last session the children were asked to
calculate the area and perimeter of specific polygons using grid paper. This
task was completed easily by all the group. The next aspect of this lesson
was to have the children use a computer program devised by Mark
Hennessey called amazing arrays. This program reinforced their
understanding of how we multiply length x width to calculate the surface
area of a regular polygons. The children were all successful at completing
this task.
Session Four
This was an explicit teaching session on how to measure the area of
irregular shapes. From this point on, I did not do any specific teaching on
perimeter but the feedback from the children via their work and reflection
indicated to me that this area was well established.
The lesson began with the children being presented with a number of
irregular shapes and we discussed in twos how we might calculate their
areas. Irregular Shapes activity allowed the children to test their
understanding and arrive at an efficient method of calculation.
After completing the task we checked their
calculations by counting the squares in the shape
and using the number sentences composed by
each child. All of the children choose to break
each shape into regular polygons (squares and
rectangles), calculate the length and width,
multiply together and then add the answers
together. The way they broke up the shapes
varied.
Shape 3 for example was broken up in the
following ways.
(5 x 7) + (4 x 3) + (4 x 7)
35 + 12 + 28
Answer = 75 cm2
Another answer provided by a child was
(5 x 2) + (5 x 2) + (13 x 3) + (4 x 2) + (4 x 2)
10 + 10 + 39 + 8 + 8
Answer = 75 cm2
One child however chose to view the shape as a rectangle that
was calculated as
13 x 7 and he then subtracted 2 x (2 x 4)
Therefore he recorded the sum as
13 x 7 – 2 x (2 x 4)
91 - 16
Answer = 75 cm2
The work allowed for valuable discussion and the children were able to
conclude that breaking the shape into regular polygons and calculating the
answers was a much more efficient method to work out the area of a
shape. They also decided that in some cases it was more efficient to
calculate the outside perimeter of the shape and subtract.
Session Five
This session began with a review of what we had learnt about calculating
the area of a regular polygon and irregular shapes. They completed a task
called ‘New Boundaries’. In this task the children were asked to divide
mainland Australia into six states of equal area and redraw the new state
boundaries. (Examples of the children’s work is attached) This was also to
be an explicit teaching session on calculating the area of a parallelogram
and a triangle. The children shared their understandings of what
constituted a parallelogram and triangle. They drew the shapes to show a
visual representation of their understanding.
The children were then given a sheet and asked to find the area of these
shapes. Parallelograms
The discussion and solutions presented indicated the various ways each
child arrived at a solution to the areas of the shape.
Some cut out the shape and made into a regular polygon, others shaded
and calculated the area; they all used the grid squares to affirm their
calculations.
We then took this further and I asked them to look at a regular polygon I
had drawn and asked them to calculate its area. All completed easily by
multiplying length x width. I then handed out the following sheet
Parallelogram 2 and asked then to answer the sheet and write about their
findings. We spoke of new terminology – base and height. It was a great
way for them to discover that the area of a quadrilateral is calculated using
a formula similar to a regular polygon – base x height
Some of the drawn diagrams of the children showed that they had
constructed triangles in their effort to calculate the area of a parallelogram.
I lead a discussion about how we could calculate the area of a triangle. Two
of the children said that their triangles were right-angled triangles and half
of the new polygon that they had drawn. After some teacher input the
children came up with a formula for working out the area of a triangle.
Area of a Triangle = base x height or ½ (base x height)
2
The question was posed – ‘Does this formula work for all triangles?’
- Isosceles triangles
- Equilateral triangles
- Scalene triangles
- Right-angled triangles.
Children tested this discovery using grid paper and formulas using the
following task. Triangles
While most children counted the
squares one child coloured the
parts of squares to prove the
formula.
Another child cut up the part
squares and rearranged into
whole squares.
Session Six
The session began with the children going on a computer and opening a
word document and formatting a table. The children were to go to clip art
and insert a picture. The others in the group where challenged to try and
work out the area of that picture.
Area Pictures Informal lesson on how to measure a circle.
Working On Area Pictures
The ‘House Project’ was introduced to the children. They were given a
design outline of what was expected to be included in their house plan
which was negotiated with the group. House Project
Session Seven
When the children first heard that their homes were to be 42 squares, all of
them imagined 42 square metres. They had all made newspaper square
metres as part of their homeroom class lessons. The Square Metre
The task for the children in this lesson was to make a house square that
equalled 9.6 square metres. The children loved this task and were amazed
with the size.
House Square
Session Eight
This session began with a lesson on how to work out the area of a circle.
Reference Curriculum @ Work.
The children then had the following problem put forward to them ‘Design
a shape that has an area of 100cm² and a perimeter of 66cms.’
The children began by inserting a 10 by 10 array on a grid and then moved
parts to increase the outside perimeter from 40cms to 66cms. Teacher
Examples. The children’s work showed that solutions to this problem are
not limited to just one answer.
The rest of the time was devoted to the children designing their house
plans. There are two groups and four individual projects. The children
looked at plans from newspapers as a guide to the set out of a plan and
symbols used to note fixtures, doors etc.
One of the groups wanted to double their house size to be 84 squares. This
was allowed but it could cause problems when blocks of land are given out,
so house design needs to be considered. We used this session also to talk
about areas that are included in the plans like verandas, garages, carports.
We spoke about a staircase and what type of staircase would take up the
most room. Position of rooms is also important; while we are not doing
plumbing and gas plumbing quotes, have all your wet areas on one side of
a house cuts costs. Children reflected where in their homes, wet areas are
located.
Session Nine
This session began with the allocation of house blocks for their plans.
House blocks are not measured in house squares but in square metres. We
had a walk around the local area and using a trundle wheel measured
house blocks to gauge the average size of blocks.
Measuring A House Block
Our school is situated in an older area but has a new housing estate close
by. The measuring that took place allowed the children to see that not all
blocks are the same, or regular in their shape and that newer homes while
being bigger have less free land. The children opted to construct their
homes on blocks found in an older area.
Session Ten
Working To Scale – In this session the children’s plans were discussed and
they were presented with a 6 x 7 grid.
This grid was to be cut up and rearranged by the grid to represent their plans.
No piece was to be discarded in the completion of this task. Photo
Session Eleven
The children were shown a computer image of a house plans and then
commenced transferring their drawn plans on to the computer and shading
in the relevant rooms of their houses. These will be imposed on to their
house blocks for final presentation.
House plan on Computer
Session Twelve
This session was where the children costed the furnishing of their
bedroom. There were lots of furnishing and electrical catalogues produced.
Teacher also brought in paint cans for children to gauge the cost of painting
and carpet / timber flooring brochures. This session also needed some
explicit teaching about the way carpet is quoted and measured – linear
metre – which is approximately 3 metres x 1 metre. The children had a
budget of $8000 to spend. Their designs indicate their creativity and
dreams of the perfect room.
Session Thirteen
Birds-Eye View Model
Children worked on their scaled birds-eye view model of their house and
placed on their allocated block. My original plan was to have the children
build a 3D model of their house using any medium they choose, but time
and the access to the children did not allow for this part of the project to
evolve. (Six of these children have lead roles in our school musical and they
were often called away for rehearsals. This is also the reason why some of
them do not have all the work requirements in their folders.)
I also wanted them to reflect on our sessions together and have the
opportunity to video their oral presentations; but once again time and access
to the children put a halt to these plans. The children have however, written
an evaluation of the project and these reflections can be found in the
individual student folders. As the teacher of this project I feel very affirmed
and pleased that the students have enjoyed our time together.
Teacher’s
Reflection
My biggest hurdle in doing this project was finding time to gather all the
children from the different classes at one time to complete the tasks. Trying
to co-ordinate time where other programs were not being interrupted was
a huge hurdle and did mean that on occasions lessons were a little rushed.
While the enthusiasm by the children for this task has been fabulous, I
would be hesitant to continue with such a project with children coming
from so many grades. It is not the class teachers’ reluctance but finding time
where we are not timetabled for specialists, sporting commitments and
musical rehearsals. I was very lucky to have the vice-principal come and
relieve me of my classroom commitments, so that I could work with all of
these boys, but her time was also limited.
While I don’t believe that individual grades should be streamed with like
abilities, my recommendation would be to timetable a class session weekly
where children of like abilities are grouped together for enrichment or
remedial help. This type of structure would overcome the dilemma I had
with finding regular time to complete this project.
I would also recommend that in each grade there is at least a pair of like
abilities. While a lot of careful planning goes into grade placements, this
year two of the senior grades have children whose abilities far outweigh
any of their classmates; having a peer with a similar ability in a particular
subject area would challenge and help to further develop ideas on topics
being studied.
Mathematics
Unit
While I was released to work with these children the rest of the grade 5/6
classes worked through the prepared Mathematics Unit on ‘Investigating
The Relationship Between Length, Perimeter and Area’.
The unit I composed and followed, used a template adopted from a model
developed by Cath Murdoch. This template is what we use to plan our
Integrated Studies Units. Area Planner
My time with Dr. Munro has affirmed my teaching practice and the
approach adopted by my team at school. We aim to have open-ended
enquiry based tasks and research projects that foster self-directed learning.
For me personally, the sessions had me reflecting on how I as a teacher
impart this type of learning in my classroom. While I encourage the
children in my care to be thinkers, risk takers and creative in their problem
solving and questioning of tasks; I have been made aware of the
importance of teaching and unpacking the creative thinking of each child.