Area and Perimeter
Using Mathematics and Using ICT Level 5
Assessment Focus
Pupil Notes
Using Mathematics
Using ICT
Level 5
Knowledge and
Understanding
Interactive
Design
•Measure
•Explore (2)*
•Number
•Evaluate
Using Mathematics
Using ICT
Part 1
Part 2
Resource
Sheet 1
•Exhibit
* Explore (2) refers to the second bullet point of Explore in
the UICT Levels of Progression.
Task Description
In the mathematics part of the task, Part 1, pupils are asked to investigate the different
numerical and spatial relationships that exist when area arrays (e.g. 4 x 6, 6 x 4) and
perimeter values are manipulated. They are also asked to express the relationships in
symbolic form.
In the Using ICT part of the task, Part 2, they are required to use programming software
to create a program that will allow the user to create an abstract ‘Mondrian’ style picture
using coloured squares.
Task code: ITE 002
Sept 2016
1
Area and Perimeter
Using Mathematics and Using ICT Level 5
Prior Knowledge/Experience
Pupils should have experience of:
Using Mathematics
• Recognising, naming and describing common
2-D shapes (Line and angle properties);
• A full rotation as 360º;
• Right angle turns as 90º;
• Using simple notation to express relationships.
i.e. expressing the area of a square as side x side or S2.
Using ICT
• Using programming software (Scratch);
• Changing pen colour and width;
• Combining commands to draw patterns and
shapes;
• Using ‘broadcast’ and ‘when I receive’;
• Creating and using variables;
• Publishing and commenting on work online.
Resources
• Crayons/colouring pencils
• Sets of small squares in three colours (16 red, 24 yellow and 36 blue)
• Squared paper
• Scissors and Glue
• Suitable programming software e.g. Scratch
Managing the Task
Pupils should be given opportunities to:
Plan
• engage in discussion to revise the properties of shape, specifically the relationships that are observable
between perimeter and the areas that it can enclose;
• discuss and demonstrate the relationship between the area of a shape and its perimeter and how they
complement each other;
• plan commands to draw 2-D shapes;
• plan ‘broadcasts’ for creating different coloured squares with a black border;
Do
• work individually or in pairs to complete each part of each task;
• practically manipulate the shapes to experiment with the concept of how a shape’s area can change when
the perimeter remains the same;
• demonstrate that different arrays of the same area can create different values for the perimeter and
similarly for area under different arrangements of the same perimeter;
Task code: ITE 002
Sept 2016
2
Area and Perimeter
Using Mathematics and Using ICT Level 5
• test commands including the use of the repeat command to draw shapes using different fill colours;
• combine commands and use ‘broadcast’ and ‘when I receive’ to create a code that will enable a user to create a ‘Mondrian’ style picture;
• save, store and retrieve their work, appropriately;
Review
• explain their conclusions;
• share their projects with the class and comment online; and
• make improvements to their programming work.
Evidence for UICT External Moderation
As well as submitting the final product, please include:
• evidence of planning
• detailed pupil evaluation at Level 5
Task code: ITE 002
Sept 2016
3
Area and Perimeter
Using Mathematics and Using ICT Level 5
Assessing Pupils’ Responses to the Task
This page sets out the requirements for Using Mathematics that are covered in this task. Alongside these
are the progression statements related to the Knowledge and Understanding required for the task and the
evidence of achievement that illustrates the standard at Level 5.
Requirements for Using
Mathematics
Progression Statements
Level 5
Evidence of using their Knowledge and
Understanding of Shape and Space
Across the curriculum, at
the level appropriate to
their ability, pupils should
be enabled to:
In structured activities, in
familiar and accessible
contexts, pupils can:
Evidence that illustrates the standard at
Level 5 may include the ability to:
•
• plan and decide how an
activity might be
approached;
• explain what they intend to do, how they
will do it and why;
• use mathematical
knowledge and concepts
accurately;
• use a range of appropriate
mathematical techniques
and notation;
• express and use formulae and/or
symbolic form;
• work systematically and
check their work;
• plan and work
systematically and
efficiently;
• work efficiently by using the most
effective methods for the activity,
following identified steps and carrying
out calculations and observations
accurately;
choose the appropriate
materials, equipment and
mathematics to use in a
particular situation;
• review their work, making
appropriate changes;
using their Knowledge and
Understanding of Measures;
•
calculate areas of squares,
rectangles and right-angled
triangles and volumes of
cubes and cuboids;
• calculate the areas of squares and
rectangles;
• calculate perimeters of a
range of shapes;
• calculate the perimeters of squares and
rectangles;
• explore ideas, make and
test predictions and think
creatively;
• identify and explain
patterns and relationships
and make predictions;
• make general statements on the
relationships between area and
perimeter of squares and rectangles;
using their Knowledge and
Understanding of Number;
• express and use formulae
in words and/or symbolic
form;
• generate a formula in words/symbols
to explain the number of possible
shapes from any numeric perimeter
value;
Task code: ITE 002
Sept 2016
4
Area and Perimeter
Using Mathematics and Using ICT Level 5
• read, interpret, organise
and present information in
mathematical formats; and
• explain their findings; and
• draw all possible combinations of
shapes made using smaller shapes
and use notation to represent findings;
• use mathematical
understanding and
language to ask and
answer questions, talk
about and discuss ideas
and explain ways of
working.
•
• describe how they carried out an
activity;
use appropriate
mathematical language to
discuss and describe their
way of working and
respond to questions.
• discuss what they found out;
• explain why they chose a particular way
to present their findings; and
• respond to questions about their work,
findings and presentation.
Task code: ITE 002
Sept 2016
5
Area and Perimeter
Using Mathematics and Using ICT Level 5
Assessing Pupils’ Responses to the Task
The first column of the Assessment Criteria Grid sets out the Requirements for Using ICT that are covered in
this task. Alongside this are the Levels of Progression and the Using ICT Desirable Features for Interactive
Design at Level 5. These Desirable Features have been produced as guidance for teachers to consider
when observing a pupil and assigning a level to a piece of work. When coming to a holistic judgement of the
pupil’s level of Using ICT competence, teachers should ensure that these Desirable Features are used in
conjunction with the Using ICT Levels of Progression.
Assessment Criteria Grid
Using ICT Requirements
Level 5
Explore
Pupils can:
• investigate, make predictions and solve problems
through interaction with digital tools.
• investigate and solve problems in a range of
digital environments;
Evaluate
•
talk about, review and make improvements to
work, reflecting on the process and outcome and
consider the sources and resources used,
including safety, reliability and acceptability.
• use appropriate ICT tools and features to carry
out ongoing improvements and evaluate process
and outcome; and
Exhibit
• manage and present their stored work and
showcase their learning across the curriculum,
using ICT safely and responsibly.
• organise, store and maintain their work within a
personalised area to showcase learning across
the curriculum.
Pupils should demonstrate, when and where appropriate, knowledge and understanding of
e-safety including acceptable online behaviour.
Task code: ITE 002
Sept 2016
6
Area and Perimeter
Using Mathematics and Using ICT Level 5
Desirable Criteria
Interactive Design
Level 5
Pupils can
• plan and solve a more complex problem or
design and create an interactive ‘product’
demonstrating a clear sense of purpose and
audience, for example plan, create and refine a
simple interactive game using ‘Scratch’; and
• carry out ongoing improvements and evaluate
their process and outcome.
Task code: ITE 002
Sept 2016
7
Area and Perimeter
Using Mathematics and Using ICT Level 5
Resource 1
Mondrian images
Task code: ITE 002
Sept 2016
8
Area and Perimeter
Pupil Notes
Part 1
James and Sarah have been asked to investigate the
areas and perimeters of different rectangles. They
have been given three stacks of small squares: 16 red,
24 yellow and 36 blue. Can you help them with their
investigation? You will need to use the same number of
red, yellow and blue squares.
1.Your first task is to find out how many rectangles and
squares that you can make using the 16 red squares.
Draw out each of the possible combinations on
squared paper and use notation e.g. ‘8 x 2’ to record
them. Repeat this process with the stack of yellow
squares and blue squares. You should note that the
8 x 2 combination is different from the 2 x 8
combination.
2.Your next task is to look carefully at each of the
squares and rectangles that you have drawn for each of the colours and investigate their perimeters.
(Think about how you might best record all your
findings as you will have to make comparisons later.)
a.Record the perimeter of each of the rectangles
you drew in question 1 using the red squares.
Repeat for the rectangles you drew using the blue
squares and also the yellow squares.
Task code: ITE 002
Sept 2016
9
Area and Perimeter
Pupil Notes
b.For each colour, determine which combination
provided the largest perimeter and which provided
the smallest perimeter.
c.Write a statement to explain what you have
observed and why you think there are differences in
the perimeters.
________________________________________
________________________________________
________________________________________
3.When James and Sarah investigated the area and
perimeters for the 16 red squares they made a very
interesting discovery. One of their combinations had
exactly the same numerical value. The area and the
perimeter were both 16. Do you think that this could
occur with any other quadrilateral? Try a few others
to check. Explain why you think that 16 is the only
number with which this can happen?
_________________________________________
_________________________________________
_________________________________________
Task code: ITE 002
Sept 2016
10
Area and Perimeter
Pupil Notes
4.Sarah and James decide to investigate how many
other rectangles and squares they could make that have a perimeter of 16 cm. How many do you think
they will find in total? Can you draw them out on your
squared sheet?
5.They decide to investigate how
many rectangles and squares they
could draw with a perimeter first
of 24 cm and then of 36 cm. Sarah
notices a link between the length
of the perimeter and the total
number of rectangles that can be
drawn and predicts how many
rectangles and squares might be
drawn from a perimeter of 100 cm.
Use the space below to explain
what she has discovered.
_________________________________________
_________________________________________
_________________________________________
Task code: ITE 002
Sept 2016
11
Area and Perimeter
Pupil Notes
Part 2
1.Look at the examples of the work of Piet Mondrian
on the Resource 1. He was a Dutch abstract painter
who created very interesting drawings using lines,
simple quadrilaterals and the primary colours; red, blue and yellow. He also used black and white.
2.You are going to create a Scratch project based on
the investigations in area and perimeters that you
have been doing in class. In this activity you will create
a simple project using Scratch that will enable
someone to create a Mondrian type picture using just
squares in the colours that Mondrian used. Take
a look at other Scratch projects on the Scratch
website or your class online discussion forum with your
teacher and comment on them.
Plan and create your project making sure that it suits
the audience you have created it for.
You will need to:
• Use a range of commands within the Events Control, Looks, Motion and Sound functions.
Task code: ITE 002
Sept 2016
12
Area and Perimeter
Pupil Notes
• Change the appearance of sprites and backgrounds
using more than one ‘Broadcast and Receive’ command
or by using an embedded ‘Broadcast and Receive’
command.
• Include two of the following functions in your project:
Sensing, Operators or Variables.
• Publish your saved Scratch project onto the Scratch
website or in your schools’ virtual learning environment
and comment on other pupils’ projects.
• Consider comments made about your project and
decide if you need to make any improvements.
•
Reflect on what you did and write an
account explaining how you carried out
the task, identifying any problems
you faced.
Task code: ITE 002
Sept 2016
13
Task code: ITE 002
Sept 2016
Area and Perimeter
Teacher Notes
Part 1
Possible Using Mathematics Solution
Q1. requires pupils to work methodically to identify all possible combinations for each of the numbers:
e.g. for 16 red squares:
1 x 16
16 x 1
2x8
4x4
8x2
24 yellow squares: 1 x 24, 2 x 12, 3 x 8, 4 x 6, 6 x 4, 8 x 3, 12 x 2, 24 x 1
36 blue squares: 1 x 36, 2 x 18, 3 x 12, 4 x 9, 6 x 6, 9 x 4, 12 x 3, 18 x 2, 36 x 1
Q2. requires the pupils to observe and articulate that while the area may remain constant, manipulating the
array will result in different perimeter values. It is sufficient for them to state that longer or narrower shapes
have a greater perimeter than shorter or broader shapes or the closer the shape is to a square shape the
smaller the perimeter will be.
Shape
Perimeter (Units)
1 x 16
18
2x8
20
4x4
16
8x2
20
16 x 1
18
Q3. requires them to check, observe and state that 16 is the only instance where the numerical value for
perimeter and area will be the same. Answers will require them to demonstrate that they understand that
area is calculated by finding the product of 2 adjacent sides while the perimeter is the product of 4 and any
side. The only occurrence where both are numerically identical is 16.
Task code: ITE 002
Sept 2016
15
Area and Perimeter
Teacher Notes
Q4. and Q5. require pupils to use a methodical approach to ensure that every possible combination of length
and breadth are used to create the rectangles given that the sides are positive integers.
Perimeter of 16 cm
1 x 7, 2 x 6, 3 x 5, 4 x 4, 5 x 3, 6 x 2, 7 x 1
Perimeter of 36 cm
1 x 17, 2 x 16, 3 x 15, 4 x 14, 5 x 13, 6 x 12, 7 x 11, 8 x 10, 9 x 9, 10 x 8, 11 x 7, 12, x 6, 13 x 5, 14 x 4,
15 x 3, 16 x 2, 17 x 1
The pattern can be stated as:
The total number of possible combinations is half the value of the perimeter minus 1; so for a
perimeter of 16 cm there are 7 possible arrangements.
Task code: ITE 002
Sept 2016
16
Area and Perimeter
Teacher Notes
Part 2
Possible Scratch Solution
This first script introduces the project, invites user interaction and uses the variable ‘answer’ to broadcast a
command to each of the drawing scripts depending on user input (R, B, W or Y).
Drawing the squares
The next four scripts are identical and each one is used to draw a different coloured square. They are each
initiated by a separate ‘Receive’ command which is activated by the ‘Broadcast’ command in the script
above. The sequence uses a repeat loop to draw a square of side 100 once and a variable to reduce the size
of the side of the square by 10 for each of the further 9 times it is drawn. This creates a fill effect impression.
A second repeat loop is used to draw a black border around the coloured square.
Task code: ITE 002
Sept 2016
17
Area and Perimeter
Teacher Notes
Illustrations © thinkstock.com
Changing the background
These scripts change the background and play music. The changes to the stage are controlled by broadcast
commands at the beginning and at the end of the first script and are activated by the receive command.
Task code: ITE 002
Sept 2016
18