Using Mathematics and Using ICT Level 5 Assessment Focus Pupil Notes Using Mathematics Knowledge and Understanding Measure Number Using ICT Interactive Design Explore (2)* Evaluate Exhibit Level 5 Using Mathematics Using ICT Part 1 Part 2 Resource Sheet 1 * 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. 1
Using Mathematics and Using ICT Level 5 Prior Knowledge/Experience Pupils should have experience of: Using Mathematics Using ICT 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 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; 2
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 3
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 Across the curriculum, at the level appropriate to their ability, pupils should be enabled to: choose the appropriate materials, equipment and mathematics to use in a particular situation; Progression Statements Level 5 In structured activities, in familiar and accessible contexts, pupils can: plan and decide how an activity might be approached; Evidence of using their Knowledge and Understanding of Shape and Space Evidence that illustrates the standard at Level 5 may include the ability to: explain what they intend to do, how they will do it and why; use mathematical knowledge and concepts accurately; work systematically and check their work; using their Knowledge and Understanding of Measures; use a range of appropriate mathematical techniques and notation; plan and work systematically and efficiently; review their work, making appropriate changes; calculate areas of squares, rectangles and right-angled triangles and volumes of cubes and cuboids; calculate perimeters of a range of shapes; express and use formulae and/or symbolic form; work efficiently by using the most effective methods for the activity, following identified steps and carrying out calculations and observations accurately; calculate the areas of squares and rectangles; calculate the perimeters of squares and rectangles; explore ideas, make and test predictions and think creatively; using their Knowledge and Understanding of Number; identify and explain patterns and relationships and make predictions; express and use formulae in words and/or symbolic form; make general statements on the relationships between area and perimeter of squares and rectangles; generate a formula in words/symbols to explain the number of possible shapes from any numeric perimeter value; 4
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. use appropriate mathematical language to discuss and describe their way of working and respond to questions. describe how they carried out an activity; 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. 5
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 investigate, make predictions and solve problems through interaction with digital tools. Pupils can: 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. 6
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. 7
Using Mathematics and Using ICT Level 5 Resource 1 Mondrian images 8
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. 9
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? 10
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. 11
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. 12
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. 13
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 2 x 8 4 x 4 8 x 2 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 1 x 16 18 2 x 8 20 4 x 4 16 8 x 2 20 16 x 1 18 Perimeter (Units) 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. 15
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. 16
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. 17
Teacher Notes 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. Illustrations thinkstock.com 18