Week 9: Exploring Mathematical Relationships Part 1

About

In this session, we will work through Investigation 1 (Polygon Fireworks Night Skyline) and the first activity from Investigation 2 (Mathematically Similar Rectangles) from Module 5: Exploring Mathematical Relationships, from the ScratchMaths Curriculum Materials.

The focus of the ScratchMaths Module 5 is the exploration of mathematical relationships with Scratch, including proportionality and ratios. As mentioned in the Module 5 Teacher Materials, the Exploring Mathematical Relationships activities could also be linked to other learning areas. For example, in Investigation 1 you will have the opportunity to create images that include backdrops of city skylines, which could be linked to lessons and concepts within the HSIE: Geography syllabus.

This Module also introduces variables, which is another computational concept and builds on the concepts you have learned in previous sessions, such as Sequences, Loops and Operators. The activities in the Module also build on mathematical concepts from previous weeks’ activities, including co-ordinates, angles, division and multiplication.

Metalanguage

algorithm, computational thinking, computational concept, coding, visual programming, sequences, loops, operators, debugging, custom block, random, conditionals, broadcasting, events, sensing, variables, data

Materials

Presentations

Introduction to Exploring Mathematical Relationships (PDF Presentation)
Exploring Mathematical Relationships Investigation 1 (PDF Presentation)
Exploring Mathematical Relationships Investigation 2 Part 1 (PDF Presentation)
End of Session Presentation (PDF Presentation)

Activities

Homework

For this week’s homework task, we would like you to create a plan for a lesson that involves teaching Coding and Mathematics. We have created a template for you to complete for this task, which has sections for the different parts of the lesson. If you would like to, you can use ideas and activities from the ScratchMaths resources in your lesson plan.

To complete this task, you can choose to either: 1) fill in the Google form linked below or 2) download the Word template and email that to Daniel when you have finished filling it in. If you complete the Google form, you will not have to send Daniel an email because, once the form is completed, he will be sent an email automatically.

If you use a different template for your lessons and would prefer to use that for this task, that is ok. In that case, please send an email with the completed template to Daniel.

Week 9 Homework Task Google Form Link
Week 9 Homework Task (Word document)

Session Outcomes

Stage 3 NSW Syllabus Outcomes

Science and Technology

Digital Technologies

Outcome	How the Outcome is addressed
ST3-3DP-T: defines problems, and designs, modifies and follows algorithms to develop solutions	In this session’s activities, you will design, modify and follow algorithms (steps of instructions for a computer to follow) when drawing patterns and shapes in Scratch.

Mathematics

Working Mathematically

Outcome	How the Outcome is addressed
MA3-1WM: describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions	In this session’s activities, you will have the opportunity to describe and represent a variety of mathematical situations. For example, in the Ask and Answer activity you will use mathematical conventions, in conjunction with Coding commands, to move the characters in the Scratch project around the Stage.
MA3-2WM: selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations	In this session’s activities, you will have opportunity to select and apply problem-solving strategies, when investigating probability, proportionality and geometry in Scratch.
MA3-3WM: gives a valid reason for supporting one possible solution over another	In this session’s activities you will reason about different solutions to the exercises. For example, in the Unplugged: Polygon Predictions activity, you will be given examples of different sets of scripts for drawing squares in Scratch and asked to discuss the differences between these.

Numbers and Algebra

Outcome	How the Outcome is addressed
MA3-4NA: orders, reads and represents integers of any size and describes properties of whole numbers	In this session’s activities, you will use whole numbers when drawing rectangles with Scratch’s pen tool. For example, in the Sequence of Squares activity you will use whole numbers when you draw a sequence of rectangles of increasing sizes.
MA3-8NA: analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian plane	In this session’s activities you will create geometric patterns and locate points on the Cartesian plane when you draw polygons in your Scratch projects. For example, in the Sky at Night activity you will change the Sprites’ positions on the Stage by using Scratch blocks that modify the x and y position of the Sprites.

Measurement and Geometry

Outcome	How the Outcome is addressed
MA3-9MG: selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length	In this session’s activities, you will calculate side lengths of shapes drawn in the Scratch projects. For example, in the Ask and Answer activity you will add blocks that will calculate the perimeter of a polygon that you draw on the Stage in Scratch.
MA3-15MG: manipulates, classifies and draws two-dimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties	In this session’s activities you will draw two-dimensional shapes with Scratch’s pen tool and investigate the ratio of these shapes’ base and height.

Statistics and Probability

Outcome	How the Outcome is addressed
MA3-19SP: conducts chance experiments and assigns probabilities as values between 0 and 1 to describe their outcomes	In this session’s activities, you will have the opportunity to explore the use of randomness in Scratch. For example, in the Ask and Answer activity, you will make a Sprite move to random positions on the Stage and draw shapes.

AITSL Professional Teacher Standards

Standard	How the Standard is addressed
2.6.2: Use effective teaching strategies to integrate ICT into learning and teaching programs to make selected content relevant and meaningful.	In this session, you will learn about different teaching strategies for the integration of ICT (specifically Coding) with Mathematics.
3.3.2: Select and use relevant teaching strategies to develop knowledge, skills, problem solving and critical and creative thinking.	In this session, you will learn about different teaching strategies for developing knowledge, skills, problem solving and critical and creative thinking, in the context of Stage 3 Mathematics.
3.4.2: Select and/or create and use a range of resources, including ICT, to engage students in their learning.	In this session, you will learn about different resources for teaching Coding, including ‘unplugged’ methods that can be used when you do not have access to a computer lab.
6.2.2: Participate in learning to update knowledge and practice, targeted to professional needs and school and/or system priorities.	In this session, you will learn about Coding and Computational Thinking can be incorporated into different areas within the Mathematics syllabus.

ACARA General Capabilities

Literacy

Literacy Element	How this Element is addressed
Visual knowledge	In the sessions’ activities, you will have the opportunity to apply your visual knowledge. For example, in the Ask and Answer activity you will create and interpret visuals when you draw the stars in the skyline with Scratch’s pen tool.

Numeracy

Numeracy Element	How this Element is addressed
Estimating and calculating with whole numbers	In this session’s activities, you will calculate with whole numbers when moving Sprites around the Stage in Scratch. For example, in the Ask and Answer activity you will use whole numbers when you create scripts to move the Beetle to different positions on the Stage.
Using spatial reasoning	In this session’s activities, you will use spatial reasoning when moving Sprites around the Stage in Scratch. For example, in the Ask and Answer activity, you will move the Beetle Sprite to random positions on the Stage.
Using measurement	In this session’s activities, you will calculate side lengths of shapes drawn in the Scratch projects. For example, in the Ask and Answer activity you will add blocks that will calculate the perimeter of a polygon that you draw on the Stage in Scratch.

Information and Communication Technology Capability

ICT Capability Element	How this Element is addressed
Creating with ICT	In this session, you will create images of night skylines using Scratch.

Critical and Creative Thinking

Creative and Creative Thinking Capability Element	How this Element is addressed
Generating ideas, possibilities and actions	In this session, you will be encouraged to be creative in the activities and to explore a variety of ideas, possibilities and actions when creating images of the skylines in Scratch.
Reflecting on thinking and processes	In this session, you will be encouraged to reflect on your thinking and processes you undertook when completing the activities through the questions in the Mathematics Connections sections.
Analysing, synthesising and evaluating reasoning and procedures	In this session, you will have the opportunity to synthesise and evaluate the reasoning and procedures you used during the session, through the Mathematics Connections sections.

Stage 3 ACARA Digital Technologies Content Descriptors

Content Descriptor	How the Descriptor is addressed
ACTDIP018: Design a user interface for a digital system	In this session’s activities, you will create a Scratch project that responds to user input (for example, clicking on a Sprite will make that Sprite move around the Stage).
ACTDIP019: Design, modify and follow simple algorithms involving sequences of steps, branching, and iteration (repetition)	In this session’s activities, you will design, modify and follow algorithms (steps of instructions for a computer to follow).
ACTDIP020: Implement digital solutions as simple visual programs involving branching, iteration (repetition), and user input	In this session, you will implement a program in Scratch, a visual programming language, that includes loops (iteration), events and user input.