TMN3704 Assignment 4 (COMPLETE ANSWERS) 2025 - DUE 14 August 2025

SECTION A: MATHEMATICAL THINKING AND UNDERSTANDING Refer to Moeli’s calculation error below and answer 1.5.1 and 1.5.2: Table 1: Addition of Fractions Question: Simplify 2/3 + 5/6 Moeli’s Response: 2/3 + 5/6 = (2×3)/(3×5) + (5×2)/(6×2) = 10/12 = 11/6 1.5.1 What error did Moeli make? (4 marks) 1.5.2 What remedial strategy would you use? Explain and illustrate. (4 marks) Define the concept of "Common Fraction". (2) 1.2 Identify and explain any two key concepts from the definition of a common fraction given above. These are terms that are central to the main points of the description of a common Fraction. (4) 1.3 Table A below indicates the focus of the lesson plan activity. Grade 5 Subject Mathematics Content Area Numbers, Operations and Relationships Topic Common Fractions Concepts and skills Calculations with Fractions Fractions of whole numbers which result in whole numbers 1.4 Carefully study the details of the topic as presented in the Curriculum and Assessment Policy Statement (CAPS) document and then answer the following questions: 1.4.1 In which term(s) is the topic ‘Common fractions’ taught in Grade 5? (3) 1.4.2 How much time is allocated to the topic ‘Common Fractions’ in Grade 5? (2) Question 1.6 Explain and illustrate how you could use base ten blocks to help learners add two three-digit numbers. (6 marks) Question 1.7 Briefly discuss the following approaches to teaching mathematics, and explain how each supports effective learning: a) Problem-solving approach b) Demonstration approach (4 + 4 = 8 marks) What is your understanding of the following concepts: aim and objectives of a lesson? (2) 2.2 As the first step to preparing an effective lesson, describe the aimof your lesson for the identified Topic: Refer to Table A.SECTION B: LEARNER ENGAGEMENT, INQUIRY AND LESSON DESIGN (40 MARKS) Beginning your planning with the learning objectives in mind will also help you to ensure that your tasks and activities are appropriate and will help your learners achieve the objectives. Write down the two objectives that you want your learners to have achieved by the end of the lesson. (NB: Objectives should be derived from the concepts and skills stated in Table A) (6) 2.4 Learning is a process of continually restructuring prior knowledge, not just adding to it. Good teaching and learning provide opportunities for learners to connect what they are learning to their prior knowledge. What prior knowledge do you think learners should bring to build on the knowledge of ‘fractions of whole numbers which result in whole numbers? Question 1.8 Differentiate skills-based teaching from concept-based teaching. Provide one example of each. (4 marks) Question 1.9 Design a lesson plan to teach patterns and equivalent forms, using the focus and concepts outlined below: Focus of the lesson: Equivalent forms Concepts and skills: Determine the equivalence of relationships presented (i) verbally, (ii) in a flow diagram, (iii) in a table. 1.9.1 How would you introduce the lesson? (5 minutes) (4 marks) 1.9.2 How would you develop the lesson? (Focus on time allocation, teacher and learner activities, media use, assessment) (8 marks) 1.9.3 How would you consolidate the lesson? (5 minutes) (4 marks) Question 1.10 Briefly discuss two challenges learners might experience when learning patterns. How could you address them? (4 marks) Question 1.11 Using Figure 2 (a labelled rectangle), explain how you would help learners make real-life connections with the perimeter formula: P = 2L + 2B, where L = length, B = breadth Illustrate and explain how this encourages conceptual understanding. (8 marks) SECTION C: CRITICAL THINKING, SOCIAL CONTEXT AND MATHEMATICAL DEVELOPMENT (20 MARKS) Question 2.1 Mathematics helps develop mental processes such as critical thinking, logical reasoning, accuracy and decision-making. What is your understanding of this view? Use examples to illustrate. (3 marks) Question 2.2 Design a mathematics activity (not on fractions) that develops a critical awareness of how mathematics relates to social relations (e.g., community, fairness, or decision-making).Complete PART 1 of Table C. (30) Identify and reflect on two learning strategy that you consider most suitable to unpack the concept and skills: Calculations with fractions focusing on ‘fractions of whole numbers which result in whole numbers’ and that could engage learners in the learning process that stimulates critical thinking Table C: Development of the fraction concept The main part of the lesson: To create a unique classroom atmosphere, according to Fraser (1998), teachers have to become innovative and use unique teaching methods and activities. PART 1: The role of the teacher (What will you do and say?) 1. How would you introduce the lesson? (5 minutes) (4) 2. How would you develop the lesson? (40 minutes). In answering this question, you should focus on the following aspects: • Time allocation for each activity (4) • the role of the teacher and learners’ activities (6) • As a teacher, you will be faced with the challenge of choosing the most effective media resources to reach your learners. But you can also design your own media to convey knowledge effectively and efficiently. Explain how learner-centred/t eacher-centred media resources would be used to build on learners’ understanding. (6) • Incorporate formative assessments into your lesson to evaluate students' understanding both during and at the end of the lesson. (6) 3. How would you consolidate your lesson? (5 minutes) (4) (3 marks) Question 2.3 Create an inquiry-based investigation where Grade 6 learners explore the properties of a square. Highlight six important ideas in your activity. (6 marks) Question 2.4 Develop an analytical rubric with at least three assessment criteria for evaluating the square properties investigation. (4 marks) (Answer all questions in this section.) 5.1 In planning assessment tasks, keep in mind the principles of universal design. In other words, consider the disabilities that learners might have and, if necessary, determine a strategy for accommodating those learners. Discuss four of such strategies. ( In planning assessment tasks, keep in mind the principles of universal design. In other words, consider the disabilities that learners might have and, if necessary, determine a strategy for accommodating those learners. Discuss four of such strategies. ( 5.2 Briefly discuss any three challenges that learners might experience in learning ‘fractions of whole numbers which result in whole numbers’. How could you (the teacher) address the identified challenges? Assessment tasks should be spaced throughout the term and include formative tasks (tasks that focus on improving performance) as well as summative tasks (tasks that focus on measuring performance). Why is this the case? Motivate (4) 5.3 What is your view on the following statement: "Pre-marking meetings or other activities are undertaken to ensure that assessors are able to clarify their understanding of the assessment criteria." Motivate by giving three points 5.2 Assessment tasks should be spaced throughout the term and include formative tasks (tasks that focus on improving performance) as well as summative tasks (tasks that focus on measuring performance). Why is this the case? Motivate (4) 5.3 What is your view on the following statement: An investigation promotes critical and creative thinking. It can be used to discover rules or concepts and may involve inductive reasoning, identifying or testing patterns or relationships, drawing conclusions and establishing general trends. 6.1 Create an inquiry/investigation in which grade 6 are expected to practically explore the properties of a square. Highlight six important ideas. (12) 6.2 Develop an analytical rubric to aid in evaluating the investigation (6)