TMN3704 Assignment 4 (100% ANSWERS) 2025 - DUE 14 August 2025

TMN3704 Assignment 4 (100% 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) 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) SECTION B: LEARNER ENGAGEMENT, INQUIRY AND LESSON DESIGN (40 MARKS) 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). (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. (8) 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: "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 (6) Question 1.1 How could you, as the teacher, use Figure 1: Decorative Texture Background as a resource for teaching mathematics concepts? Illustrate your approach by providing examples of two specific concepts. (6 marks) The main aim of this part of the lesson is to describe the instructional activities. These refer to tasks or exercises designed to facilitate learning and understanding of Calculations with fractions ‘fractions of whole numbers which result in whole numbers’. This section of the lesson plan should reflect that your lesson is learner-centred, by stating a lot more about what the learners will do than what the teacher will do. It should show learners as active participants rather than passive receivers of information. 4.1 Complete PART 1 of Table C. (30) 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) Question 1.2 If Merriam, the Grade 6 learner, could describe, sort, and compare 2-D shapes and 3-D objects in terms of number and shape of faces, vertices, and edges, what additional activities could you implement to deepen the learner’s understanding of the concept? (4 marks) Question 1.3 Although relational understanding is often thought to be a better alternative to instrumental understanding, when do you regard each type of understanding as useful, particularly in Mathematics? Illustrate with two examples. (4 marks) Question 1.4 How would you use the scenario below as a tool to teach ratio without promoting rote learning? Scenario: 25 cups of buttermilk are needed to make 40 scones. How many cups of buttermilk are required to make 2000 scones? Also, will 10 litres of buttermilk be sufficient to bake 3,000 scones? (6 marks) Question 1.5 Refer to Moeli’s response in Table 1. 1.5.1 What is the common error that Moeli made? (4 marks) 1.5.2 What is the possible remediation? Explain and illustrate. (4 marks) Question 1.6 Explain and illustrate how you could use base ten blocks to help learners learn the addition of two three-digit numbers. (6 marks) Question 1.7 Briefly discuss the following approaches to teaching mathematics and explain how each supports the effective teaching of mathematics: a) Problem-solving approach (4 marks) b) Demonstrated approach (4 marks) 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? Question 1.8 How do you differentiate skills-based teaching and learning from concept-based teaching and learning? Provide an example in each case. (4 marks) Question 1.9 Focus of the lesson: Equivalent forms Concepts and skills: Determine the equivalence of different descriptions of the same relationship or rule presented (i) verbally, (ii) in a flow diagram, and (iii) in a table. 1.9.1 How would you introduce the lesson? (5 marks) 1.9.2 How would you develop the lesson? Include time allocation, teacher and learner activities, use of media, and assessment. (10 marks) 1.9.3 How would you consolidate the lesson? (5 marks) Total for 1.9 = (20 marks) Question 1.10 Briefly discuss any two challenges that learners might experience in learning patterns. How could you, as the teacher, address the identified challenges? (4 marks) Question 1.11 How would you assist the learners to make connections with the derived perimeter formula such as P = 2L + 2B, where L is length and B is breadth of the rectangle? Use Figure 2 to illustrate your explanation. (6 marks) SECTION B: MATHEMATICS AND REAL-LIFE APPLICATIONS (Answer all questions.) Question 2.1 Mathematics helps to develop mental processes that enhance logical and critical thinking, accuracy, and problem-solving that will contribute to decision-making. What is your understanding of this view? Illustrate with examples. (3 marks) 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) 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) SECTION B: LEARNER ENGAGEMENT, INQUIRY AND LESSON DESIGN (40 MARKS) 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). (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) Question 2.2 Design an activity that develops a critical awareness of how mathematical relationships are used in social relations (not fractions). This activity should encourage flexibility within the problem context and help learners connect to real-life situations. (3 marks) 2.1 Mathematics helps to develop mental processes that enhance logical and critical thinking, accuracy and problem-solving that will contribute in decision-making. What is your understanding of this view? Illustrate with examples (3) 2.2 Design an activity that develops a critical awareness of how mathematical relationships are used in social relations (This is aimed at encouraging flexibility within the problem context so that learners can make connections to real-life situations. (NB: Use any topic NOT Fractions) (3) 1.1 How could you, as the teacher, use Figure 1 as a resource for teaching mathematics concepts? Illustrate your approach by providing examples of two specific concepts. (6) Figure 1: Decorative Texture Background Source: TMN3704_ASSIGNMENT 5_2024 10 1.2 If Merriam, the Grade 6 learner, in learning mathematics, could describe, sort and compare 2-D shapes and 3-D objects in terms of number and shape of faces, vertices and edges, what additional activities could you, as the teacher, implement to deepen the learner's understanding of the concept? (4) 1.3 Although relational understanding is often thought to be a better alternative to instrumental understanding, when do you regard each type of understanding as useful, particularly in Mathematics? Illustrate with two examples. (4) 1.4 The lack of significant change in learner performance might, in part, be due to the teachers deeply held traditional beliefs about the teaching and learning of Mathematics serving as an obstacle to implementing the reforms (Kleve 2010). If teachers continue to use the traditional approaches that yield only instrumental understanding, then the learners will continue to perform badly in tasks that focus on higher-order thinking and on the acquisition of critical analytic skills. How would you as the teacher use the following scenario as a tool to teach ratio without promoting rote learning? Scenario: 25 cup of buttermilk is needed to make 40 scones. How many cups of buttermilk are required to make 2000 scones? Also, will 10 liters of buttermilk be sufficient to bake 3,000 scones? (6) 1.5 As the numbers get larger, learners may begin to lose track of some numbers when they do calculations. Closely look at the following calculations done by Moeli and answer questions 1.5.1 and 1.5.2(Explain fully and use the correct mathematical language when interpreting your facts) Table 1: Addition of Fractions Question Moeli’s Response Simplify 23 +56 23 + 56 = 23 ×35 + 56 ×26 = 1012 = 116 TMN3704_ASSIGNMENT 5_2024 11 1.5.1 What is the common error that Seipati made? (4) 1.5.2 What is the possible remediation? Explain and illustrate. (4) 1.6 Explain and illustrate how you could use base ten blocks to help learners learn the addition of two three-digit numbers. (6) 1.7 The general view is that there is no preferred method or approach to teaching and learning mathematics. The important thing is to make sure that you as the teacher differentiate your lesson/teaching based on ability and ensure that you provide sufficient support to learners in your class. Briefly discuss the following approaches to teaching mathematics and explain how each supports the effective teaching of mathematics. a) Problem-solving approach (4) b) Demonstrated approach (4) 1.8 How do you differentiate skills-based teaching and learning from concept-based teaching and learning? Provide an example in each case (4) 1.9 The main aim of this part of the lesson is to describe the instructional activities. These refer to tasks or exercises designed to facilitate learning and understanding patterns. This section of the lesson plan should reflect that your lesson is learner-centred by stating a lot more about what the learners will do than what the teacher will do. It should show learners as active participants rather than passive receivers of information. Focus of the lesson: Equivalent forms: Concepts and skills: Determine the equivalence of different descriptions of the same relationship or rule presented (i) verbally; (ii) in a flow diagram and (iii) in a table. Learners need opportunities to see that changing the form of representation from geometric to verbal or to a flow diagram or to a table can sometimes help them understand the pattern. Learners should “translate” these geometric sequences into other forms of expression or representation. Answer the following questions to assist in guiding the development of your lesson plan in relation to the specified concepts and skills. (20 TMN3704_ASSIGNMENT 5_2024 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 12 1.9.1 How would you introduce the lesson? (5 minutes) 1.9.2 How would you develop the lesson? (40 minutes). In answering this question, you should focus on the following aspects: • Time allocation for each activity • The role of the teacher's and learners' activities • How the learner-centred media resources would be used to build on learners' understanding? • How would you assess learners' understanding? 1.9.3 How would you consolidate your lesson? (5 minutes) 1.10 2.1 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. (2) 2.3 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? Briefly discuss any two challenges that learners might experience in learning patterns. How could you (the teacher) address the identified challenges? (4) 1.1 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) 1.11 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) It is always important to introduce the mathematics concept to your learners in such a way that they are able to make connections and apply what they learned to real-life situations. In this way, you will be making Mathematics a hands-on subject, as your learners will be ‘doing the mathematics’ (CAPS, 2011). How would you assist the learners to make connections (teaching for conceptual understanding) with the derived perimeter formula such as P = 2L x 2B, where L is length and B is breadth of the rectangle. Use Figure 2 to illustrate and fully answer this question. Question 1.1 How could you, as the teacher, use Figure 1: Decorative Texture Background as a resource for teaching mathematics concepts? Illustrate your approach by providing examples of two specific concepts. (Source: (6 marks) Question 1.1 How could you, as the teacher, use Figure 1: Decorative Texture Background as a resource for teaching mathematics concepts? Illustrate your approach by providing examples of two specific concepts. (Source: (6 marks) Question 1.2 If Merriam, the Grade 6 learner, can describe, sort and compare 2-D shapes and 3-D objects in terms of number and shape of faces, vertices and edges, what additional activities could you implement to deepen the learner's understanding of the concept? (4 marks) Question 1.3 Although relational understanding is often preferred over instrumental understanding, when is each type useful, particularly in Mathematics? Use two examples to illustrate. (4 marks) Question 1.4 Using the scenario below, explain how you would teach ratio to avoid promoting rote learning and support higher-order thinking: Scenario: 25 cups of buttermilk are needed to make 40 scones. How many cups of buttermilk are needed to make 2000 scones? Will 10 litres of buttermilk be enough to bake 3000 scones? Question 1.2 If Merriam, the Grade 6 learner, can describe, sort and compare 2-D shapes and 3-D objects in terms of number and shape of faces, vertices and edges, what additional activities could you implement to deepen the learner's understanding of the concept? (4 marks) Question 1.3 Although relational understanding is often preferred over instrumental understanding, when is each type useful, particularly in Mathematics? Use two examples to illustrate. (4 marks) Question 1.4 Using the scenario below, explain how you would teach ratio to avoid promoting rote learning and support higher-order thinking: Scenario: 25 cups of buttermilk are needed to make 40 scones. How many cups of buttermilk are needed to make 2000 scones? Will 10 litres of buttermilk be enough to bake 3000 scones?