MTE1501 Assignment 4 (ANSWERS) 2024 - DISTINCTION GUARANTEED

Well-structured MTE1501 Assignment 4 (ANSWERS) 2024 - DISTINCTION GUARANTEED. (DETAILED ANSWERS - DISTINCTION GUARANTEED!)..... 1. Amongst the ideas of the early mathematics philosophers, which statement is NOT true? Options: 1. Aristotle uses empirical study emanating from experiments and observations. 2. Plato reasoned that mathematics is based on experimentation and abstraction. 3. Hilbert believed that mathematics can exist in the formal having concrete representations in the mind. 4. Aristotle said that we can understand mathematics through experimentation, abstraction, and observation. 2. Aristotle's beliefs on the nature of mathematics are based on the following: Options: 1. The objects of mathematics had an existence on their own. 2. The physical, the mathematical, and the theological into which knowledge could be divided. 3. Ideas of mathematics could be viewed as a subset of the ideas. 4. Logicism, intuitionism, and experimentation. 3. In the "modern" view of mathematics, the following is true... Options: 1. Mathematics exists in human creativity only. 2. Mathematical objects are not invented or created by humans. 3. A mathematics activity is not strictly governed by any one school of thought. 4. Learning mathematics is restricted to real-life connections, signs, symbols, definitions, and rules. 4. People have different views about Mathematics and that it is important to be learned at school. Which of the following is not how people view mathematics? Options: 1. Without special brains, you cannot do Mathematics. 2. Mathematics is made up of symbols and not words. 3. Mathematics does not require a good memory. 4. Mathematics' goal is to find answers. 5. The Egyptians realized or practiced this content area first: Options: 1. Arithmetic 2. Volume and area 3. Geometry 4. Measurement 6. Pictographs were discovered in Egypt and Mesopotamia from 3,000 BC. The best definition of a pictogram is: Options: 1. A form of abstract symbol used to represent quantities. 2. A graph that displays complex statistical data. 3. An ancient form of writing using abstract shapes. 4. A visual representation using pictures that stand for quantities. 9. The significance of time was realized by the Babylonians according to (Bassarear, 2005). What was the Babylonian approach to dividing time during the day and night? Options: 1. The day was divided into 24 hours and the night into 24 hours. 2. Both the day was divided into 24 hours and the night into 12 hours. 3. Both the day and night were divided into 12 hours. 4. The varying of the time for both the day and the night was not done in accordance with hours. 10. The plane geometry assists learners to understand: 1. The study of all flat shapes and all solid objects in geometry. 2. The study of flat, 2-D shapes like lines, circles, triangles, pentagons, etc. 3. The study of only triangles and quadrilaterals like squares. 4. The study of simple, uncomplicated geometry, or shapes in space. 11. The shape is clearly explained by which school? 1. Pythagorean 2. Ionian 3. Eleatic 4. None of the above 12. The Platonic solid octahedron has: 1. Eight equiangular faces. 2. Eight lateral faces. 3. Eight edges and eight congruent faces. 4. Four vertices, eight edges, and isosceles triangular faces. 13. This is false about the "relational understanding of mathematics": 1. A learner connects different mathematical ideas with understanding. 2. A learner remembers rules and formulae and can apply them in mathematics problems to reach the correct answer. 3. A learner knows the mathematical facts and the methods to calculate correctly. 4. A learner reaches the correct answer when they apply all the rules correctly. 14. Looking at the five strands of mathematical proficiency of Kilpatrick et al. (2001), what does it mean to have "conceptual understanding"? 1. To apply critical, creative, and self-regulated thought in mathematical tasks. 2. To enable learners to achieve high performance in mathematics. 3. To use the prescribed methods/procedures to solve a mathematical problem. 4. To understand the standard concepts in a specific phase subject. 5. To carry steps easily from one step to the other in mathematical procedures/methods. 15. According to Kilpatrick et al. (2001:115), the following are the components making up mathematics proficiency: Options: 1. Adaptive reasoning and Conceptual understanding, procedural fluency. 2. Strategic proficiency, Cognitive understanding, and adaptive strategies. 3. Productive position, Conceptual reasoning, and procedural understanding. 4. Conceptual understanding, procedural fluency, and adaptive reasoning. 16. Which one of the following assessment items requires problem-solving skills? 1. What is the area of a right-angled triangle with a base of 8 cm and the perpendicular height of 9 cm? 2. Use a cut-out equilateral triangle to illustrate how you will compare their sizes and their angles. 3. Find the length of the missing length of a right-angled triangle with a base of 8 cm and the perpendicular height of 9 cm? 4. How many faces and vertices does an octahedron have? 17. According to Nicholson (1992), what is the primary objective of a problem-solving task? 1. To engage learners in important mathematics development. 2. To encourage learners to follow predetermined procedures. 3. To promote quick solutions through well-known methods. 4. To assess learners' ability to perform routine activities/problems. 18. An Intermediate Phase learner recognizes that squares, rectangles, and parallelograms all have four sides and that two opposite sides in each of these shapes are the same length. At which level of van Hiele's levels of geometric thought is this learner? 1. Level 1: Analysis 2. Level 0: Visualization 3. Level 3: Formal deduction 4. Level 4: Rigour 19. This question is about your understanding of dimensions: • Zero dimension (0D) is a point that shows a position only. • One dimension (1D) is a line connecting two points; it has length as its one dimension. • Two dimensions (2D) is a shape with length and width as its two dimensions. • Three dimensions (3D) is an object with length, width, and height (three dimensions). a. Which of the following can be used to describe the area of a floor tile? 1. The area of the floor tile is 900 cm. 2. The area of the floor tile is 900 cm². 3. The area of the floor tile is 900 cm³. 4. The area of the floor tile is 900. 20. You use a number line to explain to a learner what the opening calibration and the closing calibration will be if you have to add 0.3 and 0.4. 1. 0 and 1 2. 0.1 and 0.4 3. 0.3 and 1 4. 0 and 0.4 21. Dienes blocks are base 10 blocks that help to teach place value, addition, and subtraction in the base 10 number system. b. What will be the difference between (two blocks + four flats + five units) and (nine flats + seven longs/rods + nine units)? Options: 1. Two flats + four flats + two longs/rods + six three units 2. Three blocks + three flats + eight longs/rods + four units 3. One block + four flats + two longs/rods + six three units 4. One block + three flats + eight longs/rods + four units Workings: • Start with two blocks, four flats, and five units. • Subtract nine flats, seven longs/rods, and nine units from that. Let's break it down: • Subtracting nine flats from four flats requires you to take one block (10 flats) and subtract from that, leaving you with one block and a remainder of three flats. • Subtracting seven longs/rods from zero requires you to take another block, leaving eight longs/rods. • Subtracting nine units from five units will leave you needing to borrow again, resulting in four remaining units. Thus, the answer is one block, three flats, eight longs/rods, and four units. 22. An important idea to understand when building number sense is equality, which means that what is to the left should be the same as what is to the right of an equal sign (=). Which number will make the following equation true? 11 - 11 × 1 + 11 = ? 1. 0 2. +11 3. -99 4. 121 23. a. Which of the following is equal to 2x - 3y + 7x + 5y? Options: 1. 7x + 10y 2. 11xy 3. 9x + 8y 4. 9x + 3y 24. Which of the following sentences best describes the difference between a digit and a number? 1. A digit is used everywhere, and digits are used in electronic devices, but numbers are used everywhere. 2. Digits are made up of numeral symbols 0-9 which are used to make up a number. 3. A digit is made up of numbers more than one. 4. None of the above. 25. Which one of the following numbers is rational? Options: 1. √2 2. π 3. 100/0 4. √144 26. What is the number represented by ∩∩∩