MDP1501 Assignment 3 2023 (ANSWERS)

MDP1501 Assignment 3 2023 (ANSWERS) Question 1 In this MFP1501, we refer to mathematical modelling as the process whereby we use abstractions of mathematics to solve problems in the real world. For example, there are 21 learners in Grade 5 that will go on an excursion to Zoo Lake. If one car will take a maximum of 6 learners, how many cars do we need to carry everyone? You may use one car to work out 21 divided by 6. This will give you 3,5. So, you would need 4 cars. Haylock (2014) argues that there are four steps involved in this reasoning. In step 1, a problem in the real world is translated into a problem expressed in mathematical symbols (21÷6, in this case). In step 2, the mathematical symbol is manipulated to obtain a mathematical solution (3,5). Step 3 is to interpret the mathematical solution back in the real world (3 cars, and a half). The final step is to check the answer against the constraints of the original solution. In this case, since you cannot have half of a car, the appropriate conclusion is that you need 4 cars. 1.1Summarise the process of mathematical modelling by first drawing a diagram similar to Figure 3.1 in the study guide. N. B it should not be the same. Be creative. (8) 1.2In each of the steps in your diagram make use of practical examples that will translate into your scenario of using abstractions of mathematics to solve problems in the real world. (15) 4 Question 2 As a mathematics teacher, you are expected to help children develop multiplicative thinking, which goes beyond repeated addition, as it may not happen for many learners. It is the intention of MFP1501 learning unit 4 to support you to do so. Jacob and Willis (2003) outline hierarchical phases through which multiplicative thinking develops, which include one-to-one counting, additive composition, many-to-one counting, and multiplicative relations. 2.1 Describe each phase through which multiplicative thinking develops. (20) 2.2 Motivate your descriptions in 2.1 with practical examples. (12) Question 3 It is important at the Foundation Phase level to start teaching multiplication with simple contexts, rather than abstract calculation, like 5 x 3. Providing contextual situations will allow meaningful discussion about multiplication. This can be achieved through acting, and modelling the situation with a diagram, and can finally be represented by means of a multiplication sentence. 3.1Multiplication applies to situations that involve equal groups. Formulate a scenario to illustrate that a problem can be solved by multiplication when we have a number of groups and the number of objects in each group. Include a diagram or picture(s) in your scenario. (10) 3.2What two division situations you must know as a Foundation Phase teacher? (2) 3.3Categorise each division situation with examples you will use for Grade 3 learners. (8) Question 4 While it's easy to order whole numbers like 1, 4, and 8 by size, it’s difficult to measure fractions immediately. Learners often experience challenges in ordering fractions. Since 4 is greater than 2, learners tend to use the whole number solution and refer to ¼ as greater than ½, which is incorrect. With fractions, more can mean less. The more you partition a unit into equal parts the smaller each part becomes. If each lower number, or denominator, is the same, you can order them like whole numbers, for instance, 1/5, 3/5, and 8/5. In contrast, 8/5 is greater than 3/5 and 1/5 because 8 of the same-size parts is greater than 3 and 1 of the same-size parts. 4.1 Create a short scenario similar to the one in the MFP1501 module site Learning unit 4 lesson and order the fractions you identified from the smallest to the biggest. (10) 4.2 Explain how you will assist a Grade 1 learner understand the difference between unitary and non-unitary fractions. Include diagrams or pictures in your explanation. (15)