SCHOOL OF EDUCATION (Edgewood Campus) MAIN EXAMINATIONS - NOVEMBER 2015 BACHELOR OF EDUCATION

Transcription

1 SCHOOL OF EDUCATION (Edgewood Campus) MAIN EXAMINATIONS - NOVEMBER 2015 BACHELOR OF EDUCATION Module Name Primary Mathematics Education 310 Code EDMA311 Duration 3 hours Marks 120 Internal Examiners Ms B. Goba Mrs E. Dowlath External Examiner Mr B.F. Shozi (MUT) Name Student Number Seat Number Instructions: Answer all questions in the spaces provided on this paper. If the space is insufficient, use the blank page at the end of the paper and indicate that you have done so. This question paper consists of 18 pages including this cover page and a blank page for extra work. Please check that you have them all. Question Marks Marks Obtained Internal External TOTAL 120

2 QUESTION 1 [40 Marks] 1.1 State whether the following statements are True or False. If false write down the correct answer The order of rotational symmetry of a rectangle is four A line joining two vertices in any polyhedron is called a diagonal The sum of the interior angles of a parallelogram is four right angles An equilateral triangle has three axes of symmetry. (8) Page 2

3 1.2 A nine sided polygon (called a nonagon ) is shown Show how you could work out the sum of the interior angles of this polygon without using a protractor. Write down this sum Hence show how you could work out the size of each of the interior angles of the regular nonagon drawn below. (5) Name the level in the van Hiele model which this activity is suited to? Explain why you say so? Write down a rule in terms of n and s to determine the sum of the interior angles of a regular polygon with n sides. (3) Page 3

4 1.2.5 Use your rule from Q to find the sum of the interior angles of regular decagon and hence the size of each angle Using mathematical instruments, construct triangle ABC with AB = 7 cm, A = 35 and B = 105 in the space below. (3) (Hint: Draw a rough sketch of the triangle to guide your construction) Page 4

5 1.3.2 Triangles are named or classified in two different ways: (i) according to the type of their interior angles; or (ii) according the length of their sides. Name the triangle which you constructed in Question according to: The types of their interior angles: The length of the sides. 1.4 When children are developing an understanding of angles, angles can be experienced in two ways: The dynamic view and the static view Differentiation clearly between these two terms. Page 5

6 1.5 Geometric transformations refer to the movement of a shape from one position to another. When a transformation is applied to a figure, a new figure is formed Study the shapes in the graph shown below Name the transformation and describe fully the transformation that maps: ABC onto Shape S ABC onto Shape V Page 6

7 ABC onto Shape P Explain the term isometries or isometric movements with reference to transformations Which van Hiele level(s) of geometric thinking is the following question suited to. Van Hiele level(s).. because Page 7 (3)

8 QUESTION 2 [20 marks] 2.1 Squares are arranged to form patterns as shown below. Study the patterns below and answer the questions which follow: Stage 1 Stage 2 Stage How many squares are there in Stage 4? How many squares are there in Stage 30? Write down an explanation (using the term Stage Number in your explanation) how you arrived at your answer. (3) Write down a general formula in terms of n to find the number of squares in Stage n Explain which Stage has 122 squares? Page 8

9 2.2 Study Pascal s triangle given below and answer the question set Name three types of sequences that are found on Pascal s triangle. List five terms of each of the three types of sequences you named. (6) 2.3 The figures below represent the first five triangular numbers. Page 9

10 2.3.1 Complete the table below with triangular numbers, from the first to the sixth. Position of the triangular number Number of boxes Use the table above to determine the number of dots in the 60 th figure. Explain your strategy. (3) Page 10

11 Question 3 [30 marks] 3.1 Define the following term: Statistics Nominal data 3.2 The data shows the marks obtained by 100 Grade 8 learners in a Mathematics test. The test marks are out of Complete the frequency table. (9) Page 11

12 3.2.2 Represent the data in a bar graph. (5) Study the bar graph. Explain any trends you observe in the data. Page 12

13 Frequency of runners 3.3 The following bar graph shows the ages of the runners taking part in a 10km road race. There were 180 runners in the race. Ages of runners in a 10km road race Ages of runners (years) How many classes are used in the graph? What is the class interval of each class? At what age does the first class start? What are the ages of the runners in the class with the highest frequency? Explain the trends in the data in your own words. Page 13

14 Question 4 [30 marks] 4.1 What is assessment? 4.2 List five different types of assessment strategies that can be used to assess learners mathematical understanding. (5) 4.3 On the 5 th October 2015, you solved the problem below during the lecture and provided an explanation of the solution in your journal. During the lectures you learnt that managing and grading journal entries go hand in hand. In addition, in order to make journal writing effective, the entries need to be read regularly. Considering the aforementioned, read the problem below and answer the questions that follow. Problem 1. Two hikers come to a fork in the trail and decided that each will take a different trail. They need to divide their supply of water evenly between them. Their water completely fills an 8-litre jug that has no markings on it. They also have two smaller jugs that are empty and unmarked- one holds 5 litres and the other 3 litres. How can they divide the water evenly so that each one has 4 litres for the rest of the hike? Student A journal entry Page 14

15 Student B s journal entry Evaluate with reasons student A s solution to the problem. (4) Evaluate with reasons student B s solution to the problem. (4) Page 15

16 4.4 In a bag there are 5 cards numbered 1, 3, 5, 7, 9. In a second bag there are 4 cards numbered 2, 4, 6, 8. One card is drawn at random from each bag Complete the sample space diagram/table showing the sum of the numbers on two cards What is the probability that: The sum is an odd number? The sum is 13? The sum is less than 10? The sum is exactly divisible by 5? Page 16

17 4.5 For each of the following statements, identify a misunderstanding in the learner s statement. What type of activities might you use to address these misconceptions? I have two bags of jellybeans. Bag A contains 5 red jellybeans and 10 white ones. Bag B contains 1 red and 1 white jellybean. I like red jellybeans. So, if I have to pick a jellybean from one bag, I will choose Bag A because it contains 5 reds which is more than the 1 red in Bag B Adrian flipped a coin 3 times and got heads each time. So, the probability of tails for that coin is zero The weatherman said the chance of rain is 50%. This means it will rain half of the day. Page 17

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