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UNIVERSITY OF THE WEST OF SCOTLAND: SCHOOL OF EDUCATION
BA Education (Hons) – YEAR 1
MATHEMATICS FOR UNDERSTANDING EXAM
EDUC 07019
Date: August 6th 2014
Time:0900 - 1100
Attempt as many questions as you can.
Section 1 answers should be written on the multiple-choice grid.
Section 2 answers should be written in a booklet.
CALCULATORS ARE NOT ALLOWED
Section 1: Personal Knowledge
(20 Marks)
1. What % of this grid is black?
A
B
C
D
45%
40%
38%
35%
2. The interior angle of a regular decagon is:
A
B
C
D
36º
144º
30º
150º
3. What is (45% of 80) + (23% of 300)?
A
B
C
D
95
115
125
105
4. The values of the 4 and the 2 in the number 1845371.0972 are:
A
B
C
D
4 Ten-Thousands; 2 ten-thousandths
4 Hundred-Thousand; 2 thousandths
4 Ten-Thousands; 2 thousandths
4 Hundred-Thousands; 2 ten-thousandths
5. First calculate 1 + then calculate 5 ÷
The difference between your answers is:
A
B
C 7
D 8
6. 2, 9, 16, 23, 30, …..
The nth term or general term of the above sequence is:
A
B
C
D
7. 0.68
n+7
7n
3n – 1
7n – 5
13
20
2
3
3
5
63%
Arranging the above in order from smallest to biggest gives:
3
2
A 5 63% 3
13
20
0.68
3
13
B 5 63% 20
2
3
0.68
2
3
0.68
C
3 13
5 20
3 13 2
D 5 20 3
8.
63%
63% 0.68
373 ÷ 23 =
A
B
C
D
16 remainder 21
16 remainder 5
16 remainder 22
15 remainder 28
9. Adding together the number of edges on a cuboid, the number of faces on a tetrahedron
and the number of vertices on a square-based pyramid gives a total of:
A
B
C
D
19
18
22
21
10. In a toy shop, I buy t teddy-bears and d dolls. The teddy-bears cost £4 each and the
dolls cost £5 each. The total cost, in £’s, is given by:
A
B
C
D
4t + 5d
t+d
5t + 4d
400t + 500d
End of Section 1
Section 2: Learning Theory
(60 Marks)
1.
(a) In the context of measurement, provide a definition of the terms transitivity and
conservation.
(b) Describe two activities, one which would assess a child’s understanding of
transitivity and another to assess understanding of conservation.
(4,4)
2.
A child is working on the calculation 1247 ÷ 23
Without using the traditional standard algorithm for ‘long division’ work out the answer to this
calculation without the use of a calculator, showing all of your working.
(2)
3.
Physical Removal is a contributory concept involved in the concept of subtraction.
(a) Name and describe another contributory concept involved in subtraction.
(b) Write word problems involving the two different contributory concepts of subtraction and
state the concept used for each example.
(2,2)
4.
(a) Sketch a fraction wall made up of 5 layers.
(b) A fraction wall can be used to demonstrate a key aspect of fractions.
State what this aspect is and describe exactly how the fraction wall can be used.
(2,3)
5. Consider the following two statements:
i The Hindu Arabic number system is a place value system
ii Zero is the identity element for addition and subtraction but not
for multiplication
Describe in detail, using examples, what is meant by each statement.
(5)
6. Define the following terms and explain the role each plays in counting:
(a i Conservation of number
ii Cardinality
iii Ordinality
(b) Describe a short activity that you would use in a primary one class to
reinforce both the cardinal and ordinal aspects of number.
(3,2)
7. Describe three different ways of carrying out the following calculation, making sure that the
correct answer is given:
37% of £180
(3)
8. Show how you would use an empty number line to calculate each of the following:
(a) 134 + 58
(b) 7.3 – 2.15
(c) 8 × 16
(d) For each of the calculations above, name the mental strategy used.
(1,1,1,3)
9.
(a) In the language of LOGO, write down the first 4 basic commands to create an
equilateral triangle.
(b) An equilateral triangle can be drawn using fewer commands with a repeat procedure.
Write down a repeat procedure to draw an equilateral triangle.
(c) Name three aspects of Mathematics which can be developed through the use of LOGO.
(2, 2, 3)
10. (a) List the problem solving strategies
(b) Give three reasons why problem solving is important.
(c) Consider the following problem.
“I think of a number. I multiply this number by 3 and then add 4. I get the answer 19.
What was my original number?”
Is this problem open, closed or both? Give a reason(s) for your answer.
(3,3,3)
11. During a group survey children completed the personal details below:
Activity
Skip
Name
Sandra
Morag
Elaine
Daniel
Michael
√
√
X
√
X
Swim
√
√
X
X
√
Ride a bike
√
√
√
√
√
(a) Organise all of the data collected in the table above, using a Carroll diagram.
(b) Organise all of the data collected in the table above, using a Venn diagram.
(3,3)
End of Paper