OPM1501/201/0/2019
Tutorial letter OPM1501 201/0/2019
Orientation to Intermediate Phase Mathematics
OPM1501
Year module
Department Mathematics Education
IMPORTANT INFORMATION:
This tutorial letter contains important
information about your module.
, OPM1501/201/2019
Assignment 02
ASSIGNMENT 02
CONTRIBUTES 35% TO YEAR MARK
Unique number: 656186
Due date: 24 May 2019
The questions are based on UNITS 2, 3 and 4 of your tutorial letter 501.
This assignment consists of parts A and B. Part A covers the content and in part B you need to
draw up a lesson plan (NB: refer to lesson plan assessment rubric at the end of this assignment).
PART A
1 Name the three strategies used to count set of objects and explain each. (3)
- tens or groups or unifix or bundles of sticks or bottle tops: this are counting in stacks of ten
and useful for counting under 100.
- ones: counted in units as single numbers. Learners will count the objects in ones until there is
nothing left to count. This strategy assists learners to numerate and to say it correctly. For
example, they will make sense to a stack of ten being built by ten ones. This strategy helps
learners to move from counting numbers from heart with counting with understanding.
- Base ten (Dienes blocks): It is used to assist learners on the structure of the mathematics and
how mathematics should be taught. This strategy is where learner employ the knowing of
stacking ones in groups of ten and then adding together with the counting of ones. This
strategy should assist earners to understand the writing of big numbers with the knowledge of
bringing in the place value, total value and face value of the number. It also provides learners
with the understanding of the worth and value of the number without confusing them and
memorising them.
2 How can learners learn to write two- digit numbers in a way that it is connected to the base 10
meaning of ones and tens? (2)
Think of the number written on two cards. 50 6 Fitted behind one behind the
other to look like 56 . The other strategy might be to use number cards with place
values tens and unit placed one on top of the other, please refer to the illustration on page: 3
of your Tut501.
2
, OPM1501/201/2019
e.g. 56
Number Place value chart Representation
56 Tens Units
5 6
3 Show a way in which a hundred chart can aid the teaching of subtraction of two-digit numbers. (2)
Any chosen number: e.g. 87 – 45
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 373 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
- You can follow the red arrows as the first option or: In the arrows, the units reduce by 1 along the
rows moving to the left, and columns reduce up by 10s (tens), explain in terms of the tens chosen
in your example. You can make use of the colours as well.
4 Draw Dienes block to show how to find the solution to: (4)
a) 58 + 37 Take 4 here to 6 to make 10
Take two ones here and add them to
eight ones/ turn ten ones into one
+ = long
3
, OPM1501/201/2019
= =
b) 83 – 28
- =
=
The 8th ten converted to 10 ones
5 Test the following numbers for divisibility by 6, 9, and 11. (Do not divide or factorise)
Refer to page 53 of Tutorial letter 501
a) 10 354 872 is divisible by 11 :1+3+4+7 = 15
0+5+8+2 = 15
10 354 872 is divisible by 11 because the difference between 15 and 15 is zero.
10 354 872 is divisible by 6: is divisible by 2 because it is an even number and it is
divisible by three because 1+0+ 3+5+4+8+7+2 = 30 = 3+0 3. Therefore 10 354 872
is divisible by 6.
10 354 872 is divisible by 9: 1+0+ 3+5+4+8+7+2 = 30. 30 is not a multiple of 9 therefor
1+0+ 3+5+4+8+7+2 is not divisible by 9
b) 19 752 606 is divisible by 6 and 9 but not divisible by 11 the same application in a
above should be applied. (4)
6 The Sieve of Eratosthenes is a well-known way to find prime numbers.
6.1 Use the method given in the chart below to find all the prime numbers between 1 and
100. List all the prime numbers. (5)
Most of you listed the prime numbers and this is not the purpose for this question. Its aim is to assist you
teach learners how to find prime numbers using the theorist who created this type of numbers.
4
Tutorial letter OPM1501 201/0/2019
Orientation to Intermediate Phase Mathematics
OPM1501
Year module
Department Mathematics Education
IMPORTANT INFORMATION:
This tutorial letter contains important
information about your module.
, OPM1501/201/2019
Assignment 02
ASSIGNMENT 02
CONTRIBUTES 35% TO YEAR MARK
Unique number: 656186
Due date: 24 May 2019
The questions are based on UNITS 2, 3 and 4 of your tutorial letter 501.
This assignment consists of parts A and B. Part A covers the content and in part B you need to
draw up a lesson plan (NB: refer to lesson plan assessment rubric at the end of this assignment).
PART A
1 Name the three strategies used to count set of objects and explain each. (3)
- tens or groups or unifix or bundles of sticks or bottle tops: this are counting in stacks of ten
and useful for counting under 100.
- ones: counted in units as single numbers. Learners will count the objects in ones until there is
nothing left to count. This strategy assists learners to numerate and to say it correctly. For
example, they will make sense to a stack of ten being built by ten ones. This strategy helps
learners to move from counting numbers from heart with counting with understanding.
- Base ten (Dienes blocks): It is used to assist learners on the structure of the mathematics and
how mathematics should be taught. This strategy is where learner employ the knowing of
stacking ones in groups of ten and then adding together with the counting of ones. This
strategy should assist earners to understand the writing of big numbers with the knowledge of
bringing in the place value, total value and face value of the number. It also provides learners
with the understanding of the worth and value of the number without confusing them and
memorising them.
2 How can learners learn to write two- digit numbers in a way that it is connected to the base 10
meaning of ones and tens? (2)
Think of the number written on two cards. 50 6 Fitted behind one behind the
other to look like 56 . The other strategy might be to use number cards with place
values tens and unit placed one on top of the other, please refer to the illustration on page: 3
of your Tut501.
2
, OPM1501/201/2019
e.g. 56
Number Place value chart Representation
56 Tens Units
5 6
3 Show a way in which a hundred chart can aid the teaching of subtraction of two-digit numbers. (2)
Any chosen number: e.g. 87 – 45
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 373 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
- You can follow the red arrows as the first option or: In the arrows, the units reduce by 1 along the
rows moving to the left, and columns reduce up by 10s (tens), explain in terms of the tens chosen
in your example. You can make use of the colours as well.
4 Draw Dienes block to show how to find the solution to: (4)
a) 58 + 37 Take 4 here to 6 to make 10
Take two ones here and add them to
eight ones/ turn ten ones into one
+ = long
3
, OPM1501/201/2019
= =
b) 83 – 28
- =
=
The 8th ten converted to 10 ones
5 Test the following numbers for divisibility by 6, 9, and 11. (Do not divide or factorise)
Refer to page 53 of Tutorial letter 501
a) 10 354 872 is divisible by 11 :1+3+4+7 = 15
0+5+8+2 = 15
10 354 872 is divisible by 11 because the difference between 15 and 15 is zero.
10 354 872 is divisible by 6: is divisible by 2 because it is an even number and it is
divisible by three because 1+0+ 3+5+4+8+7+2 = 30 = 3+0 3. Therefore 10 354 872
is divisible by 6.
10 354 872 is divisible by 9: 1+0+ 3+5+4+8+7+2 = 30. 30 is not a multiple of 9 therefor
1+0+ 3+5+4+8+7+2 is not divisible by 9
b) 19 752 606 is divisible by 6 and 9 but not divisible by 11 the same application in a
above should be applied. (4)
6 The Sieve of Eratosthenes is a well-known way to find prime numbers.
6.1 Use the method given in the chart below to find all the prime numbers between 1 and
100. List all the prime numbers. (5)
Most of you listed the prime numbers and this is not the purpose for this question. Its aim is to assist you
teach learners how to find prime numbers using the theorist who created this type of numbers.
4
