UNIVERSITY OF SOUTH AFRICA
College of Education
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
MIP1501: Mathematics for In-
termediate Phase Teachers I
Assignment 02 — Semester 1, 2026
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
MIP1501
Module Code:
Mathematics for Intermediate Phase Teach-
Module Name:
ers I
Assignment 02
Assignment:
769422
Unique Number:
01 June 2026
Due Date:
Dr PE Rankweteke
Lecturer:
100
Total Marks:
Submitted in partial fulfilment of the requirements for MIP1501 — UNISA 2026
,UNISA | MIP1501 Assignment 02
Question 1: Number Sense, Place Value and Time
1.1 Place Value and the Number 4008
(a) Is the learner’s answer correct? Motivate.
Question: A Grade 5 learner writes 4008 as “four thousand and eight”. Is the answer correct?
Motivate reasons for your answer.
Answer:
Yes, the learner’s answer is correct. The number 4008 consists of 4 thousands, 0 hundreds, 0
tens, and 8 units. Reading from left to right, the digit 4 occupies the thousands position, so
it contributes the value of four thousand. The two zeros hold the hundreds and tens positions
without adding any value of their own. The digit 8 sits in the units position and adds eight.
Combining these, the number reads as “four thousand and eight,” which matches exactly what
the learner wrote. The word “and” is commonly used in South African primary school math-
ematics to connect the thousands portion to the remaining units, so the learner’s reading is
both mathematically sound and consistent with how the number system is taught at this level
(Department of Basic Education, 2011).
Implementation Insight
In the South African Curriculum and Assessment Policy Statement (CAPS), Grade 5
learners are expected to read, write, and represent whole numbers up to at least 1 000
000. Teaching learners to name numbers correctly builds the foundation for understand-
ing place value and later work with large numbers.
(b) Write 4008 in expanded form using powers of 10.
Question: Write 4008 in expanded form using powers of 10 and briefly explain each step to a
Grade 5 learner.
Answer:
Step 1: Identify the position of each digit.
The number 4008 has four digits. Each position has a value that is a power of ten.
Page 2 of 25
,UNISA | MIP1501 Assignment 02
Digit Position Place Value Value
4 Thousands 103 = 1 000 4 × 1 000 = 4 000
0 Hundreds 102 = 100 0 × 100 = 0
0 Tens 101 = 10 0 × 10 = 0
8 Units 100 = 1 8×1=8
Step 2: Write in expanded form.
4008 = (4 × 103 ) + (0 × 102 ) + (0 × 101 ) + (8 × 100 )
4008 = 4 000 + 0 + 0 + 8
4008 = 4 000 + 8
To explain this to a Grade 5 learner: “Look at each digit and ask yourself how much it is worth
in its position. The 4 is in the thousands column, so it is worth 4 times 1 000, which gives us
4 000. The zeros in the hundreds and tens columns are worth nothing. The 8 is in the units
column, so it is worth 8 times 1, which gives us 8. Adding everything together: 4 000 + 8 =
4 008.”
(c) What do the two zeros represent in 4008?
Question: Explain to the learner what the two zeros represent in 4008.
Answer:
The two zeros in 4008 are placeholder zeros. The zero in the hundreds position tells us there
are no hundreds in this number. The zero in the tens position tells us there are no tens. With-
out these zeros, the number would look completely different. For example, if we removed both
zeros and wrote 48, that would mean something entirely different. The zeros are doing an
important job: they keep the digits 4 and 8 in their correct positions. Without them, the 4
would no longer be in the thousands place (Haylock and Manning, 2019).
Think of the zeros as empty chairs at a table. Even though nobody is sitting in those chairs,
Page 3 of 25
,UNISA | MIP1501 Assignment 02
the chairs still take up space and keep everyone else in their correct seats.
(d) Effect on value when both zeros are removed.
Question: If you remove both zeros, what number do you get? Explain the effect on the
value to Intermediate Phase learners in simple terms.
Answer:
Removing both zeros from 4008 gives the number 48.
Calculation of the change in value:
4 008 − 48 = 3 960
The value drops by 3 960. The number shrinks from four thousand and eight to only forty-
eight. That is a very large change caused simply by removing two zeros.
To explain to learners: “When you remove the zeros, the digit 4 falls from the thousands col-
umn into the tens column. It is no longer worth 4 000. Now it is only worth 40. The digit 8
stays in the units column, so it keeps its value of 8. Altogether, 40 plus 8 equals 48. We lost 3
960 in value just by removing two zero placeholders.” This shows how critical the position of a
digit is in our number system (Askew, 2016).
Quality Assurance
A common learner error is to think that removing zeros from a number has little effect
because “zero means nothing.” This question is a useful opportunity to address that
misconception directly. Zero does mean nothing on its own, but as a placeholder it
preserves the positional value of every other digit in the number.
1.2 Time Conversion: Decimals and Fractions
(a) Convert 0.3 hours to minutes and seconds.
Question: Explain to your Grade 6 learners how to convert 0.3 hours to minutes and sec-
onds, explaining each step.
Answer:
Page 4 of 25
, UNISA | MIP1501 Assignment 02
Step 1: Convert 0.3 hours to minutes.
There are 60 minutes in 1 hour.
0.3 hours × 60 minutes per hour = 18 minutes
Step 2: Convert the remaining decimal part of the minutes to seconds.
The result from Step 1 is exactly 18 minutes with no decimal remainder. There are 60 seconds
in 1 minute.
0 remaining minutes × 60 = 0 seconds
Result: 0.3 hours = 18 minutes and 0 seconds.
To explain to learners: “We know that 1 hour has 60 minutes. So if we have 0.3 of an hour, we
multiply 0.3 by 60 to find how many minutes that is. 0.3 × 60 = 18. So 0.3 hours is exactly 18
minutes. Since there is no remaining decimal part, there are zero extra seconds.”
(b) Express 45 minutes as a sexagesimal decimal.
Question: Express 45 minutes as a fraction of an hour in base-60 (as a sexagesimal decimal).
Answer:
In the sexagesimal (base-60) system, fractions of an hour are written as the number of min-
utes divided by 60. This gives a decimal coefficient in base 10, but the system represents time
in units of sixty.
Step 1: Write 45 minutes as a fraction of an hour.
45 3
= of an hour
60 4
Step 2: Express in sexagesimal decimal notation.
In base-60, the place to the right of the hours position represents sixtieths. Therefore:
45 minutes = 0; 45 (in sexagesimal notation)
Page 5 of 25
College of Education
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
MIP1501: Mathematics for In-
termediate Phase Teachers I
Assignment 02 — Semester 1, 2026
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
MIP1501
Module Code:
Mathematics for Intermediate Phase Teach-
Module Name:
ers I
Assignment 02
Assignment:
769422
Unique Number:
01 June 2026
Due Date:
Dr PE Rankweteke
Lecturer:
100
Total Marks:
Submitted in partial fulfilment of the requirements for MIP1501 — UNISA 2026
,UNISA | MIP1501 Assignment 02
Question 1: Number Sense, Place Value and Time
1.1 Place Value and the Number 4008
(a) Is the learner’s answer correct? Motivate.
Question: A Grade 5 learner writes 4008 as “four thousand and eight”. Is the answer correct?
Motivate reasons for your answer.
Answer:
Yes, the learner’s answer is correct. The number 4008 consists of 4 thousands, 0 hundreds, 0
tens, and 8 units. Reading from left to right, the digit 4 occupies the thousands position, so
it contributes the value of four thousand. The two zeros hold the hundreds and tens positions
without adding any value of their own. The digit 8 sits in the units position and adds eight.
Combining these, the number reads as “four thousand and eight,” which matches exactly what
the learner wrote. The word “and” is commonly used in South African primary school math-
ematics to connect the thousands portion to the remaining units, so the learner’s reading is
both mathematically sound and consistent with how the number system is taught at this level
(Department of Basic Education, 2011).
Implementation Insight
In the South African Curriculum and Assessment Policy Statement (CAPS), Grade 5
learners are expected to read, write, and represent whole numbers up to at least 1 000
000. Teaching learners to name numbers correctly builds the foundation for understand-
ing place value and later work with large numbers.
(b) Write 4008 in expanded form using powers of 10.
Question: Write 4008 in expanded form using powers of 10 and briefly explain each step to a
Grade 5 learner.
Answer:
Step 1: Identify the position of each digit.
The number 4008 has four digits. Each position has a value that is a power of ten.
Page 2 of 25
,UNISA | MIP1501 Assignment 02
Digit Position Place Value Value
4 Thousands 103 = 1 000 4 × 1 000 = 4 000
0 Hundreds 102 = 100 0 × 100 = 0
0 Tens 101 = 10 0 × 10 = 0
8 Units 100 = 1 8×1=8
Step 2: Write in expanded form.
4008 = (4 × 103 ) + (0 × 102 ) + (0 × 101 ) + (8 × 100 )
4008 = 4 000 + 0 + 0 + 8
4008 = 4 000 + 8
To explain this to a Grade 5 learner: “Look at each digit and ask yourself how much it is worth
in its position. The 4 is in the thousands column, so it is worth 4 times 1 000, which gives us
4 000. The zeros in the hundreds and tens columns are worth nothing. The 8 is in the units
column, so it is worth 8 times 1, which gives us 8. Adding everything together: 4 000 + 8 =
4 008.”
(c) What do the two zeros represent in 4008?
Question: Explain to the learner what the two zeros represent in 4008.
Answer:
The two zeros in 4008 are placeholder zeros. The zero in the hundreds position tells us there
are no hundreds in this number. The zero in the tens position tells us there are no tens. With-
out these zeros, the number would look completely different. For example, if we removed both
zeros and wrote 48, that would mean something entirely different. The zeros are doing an
important job: they keep the digits 4 and 8 in their correct positions. Without them, the 4
would no longer be in the thousands place (Haylock and Manning, 2019).
Think of the zeros as empty chairs at a table. Even though nobody is sitting in those chairs,
Page 3 of 25
,UNISA | MIP1501 Assignment 02
the chairs still take up space and keep everyone else in their correct seats.
(d) Effect on value when both zeros are removed.
Question: If you remove both zeros, what number do you get? Explain the effect on the
value to Intermediate Phase learners in simple terms.
Answer:
Removing both zeros from 4008 gives the number 48.
Calculation of the change in value:
4 008 − 48 = 3 960
The value drops by 3 960. The number shrinks from four thousand and eight to only forty-
eight. That is a very large change caused simply by removing two zeros.
To explain to learners: “When you remove the zeros, the digit 4 falls from the thousands col-
umn into the tens column. It is no longer worth 4 000. Now it is only worth 40. The digit 8
stays in the units column, so it keeps its value of 8. Altogether, 40 plus 8 equals 48. We lost 3
960 in value just by removing two zero placeholders.” This shows how critical the position of a
digit is in our number system (Askew, 2016).
Quality Assurance
A common learner error is to think that removing zeros from a number has little effect
because “zero means nothing.” This question is a useful opportunity to address that
misconception directly. Zero does mean nothing on its own, but as a placeholder it
preserves the positional value of every other digit in the number.
1.2 Time Conversion: Decimals and Fractions
(a) Convert 0.3 hours to minutes and seconds.
Question: Explain to your Grade 6 learners how to convert 0.3 hours to minutes and sec-
onds, explaining each step.
Answer:
Page 4 of 25
, UNISA | MIP1501 Assignment 02
Step 1: Convert 0.3 hours to minutes.
There are 60 minutes in 1 hour.
0.3 hours × 60 minutes per hour = 18 minutes
Step 2: Convert the remaining decimal part of the minutes to seconds.
The result from Step 1 is exactly 18 minutes with no decimal remainder. There are 60 seconds
in 1 minute.
0 remaining minutes × 60 = 0 seconds
Result: 0.3 hours = 18 minutes and 0 seconds.
To explain to learners: “We know that 1 hour has 60 minutes. So if we have 0.3 of an hour, we
multiply 0.3 by 60 to find how many minutes that is. 0.3 × 60 = 18. So 0.3 hours is exactly 18
minutes. Since there is no remaining decimal part, there are zero extra seconds.”
(b) Express 45 minutes as a sexagesimal decimal.
Question: Express 45 minutes as a fraction of an hour in base-60 (as a sexagesimal decimal).
Answer:
In the sexagesimal (base-60) system, fractions of an hour are written as the number of min-
utes divided by 60. This gives a decimal coefficient in base 10, but the system represents time
in units of sixty.
Step 1: Write 45 minutes as a fraction of an hour.
45 3
= of an hour
60 4
Step 2: Express in sexagesimal decimal notation.
In base-60, the place to the right of the hours position represents sixtieths. Therefore:
45 minutes = 0; 45 (in sexagesimal notation)
Page 5 of 25
