MIP1501
ASSIGNMENT 2
DUE DATE: 1 JUNE 2026
1.1 . A grade 5 learner in the mathematics classroom writes 4008 as “four thousand
and eight”.
a) Is the answer by the learner correct? Motivate reasons for your answer.
1.1 Grade 5 Learner: 4008 as "four thousand and eight"
a) Is the learner's answer correct? Motivate reasons for your answer. (3)
it is incorrect. The number 4008 should be read as "four thousand eight" without the
word "and". In mathematical language, the word "and" is used to indicate a decimal
point. For example, 4.008 is read as "four and eight thousandths". By saying "four
thousand and eight", the learner is incorrectly suggesting a decimal point between the
thousands and the units. The correct way to read 4008 is "four thousand eight".
(MIP1501 Study Guide, 2020, p. 17)
b) Write 4008 in expanded form using powers of 10 and explain each step to a
grade 5 learner. (5)
,MIP1501 ASSIGNMENT 2 2026
DUE 1 JUNE 2026
1.1 . A grade 5 learner in the mathematics classroom writes 4008 as “four thousand
and eight”.
a) Is the answer by the learner correct? Motivate reasons for your answer.
1.1 Grade 5 Learner: 4008 as "four thousand and eight"
a) Is the learner's answer correct? Motivate reasons for your answer. (3)
it is incorrect. The number 4008 should be read as "four thousand eight" without the
word "and". In mathematical language, the word "and" is used to indicate a decimal
point. For example, 4.008 is read as "four and eight thousandths". By saying "four
thousand and eight", the learner is incorrectly suggesting a decimal point between the
thousands and the units. The correct way to read 4008 is "four thousand eight".
(MIP1501 Study Guide, 2020, p. 17)
b) Write 4008 in expanded form using powers of 10 and explain each step to a
grade 5 learner. (5)
To explain to a Grade 5 learner, I would say "Let's look at the number 4008. Each digit
has a special place that tells us its value, like a house number."
Step-by-step
The digit 4 is in the thousands place – this means 4 × 1000 = 4000
The digit 0 is in the hundreds place – this means 0 × 100 = 0
The digit 0 is in the tens place – this means 0 × 10 = 0
The digit 8 is in the units (ones) place – this means 8 × 1 = 8
Now using powers of 10:
,1000 = 10³ (10 × 10 × 10)
100 = 10² (10 × 10)
10 = 10¹
1 = 10⁰
So 4008 = (4 × 10³) + (0 × 10²) + (0 × 10¹) + (8 × 10⁰)
c) Explain to the learner what the two zeros represent in 4008.
The two zeros in 4008 are placeholders.
I will explain to the learner "Imagine you have 4 thousand and 8 loose blocks. You don't
have any hundreds blocks and you don't have any tens blocks. But we need to write
something in those positions to show that they are empty. The zeros sit in the hundreds
and tens places to hold those positions open. Without them, the number would become
48, which is a much smaller number! Zero doesn't mean 'nothing' in the whole number
it means 'no hundreds' and 'no tens'." (MIP1501 Study Guide, 2020, p. 18)
d) If you remove both zeros, what number do you get? Explain the effect on the
value. (4)
If we remove both zeros from 4008, we get the number 48.
To explain to Intermediate Phase learners:
"Let me show you what happens when we remove zeros. 4008 is like having 4 thousand
and 8 individual blocks that's 4,008 blocks in total. But if we take away the zeros, we get
48 that's just forty-eight blocks. The zeros are like placeholders that keep the digits in
their correct positions. When we remove the zeros, the digit 4 moves from the
,thousands place to the tens place. So 4,000 becomes just 40! That's a huge difference
4,000 is 100 times bigger than 40. So zeros are very important. they tell us how big a
number really is."
1.2 Grade 6 Learner: Time Conversion
a) Convert 0.3 hours to minutes and seconds – explain each step. (3)
Step 1 Remember that 1 hour = 60 minutes. So to convert 0.3 hours to minutes, we
multiply 0.3 × 60.
0.3 × 60 = 18 minutes.
Step 2 Since 18 minutes is a whole number, we don't have any remaining minutes to
convert to seconds. So 0.3 hours = 18 minutes exactly.
If the minutes weren't a whole number, we would take the decimal part and multiply by
60 again to get seconds." (MIP1501 Study Guide, 2020, p. 14-15)
b) Express 45 minutes as a fraction of an hour in base-60 (sexagesimal decimal).
In base-60 (sexagesimal), 1 hour = 60 minutes. So 45 minutes as a fraction of an hour
is:
45/60 = 3/4 = 0.75 (in base-10)
In sexagesimal decimal form, we write 45 minutes as 0°45' where the ' indicates
minutes. Alternatively, as a fraction of an hour: 45/60 = 0.75₆₀ meaning 0 hours and 45
minutes.
,c) Task takes 1 hour 25 minutes – write as decimal in base-10 and base-60. Which
is more precise for exact fractions?
Base-10 decimal: 1 hour 25 minutes = 1 + 25/60 = 1 + 0.41666... = 1.416666... hours
(repeating decimal)
Base-60 decimal: 1 hour 25 minutes = 1°25' in sexagesimal notation
Which is more precise for exact fractions. The base-60 (sexagesimal) representation is
more precise for exact fractions because 25/60 is an exact fraction in base-60, whereas
in base-10 it becomes a repeating decimal (0.41666...). Base-60 is better for
representing fractions that don't convert nicely to base-10 decimals. (MIP1501 Study
Guide, 2020, p. 14-15)
1.3 Learner's Statement about Zero
a) Is the statement "Zero is nothing, so it does not affect any operation" always
true? Give an example where zero does affect the result.
The statement is not always true. While zero doesn't affect addition (5 + 0 = 5) or
subtraction (5 - 0 = 5), it DOES affect multiplication and division.
Example 5 × 0 = 0. Here, zero completely changed the result instead of getting 5, we
got 0. So zero definitely affects multiplication! Another example: 10 × 0 = 0. No matter
how large the other number is, multiplying by zero gives zero. (MIP1501 Study Guide,
2020, p. 18)
b) Explain why division by zero is undefined using a real-life situation.
, Imagine you have 12 sweets and you want to share them equally among your friends. If
you have 3 friends, each gets 4 sweets (12 ÷ 3 = 4). If you have 2 friends, each gets 6
sweets (12 ÷ 2 = 6). If you have 1 friend, that friend gets all 12 sweets (12 ÷ 1 = 12).
Now, what if you have ZERO friends? The question becomes: 'How many sweets does
each friend get?' But there ARE no friends to give sweets to! The question doesn't make
sense. You can't share something among nobody. That's why we say division by zero is
'undefined' – it has no meaning in real life."
c) What is the additive inverse of -8? Use zero in your explanation.
The additive inverse of -8 is 8.
I would saytThe additive inverse of a number is the number you add to it to get zero. For
-8, we need to find what number to add to make 0
(-8) + 8 = 0
So the additive inverse of -8 is 8. Zero is the 'additive identity' because when you add
zero to any number, that number stays the same. The additive inverse is the number
that 'cancels out' your original number to reach zero." (MIP1501 Study Guide, 2020, p.
18)
ASSIGNMENT 2
DUE DATE: 1 JUNE 2026
1.1 . A grade 5 learner in the mathematics classroom writes 4008 as “four thousand
and eight”.
a) Is the answer by the learner correct? Motivate reasons for your answer.
1.1 Grade 5 Learner: 4008 as "four thousand and eight"
a) Is the learner's answer correct? Motivate reasons for your answer. (3)
it is incorrect. The number 4008 should be read as "four thousand eight" without the
word "and". In mathematical language, the word "and" is used to indicate a decimal
point. For example, 4.008 is read as "four and eight thousandths". By saying "four
thousand and eight", the learner is incorrectly suggesting a decimal point between the
thousands and the units. The correct way to read 4008 is "four thousand eight".
(MIP1501 Study Guide, 2020, p. 17)
b) Write 4008 in expanded form using powers of 10 and explain each step to a
grade 5 learner. (5)
,MIP1501 ASSIGNMENT 2 2026
DUE 1 JUNE 2026
1.1 . A grade 5 learner in the mathematics classroom writes 4008 as “four thousand
and eight”.
a) Is the answer by the learner correct? Motivate reasons for your answer.
1.1 Grade 5 Learner: 4008 as "four thousand and eight"
a) Is the learner's answer correct? Motivate reasons for your answer. (3)
it is incorrect. The number 4008 should be read as "four thousand eight" without the
word "and". In mathematical language, the word "and" is used to indicate a decimal
point. For example, 4.008 is read as "four and eight thousandths". By saying "four
thousand and eight", the learner is incorrectly suggesting a decimal point between the
thousands and the units. The correct way to read 4008 is "four thousand eight".
(MIP1501 Study Guide, 2020, p. 17)
b) Write 4008 in expanded form using powers of 10 and explain each step to a
grade 5 learner. (5)
To explain to a Grade 5 learner, I would say "Let's look at the number 4008. Each digit
has a special place that tells us its value, like a house number."
Step-by-step
The digit 4 is in the thousands place – this means 4 × 1000 = 4000
The digit 0 is in the hundreds place – this means 0 × 100 = 0
The digit 0 is in the tens place – this means 0 × 10 = 0
The digit 8 is in the units (ones) place – this means 8 × 1 = 8
Now using powers of 10:
,1000 = 10³ (10 × 10 × 10)
100 = 10² (10 × 10)
10 = 10¹
1 = 10⁰
So 4008 = (4 × 10³) + (0 × 10²) + (0 × 10¹) + (8 × 10⁰)
c) Explain to the learner what the two zeros represent in 4008.
The two zeros in 4008 are placeholders.
I will explain to the learner "Imagine you have 4 thousand and 8 loose blocks. You don't
have any hundreds blocks and you don't have any tens blocks. But we need to write
something in those positions to show that they are empty. The zeros sit in the hundreds
and tens places to hold those positions open. Without them, the number would become
48, which is a much smaller number! Zero doesn't mean 'nothing' in the whole number
it means 'no hundreds' and 'no tens'." (MIP1501 Study Guide, 2020, p. 18)
d) If you remove both zeros, what number do you get? Explain the effect on the
value. (4)
If we remove both zeros from 4008, we get the number 48.
To explain to Intermediate Phase learners:
"Let me show you what happens when we remove zeros. 4008 is like having 4 thousand
and 8 individual blocks that's 4,008 blocks in total. But if we take away the zeros, we get
48 that's just forty-eight blocks. The zeros are like placeholders that keep the digits in
their correct positions. When we remove the zeros, the digit 4 moves from the
,thousands place to the tens place. So 4,000 becomes just 40! That's a huge difference
4,000 is 100 times bigger than 40. So zeros are very important. they tell us how big a
number really is."
1.2 Grade 6 Learner: Time Conversion
a) Convert 0.3 hours to minutes and seconds – explain each step. (3)
Step 1 Remember that 1 hour = 60 minutes. So to convert 0.3 hours to minutes, we
multiply 0.3 × 60.
0.3 × 60 = 18 minutes.
Step 2 Since 18 minutes is a whole number, we don't have any remaining minutes to
convert to seconds. So 0.3 hours = 18 minutes exactly.
If the minutes weren't a whole number, we would take the decimal part and multiply by
60 again to get seconds." (MIP1501 Study Guide, 2020, p. 14-15)
b) Express 45 minutes as a fraction of an hour in base-60 (sexagesimal decimal).
In base-60 (sexagesimal), 1 hour = 60 minutes. So 45 minutes as a fraction of an hour
is:
45/60 = 3/4 = 0.75 (in base-10)
In sexagesimal decimal form, we write 45 minutes as 0°45' where the ' indicates
minutes. Alternatively, as a fraction of an hour: 45/60 = 0.75₆₀ meaning 0 hours and 45
minutes.
,c) Task takes 1 hour 25 minutes – write as decimal in base-10 and base-60. Which
is more precise for exact fractions?
Base-10 decimal: 1 hour 25 minutes = 1 + 25/60 = 1 + 0.41666... = 1.416666... hours
(repeating decimal)
Base-60 decimal: 1 hour 25 minutes = 1°25' in sexagesimal notation
Which is more precise for exact fractions. The base-60 (sexagesimal) representation is
more precise for exact fractions because 25/60 is an exact fraction in base-60, whereas
in base-10 it becomes a repeating decimal (0.41666...). Base-60 is better for
representing fractions that don't convert nicely to base-10 decimals. (MIP1501 Study
Guide, 2020, p. 14-15)
1.3 Learner's Statement about Zero
a) Is the statement "Zero is nothing, so it does not affect any operation" always
true? Give an example where zero does affect the result.
The statement is not always true. While zero doesn't affect addition (5 + 0 = 5) or
subtraction (5 - 0 = 5), it DOES affect multiplication and division.
Example 5 × 0 = 0. Here, zero completely changed the result instead of getting 5, we
got 0. So zero definitely affects multiplication! Another example: 10 × 0 = 0. No matter
how large the other number is, multiplying by zero gives zero. (MIP1501 Study Guide,
2020, p. 18)
b) Explain why division by zero is undefined using a real-life situation.
, Imagine you have 12 sweets and you want to share them equally among your friends. If
you have 3 friends, each gets 4 sweets (12 ÷ 3 = 4). If you have 2 friends, each gets 6
sweets (12 ÷ 2 = 6). If you have 1 friend, that friend gets all 12 sweets (12 ÷ 1 = 12).
Now, what if you have ZERO friends? The question becomes: 'How many sweets does
each friend get?' But there ARE no friends to give sweets to! The question doesn't make
sense. You can't share something among nobody. That's why we say division by zero is
'undefined' – it has no meaning in real life."
c) What is the additive inverse of -8? Use zero in your explanation.
The additive inverse of -8 is 8.
I would saytThe additive inverse of a number is the number you add to it to get zero. For
-8, we need to find what number to add to make 0
(-8) + 8 = 0
So the additive inverse of -8 is 8. Zero is the 'additive identity' because when you add
zero to any number, that number stays the same. The additive inverse is the number
that 'cancels out' your original number to reach zero." (MIP1501 Study Guide, 2020, p.
18)
