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MIP1501 Assignment 2
(COMPLETE ANSWERS)
Semester 1 2025 - DUE 3
July 2025;
NO PLAGIARIAM
[Pick the date]
[Type the abstract of the document here. The abstract is typically a short summary of the contents of
the document. Type the abstract of the document here. The abstract is typically a short summary of
the contents of the document.]
, Course
Mathematics for Intermediate Phase teachers I
Book
Teaching Mathematics
MIP1501 Assignment 2 (COMPLETE ANSWERS) Semester 1 2025 - DUE 3 July
2025; 100% correct solutions and explanations
.Question 1 (36) 1.1. The following task example illustrate the Problem-
Solving level according to CAPS: 1.1.1. John had a few marbles. Today he
played and doubled his number of marbles. Then Thabo gave him three
marbles for free. Jabu has 21 marbles now. How many did he have before he
started playing? Solve this problem using a suitable model. (6)
To solve this problem using a suitable model (such as a bar model or equation), we can apply
algebraic reasoning to work backward from the total number of marbles John has now. The
problem falls under the Problem-Solving level in CAPS because it requires learners to analyze
the situation and apply logic, rather than follow a straightforward procedure.
Given:
After doubling his marbles, John received 3 more from Thabo.
Now he has 21 marbles.
We are to find how many marbles John had originally.
Step-by-Step Solution using an Equation (algebraic model):
Let the number of marbles John had before playing be x.
After doubling them:
👉 He has 2x marbles.
Thabo gives him 3 marbles:
👉 Total becomes 2x + 3.
We're told that he ends up with 21 marbles:
2x+3=212x + 3 = 212x+3=21
Solving the equation:
, 2x+3=21⇒2x=21−3⇒2x=18⇒x=92x + 3 = 21 \Rightarrow 2x = 21 - 3 \Rightarrow 2x = 18 \
Rightarrow x = 92x+3=21⇒2x=21−3⇒2x=18⇒x=9
✅ Answer:
John originally had 9 marbles before he started playing.
💡 CAPS Alignment:
This task demonstrates the Problem-Solving level in the CAPS document because:
It involves a real-life context.
The numbers are not immediately obvious, requiring learners to reason backward.
It encourages learners to use algebraic models or drawings (e.g., bar diagrams) to
represent relationships between numbers.
To solve this problem, we can use a bar model (also known as a tape diagram) or an algebraic
equation. Both are suitable models for this type of problem-solving.
Using a Bar Model
Let's represent the unknown number of marbles John had initially with a bar.
1. "John had a few marbles." [Unknown amount of marbles]
2. "Today he played and doubled his number of marbles." [Unknown amount of
marbles] [Unknown amount of marbles]
3. "Then Thabo gave him three marbles for free." [Unknown amount of marbles]
[Unknown amount of marbles] [+3 marbles]
4. "Jabu has 21 marbles now." The total length of the bar model now represents 21
marbles. [Unknown amount of marbles] [Unknown amount of marbles] [+3 marbles] =
21 marbles
Now, we work backward:
Subtract the marbles Thabo gave him: 21−3=18 marbles This means the doubled
amount of marbles was 18. [Unknown amount of marbles] [Unknown amount of
marbles] = 18 marbles
MIP1501 Assignment 2
(COMPLETE ANSWERS)
Semester 1 2025 - DUE 3
July 2025;
NO PLAGIARIAM
[Pick the date]
[Type the abstract of the document here. The abstract is typically a short summary of the contents of
the document. Type the abstract of the document here. The abstract is typically a short summary of
the contents of the document.]
, Course
Mathematics for Intermediate Phase teachers I
Book
Teaching Mathematics
MIP1501 Assignment 2 (COMPLETE ANSWERS) Semester 1 2025 - DUE 3 July
2025; 100% correct solutions and explanations
.Question 1 (36) 1.1. The following task example illustrate the Problem-
Solving level according to CAPS: 1.1.1. John had a few marbles. Today he
played and doubled his number of marbles. Then Thabo gave him three
marbles for free. Jabu has 21 marbles now. How many did he have before he
started playing? Solve this problem using a suitable model. (6)
To solve this problem using a suitable model (such as a bar model or equation), we can apply
algebraic reasoning to work backward from the total number of marbles John has now. The
problem falls under the Problem-Solving level in CAPS because it requires learners to analyze
the situation and apply logic, rather than follow a straightforward procedure.
Given:
After doubling his marbles, John received 3 more from Thabo.
Now he has 21 marbles.
We are to find how many marbles John had originally.
Step-by-Step Solution using an Equation (algebraic model):
Let the number of marbles John had before playing be x.
After doubling them:
👉 He has 2x marbles.
Thabo gives him 3 marbles:
👉 Total becomes 2x + 3.
We're told that he ends up with 21 marbles:
2x+3=212x + 3 = 212x+3=21
Solving the equation:
, 2x+3=21⇒2x=21−3⇒2x=18⇒x=92x + 3 = 21 \Rightarrow 2x = 21 - 3 \Rightarrow 2x = 18 \
Rightarrow x = 92x+3=21⇒2x=21−3⇒2x=18⇒x=9
✅ Answer:
John originally had 9 marbles before he started playing.
💡 CAPS Alignment:
This task demonstrates the Problem-Solving level in the CAPS document because:
It involves a real-life context.
The numbers are not immediately obvious, requiring learners to reason backward.
It encourages learners to use algebraic models or drawings (e.g., bar diagrams) to
represent relationships between numbers.
To solve this problem, we can use a bar model (also known as a tape diagram) or an algebraic
equation. Both are suitable models for this type of problem-solving.
Using a Bar Model
Let's represent the unknown number of marbles John had initially with a bar.
1. "John had a few marbles." [Unknown amount of marbles]
2. "Today he played and doubled his number of marbles." [Unknown amount of
marbles] [Unknown amount of marbles]
3. "Then Thabo gave him three marbles for free." [Unknown amount of marbles]
[Unknown amount of marbles] [+3 marbles]
4. "Jabu has 21 marbles now." The total length of the bar model now represents 21
marbles. [Unknown amount of marbles] [Unknown amount of marbles] [+3 marbles] =
21 marbles
Now, we work backward:
Subtract the marbles Thabo gave him: 21−3=18 marbles This means the doubled
amount of marbles was 18. [Unknown amount of marbles] [Unknown amount of
marbles] = 18 marbles
