MIP1501 Assignment 2
(COMPLETE ANSWERS)
Semester 1 2025 - DUE
3 July 2025;
NO PLAGIARIAM
[Pick the date]
[Type the company name]
, 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 at the Problem-Solving level as described by the CAPS curriculum,
learners are expected to apply higher-order thinking by modelling, interpreting, and working
backwards from the final result.
📌 Problem:
John had a few marbles.
Today he played and doubled his number of marbles.
Then Thabo gave him three marbles for free.
Now, John has 21 marbles.
How many did he have before he started playing?
✅ Step-by-step solution using a model (Working Backwards Strategy):
We will let John's original number of marbles be:
Let x = the number of marbles John had before playing
Then the problem tells us:
1. He doubles his marbles:
So now he has → 2 × x = 2x
2. Thabo gives him 3 more marbles:
So now he has → 2x + 3
3. Now he has 21 marbles:
So the equation becomes:
2x + 3 = 21
, 🧮 Solve the equation:
makefile
CopyEdit
2x + 3 = 21
2x = 21 - 3
2x = 18
x = 18 ÷ 2
x = 9
🎯 Answer:
John originally had 9 marbles before he started playing.
🧠 CAPS Problem-Solving Level Justification:
Non-routine: This problem cannot be solved with a basic operation; learners need to
analyse the situation.
Requires reasoning: Involves interpreting the word problem and constructing an
equation.
Involves working backwards, a key problem-solving strategy.
Encourages algebraic thinking: even at a primary level, this introduces unknowns and
equations.
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]
(COMPLETE ANSWERS)
Semester 1 2025 - DUE
3 July 2025;
NO PLAGIARIAM
[Pick the date]
[Type the company name]
, 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 at the Problem-Solving level as described by the CAPS curriculum,
learners are expected to apply higher-order thinking by modelling, interpreting, and working
backwards from the final result.
📌 Problem:
John had a few marbles.
Today he played and doubled his number of marbles.
Then Thabo gave him three marbles for free.
Now, John has 21 marbles.
How many did he have before he started playing?
✅ Step-by-step solution using a model (Working Backwards Strategy):
We will let John's original number of marbles be:
Let x = the number of marbles John had before playing
Then the problem tells us:
1. He doubles his marbles:
So now he has → 2 × x = 2x
2. Thabo gives him 3 more marbles:
So now he has → 2x + 3
3. Now he has 21 marbles:
So the equation becomes:
2x + 3 = 21
, 🧮 Solve the equation:
makefile
CopyEdit
2x + 3 = 21
2x = 21 - 3
2x = 18
x = 18 ÷ 2
x = 9
🎯 Answer:
John originally had 9 marbles before he started playing.
🧠 CAPS Problem-Solving Level Justification:
Non-routine: This problem cannot be solved with a basic operation; learners need to
analyse the situation.
Requires reasoning: Involves interpreting the word problem and constructing an
equation.
Involves working backwards, a key problem-solving strategy.
Encourages algebraic thinking: even at a primary level, this introduces unknowns and
equations.
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]
