MIP1501
ASSIGNMENT 02
Unique No: 178117
Due 3 July 2025
,MIP1501
ASSIGNMENT 02
UNIQUE NUMBER 178117
Closing date: 03 July 2025
Question 1
1.1 Problem-Solving Task: Marbles Problem
Problem Statement
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.
Solution Using a Model
To address this problem, a backward-working strategy is employed, as it aligns with the
problem-solving level outlined in the Curriculum and Assessment Policy Statement (CAPS)
for the Intermediate Phase. This approach is effective for teaching learners to reverse
operations systematically.
• Step 1: Define the Variable
Let ( x ) represent the initial number of marbles John had. After doubling, he has (
2x ) marbles. Thabo then gives him 3 marbles, resulting in
2𝑥 + 3
. 𝑇ℎ𝑒 𝑝𝑟𝑜𝑏𝑙𝑒𝑚 𝑠𝑡𝑎𝑡𝑒𝑠 𝑡ℎ𝑎𝑡 𝐽𝑜ℎ𝑛 𝑛𝑜𝑤 ℎ𝑎𝑠 21 𝑚𝑎𝑟𝑏𝑙𝑒𝑠, 𝑠𝑜:
2𝑥 + 3 = 21
• 𝑆𝑡𝑒𝑝 2: 𝑆𝑜𝑙𝑣𝑒 𝑡ℎ𝑒 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛
𝑆𝑢𝑏𝑡𝑟𝑎𝑐𝑡3𝑓𝑟𝑜𝑚𝑏𝑜𝑡ℎ𝑠𝑖𝑑𝑒𝑠𝑡𝑜𝑖𝑠𝑜𝑙𝑎𝑡𝑒𝑡ℎ𝑒𝑡𝑒𝑟𝑚𝑤𝑖𝑡ℎ(𝑥):
2𝑥 + 3 − 3 = 21 − 3 \𝑖𝑚𝑝𝑙𝑖𝑒𝑠 2𝑥 = 18
, 𝐷𝑖𝑣𝑖𝑑𝑒 𝑏𝑜𝑡ℎ 𝑠𝑖𝑑𝑒𝑠 𝑏𝑦 2:
18
𝑥= =9
2
Thus, John initially had 9 marbles.
• Step 3: Model Representation
To teach this to Intermediate Phase learners, a bar model (a visual tool emphasized
in CAPS) can be used:
• Draw a bar representing the final 21 marbles.
• Subtract a segment for the 3 marbles given by Thabo, leaving 18 marbles.
• Divide the remaining bar into two equal parts (since the marbles were
doubled), each representing ( x ). Since
18 ÷ 2 = 9
, 𝑒𝑎𝑐ℎ 𝑝𝑎𝑟𝑡 𝑖𝑠 9 𝑚𝑎𝑟𝑏𝑙𝑒𝑠.
This visual aids learners in understanding the inverse operations (Van de Walle et al.,
2019).
• Step 4: Verification
If John started with 9 marbles, doubling gives
2 × 9 = 18
, 𝑎𝑛𝑑 𝑎𝑑𝑑𝑖𝑛𝑔 3 𝑔𝑖𝑣𝑒𝑠
18 + 3 = 21
, which matches the problem.
Final Answer: John had 9 marbles before playing.
ASSIGNMENT 02
Unique No: 178117
Due 3 July 2025
,MIP1501
ASSIGNMENT 02
UNIQUE NUMBER 178117
Closing date: 03 July 2025
Question 1
1.1 Problem-Solving Task: Marbles Problem
Problem Statement
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.
Solution Using a Model
To address this problem, a backward-working strategy is employed, as it aligns with the
problem-solving level outlined in the Curriculum and Assessment Policy Statement (CAPS)
for the Intermediate Phase. This approach is effective for teaching learners to reverse
operations systematically.
• Step 1: Define the Variable
Let ( x ) represent the initial number of marbles John had. After doubling, he has (
2x ) marbles. Thabo then gives him 3 marbles, resulting in
2𝑥 + 3
. 𝑇ℎ𝑒 𝑝𝑟𝑜𝑏𝑙𝑒𝑚 𝑠𝑡𝑎𝑡𝑒𝑠 𝑡ℎ𝑎𝑡 𝐽𝑜ℎ𝑛 𝑛𝑜𝑤 ℎ𝑎𝑠 21 𝑚𝑎𝑟𝑏𝑙𝑒𝑠, 𝑠𝑜:
2𝑥 + 3 = 21
• 𝑆𝑡𝑒𝑝 2: 𝑆𝑜𝑙𝑣𝑒 𝑡ℎ𝑒 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛
𝑆𝑢𝑏𝑡𝑟𝑎𝑐𝑡3𝑓𝑟𝑜𝑚𝑏𝑜𝑡ℎ𝑠𝑖𝑑𝑒𝑠𝑡𝑜𝑖𝑠𝑜𝑙𝑎𝑡𝑒𝑡ℎ𝑒𝑡𝑒𝑟𝑚𝑤𝑖𝑡ℎ(𝑥):
2𝑥 + 3 − 3 = 21 − 3 \𝑖𝑚𝑝𝑙𝑖𝑒𝑠 2𝑥 = 18
, 𝐷𝑖𝑣𝑖𝑑𝑒 𝑏𝑜𝑡ℎ 𝑠𝑖𝑑𝑒𝑠 𝑏𝑦 2:
18
𝑥= =9
2
Thus, John initially had 9 marbles.
• Step 3: Model Representation
To teach this to Intermediate Phase learners, a bar model (a visual tool emphasized
in CAPS) can be used:
• Draw a bar representing the final 21 marbles.
• Subtract a segment for the 3 marbles given by Thabo, leaving 18 marbles.
• Divide the remaining bar into two equal parts (since the marbles were
doubled), each representing ( x ). Since
18 ÷ 2 = 9
, 𝑒𝑎𝑐ℎ 𝑝𝑎𝑟𝑡 𝑖𝑠 9 𝑚𝑎𝑟𝑏𝑙𝑒𝑠.
This visual aids learners in understanding the inverse operations (Van de Walle et al.,
2019).
• Step 4: Verification
If John started with 9 marbles, doubling gives
2 × 9 = 18
, 𝑎𝑛𝑑 𝑎𝑑𝑑𝑖𝑛𝑔 3 𝑔𝑖𝑣𝑒𝑠
18 + 3 = 21
, which matches the problem.
Final Answer: John had 9 marbles before playing.
