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ACI2605 Assignment 3 (Answer Guide) - Due 3 July 2025
QUESTIONS WITH 100% VERIFIED AND CERTIFIED ANSWERS. WRITTEN IN
REQUIRED FORMAT AND WITHIN GIVEN GUIDELINES. IT IS GOOD TO USE AS A
GUIDE AND FOR REFERENCE, NEVER PLAGARIZE. Thank you and success in
your academics.
UNISA, 2025.
Contents
QUESTION 1: The History of Numbers ................................................................................... 2
1.1.1 The Binary Number System ....................................................................................................... 2
1.1.2 The Decimal Number System .................................................................................................... 3
References .............................................................................................................................................. 5
QUESTION 2: Unit - Rate ......................................................................................................... 5
2.1.1 Write an equation that represents the relationship between the number of minutes m of
the morning drive and the total number of minutes t that the bus driver spends picking up and
dropping off students each day (5 marks) .......................................................................................... 6
2.1.2 Using the unit rate, graph the equation on a coordinate plane. On your graph, should the
points be connected to make a line? Explain (5 marks)................................................................... 6
2.1.3 Write a paragraph with 5 guidelines for teachers on setting up scenarios for introducing
the unit rate concept for intermediate phase learning (10 marks) .................................................. 7
References .............................................................................................................................................. 8
QUESTION 3: Number Sense .................................................................................................. 8
3.1 Describe four components that characterise number sense, with examples (8 marks) ....... 8
3.2.1 Write a report detailing 6 guidelines to take into consideration when teaching number
sense (6 marks) ...................................................................................................................................... 9
3.2.2 Classify the teaching approach underpinning the guidelines in 3.2.1 (3 marks) .............. 10
3.2.3 Explain the advantages of this teaching approach (6 marks) ............................................. 10
3.2.4 What are the disadvantages of this teaching approach? (5 marks) ................................... 11
3.3 Set up a real-life scenario of a number sense concept (3 marks) ......................................... 11
3.3.1 Describe the situation and the pattern or function which is developing (3 marks) ....... 11
3.3.2 Represent the function in a table form (3 marks) .............................................................. 12
3.3.3 Provide a solution to the function in 3.3.2 (3 marks)......................................................... 12
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References ............................................................................................................................................ 12
QUESTION 4: Application of Higher-Order Problem-Solving Skills (20 marks) ..................13
4.1 In a school, 50% of the students are younger than 10, 1/20 are 10 years old, and 1/10 are
older than 10 but younger than 12. The remaining 70 students are 12 years or older. How
many students are 10 years old? (5 marks) ..................................................................................... 13
4.2 In the rectangle below, the line MN cuts the rectangle into two regions. Find x (the length
of segment NB) so that the area of quadrilateral MNBC is 40% of the total area of the
rectangle. (5 marks) ............................................................................................................................. 14
4.3 In a school cafeteria, 4 students can sit together at one table. If two tables are placed, 6
people can sit together: ....................................................................................................................... 15
4.4 Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her R800,
what were her original savings? (5 marks) ....................................................................................... 16
References ............................................................................................................................................ 17
QUESTION 1: The History of Numbers
Steen (1988:611-6) regards mathematics as the science of patterns, explaining that
mathematicians seek and analyze patterns in various domains (numbers, space,
science, computers, imagination) and that mathematical theories connect these patterns
via functions, maps, and morphisms to produce structured and lasting knowledge.
You are asked to:
1.1 Provide a critical analysis of Steen’s (1988) definition of mathematics in relation to:
• 1.1.1 The binary number system (10 marks)
• 1.1.2 The decimal number system (10 marks)
1.1.1 The Binary Number System
Steen’s (1988) conceptualization of mathematics as a science of patterns can be
critically analyzed in relation to the binary number system, which is fundamental to
computer science and digital technology.
Analysis:
ACI2605 Assignment 3 (Answer Guide) - Due 3 July 2025
QUESTIONS WITH 100% VERIFIED AND CERTIFIED ANSWERS. WRITTEN IN
REQUIRED FORMAT AND WITHIN GIVEN GUIDELINES. IT IS GOOD TO USE AS A
GUIDE AND FOR REFERENCE, NEVER PLAGARIZE. Thank you and success in
your academics.
UNISA, 2025.
Contents
QUESTION 1: The History of Numbers ................................................................................... 2
1.1.1 The Binary Number System ....................................................................................................... 2
1.1.2 The Decimal Number System .................................................................................................... 3
References .............................................................................................................................................. 5
QUESTION 2: Unit - Rate ......................................................................................................... 5
2.1.1 Write an equation that represents the relationship between the number of minutes m of
the morning drive and the total number of minutes t that the bus driver spends picking up and
dropping off students each day (5 marks) .......................................................................................... 6
2.1.2 Using the unit rate, graph the equation on a coordinate plane. On your graph, should the
points be connected to make a line? Explain (5 marks)................................................................... 6
2.1.3 Write a paragraph with 5 guidelines for teachers on setting up scenarios for introducing
the unit rate concept for intermediate phase learning (10 marks) .................................................. 7
References .............................................................................................................................................. 8
QUESTION 3: Number Sense .................................................................................................. 8
3.1 Describe four components that characterise number sense, with examples (8 marks) ....... 8
3.2.1 Write a report detailing 6 guidelines to take into consideration when teaching number
sense (6 marks) ...................................................................................................................................... 9
3.2.2 Classify the teaching approach underpinning the guidelines in 3.2.1 (3 marks) .............. 10
3.2.3 Explain the advantages of this teaching approach (6 marks) ............................................. 10
3.2.4 What are the disadvantages of this teaching approach? (5 marks) ................................... 11
3.3 Set up a real-life scenario of a number sense concept (3 marks) ......................................... 11
3.3.1 Describe the situation and the pattern or function which is developing (3 marks) ....... 11
3.3.2 Represent the function in a table form (3 marks) .............................................................. 12
3.3.3 Provide a solution to the function in 3.3.2 (3 marks)......................................................... 12
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References ............................................................................................................................................ 12
QUESTION 4: Application of Higher-Order Problem-Solving Skills (20 marks) ..................13
4.1 In a school, 50% of the students are younger than 10, 1/20 are 10 years old, and 1/10 are
older than 10 but younger than 12. The remaining 70 students are 12 years or older. How
many students are 10 years old? (5 marks) ..................................................................................... 13
4.2 In the rectangle below, the line MN cuts the rectangle into two regions. Find x (the length
of segment NB) so that the area of quadrilateral MNBC is 40% of the total area of the
rectangle. (5 marks) ............................................................................................................................. 14
4.3 In a school cafeteria, 4 students can sit together at one table. If two tables are placed, 6
people can sit together: ....................................................................................................................... 15
4.4 Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her R800,
what were her original savings? (5 marks) ....................................................................................... 16
References ............................................................................................................................................ 17
QUESTION 1: The History of Numbers
Steen (1988:611-6) regards mathematics as the science of patterns, explaining that
mathematicians seek and analyze patterns in various domains (numbers, space,
science, computers, imagination) and that mathematical theories connect these patterns
via functions, maps, and morphisms to produce structured and lasting knowledge.
You are asked to:
1.1 Provide a critical analysis of Steen’s (1988) definition of mathematics in relation to:
• 1.1.1 The binary number system (10 marks)
• 1.1.2 The decimal number system (10 marks)
1.1.1 The Binary Number System
Steen’s (1988) conceptualization of mathematics as a science of patterns can be
critically analyzed in relation to the binary number system, which is fundamental to
computer science and digital technology.
Analysis:
