MIP1502
Assignment 2 2024
Detailed Solutions, References & Explanations
Unique number: 351863
Due Date: 10 June 2024
QUESTION 1
The concept of equality is foundational in mathematics, and it is crucial for primary school
teachers to emphasize this when students begin using symbols for number operations.
Understanding equality ensures that students grasp the concept that both sides of an
equation represent the same value, which is pivotal for their future success in algebra and
higher mathematics.
Firstly, an early understanding of equality helps students transition from arithmetic to
algebra. For example, when students see the equation (15 - x = 11), they need to
understand that the expression on the left (15 minus some number) is equal to the number
on the right (11). This lays the groundwork for solving for (x) by recognizing that (x = 4). If
students do not understand that both sides of the equation must be balanced or equal, they
might struggle with the abstraction required in algebra.
Terms of use
By making use of this document you agree to:
• Use this document as a guide for learning, comparison and reference purpose,
• Not to duplicate, reproduce and/or misrepresent the contents of this document as your own work,
• Fully accept the consequences should you plagiarise or misuse this document.
Disclaimer
Extreme care has been used to create this document, however the contents are provided “as is” without
any representations or warranties, express or implied. The author assumes no liability as a result of
reliance and use of the contents of this document. This document is to be used for comparison, research
and reference purposes ONLY. No part of this document may be reproduced, resold or transmitted in any
form or by any means.
, +27 67 171 1739
QUESTION 1
The concept of equality is foundational in mathematics, and it is crucial for primary
school teachers to emphasize this when students begin using symbols for number
operations. Understanding equality ensures that students grasp the concept that both
sides of an equation represent the same value, which is pivotal for their future success
in algebra and higher mathematics.
Firstly, an early understanding of equality helps students transition from arithmetic to
algebra. For example, when students see the equation (15 - x = 11), they need to
understand that the expression on the left (15 minus some number) is equal to the
number on the right (11). This lays the groundwork for solving for (x) by recognizing
that (x = 4). If students do not understand that both sides of the equation must be
balanced or equal, they might struggle with the abstraction required in algebra.
Secondly, equality underpins many concepts in mathematics beyond simple
operations. For instance, in geometry, the equality of two angles or sides of a shape
is crucial. In this context, failure to understand equality as a fundamental principle can
lead to misconceptions in broader areas of mathematics.
For a practical classroom example, consider the equation (3 + 4 = 7) and the equation
(7 = 3 + 4). Elementary students must recognize that these are just different ways of
showing the same relationship. Demonstrating this with physical objects, such as
counters or blocks, can help. For instance, placing 3 blocks on one side and 4 on the
other while physically combining them to show 7 blocks reinforces that the side by side
representation (3 + 4) and the total number of blocks (7) are indeed equal.
Another example is building on number patterns. By recognizing and continuing
patterns such as 2, 4, 6, 8, students can begin to understand algebraic rules like (n =
2n), where each term equals the previous term times two. This fosters algebraic
thinking and builds the important bridge from numbers to symbols.
Lastly, equality is vital for understanding operations in other math concepts such as
fractions, where students need to comprehend statements like 1/2 = 2/4 to perform
equivalence and simplification.
Disclaimer
Extreme care has been used to create this document, however the contents are provided “as is” without
any representations or warranties, express or implied. The author assumes no liability as a result of
reliance and use of the contents of this document. This document is to be used for comparison, research
and reference purposes ONLY. No part of this document may be reproduced, resold or transmitted in any
form or by any means.
, +27 67 171 1739
In conclusion, the early emphasis on equality assists students in making the critical
transition from concrete arithmetic operations to abstract algebraic reasoning. It
fosters a deep understanding of mathematical relationships and prepares them for
more complex concepts. By ensuring students grasp equality, teachers lay a strong
foundation for all future mathematical learning.
OR
Mathematics teachers in primary school must be concerned with the concept of
equality as soon as learners start writing symbols for number operations because
understanding the concept of equality is foundational to many mathematical concepts.
It is important for students to grasp the idea that the two sides of an equation are equal
from an early age in order to build a strong understanding of algebraic thinking.
For example, when a learner is asked to solve the equation 15 - n = 11, they must
understand that they need to find the value of 'n' that makes the equation true.
Similarly, when solving the equation n + 4 = 12, learners need to understand that they
must find the value of 'n' that makes the equation balanced. These simple equations
introduce the concept of equality and the idea that the left side of the equation must
be equal to the right side.
Understanding the concept of equality is crucial for students as they progress through
their mathematical education. It forms the basis for solving equations, working with
algebraic expressions, and developing problem-solving skills. Therefore, it is vital for
primary school mathematics teachers to ensure that learners have a solid
understanding of equality from the beginning of their mathematical journey.
QUESTION 2
2.1.1.
Let x be the amount Nomasizwe needs.
Disclaimer
Extreme care has been used to create this document, however the contents are provided “as is” without
any representations or warranties, express or implied. The author assumes no liability as a result of
reliance and use of the contents of this document. This document is to be used for comparison, research
and reference purposes ONLY. No part of this document may be reproduced, resold or transmitted in any
form or by any means.
Assignment 2 2024
Detailed Solutions, References & Explanations
Unique number: 351863
Due Date: 10 June 2024
QUESTION 1
The concept of equality is foundational in mathematics, and it is crucial for primary school
teachers to emphasize this when students begin using symbols for number operations.
Understanding equality ensures that students grasp the concept that both sides of an
equation represent the same value, which is pivotal for their future success in algebra and
higher mathematics.
Firstly, an early understanding of equality helps students transition from arithmetic to
algebra. For example, when students see the equation (15 - x = 11), they need to
understand that the expression on the left (15 minus some number) is equal to the number
on the right (11). This lays the groundwork for solving for (x) by recognizing that (x = 4). If
students do not understand that both sides of the equation must be balanced or equal, they
might struggle with the abstraction required in algebra.
Terms of use
By making use of this document you agree to:
• Use this document as a guide for learning, comparison and reference purpose,
• Not to duplicate, reproduce and/or misrepresent the contents of this document as your own work,
• Fully accept the consequences should you plagiarise or misuse this document.
Disclaimer
Extreme care has been used to create this document, however the contents are provided “as is” without
any representations or warranties, express or implied. The author assumes no liability as a result of
reliance and use of the contents of this document. This document is to be used for comparison, research
and reference purposes ONLY. No part of this document may be reproduced, resold or transmitted in any
form or by any means.
, +27 67 171 1739
QUESTION 1
The concept of equality is foundational in mathematics, and it is crucial for primary
school teachers to emphasize this when students begin using symbols for number
operations. Understanding equality ensures that students grasp the concept that both
sides of an equation represent the same value, which is pivotal for their future success
in algebra and higher mathematics.
Firstly, an early understanding of equality helps students transition from arithmetic to
algebra. For example, when students see the equation (15 - x = 11), they need to
understand that the expression on the left (15 minus some number) is equal to the
number on the right (11). This lays the groundwork for solving for (x) by recognizing
that (x = 4). If students do not understand that both sides of the equation must be
balanced or equal, they might struggle with the abstraction required in algebra.
Secondly, equality underpins many concepts in mathematics beyond simple
operations. For instance, in geometry, the equality of two angles or sides of a shape
is crucial. In this context, failure to understand equality as a fundamental principle can
lead to misconceptions in broader areas of mathematics.
For a practical classroom example, consider the equation (3 + 4 = 7) and the equation
(7 = 3 + 4). Elementary students must recognize that these are just different ways of
showing the same relationship. Demonstrating this with physical objects, such as
counters or blocks, can help. For instance, placing 3 blocks on one side and 4 on the
other while physically combining them to show 7 blocks reinforces that the side by side
representation (3 + 4) and the total number of blocks (7) are indeed equal.
Another example is building on number patterns. By recognizing and continuing
patterns such as 2, 4, 6, 8, students can begin to understand algebraic rules like (n =
2n), where each term equals the previous term times two. This fosters algebraic
thinking and builds the important bridge from numbers to symbols.
Lastly, equality is vital for understanding operations in other math concepts such as
fractions, where students need to comprehend statements like 1/2 = 2/4 to perform
equivalence and simplification.
Disclaimer
Extreme care has been used to create this document, however the contents are provided “as is” without
any representations or warranties, express or implied. The author assumes no liability as a result of
reliance and use of the contents of this document. This document is to be used for comparison, research
and reference purposes ONLY. No part of this document may be reproduced, resold or transmitted in any
form or by any means.
, +27 67 171 1739
In conclusion, the early emphasis on equality assists students in making the critical
transition from concrete arithmetic operations to abstract algebraic reasoning. It
fosters a deep understanding of mathematical relationships and prepares them for
more complex concepts. By ensuring students grasp equality, teachers lay a strong
foundation for all future mathematical learning.
OR
Mathematics teachers in primary school must be concerned with the concept of
equality as soon as learners start writing symbols for number operations because
understanding the concept of equality is foundational to many mathematical concepts.
It is important for students to grasp the idea that the two sides of an equation are equal
from an early age in order to build a strong understanding of algebraic thinking.
For example, when a learner is asked to solve the equation 15 - n = 11, they must
understand that they need to find the value of 'n' that makes the equation true.
Similarly, when solving the equation n + 4 = 12, learners need to understand that they
must find the value of 'n' that makes the equation balanced. These simple equations
introduce the concept of equality and the idea that the left side of the equation must
be equal to the right side.
Understanding the concept of equality is crucial for students as they progress through
their mathematical education. It forms the basis for solving equations, working with
algebraic expressions, and developing problem-solving skills. Therefore, it is vital for
primary school mathematics teachers to ensure that learners have a solid
understanding of equality from the beginning of their mathematical journey.
QUESTION 2
2.1.1.
Let x be the amount Nomasizwe needs.
Disclaimer
Extreme care has been used to create this document, however the contents are provided “as is” without
any representations or warranties, express or implied. The author assumes no liability as a result of
reliance and use of the contents of this document. This document is to be used for comparison, research
and reference purposes ONLY. No part of this document may be reproduced, resold or transmitted in any
form or by any means.
