MIP 1502
Assignment 4
Unique number: 164979
Due date: 19 August 2022
QUESTION 1
1.1. Explain how to help learners develop algebraic reasoning in the Intermediate
Phase. Give examples to justify your thinking.
using problem-solving strategies (includes guess and check, guess and improve; act
it out and use equipment, etc.)
exploring multiple approaches and multiple solutions (diagram, arithmetic, etc.)
displaying relationships visually, symbolically, numerically and verbally (graphs,
variables, etc.)
translating among different representations (functions, schemes, graphs, etc.)
interpreting information within representations (formulas, graphs, etc.)
inductive and deductive reasoning (inductive proof, logic formulas, etc.)
generalizing patterns (graphs, tables, etc.)
providing justifications (i.e., proof).
1.2. On the number line below, the numbers 𝑚 and 𝑛 are the same distance from 0.
1.2.1 What are the numbers 𝑚 and 𝑛 called?
The numbers are called rational numbers.
1.2.2 What is the sum of 𝑚 and 𝑛?
The sum of 𝑚 and 𝑛 is zero.
1.2.3 Explain how you know the sum of 𝑚 and 𝑛 using a number line?
We are given that m and n are the same distance from zero. However, from the number
line below we can see that m and n are on different sides of zero. We can visualize this
by representing m and n as directed distances on the number line:
, m n
m n
m+n
1.2.4 Explain how you know the sum of 𝑚 and 𝑛 symbolically/algebraically
Since m and n are the same distance from zero but are on opposite sides of zero, we
know that they are opposites, so n=−m. The sum of a number and its opposite is always
zero.
m + n = m + (−m)
=m–m
=0
1.3. The entities in algebra can be distinguished, but they are deeply related to one
another. Discuss the three main entities that are used in algebra and clearly indicate
how these three entities relate to each other. Relate the first entity you listed to the
second and the third, and the first entity to the third entity as well.
The entities used in algebra are
i) projection- used to project required column data from a relation
ii)selection- used to select required tuples of the relations
iii)Union-A constraint of two relations having same set of attributes
QUESTION 2
2.1 Simphiwe bought meal tickets to use at the school’s cafeteria. Each meal requires 2
tickets, and she bought 14 tickets in total. She has already used some of the tickets,
and she still has some left.
2.1.1 Write four equivalent expressions that gives the number of tickets Simphiwe has
left in terms of 𝑥, where 𝑥 is the number of meals she has already bought.
14 – 2 x
2(7– x )
Assignment 4
Unique number: 164979
Due date: 19 August 2022
QUESTION 1
1.1. Explain how to help learners develop algebraic reasoning in the Intermediate
Phase. Give examples to justify your thinking.
using problem-solving strategies (includes guess and check, guess and improve; act
it out and use equipment, etc.)
exploring multiple approaches and multiple solutions (diagram, arithmetic, etc.)
displaying relationships visually, symbolically, numerically and verbally (graphs,
variables, etc.)
translating among different representations (functions, schemes, graphs, etc.)
interpreting information within representations (formulas, graphs, etc.)
inductive and deductive reasoning (inductive proof, logic formulas, etc.)
generalizing patterns (graphs, tables, etc.)
providing justifications (i.e., proof).
1.2. On the number line below, the numbers 𝑚 and 𝑛 are the same distance from 0.
1.2.1 What are the numbers 𝑚 and 𝑛 called?
The numbers are called rational numbers.
1.2.2 What is the sum of 𝑚 and 𝑛?
The sum of 𝑚 and 𝑛 is zero.
1.2.3 Explain how you know the sum of 𝑚 and 𝑛 using a number line?
We are given that m and n are the same distance from zero. However, from the number
line below we can see that m and n are on different sides of zero. We can visualize this
by representing m and n as directed distances on the number line:
, m n
m n
m+n
1.2.4 Explain how you know the sum of 𝑚 and 𝑛 symbolically/algebraically
Since m and n are the same distance from zero but are on opposite sides of zero, we
know that they are opposites, so n=−m. The sum of a number and its opposite is always
zero.
m + n = m + (−m)
=m–m
=0
1.3. The entities in algebra can be distinguished, but they are deeply related to one
another. Discuss the three main entities that are used in algebra and clearly indicate
how these three entities relate to each other. Relate the first entity you listed to the
second and the third, and the first entity to the third entity as well.
The entities used in algebra are
i) projection- used to project required column data from a relation
ii)selection- used to select required tuples of the relations
iii)Union-A constraint of two relations having same set of attributes
QUESTION 2
2.1 Simphiwe bought meal tickets to use at the school’s cafeteria. Each meal requires 2
tickets, and she bought 14 tickets in total. She has already used some of the tickets,
and she still has some left.
2.1.1 Write four equivalent expressions that gives the number of tickets Simphiwe has
left in terms of 𝑥, where 𝑥 is the number of meals she has already bought.
14 – 2 x
2(7– x )
