TABLE OF CONTENTS
COVER PAGE PAGE 1
TABLE OF CONTENTS PAGE 2
ASSIGNMENT 4 PAGE 3- 8
BIBLIOGRAPHY PAGE 9
DECLARATION PAGE 10
, 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?
Rational numbers
1.2.2. What is the sum of 𝑚 and 𝑛?
0
1.2.3. Explain how you know the sum of 𝑚 and 𝑛 using a number line?
m and n are equal in absolute values. However n is negative value since it’s
on the left of the number line and m is positive. The sum of a positive and
negative of the same value of 0.
1.2.4. Explain how you know the sum of 𝑚 and 𝑛 symbolically/algebraically.
If m = x, therefore n = - x
m + n = x + (-x) = 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.
1) Sets of numbers and interval notation
In mathematics, a collection of elements is called a set. Several sets of
numbers are subsets (or part) of the set of real numbers. Several sets of
numbers are used extensively in algebra. Interval notation is a way of
writing subsets of real numbers as they would appear on a number line.
Note that the closed brackets [ ] are used for a closed interval, which
includes its endpoints, and the curved parentheses ( ) for open intervals,
where the endpoints are excluded. A set may have a combination of open
COVER PAGE PAGE 1
TABLE OF CONTENTS PAGE 2
ASSIGNMENT 4 PAGE 3- 8
BIBLIOGRAPHY PAGE 9
DECLARATION PAGE 10
, 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?
Rational numbers
1.2.2. What is the sum of 𝑚 and 𝑛?
0
1.2.3. Explain how you know the sum of 𝑚 and 𝑛 using a number line?
m and n are equal in absolute values. However n is negative value since it’s
on the left of the number line and m is positive. The sum of a positive and
negative of the same value of 0.
1.2.4. Explain how you know the sum of 𝑚 and 𝑛 symbolically/algebraically.
If m = x, therefore n = - x
m + n = x + (-x) = 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.
1) Sets of numbers and interval notation
In mathematics, a collection of elements is called a set. Several sets of
numbers are subsets (or part) of the set of real numbers. Several sets of
numbers are used extensively in algebra. Interval notation is a way of
writing subsets of real numbers as they would appear on a number line.
Note that the closed brackets [ ] are used for a closed interval, which
includes its endpoints, and the curved parentheses ( ) for open intervals,
where the endpoints are excluded. A set may have a combination of open
