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MIP1501 Assignment 4 COMPLETE ANSWERS) 2024 (835443 ) - DUE 18 August 2024
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Question 1 (30) 1.1. Explain in detail to an Intermediate Phase
learner the difference between real and non-real numbers, give
two examples for each. (8) 1.2. Explain in detail to an
Intermediate Phase learner the difference between rational and
irrational numbers, give two examples for each. (8) 1.3. Discuss
in detail so that an Intermediate Phase learner will understand
any four special facts to remember about the number zero. (8)
1.4. Briefly discuss the importance of absolute values so that
Grade 6 learners would understand why absolute values are
necessary, also give 2 examples. (6)
Here’s a breakdown of how to explain these mathematical
concepts to Intermediate Phase learners:
1.1. Difference Between Real and Non-Real Numbers (8 marks)
Explanation:
Real Numbers: Real numbers are numbers that can be
found on the number line. They include all the numbers
we use daily, like counting numbers, fractions, and
decimals.
o Examples: 7, -3, 2.5
Non-Real Numbers: These are numbers that cannot be
found on the number line. They often involve square roots
of negative numbers, which are called imaginary numbers.
, o Examples: √(-1), √(-4)
Intermediate Phase Language: “Imagine drawing a number
line. Real numbers are all the numbers you can place on that
line, like 2 or -3. But some numbers can’t be put on the line
because they involve the square root of negative numbers,
which are called non-real or imaginary numbers.”
1.2. Difference Between Rational and Irrational Numbers (8
marks)
Explanation:
Rational Numbers: Rational numbers are numbers that
can be written as a fraction where both the numerator and
denominator are integers (whole numbers). The
denominator cannot be zero.
o Examples: 1/2, 3, 0.75
Irrational Numbers: Irrational numbers cannot be written
as a simple fraction. Their decimal forms are non-repeating
and never-ending.
o Examples: √2, π (Pi)
Intermediate Phase Language: “A rational number is like when
you can break something down into a simple fraction or a
number with a repeating or ending decimal, like 0.5 (which is
the same as 1/2). An irrational number is when the decimals
keep going forever without repeating, like the number Pi (π).”
1.3. Four Special Facts About Zero (8 marks)
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