Lesson Notes By Weeks and Term v4 - JHS 3

Lesson Video

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Performance objectives

• Identify relationships between whole numbers, fractions, and decimals.
• Solve problems using addition, subtraction, multiplication, and division.
• Convert between fractions, decimals, and percentages.
• Apply these skills to solve real-life word problems.

Lesson summary

In our daily lives in Ghana, we use different kinds of numbers without even thinking about it. When we count the number of players on a football team, we use one type of number. When we buy waakye for GH₵ 7.50, that's another type. When we talk about a debt, we might think of a negative number. All these numbers belong to a very big family called the Real Number System. Understanding how these numbers relate to each other helps us solve complex problems in everything from market trading and construction to science and technology. This lesson will help us see the "family tree" of numbers and become experts at using them correctly.

Lesson notes

The Real Number System is like a large family with many smaller families inside it. Let's meet them one by one, from the smallest to the largest. a) The Number Sets Natural Numbers (N) These are the counting numbers we first learn as children. They are positive and do not include zero. Set: N = {1, 2, 3, 4, 5, ...} Ghanaian Example: The number of regions in Ghana is 16. The number of students in our class is a natural number. Whole Numbers (W) This family includes all the natural numbers, but they also welcome a special member: zero (0). Set: W = {0, 1, 2, 3, 4, ...} Ghanaian Example: If Hearts of Oak scores no goals in a match, their score is 0. Zero is a whole number. Integers (Z) This family includes all the whole numbers and their negative opposites. They are whole numbers that can be positive, negative, or zero. Set: Z = {..., -3, -2, -1, 0, 1, 2, 3, ...} Ghanaian Example: If you have GH₵ 10 and you owe a friend GH₵ 15, your financial situation can be represented as -5. This is an integer. The temperature at the top of Mount Afadja can be lower than on the ground, and temperatures can go below 0°C in other parts of the world. Rational Numbers (Q) This is a very large family. A number is rational if it can be written as a fraction p/q, where 'p' and 'q' are integers and 'q' is not zero. This includes: All integers (e.g., 5 can be written as 5/1). All terminating decimals (e.g., 0.75 = 3/4). All recurring decimals (e.g., 0.333... = 1/3). Ghanaian Example: The price of a bottle of Malt is GH₵ 3.50. This can be written as 7/2, so it is a rational number. If you share one loaf of bread among 4 friends, each gets 1/4, a rational number. Irrational Numbers (I or Q') These are the "strangers" in the number family. They cannot be written as a simple fraction p/q. Their decimal form goes on forever without repeating. Examples: π (Pi): Approximately 3.14159... Used to calculate the circumference of a circle. √2: The square root of 2, approximately 1.41421... Most square roots of non-perfect squares (e.g., √3, √5, √10). Ghanaian Example: If a carpenter is building a perfect square window frame with sides of 1 metre each, the length of the diagonal piece of wood needed would be √2 metres. This is an irrational number. Real Numbers (R) This is the "super family" that includes ALL rational and irrational numbers. Every number we have discussed so far is a Real Number. b) The Relationship: A Venn Diagram

A Venn diagram helps us see how these number sets are related. Think of them as boxes inside bigger boxes. The smallest box is Natural Numbers (N). This is inside the Whole Numbers (W) box (because W includes N and 0). This is inside the Integers (Z) box (because Z includes W and negatives). This is inside the Rational Numbers (Q) box (because Q includes Z, fractions, and decimals). Irrational Numbers (I) are in their own separate box. Both the Rational and Irrational boxes are inside the biggest box, the Real Numbers (R).