Basic 9 Mathematics Term 1 Week 7 Lesson Plan

Display the following numbers on the board: √3, √18, √2, √50. Ask learners, "What do these numbers have in common, and how might they be different from each other?" Share performance indicators and introduce the lesson.

Concrete-resource task: Set out these resources for each group: Number cards; Square-grid paper; Calculator. Learners manipulate the items to model the numbers or relationships and record or check their working during the task below. Briefly discuss what surds are (numbers that can't be simplified to remove a square root). Explain the terminology: the number under the square root sign is called the 'radicand'. Define a simple surd as a square root whose radicand cannot be further simplified. Provide examples, such as √2 or √3, and explain why these are simple surds (because they don't have factors which are perfect squares, apart from 1). Define a compound surd as a square root whose radicand can be simplified further by factoring out perfect squares. Use examples to illustrate. For instance, √18 can be written as √(9x2) or 3√2. Guide learners through the process of simplifying a few compound surds. Example: Simplify the compound surd: √72. Solution To simplify the compound surd √72, you can simplify it as follows: √72 = √(36 * 2) Now, simplify the square root of 36, which is 6: √(6 * 2) = 6√2 So, the simplified form of √72 is 6√2. Distribute a set of cards to each student or small groups, where each card has a surd written on it. Example: √50, √18, √98, √54, √75, etc. Ask learners to sort these cards into two piles: simple surds and compound surds. After sorting, encourage learners to pick a compound surd and simplify it. Example: Simplify √162 solution √162 = √(9 * 18) We can start by factoring 162 as = √9=3 and √18=(9*2) = 3*3√2 So, the simplified form of √162 is 9√2 Assessment 1. Simplify the compound surd: √72. 2. Is √5 a simple or compound surd? Explain your answer. 3. Simplify √45. 4. Simplify √80. 5. Simplify √28. 6. Simplify √63. 7. Simplify √112. 8. Simplify √200.

Use peer discussion and effective questioning to find out from learners what they have learnt during the lesson

Display the following expressions on the board: √4, √9, √16, and √25

Learners use the Number cards to form examples such as √2, 3√5 and √3 + √7 and place them into simple-surd and compound-surd groups. They use the Square-grid paper to record the defining features and justify each classification. The Calculator is used only to check that the roots are non-perfect and not to replace exact surd notation. Groups create two new examples for peers to classify; rules for simplifying and rationalising are reserved for the next component.

Take feedback from learners and summarize the lesson.

Ask learners, "What do you notice about these numbers, and how can you describe this pattern?" Share performance indicators and introduce the lesson.

Concrete-resource task: Set out these resources for each group: Number cards; Square-grid paper; Calculator. Learners manipulate the items to model the numbers or relationships and record or check their working during the task below. Solution: 2 / (1 + √5) = 2 / (1 + √5) * (1 - √5) / (1 - √5) = (2 * (1 - √5)) / (1^2 - (√5)^2) = (2 - 2√5) / (1 - 5) = (2 - 2√5) / -4 = -(1/2) + (1/2)√5 c c a+b√n = * Identity: Rule 6 - : a−b√n a−b√n a+b√n Introduce Rule 6, explaining that it's used for rationalizing the denominator when the denominator contains a difference. Walk through the steps: c/(a-b√n) = c/(a-b√n) * (a+b√n)/(a+b√n). Provide examples and let students practice Example 1: Rationalize the denominator in the expression 3 / (2 - √3) Solution: 3 / (2 - √3) = 3 / (2 - √3) * (2 + √3) / (2 + √3) = (3 * (2 + √3)) / (2^2 - (√3)^2) = (6 + 3√3) / (4 - 3) = (6 + 3√3) / 1 = 6 + 3√3 Example 2: Rationalize the denominator in the expression 4 / (1 - √2). Solution: 4 / (1 - √2) = 4 / (1 - √2) * (1 + √2) / (1 + √2) = (4 * (1 + √2)) / (1^2 - (√2)^2) = (4 + 4√2) / (1 - 2) = (4 + 4√2) / -1 = -4 - 4√2 Provide learners with a set of surd expressions to simplify using the rules discussed. Encourage group work and peer learning. Allow learners to check their work collaboratively. assessment 1. Apply the product rule to simplify √2 * √8. 2. Use the quotient rule to simplify √15 / √5. 3. Rationalize the denominator in the expression 1 / √2. 4. Simplify the expression 4√7 / √2 using the surd rules. 5. What is the result of applying Rule 4 to 5√3 + 2√3? 6. Use Rule 5 to rationalize the denominator in the expression 7 / (1 + √5). 7. Apply Rule 6 to rationalize the denominator in 3 / (2 - √6).

Use peer discussion and effective questioning to find out from learners what they have learnt during the lesson. Take feedback from learners and summarize the lesson.