Basic 8 Mathematics Term 1 Week 10 Lesson Plan

Revise with learners on the previous 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. The laws of indices are a set of rules that govern how we can manipulate expressions involving powers of numbers. These rules are: 1. Product rule: am * an = a(m+n) This rule tells us that when we multiply two numbers with the same base, we can add their exponents to get the exponent of the result. Example: 23 x 24 = 2(3+4) = 27 = 128 2. Quotient rule: am / an = a(m−n) This rule tells us that when we divide two numbers with the same base, we can subtract their exponents to get the exponent of the result. Example: 58 / 53 = 5(8−3) = 55 = 3125 3. Power rule: (am)n = a(m*n) This rule tells us that when we raise a number to a power and then raise the result to another power, we can multiply the exponents to get the exponent of the final result. Example: (34)2 = 3(4*2) = 38 = 6561 4. Negative exponent rule: a(−m) = 1/am This rule tells us that when we have a negative exponent, we can flip the base and make the exponent positive to get the reciprocal of the result. Example: 2−5 = 1/25 = 1/32 5. Zero exponent rule: a0 = 1 This rule tells us that any number raised to the power of zero is equal to one. Example: 70 = 1

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

Share performance indicators with learners 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. Using these rules, have learners simplify and evaluate expressions involving powers of numbers. Here are a few examples: Example 1: Simplify 43 * 45 Using the product rule, we can add the exponents: 43 * 45 = 4(3+5) = 48 = 65536 Assessment 1. Using the power rule, Evaluate (24)3 2. Using the quotient rule, Simplify 35 / 32 3. Using the negative exponent rule, Simplify 5(−2) 4. Using the zero exponent rule, Simplify 20

Take feedback from learners and summarize the lesson.

Revise with learners on the previous lesson. Share performance indicators with learners and introduce the lesson.

Concrete-resource task: Set out these resources for each group: Number cards; Square-grid paper; Calculator. Learners use the Number cards to form bases and exponents, represent square numbers and powers on the Square-grid paper where appropriate, and use the Calculator to check their solutions. Guide learners to recall that an exponential equation is an equation in which the unknown appears as an exponent. Demonstrate how to express both sides using the same base before comparing the exponents. Example 1: Solve 2^x = 16. Write 16 as a power of 2: 16 = 2^4. Therefore, 2^x = 2^4, so x = 4. Example 2: Solve 3^x = 27. Since 27 = 3^3, 3^x = 3^3, therefore x = 3. In groups, learners select Number cards to form and solve equations such as: 1) 5^x = 125 2) 4^x = 64 3) 2^(x+1) = 16 4) 3^(x-1) = 9. Learners explain how they rewrote each side using the same base and use the Calculator to verify their answers. Use the Square-grid paper to model powers such as 2^2, 3^2, 4^2 and 5^2 as square arrangements. Learners relate the side length of each square to the base and the total number of squares to the value of the power. Guide learners to solve real-life problems involving powers. Example: A square garden has an area of 144 m². If its side length is represented by 12 = 2^2 × 3, learners discuss how powers can be used to represent factors and quantities. Another example: A bacteria population doubles every hour. If it starts with 4 bacteria, the population after x hours can be represented as 4 × 2^x. How many bacteria will there be after 3 hours? Learners calculate 4 × 2^3 = 32 and verify with the Calculator. Assessment: Solve the following. 1) 2^x = 32 2) 3^x = 81 3) 5^(x-1) = 25 4) 4^(x+1) = 64 5) A culture begins with 3 cells and triples every hour. Express the number of cells after 4 hours using powers and calculate the answer.

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.