Calculations, Percentages, and Rates

Lesson Plan: Calculations, Percentages, and Rates

Year Level: 11-12
Focus Areas: Calculations, Percentages, and Rates
Duration: 6 lessons

Learning Objectives

By the end of these lessons, students will be able to:

• Solve practical problems involving basic arithmetic operations.
• Apply correct arithmetic operation order and simplify rational expressions.
• Use calculators effectively for multi-step calculations and check for accuracy.
• Estimate, round, and evaluate numbers to the required decimal places.
• Calculate and apply percentages to real-world contexts.
• Understand and solve problems involving rates and unit conversions.

Materials Needed

• Worksheets for word problems and rational expressions.
• Calculators for multi-step and approximation problems.
• Grid paper or whiteboards for guided problem-solving.

Lesson Outline

Lesson 1: Solving Practical Problems with Arithmetic Operations

Introduction

• Review basic arithmetic operations: addition, subtraction, multiplication, and division.
• Discuss the correct order of operations (BODMAS) and the importance of simplifying expressions before solving.

Activity 1: Solving Word Problems Involving Travel Rates and Weighted Averages

• Introduce real-world examples like calculating rate of travel (e.g., speed = distance/time) and weighted averages.
• Hand out worksheets with word problems that require using travel rates (ACMEM001) and weighted averages (10-HH1.3).
• Work through examples as a class, then allow students to complete a set of similar problems individually.

Activity 2: Simplifying Rational Expressions

• Explain how to simplify rational expressions and apply this concept to word problems (ACMEM002).
• Provide problems that involve multiplying, dividing, adding, and subtracting rational expressions (11-P5 and 11-P6).

Lesson 2: Estimating, Approximating, and Using Calculators for Multi-Step Problems

Introduction

• Discuss the importance of approximation strategies and the use of leading digits for estimates.
• Explain scientific notation and its relevance to comparing large and small numbers.

Activity 1: Leading-Digit Approximation and Scientific Notation

• Provide examples of numbers in scientific notation (11-B2). Ask students to compare these numbers and use leading-digit approximation strategies (ACMEM004).
• Pair students to work on problems comparing numbers written in scientific and standard notations (11-B1).

Activity 2: Multi-Step Calculations with a Calculator

• Hand out multi-step word problems involving percentages and distances (e.g., Multi-step problems with percents 11-A6, Distance between two points 11-HH3.1).
• Instruct students on how to break down the problems into manageable steps, using their calculators to check accuracy.

Lesson 3: Checking Calculation Accuracy

Introduction

• Explain how to check the accuracy of multi-step calculations, especially with systems of equations and inequalities.

Activity 1: Accuracy with Inequalities and Systems of Equations (25 minutes)

• Provide problems where students must verify whether points satisfy inequalities or systems of simultaneous equations (10-L1, 11-D1).
• Encourage students to use calculators and rounding strategies to verify their results.

Activity 2: Rounding and Evaluating Decimal Fractions

• Review rounding numbers to the required decimal places (ACMEM009).
• Provide a worksheet for students to evaluate rational expressions and round them (11-P3).

Lesson 4: Working with Percentages

Introduction

• Discuss real-life applications of percentages, such as calculating discounts, mark-ups, and GST.

Activity 1: Calculating Percentages

• Hand out problems where students calculate percentages of a given amount, express one number as a percentage of another, and solve word problems involving mark-ups, discounts, and GST (ACMEM011, ACMEM012, ACMEM013).
• Walk through a few examples with the class, then let students complete problems on their own.

Activity 2: Multi-Step Percent Problems

• Work through more complex problems involving multiple percentage steps (11-A6).
• Emphasize the importance of breaking down these problems and double-checking calculations with a calculator.

Lesson 5: Solving Practical Problems with Rates

Introduction

• Discuss rates and their applications in real life (e.g., km/h for speed, beats/min for pulse).

Activity 1: Rate Word Problems

• Provide word problems where students calculate the rate of travel (10-HH1.2) and convert units (ACMEM015).
• Have students solve practical rate problems and check their understanding of unit conversions.

Activity 2: Unit Rate Comparison and Problem-Solving

• In pairs, have students compare rates like unit prices and heart rates after exercise (ACMEM016).
• Discuss how to use rates to make decisions, such as finding the best buy or evaluating fitness data.

Lesson 6: Review and Application

Introduction

• Recap key concepts from previous lessons (arithmetic operations, rational expressions, percentages, and rates).

Activity 1: Practical Application Group Activity

• In groups, present students with a real-world problem that involves multi-step calculations, rational expressions, and percentages.
• Example scenario: planning a budget for a trip, calculating fuel costs (rates), discounts on hotel stays (percentages), and applying rational expressions for total costs.

Activity 2: Individual Review Quiz

• Hand out a quiz that covers topics from all previous lessons, including word problems with percentages, rates, and multi-step calculations.
• Students work individually, applying the skills they’ve learned over the week.

Assessment

• Classwork: Participation in group activities and completion of worksheets.
• Quiz: Assess understanding of solving practical problems involving arithmetic, rational expressions, percentages, and rates.
• Project: Completion of a group assignment that applies multiple skills in a real-world context.

Differentiation

• For Struggling Students: Provide additional practice on simplifying expressions and solving word problems. Offer step-by-step guidance and support.
• For Advanced Students: Challenge them with more complex multi-step problems involving rational expressions and more difficult percentage calculations.

Extension/Additional Activities

• Real-World Application: Ask students to research real-life uses of rates and percentages, such as in business (e.g., discounts, profit margins) or science (e.g., population growth rates, fuel efficiency).
• Extra Practice: Provide additional worksheets with varying levels of difficulty for students to work on at home or during independent study.