Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Identify different types of patterns (linear, quadratic, exponential).
• Represent relationships using tables, graphs, and equations.
• Interpret graphs and tables to make predictions.
• Calculate and explain gradients and intercepts of linear graphs.
• Solve practical problems using these skills.

Lesson summary

This week, we're diving into patterns, relationships, and representations. This topic is crucial because it allows us to understand and make sense of the world around us. From predicting monthly expenses to interpreting graphs about unemployment rates, being able to identify patterns and understand how variables relate to each other is a vital life skill, especially in a dynamic South African context. This skill helps you to analyze situations, predict outcomes, and make informed decisions in your personal and professional life. For example, understanding patterns in water consumption during different seasons can help plan for water conservation efforts in your community.

Lesson notes

This section will explain the key ideas of patterns, relationships, and representations. We will look at different types of patterns and how to represent them. 2.1 Patterns: A pattern is a sequence that repeats itself or grows according to a specific rule.

We'll focus on three common types: Linear Patterns: These patterns increase or decrease by a constant amount each time. This constant amount is called the common difference.

Quadratic Patterns: These patterns involve a squared term. The difference between consecutive terms changes, but the difference of the differences is constant.

Exponential Patterns: These patterns involve multiplying by a constant factor each time. This constant factor is called the common ratio. 2.2 Relationships: Relationships show how two or more variables are connected. A variable is a quantity that can change. Common types of relationships we will explore include: Linear Relationships: These are relationships where the variables change at a constant rate. They can be represented by straight-line graphs.

Direct Proportion: A special case of a linear relationship where one variable is directly proportional to the other (y = kx, where k is a constant).

Inverse Proportion: Where one variable increases as the other decreases (y = k/x, where k is a constant). 2.3 Representations: Representations are different ways to show patterns and relationships.

We will use: Tables: Organized data arranged in rows and columns.

Graphs: Visual representations of data, such as line graphs, bar graphs, and pie charts.

Equations: Mathematical formulas that describe the relationship between variables.

Worked example

Example 1: Linear Pattern

A street vendor sells vetkoek. The cost is R5 for one vetkoek, R10 for two vetkoek, R15 for three vetkoek, and so on.

Identify the pattern: This is a linear pattern because the cost increases by R5 for each additional vetkoek.

Represent the pattern in a table:

| Number of Vetkoek (x) | Cost (R) (y) |

| ---------------------- | ----------- |

| 1 | 5 |

| 2 | 10 |

| 3 | 15 |

| 4 | 20 |

Represent the pattern with an equation: y = 5x, where y is the cost and x is the number of vetkoek.

Represent the pattern on a graph: Draw a straight line passing through the points (1, 5), (2, 10), (3, 15), etc.

Example 2: Quadratic Pattern