Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Identify patterns and relationships.
• Represent relationships using tables, graphs, and equations.
• Analyze and interpret information from these representations.
• Apply these skills to solve real-life problems.
• Make predictions based on observed patterns.

Lesson summary

This week, we're diving into the fascinating world of patterns, relationships, and representations. Understanding these concepts is crucial for making sense of the world around us, especially in the diverse and dynamic context of South Africa. From analyzing mobile data costs to understanding population growth trends, recognizing patterns allows us to make informed decisions and predictions. We'll be looking at how information is presented in different formats (tables, graphs, and equations) and how we can use these representations to solve real-world problems.

Lesson notes

Patterns and Relationships: A pattern is a predictable regularity or order. It can be numerical (like a sequence of numbers), geometric (like repeating shapes), or even descriptive (like a recurring event). Recognizing patterns involves identifying the rule or relationship that governs the repetition. A relationship describes how two or more variables are connected. It can be a direct relationship (as one variable increases, the other also increases), an inverse relationship (as one variable increases, the other decreases), or a more complex relationship.

Representations: We can represent patterns and relationships in various ways: Tables: Tables organize data in rows and columns, making it easy to see specific values.

Graphs: Graphs provide a visual representation of the relationship between variables.

Common graph types include: Bar graphs: Used to compare different categories.

Line graphs: Used to show trends over time.

Pie charts: Used to show proportions of a whole.

Scatter plots: Used to show the relationship between two variables (correlation).

Equations: Equations use mathematical symbols to express the relationship between variables in a precise and concise way. For example, `y = 2x + 3` describes a linear relationship.

Worked example

Example 1: Mobile Data Costs

A mobile network provider charges R10 for the first 100MB of data and then R0.08 per MB thereafter.

a) Create a table showing the cost for 100MB, 200MB, 300MB, 400MB, and 500MB.

b) Draw a graph representing the cost of data.