Lesson Notes By Weeks and Term v5 - Grade 8

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.

Performance objectives

• Identify and describe numerical patterns.
• Determine input values and output values.
• Represent relationships using flow diagrams and tables.
• Write a rule or equation for a relationship.
• Use a rule to generate tables.

Lesson summary

Functions, graphs, and relationships form a cornerstone of mathematics and are crucial for understanding how different quantities relate to each other. In South Africa, understanding these concepts is vital for interpreting data presented in news articles (e.g., graphs of COVID-19 infection rates), understanding budgets (personal and national), and even in trades like carpentry and construction where understanding relationships between lengths and angles is essential. It also forms a foundation for more advanced mathematics needed in fields like engineering, finance, and science.

Lesson notes

What is a Relationship? A relationship in mathematics describes how two or more things are connected.

Think about it like a recipe: the amount of flour you use is related to the number of cakes you can bake. In mathematics, we often deal with relationships between numbers. Input and Output Imagine a vending machine. You put money in (the input), and you get a snack out (the output). A function is similar. You give it an input, and it gives you an output according to a specific rule. We can think of a function as a 'number machine'. Function Rule The function rule describes what the 'number machine' does to the input to produce the output. It's like the instructions inside the vending machine. For example, the rule could be "multiply the input by 2 and then add 1". Representing Relationships We can represent relationships in several ways: Tables: A table lists pairs of input and output values. | Input (x) | Output (y) | | --------- | ---------- | | 1 | 3 | | 2 | 5 | | 3 | 7 | Flow Diagrams: A flow diagram shows the steps involved in applying the function rule to the input. Input (x) → Multiply by 2 → Add 1 → Output (y)

Equations: An equation expresses the function rule using mathematical symbols. For the table above, the equation would be y = 2x + 1

Worked example

Example 1: Vusi's Stokvel

Vusi is part of a stokvel. Each member contributes R50 each month. The total amount collected depends on the number of members.

Input: Number of members.

Output: Total amount collected.

Function Rule: Multiply the number of members by R

5

0. Let's represent this in a table:

| Number of Members (x) | Total Amount (y) |

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

| 1 | R50 |

| 2 | R100 |

| 3 | R150 |

| 4 | R200 |