Lesson Notes By Weeks and Term v4 - JHS 3

Lesson Video

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Performance objectives

• Define and explain what a ratio is
• Solve problems involving ratios and proportions
• Understand the link between parallel vectors and ratios
• Apply ratios to compare quantities
• Demonstrate how to simplify equivalent ratios

Lesson summary

This lesson introduces the concept of parallel vectors. We will build on our previous knowledge of what vectors are (quantities with both magnitude and direction) to understand a special relationship between them. This concept is not just for the classroom; it is used in many real-world applications in Ghana, such as in construction, where walls must be parallel; in navigation, where ships or aeroplanes might travel on parallel paths; and even in designing beautiful Kente patterns which use parallel lines. Understanding this topic helps us describe the world around us using mathematics and prepares us for the BECE. The idea of parallel vectors is directly linked to Ratios and Proportion.

Lesson notes

A. Recap: What is a Vector?

A vector is a quantity that has both magnitude (size or length) and direction. We often represent vectors in geometry as a directed line segment. In calculations, we commonly use column vectors.

For example, the vector a = $\begin{pmatrix} 4 \\ 3 \end{pmatrix}$ represents a movement of 4 units to the right (positive x-direction) and 3 units upwards (positive y-direction). B. What are Parallel Vectors?

Imagine two straight footpaths in a park. If they go in the exact same direction, they are parallel. They might have different lengths, but their direction is identical.