Scale Drawing, Ratios, Conversions, Worked Examples and Uses for Primary 6

Class: Primary 6
Term: 3rd Term
Week: 8
Age: 11 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Measurement and Geometry
Previous Lesson: Volume, Prisms, Cylinder, Sphere and.
Topic: SCALE DRAWING
Subject Matter: Meaning of scale as ratio or proportion for reduction and enlargement, measuring dimensions and representing them on paper, converting lengths and distances using a given scale, solving worked examples on scale drawing, usefulness of scale drawing in building plans, quantitative aptitude on scale drawing.

Specific Objectives

By the end of the lesson, pupils should be able to:

Cognitive Domain:

• Define scale as a ratio or proportion used for reduction or enlargement.
• Convert given lengths and distances to corresponding scale values.
• Solve worked examples on scale drawing involving finding drawing length, actual length, or the scale.
• State the usefulness of scale drawing in daily life.
• Solve quantitative aptitude problems involving scale drawing.

Affective Domain:

• Appreciate the importance of scale drawing in various fields like architecture and cartography.
• Develop a positive attitude towards problem-solving in mathematics.

Psychomotor Domain:

• Draw simple scale drawings using given scales.
• Accurately measure dimensions for scale representation.

Social Domain:

• Collaborate with peers to solve scale drawing problems.

Reference Materials

The following resources were used in planning this lesson:

• 9 Years Basic Education Curriculum for Primary 6 Mathematics.
• State Unified Scheme of Work for Primary 6 Mathematics.
• New General Mathematics for Primary Schools, Book 6.

Instructional Materials

The teacher will teach this lesson with the aid of:

• Textbook
• Workbook
• Charts showing examples of scale drawings (e.g., a map, a simple house plan)
• Mathematical set (ruler, pencil, eraser)

Rationale for the Lesson

This lesson helps pupils understand how large objects or distances can be represented accurately on paper using a smaller proportion. It enables pupils to interpret maps, building plans, and other scaled representations, which is a practical skill for everyday situations.

Prerequisite/Previous Knowledge

Pupils have prior knowledge of ratios, proportions, basic units of length (cm, m, km), and simple measurements.

Lesson Content/Board Summary

SCALE DRAWING

Meaning of Scale Drawing

Scale drawing is a drawing that shows a real object with accurate sizes reduced or enlarged by a certain amount (a ratio or proportion). The scale is the ratio of the length on the drawing to the actual length of the object.

Scale can be written in different ways:

• As a ratio (e.g., 1:100)
• As a fraction (e.g., 1/100)
• In words (e.g., 1 cm represents 1 m)

Calculating with Scale

The main formula used in scale drawing is:

Scale = Drawing Length / Actual Length

From this formula, we can also find other values:

• To find the Drawing Length: Drawing Length = Scale × Actual Length
• To find the Actual Length: Actual Length = Drawing Length / Scale

Conversion of Units:

It is important that both the drawing length and the actual length are in the same units when calculating the scale or when using the scale in calculations. Here are common conversions:

• 1 meter (m) = 100 centimeters (cm)
• 1 kilometer (km) = 1000 meters (m)
• 1 kilometer (km) = 100,000 centimeters (cm)

NOTE: When converting from a smaller unit to a larger unit (e.g., cm to m), you divide. When converting from a larger unit to a smaller unit (e.g., m to cm), you multiply.

Examples of Scale Drawing Calculations

Example 1: Finding Drawing Length

A school field is 50 m long. If it is drawn to a scale of 1:1000, what is its length on the drawing?

Solution:

Step 1: Write down the given values.

Actual Length = 50 m

Scale = 1:1000 or 1/1000

Step 2: Convert the actual length to centimeters for easier calculation with the scale.

50 m = 50 × 100 cm = 5000 cm

Step 3: Use the formula for drawing length.

Drawing Length = Scale × Actual Length

Drawing Length = (1/1000) × 5000 cm

Step 4: Calculate the drawing length.

Drawing Length = 5000 / 1000 cm = 5 cm

The length of the field on the drawing is 5 cm.

Example 2: Finding Actual Length

On a map, the distance between two towns is 4 cm. If the scale of the map is 1:200,000, what is the actual distance in km?

Solution:

Step 1: Write down the given values.

Drawing Length = 4 cm

Scale = 1:200,000 or 1/200,000

Step 2: Use the formula for actual length.

Actual Length = Drawing Length / Scale

Actual Length = 4 cm / (1/200,000)

Actual Length = 4 cm × 200,000

Step 3: Calculate the actual length in cm.

Actual Length = 800,000 cm

Step 4: Convert the actual length from cm to km.

1 km = 100,000 cm

800,000 cm = 800,000 / 100,000 km = 8 km

The actual distance between the two towns is 8 km.

Example 3: Finding the Scale

A table is 2 m long. On a drawing, its length is 5 cm. Find the scale of the drawing.

Solution:

Step 1: Write down the given values.

Actual Length = 2 m

Drawing Length = 5 cm

Step 2: Convert both lengths to the same unit. Convert the actual length to centimeters.

2 m = 2 × 100 cm = 200 cm

Step 3: Use the formula for scale.

Scale = Drawing Length / Actual Length

Scale = 5 cm / 200 cm

Step 4: Simplify the ratio.

Scale = 1 / 40 or 1:40

The scale of the drawing is 1:40.

Usefulness of Scale Drawing

Scale drawings are useful in many areas, including:

• Building Plans: Architects use scale drawings to design houses and other structures.
• Maps: Cartographers use scale drawings to represent large geographical areas on paper.
• Engineering Designs: Engineers use scale drawings for designing machines, roads, and bridges.
• Fashion Design: Fashion designers create patterns for clothes using scale drawings.
• Model Making: Models of cars, aeroplanes, and buildings are made using scale.

Quantitative Aptitude on Scale Drawing

Example: A model car is built to a scale of 1:20. If the actual car is 4 m long and 1.8 m wide, what are the dimensions of the model car in cm?

Solution:

Step 1: Write down the given values.

Scale = 1:20

Actual Length = 4 m

Actual Width = 1.8 m

Step 2: Convert actual dimensions to cm.

Actual Length = 4 m = 4 × 100 cm = 400 cm

Actual Width = 1.8 m = 1.8 × 100 cm = 180 cm

Step 3: Calculate the model’s length.

Model Length = Scale × Actual Length

Model Length = (1/20) × 400 cm = 400 / 20 cm = 20 cm

Step 4: Calculate the model’s width.

Model Width = Scale × Actual Width

Model Width = (1/20) × 180 cm = 180 / 20 cm = 9 cm

The dimensions of the model car are 20 cm long and 9 cm wide.

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Set Induction

Teacher’s Activity: The teacher greets the pupils and asks them if they have seen maps or building plans. The teacher then explains that these are examples of scale drawings used to represent large areas or objects in a smaller, manageable size.

Pupils’ Activity: Pupils respond to the teacher’s questions and share their experiences with maps or plans.

Learning Point: Pupils connect the lesson to real-life applications and understand the basic concept of representing large things on paper.

Step 2: Meaning of Scale Drawing

Time: 5 minutes

Teaching Skill: Explanation/Definition

Teacher’s Activity: The teacher defines scale as a ratio or proportion used for reduction or enlargement. The teacher explains that scale tells us how many times the actual object has been reduced or enlarged in the drawing.

Pupils’ Activity: Pupils listen attentively, define scale in their own words, and copy the definition into their notebooks.

Learning Point: Pupils understand the definition of scale and its purpose.

Step 3: Converting Lengths and Distances

Time: 10 minutes

Teaching Skill: Demonstration/Explanation

Teacher’s Activity: The teacher explains the importance of unit consistency in scale drawing calculations. The teacher presents a conversion table for length units (cm, m, km) and demonstrates how to convert between them, emphasizing when to multiply or divide. The teacher guides pupils to convert given lengths and distances to corresponding scale values.

Pupils’ Activity: Pupils listen, ask questions for clarification, practice unit conversions, and copy the conversion table and notes into their notebooks.

Learning Point: Pupils learn to convert units of length accurately for scale drawing problems.

Step 4: Solving Worked Examples on Scale Drawing

Time: 10 minutes

Teaching Skill: Guided Practice/Problem Solving

Teacher’s Activity: The teacher guides pupils through worked examples on the board, demonstrating how to find drawing length, actual length, and the scale, using the formulas and conversion skills learned. The teacher encourages pupils to follow each step carefully.

Pupils’ Activity: Pupils actively participate in solving the examples, asking questions, and copying the solutions into their notebooks.

Learning Point: Pupils develop problem-solving skills for various scale drawing scenarios.

Step 5: Usefulness of Scale Drawing

Time: 5 minutes

Teaching Skill: Brainstorming/Discussion

Teacher’s Activity: The teacher asks pupils to think about where scale drawings are used in real life. The teacher then guides them to list and explain the usefulness of scale drawing in fields like building plans, maps, and engineering designs.

Pupils’ Activity: Pupils contribute ideas and discuss the practical applications of scale drawing.

Learning Point: Pupils understand the real-world relevance and importance of scale drawing.

Step 6: Quantitative Aptitude on Scale Drawing

Time: 5 minutes

Teaching Skill: Problem Solving

Teacher’s Activity: The teacher presents a quantitative aptitude problem involving scale drawing and guides the pupils through its solution, emphasizing careful reading and multi-step problem-solving.

Pupils’ Activity: Pupils attempt to solve the problem and follow the teacher’s guidance, ensuring they understand the steps.

Learning Point: Pupils apply their scale drawing knowledge to solve more complex problems.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. Define scale drawing.
2. State the formula for finding the actual length given the drawing length and scale.
3. A road is 30 km long. If it is drawn on a map with a scale of 1:500,000, what is its length on the map in cm?
4. Mention two areas where scale drawing is useful.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 0 minutes

Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the definition of scale, its applications, and the importance of unit conversions. The teacher then assigns homework related to scale drawing calculations.

Pupils’ Activity: Pupils listen to the summary and copy down the homework.

Learning Point: Pupils consolidate their understanding of scale drawing.

Home Task: Solve three new exercises on SCALE DRAWING. Show each step and check each answer.

Lesson Keywords

• Scale – The ratio of the length on a drawing to the actual length of the object.
• Ratio – A comparison of two numbers by division.
• Proportion – An equation stating that two ratios are equal.
• Reduction – Making an object smaller in a drawing.
• Enlargement – Making an object larger in a drawing.

Differentiation

For pupils who grasp the concepts quickly, the teacher will provide more challenging problems involving inverse scales or multi-step conversions. For pupils who need additional support, the teacher will provide simplified examples, offer one-on-one guidance, and use visual aids to reinforce understanding of unit conversions and formula application.

Note for teachers using this lesson plan

Ensure that pupils have a good understanding of ratios and basic measurement units before starting this lesson. Emphasize the importance of consistent units in all calculations. Encourage pupils to use rulers and pencils accurately when attempting simple scale drawings. Real-life examples like maps and building plans should be used to make the lesson relatable and practical.