Lesson Notes By Weeks and Term v3 - Junior Secondary 3
Scales and Scale Drawing
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Scales and Scale Drawing
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Subject: Basic Technology
Class: Junior Secondary 3
Term: 3rd Term
Week: 1
Theme: Drawing Practice
This page supports the lesson note with a companion video and a short classroom-ready summary.
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use the metric rule to measure lengths and compare sizes; explain scale drawings identify scales used in drawings; draw objects to given scales.
Drawing Practice Scales and Scale Drawing Term: 3rd Term Week: 9 ---
1. Overview and Learning Objectives This topic introduces students to the fundamental concepts of measurement, comparison of sizes, and the critical skill of scale drawing. Scale drawing is a vital aspect of technical communication across various fields such as engineering, architecture, cartography, and construction. It enables the representation of large objects (e.g., buildings, land areas) or very small objects (e.g., delicate machine parts) accurately on a manageable surface like paper, maintaining proportional relationships. Understanding scales allows for the accurate interpretation and creation of technical drawings, which is indispensable for planning, design, and execution of projects in Nigeria's rapidly developing infrastructure and industries. By the end of this lesson, students will be able to: Accurately measure lengths of objects using a metric rule and compare their sizes. Explain what a scale drawing is and its purpose. Identify and interpret different types of scales used in drawings. Produce simple drawings of objects accurately to a given scale. These objectives are directly applicable to real-world scenarios in Nigeria, such as reading and understanding a house plan drawn by an architect, interpreting a road map, or drawing a component for a local fabrication project.
2. Key Concepts and Explanations 2.
1. The Metric Rule and Measurement Definition: A metric rule (or ruler) is a common measuring instrument used to determine lengths, widths, and heights of objects.
It typically measures in metric units: millimetres (mm) and centimetres (cm).
Units: 10 millimetres (mm) = 1 centimetre (cm) 100 centimetres (cm) = 1 metre (m) 1000 metres (m) = 1 kilometre (km)
Reading the Metric Rule: The rule is usually marked with major divisions representing centimetres (e.g., 0, 1, 2, 3...). Each centimetre is further divided into ten smaller divisions, with each small division representing one millimetre (mm).
Procedure for Measuring Lengths:
1. Place the zero mark of the rule exactly at one end of the object to be measured.
2. Read the marking on the rule that aligns with the other end of the object.
3. Ensure the eye is perpendicular to the rule at the point of reading to avoid parallax error (inaccurate reading due to viewing angle).
Comparing Sizes: Once measurements (length, width, height) of different objects are obtained, their sizes can be numerically compared (e.g., "Object A is 5 cm longer than Object B"). 2.
2. Scale Drawing Definition: A scale drawing is a drawing that shows a real object with accurate dimensions that have been proportionally reduced or enlarged by a specific ratio, called the scale. It is a representation of an object where all linear dimensions are either increased or decreased in a fixed ratio.
Purpose: To represent objects that are too large to be drawn on paper (e.g., a building, a piece of land) by reducing their size. To represent objects that are too small to show details clearly (e.g., a watch mechanism, a microchip) by enlarging their size. To ensure accuracy and proportion in technical drawings. 2.
3. Scales Used in Drawings A scale defines the relationship between the dimensions on a drawing and the actual dimensions of the object it represents. It is always expressed as a ratio.
Types of Scales:
1. Representative Fraction (RF) or Ratio Scale: Expressed as a ratio (e.g., 1:100, 1:2, 5:1). The first number (numerator) represents the unit of length on the drawing. The second number (denominator) represents the corresponding unit of length on the actual object. Both numbers must be in the same units.
Example: A scale of 1:100 means 1 unit on the drawing represents 100 units on the actual object. If the units are cm, then 1 cm on the drawing represents 100 cm (or 1 m) on the actual object.
2. Verbal Scale: Expressed in words (e.g., "1 cm represents 5 m," or "1 inch to 10 miles"). This scale specifies the actual distance that a given unit of length on the drawing represents.
3. Graphic or Linear Scale: A line drawn on the drawing, divided into units, with the actual lengths A proposed road section is 5 kilometres long.
If it is drawn on a map with a scale of 1:50,000, what will be its length on the map in centimetres?
7. A wall in a proposed school building is 12 metres long.
If the architect uses a scale of 1:200 for the plan, how long will the wall appear on the drawing?
8. An actual rectangular field is 40 m long and 25 m wide.
Draw this field to a scale of 1:500.
9. A square tile measures 30 cm by 30 cm. Draw a plan of four such tiles laid together, using a scale of 1:10.
1
0. A drawing of a tiny component has a dimension of 4 cm.
If the scale used is 8:1, what is the actual dimension of the component in millimetres?
6. Evaluation and Assessment 6.
1. Formative Assessment: Observation: Monitor students' ability to handle the metric rule correctly, perform calculations, and draw accurately during activities.
Question & Answer: Ask probing questions during explanations to check understanding (e.g., "What if the scale was 1:1?", "Why do we need to reduce sizes for buildings?").
Quick Check: Have students show their calculated dimensions before drawing to check for understanding of conversion. 6.
2. Summative Assessment: (Aligns directly with the Evaluation Guide provided)
1. Measure lengths and compare sizes: Measure the length and width of your Basic Technology textbook using a metric rule. State the measurements and calculate the perimeter of the textbook.
Marking Scheme: 1 mark for length, 1 mark for width, 1 mark for correct perimeter calculation, 1 mark for correct units. (4 marks)
2. Identify scale drawings: What is a scale drawing? Give two examples of where scale drawings are used in real life in Nigeria.
Marking Scheme: 2 marks for definition, 1 mark each for two relevant Nigerian examples (e.g., architectural plans, road maps, machine diagrams). (4 marks)
3. Describe scales used in drawings: Explain the meaning of a scale of 1:50 on a building plan. If a wall on the plan measures 10 cm, what is its actual length?
Marking Scheme: 2 marks for explaining 1:50, 1 mark for correct calculation of actual length (500 cm or 5 m), 1 mark for correct units. (4 marks)
4. Draw objects to given scales: A rectangular plot of land is 20 metres long and 15 metres wide.
Draw this plot to a scale of 1:100. (Show your calculations).
Marking Scheme: 1 mark for converting length to drawing length, 1 mark for converting width to drawing width, 2 marks for drawing a correct rectangle with correct dimensions, 1 mark for labeling scale. (5 marks)
7. Real-life Applications / Integration
1. Architecture and Building Construction: Scale drawings are fundamental in creating blueprints and floor plans for houses, schools, hospitals, and commercial buildings across Nigeria.
Architects use scales like 1:50, 1:100, or 1:200 to represent large structures on paper, allowing builders, masons, and carpenters to understand dimensions and construct accurately. For instance, when constructing a new police station in a local community, the entire project relies on detailed scale drawings.
2. Cartography and Urban Planning: Maps of Nigerian states, cities, or even small villages are all scale drawings. Urban planners use large-scale maps (e.g., 1:10,000) to design new estates, roads, and drainage systems, like in the ongoing development of new towns or industrial layouts in places like Ogun State or FCT Abuja. Even using Google Maps on a phone is interacting with a dynamic scale drawing.
3. Engineering and Fabrication: Engineers in Nigeria's oil and gas, manufacturing, or automotive industries use scale drawings for designing machine parts, engines, and equipment. For instance, a local mechanic or welder fabricating a new component for a damaged truck might first sketch it to an appropriate scale to ensure correct fitting and functionality. Small components might be drawn to an enlargement scale (e.g., 2:1) to show intricate details.
8. Differentiation, Remediation and Extension 8.
1. Differentiation (for struggling learners): Simplification: Provide pre-filled tables for measurement and calculation tasks, requiring only specific blanks to be filled. * Visual Aids: Use large, clearly marked charts for one is longer and by how much.
Solution: Teacher's textbook length (example): 28.5 cm Exercise book length (example): 20.0 cm Comparison: The Basic Technology textbook is longer.
Difference: 28.5 cm - 20.0 cm = 8.5 cm.
Commentary: This question assesses the student's ability to accurately use a metric rule and compare lengths. Expected accuracy within +/- 0.1 cm.
Question 2 (Objective 3): A drawing shows a map of a new estate in Lekki, Lagos.
It has a scale of 1:5000. a) What does this scale mean? b) If the distance between two blocks on the map is 5 cm, what is the actual distance in metres?
Solution: a)
The scale 1:5000 means that 1 unit of measurement on the map represents 5000 units of the same measurement on the actual ground. For example, 1 cm on the map represents 5000 cm (or 50 m) on the actual estate ground. b) Given map distance = 5 cm. Scale = 1:
5
0
0
0. Actual distance = Map distance × Scale Factor Actual distance = 5 cm × 5000 = 25,000 cm To convert to metres: 25,000 cm / 100 cm/m = 250 metres. The actual distance between the two blocks is 250 metres.
Commentary: This question assesses the ability to interpret a representative fraction scale and perform calculations for actual dimensions.
Question 3 (Objective 4): A rectangular plot of land in Kaduna is 30 metres long and 20 metres wide. Calculate the dimensions you would use to draw this plot on paper to a scale of 1:
1
0
0
0. Solution: Scale = 1:
1
0
0
0. This means 1 cm on paper represents 1000 cm (or 10 m) on the actual ground.
Convert actual dimensions to centimetres: Actual length = 30 m = 30 × 100 cm = 3000 cm. Actual width = 20 m = 20 × 100 cm = 2000 cm.
Calculate drawing dimensions: Drawing length = Actual length / Scale Factor = 3000 cm / 1000 = 3 cm. Drawing width = Actual width / Scale Factor = 2000 cm / 1000 = 2 cm. The dimensions to draw the plot are 3 cm (length) by 2 cm (width).
Commentary: This question assesses the ability to convert real-world dimensions to drawing dimensions using a reduction scale.
Question 4 (Objective 4): Draw a square table top that measures 80 cm by 80 cm, using a scale of 1:
2
0. Solution: Scale = 1:
2
0. This means 1 cm on paper represents 20 cm on the actual table top. Convert actual dimensions to drawing dimensions: Actual side = 80 cm. Drawing side = Actual side / Scale Factor = 80 cm / 20 = 4 cm.
Drawing: (Students should draw a square with each side measuring 4 cm on their paper). [Visual representation: A 4cm x 4cm square should be drawn] Label: "Side = 4 cm", "Scale = 1:20"
Commentary:* This question assesses the practical application of scale calculation to produce a drawing. Neatness and accuracy of the drawing are important.
5. Independent Practice (Questions Only)
1. Measure the length of your pencil and the width of your palm using a metric rule. Record your readings.
2. Which of the two items in question 1 is longer? By how much?
3. Explain in your own words what "scale drawing" means.
4. A technical drawing of a small machine part has a scale of 5:
1. What does this scale tell you about the drawing compared to the actual part?
5. Convert the verbal scale "1 cm represents 2 metres" into a representative fraction (RF).
6. A proposed road section is 5 kilometres long.
If it is drawn on a map with a scale of 1:50,000, what will be its length on the map in centimetres?
7. A wall in a proposed school building is 12 metres long.
If the architect uses a scale of 1:200 for the plan, how long will the wall appear on the drawing?
8. An actual rectangular field is 40 m long and 25 m wide.
Draw this field to a scale of 1:500.
9. A square tile measures 30 cm by
Example 1 (Reduction Scale):
A rectangular classroom in Abuja is 8 metres long and 6 metres wide. Draw the plan of the classroom to a scale of 1:
2
0
0. Step 1: Understand the scale.
Scale = 1:
2
0
0. This means 1 unit on the drawing represents 200 units on the actual classroom.
Let's use centimetres. 1 cm on drawing = 200 cm (or 2 m) on actual classroom.
Step 2: Convert actual dimensions to drawing dimensions.
Length: Actual length = 8 m = 800 cm.
Drawing length = Actual length / Scale Factor = 800 cm / 200 = 4 cm.
Width: Actual width = 6 m = 600 cm.
Drawing width = Actual width / 200 = 600 cm / 200 = 3 cm.
Step 3: Draw the object.
Using a metric rule and pencil, draw a rectangle with a length of 4 cm and a width of 3 cm. Label the dimensions and the scale used.
Example 2 (Enlargement Scale):
A tiny bolt head measures 5 mm in diameter.
Draw it to a scale of 4:
1. Step 1: Understand the scale.
Scale = 4:
1. This means 4 units on the drawing represent 1 unit on the actual bolt head. The drawing will be 4 times larger.
Step 2: Convert actual dimensions to drawing dimensions.
Diameter: Actual diameter = 5 mm.
Drawing diameter = Actual diameter Scale Factor = 5 mm 4 = 20 mm (or 2 cm).
Step 3: Draw the object.
Draw a circle with a diameter of 2 cm. Label the diameter and the scale used.
Example 3 (Verbal Scale Conversion):
A map has a verbal scale "1 cm represents 5 km". Convert this to a representative fraction (RF).
Step 1: Write the verbal scale as a ratio of drawing distance to actual distance.
1 cm (drawing) : 5 km (actual)
Step 2: Convert both units to the same unit (usually cm or mm for small scales).
1 cm : (5 km 1000 m/km 100 cm/m)
1 cm : (5 1000 100) cm
1 cm : 500,000 cm
Step 3: Express as a representative fraction.
RF = 1:500,000
Teaching and Learning Activities
3. 1. Teacher Activities
Introduction (10 min):
Review previous knowledge on basic measurement and units.
Ask students how engineers, architects, or surveyors represent large objects like buildings or roads on paper. Introduce the concept of "Scale Drawing."
Present the lesson objectives clearly.
Measuring and Comparing (15 min):
Distribute metric rules and various classroom objects (e.g., exercise books, pencils, geometry sets, a piece of wood).
Demonstrate correct technique for measuring length, width, and thickness using the metric rule, emphasizing starting from zero and avoiding parallax error.
Guide students to measure assigned objects and record their measurements in a table.
Facilitate comparison of sizes based on recorded measurements.
Explaining Scale Drawings and Scales (20 min):
Use charts or real-life examples (e.g., a simple house plan, a road map of a local government area like Surulere in Lagos, a diagram of a bicycle part) to explain what a scale drawing is.
Define and explain the three types of scales: Representative Fraction (RF), Verbal Scale, and Graphic Scale.
Focus on RF and verbal scale for calculations, explaining reduction (1:X), enlargement (X:1), and full size (1:1) scales.
Walk through Example 1 (classroom plan) and Example 2 (bolt head) from the Key Concepts section, step-by-step, explaining the calculations for converting actual dimensions to drawing dimensions.
Drawing to Scale Demonstration (15 min):
On the whiteboard or a large chart, demonstrate drawing a simple rectangular object (e.g., a school gate) to a specified scale, showing the calculations and the actual drawing process using a large ruler.
Emphasize neatness, accuracy, and clear labeling of dimensions and scale.
Consolidation & Wrap-up (5 min):
Recap key definitions and procedures.
Address any student misconceptions.
Assign homework.