Scale Drawing

Subject: 

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MATHEMATICS

Term:

FIRST TERM

Week:

WEEK 9

Class:

PRIMARY 6 / BASIC 6

Topic:

SCALE DRAWING

• Objects
• Maps
• Distance

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Previous lesson: 

The pupils have previous knowledge of

Order of Operation

that was taught as a topic in the previous lesson

Behavioural objectives:

At the end of the lesson, pupils should be able to

• draw plane shapes according to a given scale
• apply and use scale drawing in converting lengths and distances of objects in their environment with a given scale
• interprete and solve real life problems on scale drawing

Instructional Materials / Learning Resources 

• Wall charts
• Pictures
• Related Online Video
• Flash Cards
• Ruler
• Type rule
• Pencil
• Cardboard paper

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Methods of Teaching:

• Class Discussion
• Group Discussion
• Asking Questions
• Explanation
• Role Modelling
• Role Delegation

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Reference Materials:

• Scheme of Work
• Online Information
• Textbooks
• Workbooks
• Lagos State Basic Education Curriculum

Content:

WHAT IS SCALE DRAWING

In mathematics, scaling refers to the process of multiplying a quantity by a factor or ratio. Scaling can be applied to a variety of mathematical objects, such as numbers, vectors, and functions.

For example, if you have a set of numbers and you want to scale them up by a factor of 2, you would multiply each number in the set by 2. If you want to scale them down by a factor of 2, you would divide each number by 2.

Scaling can also be applied to vectors, which are quantities that have both magnitude (size) and direction. When you scale a vector, you can change its magnitude without changing its direction. For example, if you have a vector pointing north and you want to scale it up by a factor of 2, you would multiply the vector’s magnitude by 2, but it would still point north.

Also , scaling can also be applied to functions. When you scale a function, you can change the values of the function at different points without changing the shape of the curve. For example, if you have a function that describes the height of a person as a function of time, and you want to scale the function up by a factor of 2, you would multiply the height of the person at each time point by 2.

Scaling is a fundamental concept in mathematics that has many applications in science, engineering, and other fields

SCALE DRAWING OF OBJECTS 

Scaling in mathematics can be used to draw objects by allowing you to resize them without distorting their shape. This can be especially useful when working with technical drawings or diagrams, where precise dimensions are important.

To use scaling to draw an object, you can start by drawing a rough outline of the object at a smaller scale. Then, you can use scaling to enlarge the object to the desired size while maintaining the correct proportions.

For example, suppose you want to draw a blueprint of a building that is 50 feet long and 30 feet wide. You could start by drawing the building at a smaller scale, say 1 inch = 10 feet. This means that if you draw a line that is 1 inch long on your paper, it represents a distance of 10 feet in the actual building.

Then, to scale the drawing up to the correct size, you would simply multiply all of the dimensions by the scaling factor. In this case, the scaling factor would be 5, since 50 / 10 = 5. This means that each line you drew on the paper would need to be 5 times as long as it was originally.

Scaling can also be useful for creating computer graphics, where you may need to scale an object up or down to fit a particular screen size or resolution. In these cases, you can use mathematical scaling techniques to resize the object without distorting its shape.

Importance and Usefulness of Scale Drawing when it comes to map reading 

Scale drawings are an important tool for map reading because they allow you to accurately measure distances on a map. A scale drawing is a representation of an object or area that is drawn to a specific size relative to the original. For example, a map of a city might be drawn at a scale of 1 inch = 1 mile, which means that 1 inch on the map represents 1 mile in the real world.

Using a scale drawing can help with map reading because it allows you to measure distances on the map and compare them to real-world distances. For example, if you wanted to know how far it is from one city to another on a map, you could use the scale to measure the distance on the map and then multiply that distance by the scaling factor to get the actual distance in miles.

Scale drawings are also useful for finding your way around an unfamiliar area. By using a map with a scale, you can determine how far it is from your current location to your destination, and you can use this information to plan the best route.

And also, scale drawings are an essential tool for map reading because they allow you to accurately measure and compare distances, and they can help you navigate unfamiliar areas more effectively.

The importance of Scale drawing to surveyor, Architect, pilots and other professionals

1. Surveyors: Scale drawings are important for surveyors because they allow them to accurately measure distances and angles on a map or aerial photograph. This can be especially useful when surveyors are working on large projects, such as building roads or bridges, or when they need to measure distances over long distances.
2. Architects: Scale drawings are also important for architects because they allow them to create detailed plans and drawings of buildings and other structures. By using scale drawings, architects can ensure that their designs are accurate and to scale, which is essential for the construction process.
3. Pilots: Scale drawings are useful for pilots because they allow them to accurately measure distances on a map or aerial photograph. This can be especially important when pilots are navigating unfamiliar areas or when they need to plan a flight route.
4. Other professionals: There are many other professionals who use scale drawings in their work, including cartographers, engineers, and geologists. Scale drawings are an important tool for these professionals because they allow them to accurately measure and compare distances and angles, which is essential for their work.

How to draw plane shapes according to a given scale

To draw plane shapes according to a given scale, you will need to determine the scaling factor that you will use. The scaling factor is the ratio of the size of the drawing to the size of the actual object or area.

Once you have determined the scaling factor, you can use it to create your drawing. For example, suppose you want to draw a square with sides that are 10 feet long, and you are using a scale of 1 inch = 2 feet. To draw the square at this scale, you would need to draw a line that is 5 inches long (10 / 2 = 5). You would then draw the other three sides of the square using the same scaling factor, so that the sides of the square are all 5 inches long.

You can use this same process to draw other plane shapes, such as circles, triangles, and rectangles. Simply determine the size of the shape you want to draw and the scaling factor you are using, and use these values to create your drawing.

It is important to carefully measure and draw the shapes to ensure that they are accurate and to scale. This can be especially important when you are working on technical

Drawing tools that are needed for scale drawing.

There are a variety of drawing tools that can be used for scale drawing, including the following:

1. Pencils: Pencils are a classic drawing tool that can be used to create scale drawings. They are easy to erase and can be sharpened to a fine point, which is useful for creating precise lines and details.
2. Erasers: Erasers are an important tool for scale drawing because they allow you to correct mistakes or make adjustments to your drawing.
3. Rulers: Rulers are useful for creating straight lines and measuring distances on a scale drawing. They can be especially useful for drawing shapes and objects that require precise dimensions.
4. Compasses: Compasses are used to draw circles and arcs. They can be especially useful for drawing circular objects or for creating curves on a scale drawing.
5. Protractors: Protractors are used to measure angles. They can be useful for creating precise angles on a scale drawing, or for measuring the angles of existing objects.
6. Drawing board: A drawing board is a flat surface that is used to support a piece of paper or other drawing media. It can be useful for scale drawing because it provides a stable surface for drawing and allows you to easily make precise measurements.

Example

Interpret the following ratios as scales. Explaining what 1cm represents 1:100000

Solution

A ratio of 1:100,000 can be interpreted as a scale that represents a relationship between two quantities, with the first quantity being 1 unit and the second quantity being 100,000 units.

In this case, the scale indicates that 1 centimeter on the drawing represents 100,000 units in the actual object or area. This means that if you measure a distance of 1 centimeter on the drawing, it represents a distance of 100,000 units in the real world.

This scale is often used for maps, where it allows you to represent large areas on a small piece of paper. For example, a map of a city might be drawn at a scale of 1:100,000, which means that 1 centimeter on the map represents 100,000 feet in the real world. This allows you to see the entire city on a single map, even if it is very large.

Interpret the following ratios as scales. Explaining what 1cm represents

• 1: 1000000
• 1: 30000
• 1: 12000000
• 1: 50
• 1 : 20000

Rewrite the following scales as ratios 

• 1 cm represents 50km
• 1 cm represents 30 km
• 1cm represents 12 m
• In cm represents 1.4km
• 1cm represents 17.8 km

Presentation. 

The topic is presented step by step

Step 1:

The class teacher revises the previous topics

Step 2.

He introduces the new topic

Step 3:

The class teacher allows the pupils to give their own examples and he corrects them when the needs arise

Evaluation

1. What is scaling or scale drawing
2. Mention three professionals that use scale drawings
3. Mention three scale drawing tools
4. Mention four areas in life that scale drawing may be of useful in solving real problems life problems.

Conclusion

In conclusion, scale drawing is a valuable tool that is used in a variety of fields, including surveying, architecture, and map reading. It involves creating a representation of an object or area that is drawn to a specific size relative to the original. Scale drawings are useful because they allow you to accurately measure and compare distances and angles, and they can be used to create detailed plans and diagrams. They are an essential tool for many professionals, and they have many practical applications in real-life situations

The class teacher wraps up or concludes the lesson by giving out short notes to summarize the topic that he or she has just taught.

The class teacher also goes round to make sure that the notes are well copied or well written by the pupils.

He or she does the necessary corrections when and where the needs arise.