GCSE Maths - Using Scales on Maps and Scale Diagrams

Summary

This educational video script explores the concept of scale in images, diagrams, and maps, explaining how they represent real-world objects in a reduced or enlarged form while maintaining correct proportions. It clarifies terminology, such as 'scale drawing' and 'scale diagram,' and emphasizes the importance of a scale or key for accurate representation. The script provides step-by-step examples of how to calculate distances and areas using different types of scales, including numerical ratios and linear measurements, and highlights common mistakes to avoid in exam questions related to scale.

Takeaways

• 📐 All three images in the script are scale representations, meaning they are either larger or smaller than the actual objects they depict but maintain correct proportions.
• 🌍 The example of the United Kingdom being three centimeters wide is used to illustrate the concept of scale, emphasizing that the image is a representation of a much larger reality.
• 🏠 The script clarifies the terminology used for scale images: photos are called photos, drawings are scale drawings, diagrams are scale diagrams, and maps can be referred to simply as maps.
• 🔍 Scale diagrams and maps should include a scale or key to help interpret the real-life distances represented by the images.
• 📏 The script introduces three main types of scales: a specific measurement per unit (e.g., 1 cm represents 5 km), a ratio scale (e.g., 1:600), and a line scale where a certain length represents a specific distance.
• ✂️ To use a line scale, one must measure the length on the diagram and then apply the scale to find the real-life distance.
• 📝 The script provides an example of how to calculate the distance between two points on a map using a ratio scale.
• 📐 It explains the process of converting diagram measurements to real-life measurements and vice versa, using the example of Jennifer's garden.
• 🏡 The area of a patio in Jennifer's garden is calculated by first determining the real-life dimensions from the scale drawing and then multiplying them to find the area in square meters.
• 💧 The script addresses a common mistake of converting square centimeters to square meters incorrectly and emphasizes the importance of using the scale for linear measurements only.
• 🎨 Part B of the script involves drawing a pond onto a scale drawing, demonstrating the process of converting real-life measurements to scale drawing measurements.

Q & A

What is the common feature of the images discussed in the script?

The common feature of the images is that they represent things either much larger or smaller than the images themselves, maintaining correct proportions while being scaled to fit on the screen.

What is the term used for images that are scaled to represent real-life objects or places?

Images that are scaled to represent real-life objects or places are referred to as 'scale drawings' if they are drawings, 'scale diagrams' if they are diagrams, and simply as 'maps' in the case of geographical representations.

Why is it important for scale diagrams or maps to have a scale or key?

A scale or key is important because it allows users to understand and calculate the real-life distances that the images represent, providing a reference for the size and proportion of the depicted objects or areas.

What are the three main types of scales mentioned in the script?

The three main types of scales mentioned are: a direct scale (e.g., 1 cm on the map represents 5 km in reality), a ratio scale (e.g., 1:600 meaning everything on the image is 600 times smaller than the real thing), and a line scale where a specific line length represents a certain distance (e.g., 2.5 cm represents 20 km).

How can you convert a ratio scale to a more workable form?

A ratio scale can be converted to a more workable form by expressing it as '1 centimeter on the image equals X centimeters (or meters) in real life', which makes it easier to calculate real-life distances based on the image measurements.

What is the process of finding the distance between two points on a map using the scale?

First, identify the scale of the map. Then, measure the distance between the two points on the map using a ruler. Finally, apply the scale to convert the measured distance into real-life distance.

How do you calculate the area of a shape on a scale drawing?

First, measure the length and width of the shape on the scale drawing. Then, convert these measurements into real-life measurements using the scale. Multiply the converted length by the converted width to find the area in square units of the real-life measurement.

What is a common mistake made when calculating the area of a shape on a scale drawing?

A common mistake is calculating the area of the drawing in square centimeters and then incorrectly trying to convert it directly to square meters using the scale, which only applies to linear measurements, not square measurements.

How can you represent a real-life object with specific dimensions on a scale drawing?

Determine the scale factor between the drawing and real life. Then, reduce the real-life dimensions by this scale factor to represent the object on the scale drawing.

What is the purpose of the learning platform mentioned by Amadeus at the end of the script?

The learning platform is designed to provide additional resources for learners, including videos, practice questions, and progress tracking for subjects like science and math. It is offered as a free service.

How can viewers access the learning platform and the specific lesson related to the video?

Viewers can access the learning platform by clicking on the logo on the right of the video or by following the link provided in the video description for the specific lesson.

Outlines

00:00

📏 Understanding Scale in Images and Diagrams

This paragraph explains the concept of scale in images and diagrams, emphasizing that even though images may represent objects at different sizes, the proportions are maintained. It clarifies the terminology used for different types of scaled images, such as photos, scale drawings, and scale diagrams, with a special mention of maps. The importance of including a scale or key in diagrams and maps is highlighted, with three main methods explained: a direct scale (e.g., 1 cm represents 5 km), a ratio scale (e.g., 1:600), and a representative fraction scale. The paragraph also demonstrates how to apply these scales to solve problems, such as finding distances between points on a map using the given scale.

05:01

📐 Solving Problems with Scale Drawings and Diagrams

The second paragraph delves into solving practical problems using scale drawings and diagrams. It discusses how to measure distances on a diagram and convert them to real-life measurements using the scale provided. An example is given where a map's scale of 1 to 500 is used to calculate the distance between two points, converting centimeters on the map to meters in reality. The paragraph also addresses a common mistake of converting square centimeters to square meters incorrectly and provides the correct method for calculating areas on scale drawings. Another example involves calculating the area of a patio from a grid-based scale drawing and converting real-life measurements to scale drawing measurements, as demonstrated by drawing a pond onto Jennifer's garden plan.

Keywords

💡Scale

Scale refers to the ratio or proportion between the dimensions of a representation, such as a drawing, map, or model, and the actual dimensions of the object it represents. In the video, scale is crucial for understanding how the size of objects in images relates to their real-world size. For example, the script mentions that a map of the United Kingdom is not actually three centimeters wide, but is scaled down to fit on the screen.

💡Scale Drawing

A scale drawing is a type of illustration where the size of the objects is reduced or enlarged proportionally to fit within a specific space while maintaining their relative proportions. The script explains that when a drawing is to scale, it is called a scale drawing, which is important for accurately representing real-world distances and dimensions.

💡Scale Diagram

A scale diagram is similar to a scale drawing but is often used to represent more abstract concepts or systems. The script clarifies that when a diagram is to scale, it is referred to as a scale diagram, emphasizing the importance of maintaining accurate proportions for conveying information effectively.

💡Map

A map is a graphical representation of an area, usually on a flat surface, that shows the spatial relationships among various features. The script notes that in the special case of a map, it can simply be called a map, but it should still maintain a scale to represent real-world distances accurately.

💡Key

In the context of the video, a key is a tool or set of instructions that helps interpret the scale of a map or diagram. The script explains that scale diagrams or maps should have a key to allow users to understand the real-life distances represented by the images.

💡Ratio

A ratio is a comparison of two quantities, often expressed as a fraction or with a colon. In the script, the ratio '1 to 600' is used to describe the scale of an image, meaning that every unit on the image is 600 times smaller than the actual object.

💡Centimeter

The centimeter is a unit of length in the metric system, equal to one hundredth of a meter. The script uses centimeters as a common unit for expressing scale, such as when explaining that one centimeter on a map might represent 500 centimeters or 5 kilometers in real life.

💡Meter

The meter is the base unit of length in the International System of Units (SI). The script mentions meters when converting distances from the scale of a drawing to real-world measurements, such as converting centimeters to meters to find the actual distance between two points.

💡Area

Area refers to the amount of space enclosed within a two-dimensional figure or shape. The script discusses calculating the area of a patio in a scale drawing, emphasizing the need to convert the scaled measurements to real-world dimensions to find the actual area in square meters.

💡Conversion

Conversion is the process of changing from one system of measurement to another. The script demonstrates conversion by explaining how to change the scale from a ratio to a more workable form, such as converting '1 to 500' to '1 centimeter equals 500 centimeters' for easier calculation.

💡Grid

A grid is a structure made up of a series of parallel horizontal and vertical lines, often used as a guide for measurement or organization. The script mentions a grid used in a scale drawing of Jennifer's garden, where each square represents one centimeter by one centimeter, facilitating the measurement of distances and areas.

Highlights

Images can represent objects larger or smaller than themselves by scaling them to fit on a screen.

All proportions in scale images are correct, maintaining the relative measurements of the actual objects.

Scale images are categorized as photos, scale drawings, or scale diagrams depending on their type.

Scale diagrams and maps should include a scale or key to interpret real-life distances.

Three main methods of scale representation: direct measurement, ratio, and specific distance representation.

Direct measurement scale means a certain unit on the image corresponds to a fixed real-life distance.

Ratio scales express that the image is a certain multiple smaller than the actual object.

Specific distance scales indicate a particular length on the image corresponds to a set real-life distance.

Exam questions often require using the scale to find distances between points on a map.

Changing scale ratios to a more workable format can simplify calculations.

Measuring distances on a diagram and applying the scale to find real-life distances.

Converting measurements from the diagram to real-life measurements using the scale.

Avoiding common mistakes in converting square centimeters to square meters using scale.

Calculating the area of objects on a scale diagram by finding real-life dimensions.

Understanding that the area of a rectangle is found by multiplying its length by its width.

Drawing objects on a scale diagram by converting real-life measurements to the diagram's scale.

The importance of correctly applying scales to avoid errors in representation and calculations.

Amadeus offers a learning platform for further study and practice with progress tracking.

The availability of a playlist for organized learning of the subject matter.

Transcripts

if you look at these three images what

they all have in common is that they're

representing things much larger or

smaller than the images themselves

for example the united kingdom isn't

really three centimeters wide

and neither is a cell or a horse

we've just made them smaller or larger

than the real things so that we can show

them neatly on the space of the screen

however the important thing to notice is

that the images are to scale

which means that all the proportions are

correct

for example the horse's height relative

to its length is correct

there's a bit of confusion around what

we call images like this because it

depends on what type of image we have

if we have a photo then we just call it

a photo

because they should always be the scale

when we have a drawing that's the scale

though we call it a scale drawing

and when we have a diagram master scale

we call it a scale diagram

although in the special case of a map we

can also just call it a map as well

now something else that all scale

diagrams or maps should have is some

kind of scale or key

which allows you to work out the real

life distances that the images represent

there's a few different ways they can do

this but the main ones are these three

this first type is the easiest to work

with and in this case it just means that

every one centimeter on your map or

drawing

represents five kilometers in real life

so two centimeters would represent 10

kilometers three centimeters would

represent 15 kilometers and so on

his second one

one to 600 is basically a ratio

and means that everything on the image

is 600 times smaller than the real thing

or in other words every one centimeter

on the image would be 600 centimeters in

real life

so we could rewrite it as one centimeter

equal 600 centimeters

or even one centimeter equal six meters

because 600 centimeters and six meters

are the same distance

this last type is the trickiest of the

three

but just means that this distance here

represents 20 kilometers

so what we normally do is measure the

line with a ruler

which in this case would be 2.5

centimeters

and then we know that every 2.5

centimeters represents 20 kilometers

which is a much easier scale to use

and if you wanted you could make it even

easier by dividing both sides by 2.5

to find that one centimeter represents 8

kilometers

now that we've covered the basics let's

have a go at a couple of exam questions

so in this question we're being asked to

use the map to find the distance between

the two points a and b

and if we look at our map we can see the

two points they're talking about

and we can also see the scale in the

bottom right corner

which says 1 to 500

which means that our diagram is 500

times smaller than in real life

now you don't have to do this but what i

like to do is change the 1 to 500

to 1 centimeter equals 500 centimeters

because it means exactly the same thing

but it'll be a bit easier to work with

later

the next thing we're going to have to do

is find the distance between a and b on

our diagram

which we can do by measuring with a

ruler

and on my screen that's 9 centimeters

then because we know from our scale that

each one centimeter on our diagram

represents 500 centimeters in real life

we can work out what that nine

centimeters must represent

so because nine centimeters is nine

times bigger than one centimeter

we also have to multiply the 500

centimeters by nine

to get four thousand five hundred

centimeters

and then to finish all we need to do is

convert that into meters by dividing it

by 100

to get 45 meters

so we now know that the point a and b

are 45 meters apart in real life

okay let's try a slightly different one

this time

in this question we're told that the

image below is a skill drawing of

jennifer's garden

where each centimeter on the diagram

represents 0.5 meters in the real world

and for part a we're being asked to find

the area of the patio in square meters

now you might have noticed that they've

done this drawing over a grid

and they actually do this quite a lot in

exams

where each square is often one

centimeter by one centimeter

and this makes it easier for us to

measure distances

however the squares could also be

different sizes so it's always worth

checking with a ruler

for this question we'll assume that the

squares are all one centimeter by one

centimeter

so in order to find the area of the

patio we're first of all going to need

to find the real length and real width

because we'll then be able to multiply

them together to get the area

to do this we first need to measure how

long they are on our diagram

which we can do using a ruler which

would give us eight centimeters and six

centimeters

or by counting the squares

which would give us the same thing

because remember each square is one

centimeter

and now that we have these values from

the drawing we can convert them into

real life values

so because one centimeter is equivalent

to 0.5 meters

eight centimeters which is eight times

larger must be four meters

while six centimeters which is six times

larger must be three meters

so in real life the patio area is four

meters long and three meters wide

and lastly because the area of a

rectangle is equal to its length times

its width

we just do four times three

to find that the area of the patio is 12

square meters

now one thing i want to point out here

is that a common mistake with this type

of question and exams is to find the

area of the drawing in square

centimeters

and then try to convert that value

straight to square meters

which unfortunately doesn't work

for example if we found the area of the

drawing

by doing the length of 8 centimeters

times the width of 6 centimeters to get

48 square centimeters

we couldn't then use our scale to

convert that to 24 square meters

because our scale only converts

centimeters to meters

not square centimeters to square meters

if we rub all of this working out let's

have a go at a part b before we finish

this one says that jennifer wants to

have a one meter by one meter square

pond installed

and we need to draw the pond onto the

scale drawing

so this is kind of the opposite of part

a

this time we're converting from real

life values of one meter by one meter to

the scale drawing values

so if one centimeter is 0.5 meters

and our pond has a side length of one

meter

that's two times bigger so on our

drawing it will be two centimeters

which means that all we have to do is

draw a two centimeter by two centimeter

square somewhere on this diagram

for example down here or over here

it doesn't really matter where you just

need to plop it on and then label it

pond

hey everyone amadeus here i just wanted

to let you know that we also have a

learning platform where you can watch

all of our videos

practice what you've learned with

questions and keep track of all of your

progress for the sciences and maths

it's completely free so if you haven't

already you can check it out by clicking

on our logo here on the right

or if you'd like to do the lesson for

this particular video we put the link to

that in the description down below

we've also arranged all the videos for

this subject in a playlist for you here

that's all though so hope you enjoy and

i'll see you next time thanks