Keiran McLean: We’re in the office of world famous architect Zara Jones who’s about to reveal her new design.
Zara Jones: Ladies and Gentlemen, I give you my ‘House for a Geometry Lover’.
Keiran McLean: Brilliant! What a beautiful model. Now, what scale is it?
Zara Jones: Scale?
Keiran McLean: Yes, scale. You know, is the model 1:50? So, if it’s 1 centimeter on a map or model, it’ll be 50 centimeters in real life?
Zara Jones: No.
Keiran McLean: What is the scale then?
Zara Jones: No. No. Stop. I’m not interested in the maths. I don’t bother with scale. It’s too hard. No.
Keiran McLean: So, it’s 1:1. The Model is the same size as the actual building you’re going to build.
Zara Jones: Yes. 1:1. Whatever you say. This IS the building. It’s finished.
Zara Jones: Infact. You can go inside if you like.
Keiran McLean: Really? But how will I fit through the door?
Zara Jones: Oh really. Must I do all the work round here?
Zara Jones: Let me just give you a guided tour.
Narrator: Scale and Coordinates. Sounds coordiplated. I mean, complicated. But, don’t panic.
V.O: Let’s kick some Maths!!
Narrator: Hear Scale think size. In real life, my house is 100 meters from this tree.The distance between them on this map is 10 cm.You already know that 1m is the same as 100cm, so 100m equals 100 X 100cms, and that’s 10000cm.
Narrator: So how much bigger is the real distance than our map? Well, 10000 ÷ 10 = 1000, so the real distance is 1000 times bigger than the map. We say that the map has a ratio of 1:1000. Objects in real life are 1000 times bigger than they are on the map.
Narrator: Maps also have a grid of squares on them and numbers at the sides. This is so we can find a point on the map by using numbers that we call coordinates. We can use coordinates to help us make a shape bigger or smaller using a scale factor.
Narrator: The X axis is horizontal. It goes across. The Y axis is vertical. It goes up. The X axis and Y axis stretch into minus territory. And where they cross is called the origin.
Narrator: Now let’s make a point A there. We mark down the coordinates by going ACROSS first, THEN UP.
Det. Lewis Stinker: Okay Sgt. Let’s be Methodological! Go into the house! And up the stairs!
Sgt Janice Fungal: Just like when we mark down coordinates. Across and up! Okay!
Det. Lewis Stinker: You could have opened the door!
Narrator: So X first, 2, then followed by Y, 2. It’s really important to get that in the right order, X first, then Y, just like they are in the alphabet. So we write a 2,2. If I gave you b 6,4 and c 4,6, we’d end up with a triangle.So, now we have coordinates for a shape. Just think of them as a recipe.
Baker: TRIANGLES!
Narrator: What if we want to make it larger or smaller? That’s when we use a Scale Factor – which is how much bigger or smaller you want something to be. And it’s really very easy. If we had a Scale Factor of 2, then we’d want our triangle twice as big, so we multiply our coordinates. Look. By multiplying each coordinate by 2, so that a (2, 2) becomes (4,4) we can find out the coordinates for our new twice as big triangle.
Narrator: But not all Scale Factors will make things bigger. A Scale Factor of ½ will halve the size of our original, so again, multiply your original coordinates by a half and you get (1,1), (3,2), and (2,3).
Narrator: Sometimes, you won’t have a Scale Factor, and you’ll be asked to find one. But don’t worry, you’ll be able to work it out… If we look at these two rectangles, we know that these corresponding sides are 3 and 9. The bigger shape is our copy and it’s always copy over original, so 9 over 3 is, well, 3. Our Scale Factor is 3, which means our copy is three times as big as the original.
Narrator: Now, how to find out the missing length of the larger rectangle? Again, we’re using what we know to find out what we don’t know. We multiply the known length of 4 by our Scale Factor or 3 to get 12! The length of our missing side is 12 centimetres!
Narrator: So, now you know how to do all that, I expect you’ll all grow up to be World Famous Architects and Engineers. Which reminds me. I wonder how the world famous architect Zara Jones is getting on?
Lady: Can I have a proportion of Fish & Chips please.
Server: A portion of Fish & Chips coming right up.
Lady: No! I said a proportion of Fish & Chips please.
Server: A proportion…
Lady: Yes please. A large proportion. Let’s scale it up to twice the size!
Server: Ok
Lady: That’s not in proportion! Double the fish! Double the chips!
Lady: That’s better. The large portion is now in proportion to the smaller one. Same proportions!
Lady: Thanks. Glad to see you know all about proportion now.
Server Salt & Vinegar?
Video summary
We see a demonstration of converting distance on a map to real-life distance and learn how to calculate scale factor given the actual distance on a map.
Reading coordinates and placing coordinates on a set of axes is explained, which leads on to enlargement using scale factors on a coordinate plane.
An example of calculating unknown sides of an enlarged shape is shown.
The end sketch illustrates the idea of proportion.
This clip is from the series Kick Sum Maths.
Teacher Notes
Pupils could use scale factors to enlarge shapes on a coordinate plane or to read maps.
They could create scale drawings and models of objects or places, for example a map of the school.
These clips could be used for teaching Maths at KS2 or at a beginner level in England, Wales and Northern Ireland and 1st and 2nd Level in Scotland.
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