Keiran McLean: Building your own home is an exciting adventure for any family, but for one couple, Hugh and Daisy Watson, they鈥檙e really embracing the unknown.
Hugh Watson: Hi
Keiran McLean: Hello!
Keiran McLean:So, tell me about the architect who鈥檚 designing your new home?
Daisy Watson: Yes, he鈥檚 Cosmo Wunderlich. Ignores all the boring rules. Can鈥檛 wait to see his design.
Keiran McLean: So tell me about your exciting new design!
Cosmo Wunderlich: I can鈥檛.
Keiran McLean: Is it a secret?
Cosmo Wunderlich No. It鈥檚 just that I don鈥檛 use the language of geometry.
Keiran McLean: Is your building square? Rectangular? Triangular roof? Any parallel lines? Right angles? Any parallelograms?
Cosmo Wunderlich: Ha! You just made that word up. Parallel o gram鈥 There鈥檚 no such thing!
Keiran McLean: Yes there is. A parallelogram is a ~
Cosmo Wunderlich:Listen you boring man, it鈥檚 the 21st Century! I don鈥檛 need to know this building blocks stuff. I am not a child. I will build a house for Hugh & Daisy and it will be beautiful. Geometry! HA! Who needs it!?!?
Keiran McLean: It鈥檚 a year later, let鈥檚 see what he鈥檚 built.
Narrator: Don鈥檛 worry. I鈥檓 sure they鈥檙e absolutely fine underneath there. clears throat. You see, Geometry is serious stuff. There鈥檚 a bit to learn, but don鈥檛 panic. You can do it! Now ~
V.O: Let鈥檚 kick some Maths!!
Narrator: Geometry is how Math鈥檚 measures and describes the world around us, and can describe simple shapes like squares or triangles Right up to the most complicated shapes. But you don鈥檛 have to worry about the complicated stuff now. Or 3D shapes just yet.
Narrator: What鈥檚 important to understand is that geometry has rules, has facts you need to know. Here鈥檚 a rule you probably know: that a shape with 4 right angles and 4 equal sides is a square! What鈥檚 an angle again? It鈥檚 a measure of the amount of turn between two lines! A box in the corner means that it鈥檚 a right angle!
Narrator: These two lines are perpendicular, which just means they are on either side of a right angle. The lines facing each other are parallel. This means they鈥檙e always the same distance apart. They鈥檇 never meet, even if they stretched on forever! We use matching arrows to show parallel lines.
No matter the length of the sides, as long as they鈥檙e equal and there are 4 right angles of 90 degrees 鈥 it鈥檚 a square! It鈥檚 always a square!
Narrator: But what if I squeeze this square? Two angles get wider and two get narrower. Now, it鈥檚 still got four equal sides, but it鈥檚 not a square, it鈥檚 a rhombus! All its angles add up to 360 degrees, just the same as any four sided shape. But a rhombus has matching pairs of opposite angles. Two are acute angles, smaller than 90 degrees. And two are obtuse angles, bigger than 90 degrees. That angle is 65 degrees. Can you work out the others?
Narrator: Don鈥檛 panic. You have all the information you need to beat this problem. And this is pretty much what geometry and a lot of Maths is about. Using what you know to find out what you don鈥檛. The answer is staring you in the face. So stare back. And Kick Sum Maths!
Narrator: So, we know the angles add up to 360 degrees, and that the angles that face each other match, so right away you can fill in that as 65 degrees too. Now, the other 2 angles must match too 鈥 but what are they? Well, if ALL the angles add up to 360 degrees, then how about this? Take the sum of those angles, 65 + 65 = 130 from the total of 360 and you get 230. The other two must add up to 230, so divide 230 by 2 and you get 115! Easy!
Narrator: You鈥檒l be asked a lot of questions about triangles.
NEFERTITI: Tell me about it.
Narrator: So, it鈥檚 important to know that there are 4 different types of triangles. An equilateral triangle has equal sides and equal angles.
Narrator: An Isosceles triangle, has 2 equal sides and 2 angles that are equal.
Narrator: A right angled triangle has a right angle in it, but not necessarily any equal sides.
Narrator: And a scalene triangle has different sides and different angles. But remember, all the angles in a triangle add up to 180 degrees
Narrator: So, if I were to ask you what the missing angle is ~ here?
You鈥檇 be able to use what you know to find out what you don鈥檛. That is a right angle, and that is 40 degrees so, 180 minus 90 minus 40 equals 50! And that鈥檚 the magic of geometry! Whatever the problem is, use the information you are shown, plus the information you already know, with a careful step by step method to find the answer. And that鈥檚 Maths explaining itself right there!
Narrator: Isn't that right maths lamb?
Maths Lamb: Maaaaaaaath
HOST: Ladies and gentlemen, boys and girls, it鈥檚 time for another exciting addition of the geometry based gameshow, that you can play along at home. Name That Shape!
So without further ado, contestant Number 1鈥
Can you鈥 Name That Shape?!
Number1: Errr鈥mmm鈥
HOST: I can tell you it's got 4 sides鈥
Number 1: A quadrilateral, hmm, rectangle, kite, rhombus, trapezium鈥
HOST: And all the sides are equal.
Number 1: It could be a rhombus, or maybe a square鈥
HOST: What if I told you that all the corners are right angled?
Number 1: Are you telling me that?
HOST: Yes
Number 1: It鈥檚 a square.
HOST: It is a square! Well done contestant number 1. You鈥檝e won an all expenses paid luxury holiday to the planet Mars!
Number 1: Yeah!!!
HOST: Contestant Number 2鈥
Can you鈥 Name That Shape?!
Number 2: A triangle!
HOST: I鈥檓 going to have you to be more specific. What type of triangle?
Number 2: Uh鈥 A big one?
HOST: All the interior angles are equal鈥
Number 2: Oh an equilateral triangle!
HOST: It is an equilateral triangle. You really know your geometry contestant Number 2鈥 and you鈥檝e one鈥 a lifetimes worth of chocolate ice cream!
Number 2: Hmmm Yeah!! I like icecream
HOST : Okay contestant Number 3 I鈥檝e got a very simple shape for you鈥or your chance to win your very own magical wish granting unicorn, can you Name That Shape?!
Number 3: Err鈥rr鈥
HOST: I鈥檓 going to have to hurry you!
Number 3: A sausage?
HOST: No I鈥檓 sorry- a sausage??
Number 3: A squid?.. A squirrel?.. A squid riding a squirrel?
HOST: You鈥檙e really going to kick yourself when I tell you鈥 It was a GOMBOC! I鈥檓 sorry contestant Number 3 but for getting that wrong you lose a million points and have to spend a week in the horrible dungeon of nasty smellyness!
Number 3: No please, anything but the horrible dungeon of nasty smellyness!
HOST: Well that鈥檚 all for this weeks show, but make sure you tune in next time when we鈥檒l be playing鈥 Name That Squirrel!.. I mean shape! Name That Shape!!
Johnny James: What is it you want boss?
Editor: You鈥檙e the best young reporter at this newspaper Johnny.
Johnny James: Thanks boss.
Editor: And I鈥檓 sure you鈥檝e heard the news. There鈥檚 a giant parallelogram that鈥檚 escaped from a geometry research laboratory. Those crazy geometrists always thinking they can play god. When will they ever learn!!! It鈥檚 the 鈥渢eaching a triangle to sing鈥 debacle all over again.
Johnny James: What do you want me to do about it boss?
Editor: It鈥檚 a beserk giant parallelogram. I want you to go out and get the 鈥渁ngle鈥 on this story.
Johnny James: Right away boss!
Johnny James: I think I鈥檝e got the right angle for the story boss!
Editor: It鈥檚 a right angle sure. But it鈥檚 a parallelogram so a right angle is the WRONG angle! Now go out again and get me the angle on this story.
Editor: That鈥檚 a straight line! The only angle you鈥檒l get from that is 180 degrees and that鈥檒l turn everything upside down.
Editor: Now THAT鈥橲 the angle I鈥檓 looking for. Well done Johnny. You鈥檝e knocked this story into shape.
Scientist: Behold Igor, my latest and most fantastical creation. The like of which the world has never seen!
Scientist: I call it a 鈥淔rankencube!鈥. It鈥檚 like a square, with pairs of sides that are equal in length and parrallel, but look closely my mutant chum and you will see that there are NO RIGHT ANGLES!! AH-HA-HA-HA-HA!!!
Igor: It鈥檚 a rhombus
Scientist: What?
Igor: A rhombus. It鈥檚 what you鈥檚 get if you stitch two triangles together.
Scientist: So it鈥檚 not a new shape?
Igor: No master. In fact it鈥檚 quite common.
Scientist: Oh dear. Back to the drawing board.
Igor: What do you want me to do with your creation?
Scientist: Dispose of it Igor. I have new shapes to create!
Rhombus: Rhombus want to live!
Igor: Oh look master, he鈥檚 left a hole. It鈥檚 in the shape of a Frankencube!
Video summary
A demonstration of the importance of using correct mathematical language.
Descriptions of acute, right and obtuse angles as well as parallel and perpendicular lines.
We compare and contrast the geometric properties of different triangles and quadrilaterals.
A sketch explores naming shapes through their properties, while another looks at different types of angles and how they relate to shapes.
One final sketch explores the properties of a rhombus.
This clip is from the series Kick Sum Maths.
Teacher Notes
Pupils could work in pairs. One has a 2D shape and describes it to their partner using mathematical language. The other student attempts to draw the shape. Compare the shape drawn to the shape described.
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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Decompose numbers into prime factors. End sketches look at primes and simple sequences.
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