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# Circumference of Circles

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## Mr Mattock

on 28 September 2016

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#### Transcript of Circumference of Circles

Circumference of Circles
Starter
3U + 1T.

3U + 1T means 3 x the units figure + 1 x the tens figure.

So 24 > 3 x 4 + 1 x 2 = 12 + 2 = 14
Then 14 > 3 x 4 + 1 x 1 = 12 + 1 = 13

Continue this rule until you get back to 24.

Repeat using any number less than 30 that you have not already used.
There is a loop of 28 numbers.

24 -> 14 -> 13 -> 10 -> 1 -> 3 -> 9 -> 27 -> 23 -> 11 -> 4 -> 12 -> 7 -> 21

8 <- 22 <- 17 <- 25 <- 18 <- 6 <- 2 <- 20 <- 26 <- 28 <- 19 <- 16 <- 15 <- 5

The only number left is 29 which is a rather special number as;

29 -> 3 x 9 + 1 x 2 = 27 + 2 = 29.
Circumference of Circles
L.O. - Find the circumference of circles, by calculating using the diameter/radius.
What have we discovered?
Circumference

Diameter
= Pi
Circumference = Pi x Diameter
7 cm
Examples
5 mm
Red:
1) 25.1 cm 2) 37.7 cm 3) 62.8 cm
4) 113 m 5) 50.3 m 6) 44.0 m
7) 37.7 cm 8) 50.3 cm 9) 75.4 cm
10) 7.23m 11) 53.4 m 12) 72.3 m

Amber:
1) 6.366 cm 2) 33.42 cm 3) 0.7321 m
4) 4.775 m 5) 81.49 cm 6) 56.02 m

Green
1) 786 cm 2) 786 m 3) 26 m
4) 579 turns 5) 21 turns 6) 979 turns
7) 55 cm 8) 408 cm 9) 54 m
Left
Right
Main Activity
Complete the RAG Worksheet

Red -
Find the circumference of the circles.

Amber -
Find the diameters of the circles given the circumferences.

Green -
Solve the circumference problems.
Circumference of Circles
7 cm
x 7 = 21.99 cm
Examples
5 mm
x 10 = 31.4 mm
(a) Circumference =
0.5 x = 1.570796327 metres

100 rotations = 100 x 1.570796327 = 157.1 metres
(b)
5000/1.570796327 = 3183.1 turns
Key
Examples

Activities
Activity