Costume 2 · machines + correctionsSun 13 September1 / 4
Gears, and this week's corrections
A lowest common multiple you can actually watch turning
Name Date
Think about thisA 12-tooth gear meshes with an 18-tooth gear. Both marks start pointing straight up.
After how many teeth do both marks point up again?
1Answer the question above.
2By then, how many turns has the 12-tooth gear made? And the 18-tooth one?
Once you have both numbers, look at them carefully. Notice anything?
This is the important part todayNot 12 x 18 ＝ 216.
Multiplying takes you far past the first time they line up. Make sure you can say in words why the answer is 36 and not 216.
3Write, in words, why the answer to question 1 is not 216.
Different gears
4With an 8-tooth and a 12-tooth gear, after how many teeth do they line up again?
5A bicycle has 48 teeth on the front gear and 16 on the back. One turn of the pedals turns the back gear how many times?
48 ÷ 16. This one is division, not a common multiple.
This week's corrections
6Pick two questions you got wrong this week and do them again.
Solve them again — do not copy the answer across.
Classic problem — cycles
7Red, blue and yellow lights flash in that order, over and over. The 1st is red. What colour is the 50th?
Think about the remainder when you divide by 3.
8With the same three lights, what colour is the 100th?
More of it — reading the remainder
9Red, blue, yellow, green repeat in that order, starting with red. What colour is the 60th?
10In question 9 the remainder came out 0. What does a remainder of 0 mean here? Say it in words.
The important question today.
11If 1 January is a Thursday, what day is 29 January?
12The gear questions used the lowest common multiple. What did the repeating-colour questions use? One phrase is enough.
Extra · you may skip thisAdd a third gear with 36 teeth. After how many teeth are all three back where they started?