Gear Activity You have 2 gears, one small one and one big one. Think about the following questions: 1. If the small gear turns clockwise, which direction does the big gear turn? Why? Will this always be true? Why? 2. If you turn the small gear a certain number of times, does the big gear turn more revolutions, fewer, or the same amount? How can you tell? 3. Devise a way to keep track of how many revolutions Gear A makes. Devise a way to keep track of the revolutions Gear B makes. How can you keep track of both at the same time?
You have 2 gears, one small one and one big one. Think about the following questions: 1. Last time you found out that the small gear has 2/3 of the number of total teeth that the big gear has. How does this relate to the rotations the gears make? Justify your answer. 2. What is the relationship between the number of teeth on the gears and the number of rotations that the gears make?
The following table contains pairs of rotations for a small and a big gear. Did all of these entries come from the same gear pair, or did some of them come from different gears altogether? How can you tell? Small Big 7 1/2 5 27 18 4 1/2 3 16 10 2/3 1/10 1/15
Ricardo was working with the small gear and the big gear (8 teeth and 12 teeth). He turned the small gear a certain number of times he wasn t quite sure exactly how many times, because he lost count. Then he turned the small gear 1 extra rotation. How many extra rotations did the big gear turn while he did that?
Say you had 2 gears that had 5 teeth and 7 teeth, instead of 8 teeth and 12 teeth like we ve been working with. What would be the relationship between the number of turns the small gear makes and the number of turns the big gear makes in this case?
Say we re working with the small gear (8 teeth) and the big gear (12 teeth). 4. If you could replace the small gear with a different gear that would make the big gear turn twice as fast, how many teeth would that different gear have? 5. What if you wanted to replace the small gear with a different gear to make the big gear turn twice as slow instead of twice as fast. How many teeth would that different gear have?
Now let s work with 3 gears: small (8 teeth), middle (12 teeth), and large (16 teeth). Connect the small to the middle and the middle to the large. 1. You already know about the relationship between the small gear and the middle gear. What about the middle gear and the large gear? How many turns does the large gear make in relationship to the middle gear? 2. How many times do you have to turn the small gear to make the LARGE gear turn once? 3. How many times will you have to turn the small gear so that the middle gear AND the large gear both turn a whole-number amount of revolutions, with no fractions?
Say you had this table: Small Big 7 1/2 5 27 18 16 12 12 9 Another student explained that since the cross products with the first 2 pairs and the cross products with the 2 nd 2 pairs equal each other, then they all came from the same gear. Do you agree or disagree? Why? Explain your thinking.
Gear A has 6 teeth. You hook it up to Gear B, and turn it a certain number of times. Gear B turned 1/4 of the number of turns that Gear A turned. How many teeth would Gear B have to have? **********************************************************************
Gear A has 15 teeth. If you turn it 12 times, Gear B turns 10 times. How many teeth does Gear B have to have?
Gear A has 5 teeth and Gear B has 8 teeth. Gear A starts spinning on its own, before it s connected to Gear B. It spins 6 times. Then Gear B is plopped down and they spin together. 3. If Gear A spun a TOTAL of 48 times, how many times did B spin? 4. If Gear B spun 15 times, how many times did A spin? 5. Write an algebraic expression that describes this situation.
Gear A has 24 teeth. You hook it up to Gear B, and turn it a certain number of times. Gear B turned 4/5 of the number of turns that Gear A turned. How many teeth would Gear B have to have? **********************************************************************
Gear A has 15 teeth. You hook it up to Gear B, and turn it a certain number of times. Gear B turned 1 and 2/3 of the number of turns that Gear A turned. How many teeth would Gear B have to have? **********************************************************************
Gear A has 24 teeth. You hook it up to Gear B, and turn it a certain number of times. Gear B turned 4/5 of the number of turns that Gear A turned. How many teeth would Gear B have to have? Another student said that all you would have to do would be to multiply A s teeth by 5/4 to figure out how many teeth B has. Do you agree or disagree? Why?
Gear A has 5 teeth and Gear B has 8 teeth. Gear A starts spinning on its own, before it s connected to Gear B. It spins 6 times. Then Gear B is plopped down and they spin together. 6. If Gear A spun a TOTAL of 48 times, how many times did B spin? 7. If Gear B spun 15 times, how many times did A spin? 8. Write an algebraic expression that describes this situation. 9. Make a table of pairs of rotations for A and B. How is your table different from the ones you ve made before? How is it similar?
The following table represents pairs of gear rotations: A B 2 0 10 5 16 10 18 11 2/3 A. Do all of the pairs come from the same gear combination? How can you tell? B. Describe the gear situation(s) that generated these pairs. ****