Free Activity: LEGO® Education Simple and Motorized Mechanisms Lesson – Using Ratios with Gears

 
 
 
 
Estimated Completion Time

·         45-50 minutes

Grade Level: 6

·         Math

 Learning Outcomes

·         Understanding the concept of a ratio and using ratio language to describe a ratio relationship between two quantities

·         Understanding the concept of a unit rate a/b associated with a ratio a:b with b ‡ 0, and using rate language in the context of a ratio relationship

 LEGO® Education Materials

·         LEGO® Education Simple and Motorized Mechanisms Base Set

·         Book III G2

 Vocabulary

Encourage the use of these words during the activity:

·         gear ratio

·         gear tooth

·         ratio

·         revolution

 

Connect

·         Have students count the number of teeth on each gear. Choose two gears and ask about the ratio – 8-tooth and 40-tooth gear would be 8:40, but we reduce to lowest terms, which is 1:5. Have students explain why it is 1:5 using the terms tooth/teeth and ratio.

·         Now, have students predict how many revolutions the 8-tooth gear will go when the 24-tooth or the 40-tooth gear is turned once.

 Construct

·         Using Book III G2 as a guide, construct the model using the 8-tooth and 24-tooth gears.

·         Have students carefully turn the handle on the 24-tooth gear so that it makes one complete revolution. Count how many times the 8-tooth gear turns in a complete circle. Make sure students try this 4-5 times to be sure they get the same count. Have them put the data they obtain into the table.

·         Change the gears so that the 40-tooth gear is used in place of the 24-tooth gear. The students will have to change the position of the axle that holds the gear. Have students carefully turn the handle on the 40-tooth gear so that it makes one complete revolution.

·         Count how many times the 8-tooth turns in a complete circle. Make sure students try this 4-5 times to be sure they get the same count. Have them put the data they obtain into the table.

 Contemplate

·         Have students complete the table. Discuss the ratios that were made. Ask students to describe the relationship between the number of teeth, using ratios.

·         Ask students to describe the relationship between the revolutions using ratios and to describe the rate of motion. Is there a correlation that they can see between the two ratios?

Continue

·         Ask students to determine – without trying the gears – the ratio of a 12-tooth gear to an 8-tooth gear. Then, ask them to predict how many complete rotations the 8-tooth gear will make when the 12-tooth gear makes two complete rotations. Ask students to check their predictions. Students will not be able to use the blue beam as a guide, so tell them they will have to create their own test.

 Guiding Questions

·         What is the relationship between the gear ratio and the revolution ratio?

·         Will a ratio always be reducible to 1:X or X:1? Why or why not?

 Extension

·         Have students test the 40-tooth gear and the 24-tooth gear and create gear ratios and revolution ratios.

·         Have students write a word problem that involves using the gear ratios.

·         Talk about gearing up and gearing down and the relationships using gear ratios. Then, ask students what the driver and driven gears would be in a given situation. How can they determine if a gear ratio represents gearing up or gearing down?

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