**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?