So you want to take a walk Standard 7.RP: Compute unit rates associated with ratios of fractions. Please discuss in your groups What is the relationship between rate, time and distance? Be prepared to discuss with the entire class How do we talk about distance, time and rate? • If you were going to tell me how fast you were walking how would you express it? • How are rate, time and distance reflected in your explanation of how fast you walked? • How would you express it if you were driving, or running. Is the underlying concept any different? Discuss in groups and be prepared to discuss it as a class. Metric System Conversion Chart Abbreviations • Common Length Unit Abbreviations: • millimeters = mm centimeters = cm inches = in meters = m feet = ft kilometers = km miles = miles Conversion tables Metric Conversions 1 centimeter 1 meter 1 kilometer = 10 millimeters = 100 centimeters = 1000 meters 1 cm 1m 1 km = 10 mm = 100 cm = 1000 m Standard Conversions 1 foot 1 yard 1 yard 1 mile = 12 inches = 3 feet = 36 inches = 1760 yards 1 ft 1 yd 1 yd 1 mi = 12 in = 3 ft = 36 in = 1760 yd Metric to Standard 1 millimeter 1 centimeter 1 meter 1 meter 1 meter 1 kilometer 1 kilometer = 0.03937 inches = 0.39370 inches = 39.37008 inches = 3.28084 feet = 1.09361 yards = 1093.6133 yards = 0.62137 miles 1 mm 1 cm 1m 1m 1m 1 km 1 km = 0.03937 in = 0.39370 in = 39.37008 in = 3.28084 ft = 1.09361 yd = 1093.6133 yd = 0.62137 mi Standard to Metric 1 inch 1 foot 1 yard 1 yard 1 mile 1 mile = 2.54 centimeters = 30.48 centimeters = 91.44 centimeters = 0.9144 meters = 1609.344 meters = 1.609344 kilometers 1 in 1 ft 1 yd 1 yd 1 mi 1 mi = 2.54 cm = 30.48 cm = 91.44 cm = 0.9144 m = 1609.344 m = 1.609344 km • If a person walks ½ mile in each ¼ hour, compute the unit rate as the complex fraction ½ / ¼. Questions to consider How is this fraction related to a ratio? Is there any difference? What elements are we using to explain our rate? Solve this using a mathematical model in groups. Be prepared to discuss your model with your class. Have them count in non standard measurement • We are going to use the Outside Unit Packet • With a partner count the number of steps in 10 feet then switch and have your partner count. Are they the same. Why or why not? • With a partner count the number of Mississippi's in 10 feet then switch. Are they the same. Why or why not? • How is counting using Mississippi potentially problematic? Discuss in groups and then be prepared to discuss as a class. Outside Unit Tables You Partner Number of steps taken in 10 feet Number of Mississippi’s taken in 10 feet Multiply Steps taken in 100 feet Steps taken in 10 feet You Partner Mississippi’s taken in 10 feet You Partner X 10 X 10 Mississippi’s taken in 100 feet X 10 X10 Multiply Steps taken in 1000 feet Steps taken in 10 feet You Partner Mississippi’s taken in 10 feet You Partner X 100 X 100 Mississippi’s taken in 1000 feet X 100 X100 Multiply Steps taken in 10000 feet Steps taken in 10 feet You Partner Mississippi’s taken in 10 feet You Partner X 1000 X 1000 Mississippi’s taken in 10000 feet X 1000 X1000 Putting it together You Rate =D T steps Mississippi’s Partner Partner steps Mississippi’s Time = D T Number of Mississippi’s (taken from first table) Number of Mississippi’s (taken from first table) Distance =R T Number of steps (taken from first table) 10 feet Number of steps (taken from first table) Question: Based on the data from your table how long would it take you to travel 5 miles? How long would it take your partner to travel 5 miles? Draw a table to organize your information. Hint Use your rate and times from the above table. There are 5,280 feet in a mile. Extension Challenge: How long would it take you to travel 5 Kilometers? Hint there are 2.54 cm in one inch. Please make use of the metric system graphic organizer on the website.