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Rules, Tables, and Graphs: Lesson 10.4 By Jenna Max, April 2010 LEQ: How do I develop representational forms for rates? Standard 2.5.5.B: Use appropriate mathematical terms, vocabulary, language, symbols, and graphs to explain clearly and logically solutions to problems Standard 2.8.5.B: Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) and explain the method of solution. Standard 2.8.5.C: Recognize, describe, extend, create, replicate, and form a rule for a variety of patterns, sequences, and relationships verbally, numerically, symbolically, and graphically. Standard 2.8.5.D: Determine a functional rule from a table or graph. Standard 2.8.5.E: Use concrete objects and combinations of symbols and numbers to create expressions, equations, and inequalities that model mathematical situations. Standard 2.8.5.F: Describe data represented in equations, inequalities, tables, or graphs and/or create a story that matches that data. Mental Math TE 804 and top of Math Journal 346 Rate • Rate describes a relationship between two quantities or amounts • Each quantity in a rate has a different unit: Miles and hours: rate would be miles per hour Dollars and pounds: rate would be dollars per pound Rate Continued… • Rate tells how many of one type of thing there are for a certain type of another thing • Example: Speed/pace – A speed tells how many units of distance there are for a given unit of time – 60 miles per hour is a rate that says a distance of 60 miles is traveled for each hour of time Rate Continued… • With rate, we often see the word “per” (50 miles per hour, 5 dollars per pound, 10 rainy days per month) • Rate can be displayed in FRACTIONS: 3 apples 89 cents 12 inches 24 hours 36 inches 1 yard Let’s try this together • MJ 346 Math Journal 346 Number Model: _________________ 480 1hour 60 minutes 1 hour 480 60 60 60 480/60= 8 miles per minute Explain it: Because there are 60 minutes in an hour, divide 480 by 60. This gives us the distance traveled per minute! 480 60 60 60 480/60= 8 miles per minute Let’s try another At 8 miles per minute, how far will a plane travel in 10 minutes? 8 miles 1 min. 10 10 = 80 miles 10 minutes Let’s practice graphing our data: MJ 347