Dimes & Quarters [for teachers]

Topic:
Algebra
The Dimes & Quarters applet represents the same problem in two different ways. Jane has 8 coins. Some are dimes & some are quarters. The total value of the coins is $ 1.55. How many dimes and how many quarters does Jane have? [answer 3 dimes, 5 quarters] One representation shows the problem in the {$ value, coin #} plane and the other representation shows the problem in the {dimes, quarters} plane. [the 'answer' to the question posed in the problem is 3 dimes and 5 quarters - the point {3 dimes, 5 quarters} is plotted in the right panel - the point {8 coins, $ 1.55} is plotted in the left panel.] You can choose to set the number of quarters and dimes in the right panel by dragging the GREEN and BLUE DOTS, or - you can choose to set the $ value and the number of coins in the left plane by dragging the GREEN and BLUE DOTS. Study the two representations carefully - How are the number of dimes and the number of quarters represented in the {$ value, coin #} plane ? How are the value of the coins and their number represented in the {dimes, quarters} plane ? How are the quantities $/dime and $/quarter represented in each of the two planes? Which representation do you think provides you with more insight? Why? - How can you use this applet to generate more problems of this sort? - What questions could/would you ask your students? - What have you learned about word problems from this applet?
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