Word Problems & Multiple Graphical Representations
[b]This is a series of applets drawn from the website mathMINDhabits [[url]sites.google.com/site/mathmindhabits[/url]] that is designed for teachers of mathematics who want to deepen their understanding of the mathematics they teach and that their students are expected to learn.[/b] For background on this collection of applets, please read the essay entitled "Hens & Rabbits, Feet & Animals; Some Thoughts on Representing Word Problems Graphically" on the mathMINDhabits website.
Table of Contents
- Two graphical repesentations for each of 6 classical word problems
- Adult tickets & Child tickets - in {child, adult} space
- Adult Tickets & Child Tickets - in {dollar, ticket} space
- Coffee Mixture Problem - in {weight, price} space
- Coffee Mixture Problem - in {cheap, expensive} coffee space
- Hens & Rabbits - in {hen, rabbit} space
- Hens & Rabbits - in {animal, feet} space
- Dimes & Quarters - in {dimes, quarters} space
- Dimes & Quarters - in {coins, value} space
- Combining rates - Joe & Sam paint a wall
- Combining rates - Joe & Sam paint a wall - revisited
- Combining rates - upstream, downstream in {time, distance} plane
- Combining rates - upstream, downstream - {time, speed} plane
- A closer look at the role of simultaneous multiple representations
- Hens & Rabbits [for teachers]
- Two Lap Average [for teachers]
- Isomorphic word problems
- Word Problem Duo - Distance,Time,Rate
- Word Problem Duo - Mass,Volume,Density
Adult tickets & Child tickets - in {child, adult} space
The two Adult Tickets & Child Tickets applets allow the user to explore the same problem in two different graphical representations[br][br]Tickets for a minor league baseball game cost $10 for an adult and $4 for a child. A total of 400 tickets were sold and $3,400 was collected.[br][br]How many adult tickets were sold and how many children’s tickets were sold?[br][br]Now make up (and solve) two other similar problems. Explain what makes the new problems similar.[br][br]Explain how this problem is similar to the ones in the ‘Coin problem’ environment and the ‘Coffee mixture’ environment
Hens & Rabbits [for teachers]
The Hens & Rabbits applet describes a well-known word problem in two different representations.[br][br]A farmer has 50 animals. Some are hens & some are rabbits. Among them they have a total of 140 legs. How many hens and how many rabbits does the farmer have? [br][br]One representation of the problem shows the {animals, feet} plane and the other representation shows the {hens, rabbits} plane. [[size=85]the '[i]answer' to the question posed in the problem is 30 hens and 20 rabbits - the point {30 hens, 20 rabbits} is plotted in the right panel - the point {50 animals, 140 feet} is plotted in the left panel.[/i][/size]][br][br]You can choose to set the number of rabbits and hens in the right panel by dragging the GREEN and BLUE DOTS, [i][b][size=200]or[/size][/b][/i][br][br]- you can choose to set the number of feet and animals in the left plane by dragging the GREEN and BLUE DOTS. [br][br]Study the two representations carefully -[br][br]How are the numbers of rabbits and the number of hens represented in the {animals, feet} plane?[br][br]How are the number of animals and the number of feet represented in the {hens, rabbits} plane?[br][br]How are the quantities feet/rabbit and feet/hen represented in each of the two planes?[br][br]Which representation do you think provides you with more insight? Why?[br][br][color=#ff0000][i][b]How can you use this applet to generate more problems of this sort?[br][br]What questions could/would you ask your students? [br][br]What have you learned about word problems from this applet?[/b][/i][/color]
Word Problem Duo - Distance,Time,Rate
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How does this pair of graphical representations of a distance traveled down a road correspond to the graphical representations of the Word Problem Duo - Mass,Volume,Density ? |
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