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| Introduction Courtney finds many puzzling things when she plays the computer game "Number Between". She interprets the decimal part of the number as the denominator of a fraction (ie. as the number of pieces something has been divided into). She is unable to find a number between 0.45 and 0.5, because she is searching between 1/45 and 1/5. Comments: Text in italics Interviewer: Text in red Courtney: Text other colour |
In this game you have to type a number which fits on the numberline. You can see the two endpoints on the screen. For this turn they are point 3 and point 5. |
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I think it must be point 4 Courtney thinks that 0.3 is 1/3 and 0.5 is 1/5, so the numberline is, for her, reversed, with the larger number on the left. |
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OK, the computer has accepted your answer and now it will change the number line for your next turn. |
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But there is no number between 4 and 5! (pause)... Interviewer: Try point four five. Courtney enters 0.45 and is surprised when it is accepted. |
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That's weird! The computer presents the new numberline. |
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Now there are lots of numbers there, between 5 and 45 pieces... Interviewer: Just choose one of them Courtney: OK, that's easy, maybe 28 pieces.. so point two eight. |
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Courtney: This is strange... if it has to be bigger than 28...maybe 9 pieces Since 0.28 is too small, Courtney thinks that she needs a number between 5 and 28. |
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Courtney: This doesn't make sense... there is something wrong with this game |
You are using the online sample of the Teaching and Learning about Decimals CDROM. Not all linked pages are accessible in this version. For further information about the complete CDROM please click here.
Reciprocal Thinking
Number Between
| Introduction Courtney finds many puzzling things when she plays the computer game "Number Between". She interprets the decimal part of the number as the denominator of a fraction (ie. as the number of pieces something has been divided into). She is unable to find a number between 0.45 and 0.5, because she is searching between 1/45 and 1/5. Comments: Text in italics Interviewer: Text in red Courtney: Text other colour |
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In this game you have to type a number which fits on the numberline. You can see the two endpoints on the screen. For this turn they are point 3 and point 5. |
|
I think it must be point 4 Courtney thinks that 0.3 is 1/3 and 0.5 is 1/5, so the numberline is, for her, reversed, with the larger number on the left. |
|
OK, the computer has accepted your answer and now it will change the number line for your next turn. |
|
But there is no number between 4 and 5! (pause)... Interviewer: Try point four five. Courtney enters 0.45 and is surprised when it is accepted. |
|
That's weird! The computer presents the new numberline. |
|
Now there are lots of numbers there, between 5 and 45 pieces... Interviewer: Just choose one of them Courtney: OK, that's easy, maybe 28 pieces.. so point two eight. |
|
Courtney: This is strange... if it has to be bigger than 28...maybe 9 pieces Since 0.28 is too small, Courtney thinks that she needs a number between 5 and 28. |
|
Courtney: This doesn't make sense... there is something wrong with this game |