Measuring Up Prototypes for Mathematics Assessment (1993) / Chapter Skim
Currently Skimming:
The Taxman
The Taxman
Pages 101-114
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 101... ...
lowing a videotaped introduction Task Assumec/ background/: This task assumes that chi~dren are familiar with the concept of factors of whole numbers and, in particular, with prime numbers. It also assumes that they have had some experience in deve~opi ng m u lti-step strategies and i n articu ~ ati ng those strategies coherently.
|
From page 102... ...
(If a tape is not available, the classroom teacher can use the script as a guide to introducing the game.) The scene opens in a classroom setting, with a teacher anc/ There is a cha/kboarc/ on one wa//.
|
From page 103... ...
The only other rule is this: 2. When none of the numbers in the list has any factors left in the fist, then the game is over, and the Taxman gets aid the numbers that are left in the list.
|
From page 104... ...
The Taxman only gets 1. records scores]
|
From page 105... ...
3 You Taxman 5 4 St ~6 1 2 Student E: And now you can choose the 6 because the 3 is still left for the Taxman. [Crosses off and records scores.]
|
From page 106... ...
Remind the students that the Taxman must a/ways get something Student assessment activity: See the following pages. A Spanish translation is provided after the English version.
|
From page 107... ...
Be sure to show which numbers you took and the order in which you took them, not just the final score.
|
From page 108... ...
l l ll Fecha Juega varios partidos de el Cobrador de Impuestos con estos diez numeros: 1 2 3 4 5 6 7 8 9 10 A medida que investigas el juego de el Cobrador de Impuestos con los diez numeros, contesta las siguientes preguntas: 1. ~Puedes ganar~e a~ cobrador de impuestos?
|
From page 109... ...
The widespread availability of videocassette recorders in classrooms now makes it feasible to introduce problem settings that would previously have been too complex to replicate reliably from one classroom to another. Certain features of the Taxman task and other potential assessment tasks make a uniform introduction even more important.
|
From page 110... ...
It's harder to see that 91 is also not a prime, and that in fact the largest available prime (and therefore one's best first move)
|
From page 111... ...
A related point: One should be aware that there may be cultural or personality effects operating in question 3. Some children will think that it is generally unseemly or boastful to claim that anything they do is "best." Others may think that it is important to put up a front of asserting that whatever they do is "best." Or perhaps prior personal experiences have convincecl the chilcl that nothing he or she does couch be "best." Thus the answers given to question 3 may depend on factors other than those that are really relevant to the mathematics.
|
From page 112... ...
An opening move of 6 would result in a tie, 6 to 6. The following questions would be of interest: "Which opening moves result in You leading, which result in the Taxman leading, and which result in a tie?
|
From page 113... ...
A somewhat less advanced response is simply that 89 is the largest number on the list that has only one factor on the list. An even less satisfactory response is to declare that the largest prime is the optimal opening move, but then to misidentify 91, 93, or 95 as a prime.
|
From page 114... ...
1 1 4 Measuring Up to depend on the best game that the students can find. If a less-than-optimal game is described, then an answer of "Yes" is correct here.)
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.