Grade 5 – Statistics and Probability Alex’s Tiles Alex had a bag filled with colored tiles. It contained: 4 red tiles, half as many green tiles as red tiles, 8 purple tiles, twice as many blue tiles as purple tiles, and 3 times as many yellow tiles as green tiles. If Alex reached into his bag and pulled out 1 tile without looking, what is the probability that he will pull out a yellow tile? Alex tenía una bolsa llena de losas coloreadas que contenía: 4 losas rojas, la mitad del número de losas rojas en color verde, 8 losas moradas, dos veces más que el número de losas moradas en color azul, y 3 veces más el número de losas verdes en color amarillo. Si Alex buscara en su bolsa y sacara 1 losa sin mirar, ¿cuál es la probabilidad de que sacará una losa amarilla? У Алекса был пакет с цветными плитками. В пакете было 4 красных плитки; зелёных плиток было наполовину меньше, чем красных; 8 фиолетовых плиток; синих плиток было в 2 раза больше, чем фиолетовых; а жёлтых плиток было в три раза больше, чем зелёных. Если бы Алекс засунул руку в пакет и, не глядя, вытащил 1 плитку, какая вероятность того, что он вытащил бы жёлтую плитку?

Alex’s Tiles KEY CONCEPTS: Find unknown tiles; Ratio of yellow to total Theoretical probability (not experiential) How to determine number of tiles for each color –terminology (math vocab. /parameters) Probability is expressed in (fraction, ratio, percent) 5 – 1 - 1 CU 6 The paper shows an understanding of each of the key concepts (the

terminology from the task, the need to find the unknown quantities of tiles, the need to find the total number of tiles, and the need for theoretical probability). In addition, the paper shows an understanding of desired sized parts out of the whole, and also an understanding of odds. The combination of these three parts makes the translation enhanced.

PS 6 The first process (finding the unknown numbers tiles, finding the total

numbers of tiles, and comparing the number of yellow tiles to the total number of tiles is thoroughly developed. This work is then enhanced by the first part of the check seeing the 6 out of 36 as equal to 1 out of 6, and the second part of the check showing what the odds are.

V 6 The review is definitely related to the task, and enhanced by the different

perspective used to show the 1 out of 6. Additionally, s/he shows what the odds would be for pulling yellow from the bag of tiles. [The combination of these parts is more than what is needed for a 6.]

C 6 The connecting path is enhanced by the thorough recording of each of the

parts accompanied by the graphics (with their keys) and the verbiage – allowing the reader to move easily and make connections from one thought to another.

Acc 5 6/36 or 1/6 is a mathematically justifiable solution to the task and is

supported by the work.

Alex’s Tiles KEY CONCEPTS: Find unknown tiles; Ratio of yellow to total Theoretical probability (not experiential) How to determine number of tiles for each color –terminology (math vocab. /parameters) Probability is expressed in (fraction, ratio, percent) 5 – 1 – 2 CU 4 The paper shows an understanding of the terminology in the task, what

theoretical probability is, and of how probability is expressed in words. The translation is complete.

PS 4 Although the process of finding the numbers of unknown tiles is not

recorded in the original solution (and could have been done mentally), the numbers of tiles are what the reader expects to see. Finding the unknowns, then the total number of tiles, and finally expressing the yellow tiles out of the total is complete.

V 5 The second look contains a thoroughly developed/recorded: review

(restatement) of the key concepts, process for finding the numbers of unknown tiles and for finding the total number of tiles, and again records the probability as the number of yellow tiles out of the total number of tiles.

C 4 The path connecting the translation of the concepts to the process for

finding the total number of tiles to the initial answer and then to the thoroughly developed verification is complete.

Acc 5 6 out of 36 chance is a mathematically justifiable solution to the task and

is supported by the work.

Alex’s Tiles KEY CONCEPTS: Find unknown tiles; Ratio of yellow to total Theoretical probability (not experiential) How to determine number of tiles for each color –terminology (math vocab. /parameters) Probability is expressed in (fraction, ratio, percent) 5 – 1 – 3 CU 2 In recording the “facts” the work shows an understanding of the need to

find the unknown numbers of tiles, accompanied by the hint of understanding of probability – “the yellow would not have a probability of getting chosen”. However, there is no evidence of translating the task into theoretical probability. Overall this makes an underdeveloped translation.

PS 2 The process of finding and recording the unknown numbers of tiles is

more than a minimal beginning to the task. However, s/he doesn’t show evidence of knowing how to actually find probability (beginning with finding the total number of tiles), or how probability is expressed.

V 3 The graphical display of the numbers of each color of tiles is a review of

part of the key concepts, and a review of the first step of the process. There is no other evidence of reviewing how s/he arrived at the answer. Overall, the review is partially effective.

C 3 The significant gap in the path occurs between the process of finding the

unknown numbers of tiles and the answer of “yellow would not have a probability of getting chosen”.

Acc 1 Yellow would not have a probability of getting chosen is not a

mathematically justifiable solution to this task.