EIGHTH GRADE TRAINING GUIDE

1994 Mathematics Rubric - Eighth Grade


FORM F

6. There are 6 teams in a school football league. If each team plays each other team once during the season, how many games are played during the season? Explain your answer.

ITEM SCORE SCALE

0 Answer does not address task, or is unrelated or inappropriate. Answer contains nothing correct.
1 Answer is partially correct. Answer contains something correct in the process of calculating the number of games played or, a correct answer of 15 games is given without explanation or with unclear explanation.
2 Answer is nearly correct. The answer or explanation contains a minor error, omission, or lack of clarity.
3 Answer and explanation are complete and correct.


STUDENT RESPONSES

QUESTION

6. There are 6 teams in a school football league. If each team plays each other team once during the season, how many games are played during the season? Explain your answer.


STUDENT RESPONSE NUMBER ONE

If there are 6 teams and they play each other once Then there are twelve football games played.

RUBRIC SCORING

0 --Nothing correct.


STUDENT RESPONSE NUMBER TWO

30 games

6 teams have to play 5 other teams because they can't play themselves.

RUBRIC SCORING

1 -- The answer of 30 is incorrect, but there is a correct beginning strategy (multiplying 6 teams by 5 teams).


STUDENT RESPONSE NUMBER THREE

15 games

each team gets a turn playing each other. The first team gets to play them first, then the second, third, and so on.

RUBRIC SCORING

1 -- A correct answer is given with an explanation which shows a major lack of clarity.


STUDENT RESPONSE NUMBER FOUR

15 games

There are 6 teams.

Teams 1, 2, 3, 4, 5, 6

1 & 2 = 12 & 3 = 13 & 4 = 1
1 & 3 = 12 & 4 = 13 & 5 = 1
1 & 4 = 12 & 5 = 13 & 6 = 1
1 & 5 = 14 & 5 = 15 & 6 = 1
4 & 6 = 1

RUBRIC SCORING

2 -- A correct answer is given. Explanation lacks verbal detail/full clarity.


STUDENT RESPONSE NUMBER FIVE

16 games

aabacadaeaf
bbcbdbebf
ccdcececf
ddedf
eef
f

I got this answer by counting how many combinations of games could be played.

RUBRIC SCORING

2 -- A minor error is made: the combination ce is counted twice.


STUDENT RESPONSE NUMBER SIX

15

If one team plays all the others that would be 5 games played. Then the 2nd team has to play all of the other teams except team 1 which they have already played. That makes 4 games played. The team 3 would have already played 2 of the other teams so that leaves 3 more games & so on. Then you add them all up. 5 + 4 + 3 + 2 + 1 = 15.

RUBRIC SCORING

3 -- Answer and explanation are complete and correct.