Read the questions carefully. Take your time and write a complete answer on your paper before
checking your answers by clicking on the answer ink
There are no calculators allowed for these questions.
9. A worker placed white tiles around black tiles in the pattern shown in the three figures below.
n, of black tiles. Show or explain your work.a. Based on this pattern, how many white tiles would be needed for 4 black tiles?
b. Based on this pattern, how many white tiles would be needed for 50 black tiles?
c. Make a scatterplot of the first five figures in this pattern showing the
relationship between the number of white tiles and the number of black
tiles. Be sure to label the axes.
d. Based on this pattern, explain how you could find the number of white tiles
needed for any number,
link to answer for test item 9
22. Lionel and Tracy are playing a game using two six-sided number cubes.
The faces of each cube are numbered as shown below.
Lionel has a red cube and Tracy has a green cube. To play the game they both
roll their cubes at the same time.
• The numbers that show face up when the cubes stop rolling are used to
make a fraction.
• The number on the red cube is used for the numerator and the number on
the green cube is used for the denominator.
For example, the results shown below would make the fraction 1/2 .
• Lionel wins 1 point if the fraction formed has a value less than one.
• Tracy wins 1 point if the fraction has a value greater than one.
• No one gets a point if the fraction is equal to one.
a. Make a list or a table in your Student Answer Booklet of all of the fractions
possible from rolling 1 red and 1 green cube. How many total different
fractions are there?
b. If Lionel (red cube) rolls a 3, what is the probability that Tracy (green cube)
wins 1 point? Show your work or explain how you obtained your answer.
c. Using your table, what is the probability of each player winning a
point on a given turn? Do you think this game is fair to both players?
Show your work or explain how you obtained your answer.
link to answer for test item 22
a.
| black | 1 | 2 | 3 | 4 |
| white | 8 | 10 | 12 | 14 |
| when black adds 1 white adds 2 | ||||
b. How many white tiles will be needed for 50 black tiles?
In part-a we learned that white adds two every time black adds 1. Using the pattern we see
black is 1 when white is 8. If I add 3 more to make 4 I need to add 6 more white to make 14.
so 1 +49= 50 black
then 8 + (2x49) = white
so calculators are allowed so the mental math solution is:
2 times 40 = 80
2 times 9 = 18
therefore 98 is 2 x 49add the 8 the answer is 106 white
c. to make a scatter plot first I need to know the x and y coordinates for the first five figures.
using the table from part-a I call black x and white y
| x | 1 | 2 | 3 | 4 | 5 |
| y | 8 | 10 | 12 | 14 | 16 |
y
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| 16 |
x |
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| 15 |
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| 14 |
x |
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| 13 |
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| 12 |
x |
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| 11 | |||||
| 10 | x | ||||
| 9 | |||||
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8 x |
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| 7 | |||||
| 6 | |||||
| 5 | |||||
| 4 | |||||
| 3 | |||||
| 2 | |||||
|
1 |
2 | 3 | 4 | 5 |
X
d. 2(n - 1 black)=
white+ 8
so if n is 50 then
2(50-1) is98
98= w-8
98+8=w
106= w
a.
| 1/1 | 2/1 | 3/1 | 4/1 | 5/1 | 6/1 |
| 1/2 | 2/2 | 3/2 | 4/2 | 5/2 | 6/2 |
| 1/3 | 2/3 | 3/3 | 4/3 | 5/3 | 6/3 |
| 1/4 | 2/4 | 3/4 | 4/4 | 5/4 | 6/4 |
| 1/5 | 2/5 | 3/5 | 4/5 | 5/5 | 6/5 |
| 1/6 | 2/6 | 3/6 | 4/6 | 5/6 | 6/6 |
there are 36 different fractions but some have equal value
b. rolling a 3 there is a 2 out of 6 (2/6) which simplifies to 1/3 chance that the other roll will make the value more than one. if a 1 came the value is 3/1 or 3. If a 2 comes the value is 3/2 or, 1 and 1/2.
c.
Lionel wins 1 point if the fraction formed has a value less than one.
in column 1 there are 5 values of less than one
in column 2 there are 4 values of more than one
in column 3 there are 3 values of less than one
in column 4 there are 2 values less than one
in column 5 there is 1 value less than one
in column 6 there is 0 value less than one
Lionel has a 15:36 or 5/12 chance of winning
Tracy wins 1 point if the fraction has a value greater than one.
in column 1 there are 0 values of more than one
in column 2 there is 1 value of more than one
in column 3 there are 2 values of more than one
in column 4 there are 3 values of more than one
in column 5 there are 4 values of more than one
in column 6 there are 5 values of more than one
Tracy has a 15:36 or 5/12 chance of winning too.
It is a fair game. Both have 15 chances out of 36 to
win a point.
There are 6 of 36 chances no one scores.