Name Date

Question

Soccer Shootout
Part 1

© 2017 Connections Education LLC. All rights reserved.
The Blue Knights soccer team is practicing kicking the soccer ball into the goal. To
begin, each player attempts kicks for 2 minutes and then reports the fraction of
goals they made. Brad, Alice, and Andre report the following fractions:
Player Goals Made
Brad
4
5
Alice
1
2
Andre
4
6
Graph each fraction on a number line.
1. Which of these players made the greatest fraction of goals?
2. Brad took 5 kicks and made 4 goals:
4
5
. Sydney will take 10 shots and she
wants to make an equivalent fraction of the goals. How many goals must she
make?
4
5 10
 

2
3. Andre took 6 kicks and made 4 goals:
4
6
. Tom wants to take more than 20
kicks and make an equivalent fraction to Andre. What are two possible
fractions of goals Tom can make?
3.
1
4
of the players on every team are girls. Write 3 fractions equivalent to
1
4
.
© 2017 Connections Education LLC. All rights reserved.
2. 32 players show up to practice one day, and the coach realizes she can't
make equal teams of 6. With 32 players, how many players can the coach
put on each team so that each player is on a team and every team has the
same number of players?
Part 2
1. After kicking, one coach likes to play practice games with 6 players on each
team. She doesn’t like any team to have more or fewer than 6 players and
she doesn’t like anyone to be left off a team. What are the possible numbers
of players who must show up to practice so that the coach can make these
teams?

Answer 1

Let's go through this step-by-step:

Part 1

Fractions Reported:

• Brad: \( \frac{4}{5} \)
• Alice: \( \frac{1}{2} \)
• Andre: \( \frac{4}{6} = \frac{2}{3} \) (simplified)

1. Which of these players made the greatest fraction of goals?

To compare the fractions, let's convert them to a common denominator or decimal form:

• \( \frac{4}{5} = 0.8 \)
• \( \frac{1}{2} = 0.5 \)
• \( \frac{2}{3} \approx 0.67 \)

Conclusion: Brad made the greatest fraction of goals with \( \frac{4}{5} \).

---

2. Calculate how many goals Sydney must make:

If Sydney wants to achieve the same fraction \( \frac{4}{5} \) making 10 shots, we set up the equation:

\[ \frac{4}{5} = \frac{x}{10} \]

Where \( x \) is the number of goals she must make. We solve for \( x \):

\[ 4 \times 10 = 5x \ 40 = 5x \ x = \frac{40}{5} = 8 \]

Sydney must make 8 goals.

---

3. Find two possible fractions for Tom:

Tom wants to maintain the same fraction \( \frac{2}{3} \) that Andre had, while taking more than 20 kicks.

Let \( y \) be the number of goals Tom makes and \( n \) be the number of kicks he takes:

\[ \frac{2}{3} = \frac{y}{n} \]

Two possible fractions, provided \( n > 20 \), can be found by selecting multiples of 3 (for \( n \)) and corresponding \( y \):

• If \( n = 24 \): \[ \frac{y}{24} = \frac{2}{3} \Rightarrow y = \frac{2}{3} \times 24 = 16 \ \Rightarrow Tom can make \( \frac{16}{24} \) \]

• If \( n = 27 \): \[ \frac{y}{27} = \frac{2}{3} \Rightarrow y = \frac{2}{3} \times 27 = 18 \ \Rightarrow Tom can make \( \frac{18}{27} \) \]

Therefore, two possible fractions are \( \frac{16}{24} \) and \( \frac{18}{27} \).

---

4. Finding equivalent fractions to \( \frac{1}{4} \):

Three fractions equivalent to \( \frac{1}{4} \) can be made by multiplying the numerator and the denominator by the same non-zero integer:

• \( \frac{2}{8} \)
• \( \frac{3}{12} \)
• \( \frac{5}{20} \)

---

5. Players for Equal Teams:

For the coach to create equal teams of 6 with no one left out from a total of 32 players, the total number of players must be a multiple of 6.

To find suitable numbers, we can do:

\[ 6, 12, 18, 24, 30 \]

As these are all multiples of 6, each allows equal team formation where no one is left out.

Conclusion: Possible numbers of players who must show up to practice = {6, 12, 18, 24, 30}.

For a total of 32 players specifically, they cannot make groups of 6 as 32 is not a multiple of 6; hence adjustments would be necessary.