
or
Colin loves to play the piano but doesn't like practicing the exercises his piano teacher assigns. Colin knows the exercises will help him play better though, so he tries to motivate himself using his favorite treat—chocolate chip cookies.
There is a proportional relationship between the amount of time (in hours) that Colin practices the piano, x, and how many cookies he gives himself, y.
x (hours)	y (cookies)
1	5
2	10
3	15
4	20
What is the constant of proportionality? Write your answer as a whole number or decimal.

To find the constant of proportionality in this situation, we need to look at the ratio between the number of cookies \( y \) and the number of hours \( x \) Colin practices. 

Since there is a proportional relationship between \( x \) and \( y \), we can use the formula:

\[
y = kx
\]

where \( k \) is the constant of proportionality. To solve for \( k \), we can rearrange this formula as:

\[
k = \frac{y}{x}
\]

Using any of the given data points, we can calculate \( k \):

For \( x = 1 \) and \( y = 5 \):

\[
k = \frac{5}{1} = 5
\]

Checking with other data points, we find the same result:
- For \( x = 2 \) and \( y = 10 \): \( k = \frac{10}{2} = 5 \)
- For \( x = 3 \) and \( y = 15 \): \( k = \frac{15}{3} = 5 \)
- For \( x = 4 \) and \( y = 20 \): \( k = \frac{20}{4} = 5 \)

So, the constant of proportionality is:

\[
\boxed{5}
\]

Would you like further details or have any questions?

---

**Relative Questions:**
1. How would you use the constant of proportionality to predict cookies for 6 hours of practice?
2. What does a proportional relationship imply in real-world terms?
3. If Colin practiced for 0.5 hours, how many cookies would he reward himself with?
4. How would the relationship change if the constant of proportionality was 3 instead of 5?
5. Can we calculate the total cookies for any fractional hour of practice with this constant?

**Tip:** When you identify a proportional relationship, the constant of proportionality remains the same across all points in the data.

Colin loves to play the piano but doesn't like practicing the exercises his piano teacher assigns. Colin knows the exercises will help him play better though, so he tries to motivate himself using his favorite treat—chocolate chip cookies. There is a proportional relationship between the amount of time (in hours) that Colin practices the piano, x, and how many cookies he gives himself, y.

x (hours)   y (cookies)
1           5
2          10
3          15
4          20

What is the constant of proportionality? Write your answer as a whole number or decimal.

Explore how to find the constant of proportionality between Colin's piano practice hours and the number of cookies he rewards himself with. Using a proportional relationship and the formula y = kx, this problem demonstrates how consistent ratios lead to a constant of proportionality of 5. Suitable for students in Grades 6-8.

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