Math worksheet focusing on identifying the constant of proportionality in various scenarios, including graphs, tables, and word problems.

Let's solve each row of this "Odd Man Out" worksheet step by step. The goal is to:

1. Find the constant of proportionality (k) for each box.
2. Identify which box in each row does not match the others — that’s the “odd man out.”
3. Shade or mark the one that doesn’t belong.

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🔹 Row 1

We have four boxes:

#### Box A: Graph
- Points: (1, 12), (2, 24), (3, 36)
- This is a straight line through origin → proportional.
- Constant of proportionality:
$ k = \frac{y}{x} = \frac{12}{1} = 12 $

✔ So, k = 12

#### Box B: Word Problem – Jaylin’s Earnings
- $36 for 3 hours → $36 / 3 = $12/hour
- $60 for 5 hours → $60 / 5 = $12/hour
- So, rate = $12 per hour

✔ k = 12

#### Box C: Table
| x | 12 | 24 | 60 |
|---|----|----|----|
| y | 1 | 2 | 5 |

Check ratios:
- 1/12 = 0.0833...
- 2/24 = 0.0833...
- 5/60 ≈ 0.0833...

All are equal: $ \frac{y}{x} = \frac{1}{12} $ → so k = 1/12

Wait! But earlier ones had k = 12. This is not the same.

Hold on — if k = y/x, then here k = 1/12, but others have k = 12.

So this one is different!

But let’s check again: Is it possible they meant k = x/y?

No — constant of proportionality is y = kx, so k = y/x.

Here:
- For x=12, y=1 → k = 1/12
- x=24, y=2 → k = 2/24 = 1/12
- x=60, y=5 → k = 5/60 = 1/12

So k = 1/12

But other boxes have k = 12

So this one is different.

#### Box D: Equation
- y = 12x → clearly k = 12

✔ k = 12

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✔ Conclusion for Row 1:

- A: k = 12
- B: k = 12
- C: k = 1/12 ← ODD MAN OUT
- D: k = 12

➡️ Shade Box C (the table)

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🔹 Row 2

#### Box A: Word Problem – Sophie’s Reading
- 4 books in 2 months → 4/2 = 2 books/month
- 10 books in 5 months → 10/5 = 2 books/month
→ Rate = 2 books per month

So, y = 2x → k = 2

But wait: Is it proportional? Yes, since rate is constant.

So k = 2

#### Box B: Table
| x | 0.1 | 2.6 | 15 |
|---|-----|-----|----|
| y | 0.1 | 2.6 | 15 |

Check ratios:
- 0.1 / 0.1 = 1
- 2.6 / 2.6 = 1
- 15 / 15 = 1

So k = 1

Wait — but we just said k = 2 from the word problem.

So this table has k = 1 → different.

But hold on — is the table consistent with y = x? Yes, because y = x → k = 1.

But the word problem has k = 2.

So conflict.

Wait — maybe I misread.

Let’s recheck:

- Sophie read 4 books in 2 months → 2 books/month → k = 2
- So if x = months, y = books → y = 2x → k = 2

But the table says: when x = 0.1, y = 0.1 → k = 1

So this table does NOT match.

So Box B is odd?

But let’s look at the rest.

#### Box C: Equation
- y = x → k = 1

✔ k = 1

#### Box D: Graph
- Points: (1,1), (2,2), (3,3), (4,4), (5,5) → y = x → k = 1

✔ k = 1

So:
- A: k = 2
- B: k = 1
- C: k = 1
- D: k = 1

So A is the odd one out

Because only A has k = 2, others have k = 1

➡️ Shade Box A (Sophie’s reading problem)

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🔹 Row 3

#### Box A: Equation
- y = (1/3)x → k = 1/3

✔ k = 1/3

#### Box B: Graph
- Points: (2,6), (4,12), (6,18), (8,24), (10,30)
- Check ratio: 6/2 = 3, 12/4 = 3, 18/6 = 3 → k = 3

So k = 3

But A has k = 1/3 → not matching

Wait — so already different.

Let’s continue.

#### Box C: Table
| x | 4 | 6 | 9 |
|---|---|---|---|
| y |12 |18 |27 |

Check:
- 12/4 = 3
- 18/6 = 3
- 27/9 = 3 → k = 3

✔ k = 3

#### Box D: Word Problem – Alexis’ Cookies
- 24 cookies with 8 tsp sugar → 8/24 = 1/3 tsp per cookie
- 45 cookies with 15 tsp sugar → 15/45 = 1/3 tsp per cookie

So sugar per cookie = 1/3 → y = (1/3)x → k = 1/3

✔ k = 1/3

So:
- A: k = 1/3
- B: k = 3
- C: k = 3
- D: k = 1/3

So two with k = 1/3 (A and D), two with k = 3 (B and C)

But the question says one odd man out.

Wait — perhaps I made a mistake.

Wait: In the graph, is it y = 3x or x = 3y?

Points: (2,6): y = 6, x = 2 → y = 3x → yes, k = 3

But the equation is y = (1/3)x → so k = 1/3

So:
- A: k = 1/3
- B: k = 3
- C: k = 3
- D: k = 1/3

So two groups: A and D → k = 1/3
B and C → k = 3

But only one should be odd.

Wait — unless I misread the graph.

Wait — the graph shows increasing values: (2,6), (4,12), etc. → y = 3x → k = 3

But A says y = (1/3)x → k = 1/3

So both A and D have k = 1/3, while B and C have k = 3

So which one is the odd one out?

Wait — maybe the equation is correct, and the graph is wrong?

No — the task is to find which one doesn't belong.

But there are two with k = 1/3 and two with k = 3.

But the instruction says: "there is an ODD MAN OUT" — meaning only one is different.

Hmm — contradiction.

Wait — let’s double-check the table.

Table: x=4, y=12 → y/x = 3
x=6, y=18 → 3
x=9, y=27 → 3 → k = 3

Graph: points show y = 3x → k = 3

Equation: y = (1/3)x → k = 1/3

Word problem: sugar per cookie = 1/3 → k = 1/3

So A and D have k = 1/3
B and C have k = 3

So no single odd one out?

But the problem says there is an odd man out.

Wait — maybe I misread the equation.

It says: y = 1/3x → which is y = (1/3)x → k = 1/3

But maybe the graph is actually inverse?

No — the graph clearly shows y increases faster than x.

(2,6): y = 3x → k = 3

But equation says k = 1/3 → so if y = (1/3)x, then when x=2, y=0.666... but graph shows y=6

So graph ≠ equation

So the equation is inconsistent with the graph.

But both the equation and word problem have k = 1/3

And graph and table have k = 3

So maybe the equation is the odd one?

Wait — no: the equation is y = 1/3x → k = 1/3

But the graph has k = 3 → so it's different.

But the word problem also has k = 1/3 → so it matches the equation.

So:
- A: y = (1/3)x → k = 1/3
- B: graph → k = 3
- C: table → k = 3
- D: word problem → k = 1/3

So A and D have k = 1/3
B and C have k = 3

So two pairs, but only one odd?

Wait — unless the graph is supposed to represent the same as the others?

But it clearly doesn’t.

Wait — maybe the equation is wrong?

Or maybe the table is wrong?

Wait — let’s look at the table:

x: 4, 6, 9
y: 12, 18, 27

This is y = 3x → k = 3

Graph: same → k = 3

Equation: y = (1/3)x → k = 1/3

Word problem: k = 1/3

So equation and word problem agree (k = 1/3)
graph and table agree (k = 3)

So both A and D are different from B and C.

But the problem says only one odd man out.

Unless I made a mistake in interpreting the word problem.

Alexis made 24 cookies with 8 tsp sugar → sugar per cookie = 8/24 = 1/3 tsp

45 cookies with 15 tsp → 15/45 = 1/3 tsp

So sugar per cookie = 1/3 → so if y = sugar, x = cookies → y = (1/3)x → k = 1/3

So correct.

Now, what about the equation? It says y = 1/3x → k = 1/3 → matches

But the graph shows y = 3x → k = 3 → does not match

The table shows y = 3x → k = 3 → does not match

So both graph and table have k = 3, while equation and word problem have k = 1/3

So either graph or table is the odd one, but they are the same.

Wait — maybe the graph is not showing y = 3x?

Let’s check the graph:

- x-axis: 2,4,6,8,10
- y-axis: 6,12,18,24,30
- Points: (2,6), (4,12), (6,18), (8,24), (10,30)

Yes → y = 3x → k = 3

So it's correct.

So the equation says y = (1/3)x → which would give (2, 0.666...) but graph shows (2,6)

So equation is wrong compared to the others.

But the word problem supports k = 1/3

So why is the equation labeled as y = 1/3x?

Wait — maybe the equation is the odd one out?

But it matches the word problem.

Unless the word problem is about cookies per sugar?

No — it says: "made 24 cookies with 8 tsp sugar"

So sugar used per cookie = 8/24 = 1/3 tsp

So if x = number of cookies, y = sugar → y = (1/3)x

So correct.

But the graph and table show y = 3x

So either the graph/table are wrong, or the equation/word problem are wrong.

But the equation and word problem both say k = 1/3

The graph and table both say k = 3

So two vs two — no odd one?

But the problem says one odd man out.

Wait — unless I misread the table.

Look at the table:

| x | 4 | 6 | 9 |
|---|---|---|---|
| y |12 |18 |27 |

Yes, y = 3x

But maybe it’s supposed to be x = 3y? No, that would be inverse.

Alternatively, maybe the constant of proportionality is defined as x/y?

No — standard is y = kx, so k = y/x

So k = 3 for table and graph

k = 1/3 for equation and word problem

So the equation and word problem are consistent, and graph and table are consistent

But only one should be odd.

Wait — maybe the equation is written incorrectly?

But it says: y = 1/3x → which is correct for the word problem.

But the graph and table are for a different scenario.

So perhaps the graph is the odd one?

But it matches the table.

Wait — unless the table is mislabeled?

No.

Wait — look at the graph: it goes from (2,6) to (10,30)

But the equation says y = (1/3)x → so at x=2, y=0.666...

But the graph shows y=6 → so it’s off by a factor of 9.

Wait — unless the graph is for x = (1/3)y?

Then y = 3x → which matches the graph.

So maybe the equation is wrong.

But it says y = 1/3x

But the word problem supports y = (1/3)x

So why is the graph showing y = 3x?

Unless the graph is for number of cookies vs sugar?

But it’s labeled as x and y, no units.

But in the table, it's x and y — no labels.

But the word problem is about sugar and cookies.

So likely, the equation and word problem are for sugar vs cookies → y = (1/3)x

The graph and table are for cookies vs sugar → y = 3x

So they are inverses.

But the constant of proportionality depends on how you define variables.

But in the table, it's x and y, and y = 3x → k = 3

In the equation, y = (1/3)x → k = 1/3

So they are different.

But the word problem supports k = 1/3

The graph and table support k = 3

So which one is the odd one?

But notice: the equation is labeled as y = 1/3x

The graph shows y = 3x

So the equation and the graph are inconsistent.

But the table also shows y = 3x

So equation is the only one with k = 1/3

But the word problem also has k = 1/3

So equation and word problem match

graph and table match

So two pairs

But the problem says one odd man out.

Wait — unless the table is the odd one?

Let’s check the table again.

x: 4, 6, 9
y: 12, 18, 27

Is this proportional? Yes, y = 3x

But look at the values: 4→12, 6→18, 9→27

But the word problem says: 24 cookies with 8 tsp sugar

So if x = sugar, y = cookies → then 8 tsp → 24 cookies → y = 3x → k = 3

Ah! Wait — maybe the word problem is about cookies per teaspoon of sugar?

Yes: 8 tsp → 24 cookies → 24/8 = 3 cookies per tsp

So y = 3x → k = 3

I think I flipped it!

Let’s re-read:

> "Alexis made 24 cookies with 8 teaspoons of sugar and 45 cookies with 15 teaspoons of sugar."

So cookies = y, sugar = x

Then:
- x = 8, y = 24 → y/x = 3
- x = 15, y = 45 → y/x = 3

So y = 3x → k = 3

Oh! I had it backward!

I thought y was sugar, but it's cookies = y, sugar = x

So k = 3

So k = 3

Similarly, the equation says y = (1/3)x → k = 1/3 → this is wrong

So now:
- A: y = (1/3)x → k = 1/3
- B: graph → y = 3x → k = 3
- C: table → y = 3x → k = 3
- D: word problem → y = 3x → k = 3

So only A has k = 1/3

Others have k = 3

➡️ Shade Box A (the equation y = 1/3x)

It's the odd one out.

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🔹 Row 4

#### Box A: Word Problem – Jazmyn’s Paint
- 2 gallons for 5 walls → 2/5 = 0.4 gallons per wall
- 4 gallons for 10 walls → 4/10 = 0.4 gallons per wall
→ So constant: 0.4 gallons/wall

So k = 0.4 = 2/5

#### Box B: Table
| x | 0.5 | 1.5 | 3.5 |
|---|-----|-----|-----|
| y | 0.2 | 0.6 | 1.4 |

Check ratios:
- 0.2 / 0.5 = 0.4
- 0.6 / 1.5 = 0.4
- 1.4 / 3.5 = 0.4

So k = 0.4 = 2/5

✔ k = 2/5

#### Box C: Graph
- Points: (2,5), (4,10), (6,15), (8,20), (10,25)
- y/x = 5/2 = 2.5, 10/4 = 2.5, etc. → k = 2.5 = 5/2

Wait — this is not 0.4

So k = 2.5

But others have k = 0.4

So this is different.

#### Box D: Equation
- y = 2/5x → k = 2/5 = 0.4

✔ k = 0.4

So:
- A: k = 0.4
- B: k = 0.4
- C: k = 2.5
- D: k = 0.4

So C (graph) is the odd one out

➡️ Shade Box C (the graph)

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🔹 Row 5

#### Box A: Table
| x | 1 | 2 | 3 |
|---|---|---|---|
| y |1.2|2.4|3.6|

Check:
- 1.2/1 = 1.2
- 2.4/2 = 1.2
- 3.6/3 = 1.2 → k = 1.2

But the equation says y = 1.25x → k = 1.25

So not matching.

But let’s see.

#### Box B: Equation
- y = 1.25x → k = 1.25

#### Box C: Word Problem – Grapes
- 4 lbs cost $5 → $5/4 = $1.25/lb
- 7 lbs cost $8.75 → $8.75/7 = ?
8.75 ÷ 7 = 1.25 → yes, $1.25 per pound

So k = 1.25

#### Box D: Graph
- Points: (4,5), (8,10), (12,15), (16,20), (20,25)
- y/x = 5/4 = 1.25, 10/8 = 1.25, etc. → k = 1.25

So:
- A: k = 1.2
- B: k = 1.25
- C: k = 1.25
- D: k = 1.25

So A (table) has k = 1.2, others have k = 1.25

➡️ Shade Box A (the table)

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✔ Final Answers:

| Row | Odd Man Out | Reason |
|-----|-------------|--------|
| 1 | Table (x,y) | k = 1/12 vs others k = 12 |
| 2 | Sophie’s reading | k = 2 vs others k = 1 |
| 3 | Equation y = 1/3x | k = 1/3 vs others k = 3 |
| 4 | Graph | k = 2.5 vs others k = 0.4 |
| 5 | Table (x,y) | k = 1.2 vs others k = 1.25 |

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📌 Summary of Shading:

- Row 1: Shade the table (third box)
- Row 2: Shade the word problem (first box)
- Row 3: Shade the equation (first box)
- Row 4: Shade the graph (third box)
- Row 5: Shade the table (first box)

Let me know if you want a visual guide!