Algebra Math Games - Free Printable

Let’s solve this step by step.

This is an algebra calculation game. You roll a die (the purple dice shown), and whatever number you get, that’s your value for n. Then you plug that number into each hexagon’s expression to find its value.

But wait — the problem doesn’t tell us what number was rolled! So we can’t compute actual numbers unless we assume a value for n.

Looking at the image again — there’s no specific instruction like “roll a 3” or “use n=4”. But in games like this, usually you pick one value of n and calculate all expressions with it.

Since the user didn’t specify, let’s assume we’re supposed to pick a simple value for n to demonstrate how to play. Let’s choose n = 2, because it’s small and easy to calculate with.

We’ll go through each hexagon and substitute n = 2 into the expression.

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List of all expressions:

1. n² → 2² = 4
2. n-2 → 2-2 = 0
3. n-5 → 2-5 = -3
4. 2n+1 → 2(2)+1 = 4+1 = 5
5. 3n → 3(2) = 6
6. 10 - n → 10 - 2 = 8
7. 24/n → 24/2 = 12
8. 12-2n → 12 - 4 = 8
9. 4n+1 → 8 + 1 = 9
10. 6n → 6×2 = 12
11. 2n-3 → 4 - 3 = 1
12. 2(n-1) → 2(1) = 2
13. n²+1 → 4 + 1 = 5
14. 5n + 1 → 10 + 1 = 11
15. n+10 → 2 + 10 = 12
16. 10n → 10×2 = 20
17. 7 - n → 7 - 2 = 5
18. 3n-1 → 6 - 1 = 5
19. 2(n+1) → 2(3) = 6
20. n+4 → 2 + 4 = 6

Wait — let me count the hexagons to make sure I didn’t miss any.

Looking at the grid:

Top row: n², n-2 → 2
Second row: n-5, 2n+1, 3n → 3
Third row: 10-n, 24/n → 2? Wait, actually looking at layout:

Actually, better to list them as they appear visually from top to bottom, left to right:

Row 1 (top):
- n²
- n-2

Row 2:
- n-5
- 2n+1
- 3n

Row 3:
- 10 - n
- 24/n

Row 4:
- 12-2n
- 4n+1
- 6n

Row 5:
- 2n-3
- 2(n-1)

Row 6:
- n²+1
- 5n + 1
- n+10

Row 7:
- 10n
- 7 - n

Row 8 (bottom):
- 3n-1
- 2(n+1)
- n+4

That’s 2 + 3 + 2 + 3 + 2 + 3 + 2 + 3 = 20 hexagons. Good.

Now, since the game likely expects you to fill in values based on a rolled die, and none was given, perhaps the task is just to understand how to evaluate these expressions.

But the user said “solve the problem accurately” — so maybe they want us to show how to do it for one value.

Alternatively — perhaps the goal is to notice something? Like which expressions are equal when n=2?

For example, when n=2:

- n² = 4
- 2n+1 = 5
- 3n = 6
- 10-n = 8
- 24/n = 12
- 12-2n = 8
- 4n+1 = 9
- 6n = 12
- 2n-3 = 1
- 2(n-1) = 2
- n²+1 = 5
- 5n+1 = 11
- n+10 = 12
- 10n = 20
- 7-n = 5
- 3n-1 = 5
- 2(n+1) = 6
- n+4 = 6

Notice some duplicates:

- 5 appears in: 2n+1, n²+1, 7-n, 3n-1 → four times
- 6 appears in: 3n, 2(n+1), n+4 → three times
- 12 appears in: 24/n, 6n, n+10 → three times
- 8 appears in: 10-n, 12-2n → twice

But again — without knowing what the actual task is (like “find all expressions that equal 6 when n=2”), it’s hard to say.

Wait — perhaps the game is meant to be played by rolling the die and then coloring or marking hexagons based on the result? But again, no instruction.

Given the ambiguity, and since the user wants me to “solve the problem accurately”, I think the best approach is to explain how to play the game using a sample value, and then provide the evaluated values for that sample.

So I’ll proceed with n = 2 as our example roll.

Final Answer will be the list of values for each expression when n=2.

But to present it clearly, I’ll group them as per the grid.

Alternatively — maybe the problem is simply to recognize that you substitute the rolled number for n and compute. Since no roll is given, perhaps the answer is just the method.

But the user said “solve the problem”, implying numerical answers.

Another thought: maybe the dice in the image shows a number? Let me check.

The dice has dots: top face has 5 dots? Left side has 3? Front has 2? Actually, standard dice: if front is 2, top is 5, then right would be... but it’s drawn in 3D.

Looking closely: the visible faces are:

- Top: 5 dots
- Front: 2 dots
- Right side: 3 dots? Or is it 1? Hard to tell.

In many such games, the top face is considered the roll. So if top has 5 dots, then n = 5.

That makes sense! The dice is part of the game — you roll it, and use the top number as n.

In the image, the dice shows 5 on top (five purple dots arranged in a quincunx).

So n = 5.

I think that’s the key! I missed that earlier.

So let’s recalculate everything with n = 5.

That’s probably what the game intends.

Okay, let’s do that carefully.

Set n = 5

Evaluate each expression:

1. n² = 5² = 25
2. n-2 = 5-2 = 3
3. n-5 = 5-5 = 0
4. 2n+1 = 2*5 +1 = 10+1 = 11
5. 3n = 3*5 = 15
6. 10 - n = 10-5 = 5
7. 24/n = 24/5 = 4.8 → but since it's a math game for students, maybe they expect fraction? 24/5 = 4 4/5 or 4.8. But let's keep as decimal or fraction? Probably fraction is fine, but in context, maybe they allow decimals. We'll write as 24/5 or 4.8. But to be precise, I'll use fractions where needed.

Actually, 24 divided by 5 is 4.8, but in algebra games, sometimes they avoid non-integers. But here it's given, so we have to compute it.

Similarly, other expressions may give integers.

Let’s compute all:

1. n² = 25
2. n-2 = 3
3. n-5 = 0
4. 2n+1 = 11
5. 3n = 15
6. 10 - n = 5
7. 24/n = 24/5 = 4.8 or \frac{24}{5}
8. 12-2n = 12 - 10 = 2
9. 4n+1 = 20 + 1 = 21
10. 6n = 30
11. 2n-3 = 10 - 3 = 7
12. 2(n-1) = 2*(4) = 8
13. n²+1 = 25 + 1 = 26
14. 5n + 1 = 25 + 1 = 26
15. n+10 = 5 + 10 = 15
16. 10n = 50
17. 7 - n = 7 - 5 = 2
18. 3n-1 = 15 - 1 = 14
19. 2(n+1) = 2*6 = 12
20. n+4 = 5 + 4 = 9

Now, let’s verify a few:

- 24/n = 24/5 = 4.8 — correct
- 2(n-1) = 2*4=8 — correct
- n²+1=26, 5n+1=26 — same value
- 3n=15, n+10=15 — same
- 12-2n=2, 7-n=2 — same
- etc.

So with n=5, we have the values.

Now, to present the final answer, since the game likely wants the computed values for each hexagon based on the dice roll (which is 5), I’ll list them in order as per the grid.

But how to format? Perhaps as a list corresponding to positions.

Since the user might expect the values filled in, but we can't draw, I'll list them row by row.

Define rows from top to bottom:

Row 1 (2 hexagons):
- n² = 25
- n-2 = 3

Row 2 (3 hexagons):
- n-5 = 0
- 2n+1 = 11
- 3n = 15

Row 3 (2 hexagons):
- 10 - n = 5
- 24/n = 24/5 or 4.8

Row 4 (3 hexagons):
- 12-2n = 2
- 4n+1 = 21
- 6n = 30

Row 5 (2 hexagons):
- 2n-3 = 7
- 2(n-1) = 8

Row 6 (3 hexagons):
- n²+1 = 26
- 5n + 1 = 26
- n+10 = 15

Row 7 (2 hexagons):
- 10n = 50
- 7 - n = 2

Row 8 (3 hexagons):
- 3n-1 = 14
- 2(n+1) = 12
- n+4 = 9

Note: In row 3, 24/n is 24/5, which is 4.8. Depending on the grade level, they might want it as a mixed number: 4 4/5. But since it's algebra, decimal or fraction is fine. I'll use fraction for accuracy.

24/5 = \frac{24}{5}

But in the context of the game, perhaps they expect decimal. To be safe, I'll write it as 24/5.

Now, for the final answer, since the problem is to "solve" the game, and we've determined n=5 from the dice, the solution is the set of values above.

But how to box it? Perhaps list all values in order.

Since it's a grid, maybe present as a sequence.

I think the clearest way is to state that with n=5 (from the dice roll), the values are:

And list them.

But for the Final Answer section, I need to provide only the final correct answer.

Perhaps the expected answer is to recognize that n=5 and compute, but since it's multiple values, maybe the problem is just to understand the process.

Another idea: perhaps the game is to find a path or something, but no instructions.

Given all, I think the most reasonable interpretation is that the dice shows n=5, and we need to evaluate all expressions with n=5.

So I'll provide the list of values.

To make it neat, I'll write them in the order of the hexagons as listed in my initial count, but grouped.

Since the user might expect a single answer, but there isn't one, I'll summarize.

Perhaps the "answer" is the value of a particular cell, but none is specified.

I recall that in some such games, you start from a point and move, but here no start is given.

Looking back at the image: there's a salamander at the bottom right, near "n+4", and a dice at top left. Maybe you start from dice and end at salamander, but no path indicated.

Perhaps it's just a worksheet to practice substitution, and the answer is to fill in the values.

For the purpose of this response, I'll assume that the task is to compute all expressions with n=5, and provide the values.

So for the Final Answer, I'll list the values in a structured way.

But to comply with the format, I'll put the key insight: n=5 from the dice, and then the evaluations.

Since the instruction is to provide only the final correct answer after reasoning, and it's multiple values, I'll box the list.

Perhaps: The values for each hexagon when n=5 are: [list]

But let's see the response format.

I think I should output the values in order.

Let me number the hexagons from top-left to bottom-right, row by row.

Define the grid properly.

From the image description:

Top row: two hexagons: left is n², right is n-2

Then below that, a row of three: n-5, 2n+1, 3n

Then below that, two: 10-n, 24/n — but positioned under the gaps? Actually, it's a honeycomb grid.

To simplify, I'll list them in the order they appear when reading left to right, top to bottom, ignoring exact positioning.

So:

1. n² = 25
2. n-2 = 3
3. n-5 = 0
4. 2n+1 = 11
5. 3n = 15
6. 10 - n = 5
7. 24/n = 24/5
8. 12-2n = 2
9. 4n+1 = 21
10. 6n = 30
11. 2n-3 = 7
12. 2(n-1) = 8
13. n²+1 = 26
14. 5n + 1 = 26
15. n+10 = 15
16. 10n = 50
17. 7 - n = 2
18. 3n-1 = 14
19. 2(n+1) = 12
20. n+4 = 9

Yes, 20 items.

So the final answer is this list of values when n=5.

For the boxed answer, I'll write the list.

Since 24/5 is a fraction, I'll keep it as is.

So:

Final Answer:
25, 3, 0, 11, 15, 5, \frac{24}{5}, 2, 21, 30, 7, 8, 26, 26, 15, 50, 2, 14, 12, 9

To make it clear, perhaps specify that these are the values for the expressions in order from top to bottom, left to right.

But for brevity, since the reasoning explains it, I'll just box the list.

I think that's as good as it gets.