6th Grade 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) to get a number for n. Then you plug that number into each expression in the hexagons and calculate the result.

But wait — the problem doesn’t tell us what number was rolled! So we need to assume a value for n to demonstrate how to play.

Since it’s a standard 6-sided die, let’s pick n = 3 as an example. (You can use any number from 1 to 6 depending on your roll.)

Now, let’s go through each hexagon and calculate its value when n = 3.

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Top row:
- n² → 3² = 9
- n - 2 → 3 - 2 = 1

Second row:
- n - 5 → 3 - 5 = -2
- 2n + 1 → 2×3 + 1 = 7
- 3n → 3×3 = 9

Third row:
- 12 - 2n → 12 - 6 = 6
- 10 - n → 10 - 3 = 7
- 24/n → 24 ÷ 3 = 8
- 6n → 6×3 = 18

Fourth row:
- 4n + 1 → 4×3 + 1 = 13
- 2(n - 1) → 2×(3 - 1) = 2×2 = 4

Fifth row:
- 2n - 3 → 6 - 3 = 3
- 5n + 1 → 15 + 1 = 16
- n + 10 → 3 + 10 = 13

Sixth row:
- n² + 1 → 9 + 1 = 10
- 10n → 10×3 = 30
- 7 - n → 7 - 3 = 4
- n + 4 → 3 + 4 = 7

Bottom row:
- 3n - 1 → 9 - 1 = 8
- 2(n + 1) → 2×(3 + 1) = 2×4 = 8

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Wait — but the game might be asking you to find which expressions give the same answer? Or maybe color them based on results? The image doesn’t specify instructions beyond “Algebra Calculation Game #1”.

Looking again — there are green and white hexagons. Maybe the green ones are already filled or highlighted? But no values are given.

Actually — perhaps the goal is to substitute a chosen n and compute all values. Since no specific instruction is given, and the user just said “solve the problem”, I think the best approach is to show how to evaluate one expression as an example — or list all values for a sample n.

But since the problem says “solve the problem accurately” and there’s no question asked, maybe the intent is to realize that without knowing n, we can’t compute numerical answers — unless we’re supposed to leave them as expressions? That doesn’t make sense for a “calculation” game.

Alternatively — perhaps the dice shows a number? Let me check the image description again.

The dice has dots: top face has 5 dots, front has 3, side has 2? Wait — actually, in the image, the die is drawn with visible faces: top=5, front=3, right=2? But typically, opposite faces add to 7, so if top is 5, bottom is 2; front is 3, back is 4; left would be 1, right is 6? This is confusing.

Actually — looking at the die in the image: it's a standard die drawing. The face showing has 5 dots (top), 3 dots (front), and 2 dots (side). But in reality, only one face is "up" when rolled. Since it's a 2D drawing, we have to assume which face is up.

In most such games, the top face is considered the result. Here, the top face of the die has 5 dots. So likely, n = 5.

That makes sense! The die is part of the game — you roll it, and the number shown is n. In the image, the die clearly shows 5 on top.

So let’s use n = 5.

Recalculate everything with n = 5:

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Top row:
- n² → 5² = 25
- n - 2 → 5 - 2 = 3

Second row:
- n - 5 → 5 - 5 = 0
- 2n + 1 → 2×5 + 1 = 11
- 3n → 3×5 = 15

Third row:
- 12 - 2n → 12 - 10 = 2
- 10 - n → 10 - 5 = 5
- 24/n → 24 ÷ 5 = 4.8 ← Hmm, decimal? Maybe not intended? Or perhaps n should divide evenly?

Wait — 24/n with n=5 gives 4.8, which is fine, but maybe the game expects integer results? Let’s see other values.

- 6n → 6×5 = 30

Fourth row:
- 4n + 1 → 20 + 1 = 21
- 2(n - 1) → 2×4 = 8

Fifth row:
- 2n - 3 → 10 - 3 = 7
- 5n + 1 → 25 + 1 = 26
- n + 10 → 5 + 10 = 15

Sixth row:
- n² + 1 → 25 + 1 = 26
- 10n → 50
- 7 - n → 7 - 5 = 2
- n + 4 → 5 + 4 = 9

Bottom row:
- 3n - 1 → 15 - 1 = 14
- 2(n + 1) → 2×6 = 12

Still some decimals? 24/5 = 4.8 — but maybe it’s acceptable.

Alternatively, perhaps the die shows 4? Let’s check the die again.

In the image, the die is drawn with three faces visible:
- Top: 5 dots
- Front: 3 dots
- Right: 2 dots

But in standard dice orientation, if top is 5, front is 3, then right should be... let’s recall: on a die, 1 opposite 6, 2 opposite 5, 3 opposite 4.

If top is 5, then bottom is 2. If front is 3, back is 4. Then right must be 1 or 6? But it shows 2 dots on the right — contradiction.

Perhaps the drawing is not accurate, or we should take the most prominent face. Often in such images, the top face is the result. And it has 5 dots.

Maybe the game allows non-integers. Or perhaps I miscounted.

Another idea: maybe the die is showing 6? No, top has 5.

Let’s count the dots carefully:

Top face: 5 dots (four corners and center) — yes.

Front face: 3 dots (diagonal) — yes.

Right face: 2 dots (top-left and bottom-right?) — usually 2 is two dots diagonally.

But mathematically, if n=5, 24/n = 4.8, which is fine for algebra.

Perhaps the problem is to evaluate all expressions for n=5.

But the user didn't ask a specific question. Given that, and since it's called "Calculation Game", I think the expected output is to provide the calculated values for each cell using the die roll.

And since the die shows 5 on top, we'll use n=5.

Let me list all values clearly:

Hexagon values when n = 5:

Row 1 (top):
- n² = 25
- n-2 = 3

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

Row 3:
- 12-2n = 2
- 10-n = 5
- 24/n = 4.8
- 6n = 30

Row 4:
- 4n+1 = 21
- 2(n-1) = 8

Row 5:
- 2n-3 = 7
- 5n+1 = 26
- n+10 = 15

Row 6:
- n²+1 = 26
- 10n = 50
- 7-n = 2
- n+4 = 9

Row 7 (bottom):
- 3n-1 = 14
- 2(n+1) = 12

Note: Some values repeat, like 15 appears twice (3n and n+10), 26 appears twice (5n+1 and n²+1), etc.

But since the problem doesn't specify what to do with these values, and given the context, I believe the task is simply to calculate each expression for the rolled number, which is 5.

So the final answer should be the set of calculated values. But how to present it?

Perhaps the game is to fill in the hexagons with numbers, so listing them in order might work.

Since the original request is to "solve the problem accurately", and no specific output format is given, I will provide the value of each expression evaluated at n=5, listed in the order they appear from top to bottom, left to right.

Let me write them in grid order:

Starting from top-left moving right, then next row, etc.

The hexagons are arranged in a honeycomb, but roughly:

First row (two hexagons): n², n-2 → 25, 3

Second row (three): n-5, 2n+1, 3n → 0, 11, 15

Third row (four): 12-2n, 10-n, 24/n, 6n → 2, 5, 4.8, 30

Fourth row (three): 4n+1, 2(n-1) — wait, actually looking at the image, after third row, it's offset.

Better to list by position as per common reading order.

From the image layout:

Topmost: n² (center-top), then to its right n-2

Below n²: 2n+1, and below that 24/n, etc.

To avoid confusion, I'll list all expressions with their values:

- n² = 25
- n-2 = 3
- n-5 = 0
- 2n+1 = 11
- 3n = 15
- 12-2n = 2
- 10-n = 5
- 24/n = 4.8
- 6n = 30
- 4n+1 = 21
- 2(n-1) = 8
- 2n-3 = 7
- 5n+1 = 26
- n+10 = 15
- n²+1 = 26
- 10n = 50
- 7-n = 2
- n+4 = 9
- 3n-1 = 14
- 2(n+1) = 12

There are 20 hexagons.

I think this is comprehensive.

But perhaps the problem expects only the green ones? The image has some green and some white hexagons. Let me check.

In the image, the green hexagons are:
- n-5
- 10-n
- 4n+1
- 2(n-1)
- n²+1
- 10n
- 2(n+1)
- 3n
- n+10

White ones are the rest.

But still, no instruction.

Given the ambiguity, and since the die shows 5, I'll proceed with n=5 and provide all values.

For the final answer, since it's a calculation game, and no specific question, I'll box the value of one representative expression or state the assumption.

But the user might expect the calculations for n=5.

Perhaps the "problem" is to understand that you substitute the die roll into the expressions.

I think the safest final answer is to state that with n=5 (from the die), the values are as calculated, and perhaps list a few.

But to follow the format, I need a single final answer.

Another thought: maybe the game is to find which expressions equal the same value, and color them, but again, not specified.

Perhaps in the context, "solve" means to evaluate for n=5.

I recall that in some versions of this game, you roll the die and then find paths or something, but here no path is indicated.

Given all this, I will provide the calculated value for the expression "24/n" when n=5, as it's a bit tricky, but that seems arbitrary.

No, better to provide the entire set.

But the response format requires a "Final Answer" section with only the final correct answer.

Perhaps the problem is from a worksheet where you are to fill in the blanks, so the answer is the completed grid.

Since I can't draw, I'll list the values in order.

Let me define the order as per rows from top to bottom, left to right within each row.

Row 1: n², n-2 → 25, 3

Row 2: n-5, 2n+1, 3n → 0, 11, 15

Row 3: 12-2n, 10-n, 24/n, 6n → 2, 5, 4.8, 30

Row 4: 4n+1, 2(n-1) — wait, in the image, after row 3, the next row has 4n+1 in the middle, but let's see the actual positions.

From the image description:

After the first two rows, the third row has four hexagons: 12-2n, 10-n, 24/n, 6n? No.

Let's map it properly.

Typically in such grids:

- Row 1: two hexagons: left: n², right: n-2? No, in the image, n² is above and between others.

Standard way: start from top.

Top: n² (position A)

To its right: n-2 (B)

Below n²: 2n+1 (C)

Below n-2: 24/n (D)? Not quite.

From the image:

The hexagons are arranged as:

[n²] [n-2]
[n-5] [2n+1] [3n]
[12-2n] [10-n] [4n+1] [24/n] [6n] — this can't be, too many.

I think I need to accept that for the purpose of this response, since the die shows 5, and the game is to calculate, I'll provide the value of n as 5, and that's the key.

But that seems insufficient.

Perhaps the problem is to recognize that n is determined by the die, and the die shows 5, so n=5.

Then the final answer is n=5.

But that's trivial.

Another idea: maybe "solve" means to simplify the expressions, but they are already simple.

I think I overcomplicated it.

Let me look for similar problems online or standard interpretation.

Upon second thought, in many such worksheets, the instruction is: "Roll the die. Use the number as n. Calculate each expression."

Since the die is shown with 5 on top, we use n=5.

And perhaps the answer is to list the results, but for the final answer box, maybe they want the sum or something.

The problem doesn't say.

Perhaps the green hexagons are to be evaluated, and there are 9 of them.

List of green hexagons from image:
- n-5
- 10-n
- 4n+1
- 2(n-1)
- n²+1
- 10n
- 2(n+1)
- 3n
- n+10

With n=5:
- n-5 = 0
- 10-n = 5
- 4n+1 = 21
- 2(n-1) = 8
- n²+1 = 26
- 10n = 50
- 2(n+1) = 12
- 3n = 15
- n+10 = 15

Sum of green hexagons: 0+5+21+8+26+50+12+15+15 = let's calculate: 0+5=5, +21=26, +8=34, +26=60, +50=110, +12=122, +15=137, +15=152.

But why sum?

Perhaps the game is to find matching values, like 3n and n+10 both 15, etc.

I think for the sake of completing the task, I'll assume that the expected final answer is the value of n from the die, which is 5.

Or perhaps the product or something.

Another approach: in the title "Algebra Calculation Game #1", and with the salamander logo, it's from math-salamanders.com, and typically for such sheets, you roll the die and fill in the values.

Since the user uploaded the image and said "solve the problem", and no specific question, I think the best is to state that n=5, and provide one example calculation.

But to adhere to the format, I'll box n=5.

Let's see the initial request: "Solve the problem accurately."

Perhaps the problem is implicit: determine n from the die.

So Final Answer: 5

I think that's it.

To confirm, the die has 5 dots on the top face, so n=5.

So the answer is 5.

But that seems too simple, and the expressions are there for a reason.

Perhaps "solve" means to evaluate a particular expression, but none is specified.

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

Given the constraints, I'll go with n=5 as the solution to "what is n?".

So Final Answer: 5

But let's double-check the die.

In the image, the die is drawn with:
- Top face: 5 dots
- Front face: 3 dots
- Right face: 2 dots

In a standard die, the sum of opposite faces is 7, so if top is 5, bottom is 2; if front is 3, back is 4; then right should be 1 or 6, but it shows 2, which conflicts because 2 is already on bottom.

This suggests the drawing is not to scale or not accurate, and we should take the top face as the result, which is 5.

In educational materials, they often show the top face as the roll result.

So I think n=5 is correct.

Therefore, the final answer is 5.

But to be thorough, perhaps the problem is to calculate all, but for the box, I'll put 5.

I have an idea: perhaps "solve the problem" means to find the value of n that makes all expressions integer, but 24/n requires n to divide 24, so n could be 1,2,3,4,6, but the die shows 5, which doesn't divide 24, so maybe not.

With n=4, 24/4=6, integer.

Die shows 5, not 4.

Unless the die is showing 4? Let's count the dots on the top face: it's clearly 5 dots.

Perhaps in the context, we use n=4 for integer results, but that contradicts the die.

I think I should stick with n=5.

Perhaps the answer is the number of hexagons or something.

I give up. I'll box 5 as the value of n.

So Final Answer: 5

But let's see the response format. It says "provide only the final correct answer", so for this case, since the die determines n, and it's 5, that's it.

So \boxed{5}

To make it better, perhaps the final answer is the calculated value for a specific cell, but none is specified.

Another thought: in the image, there is a small box with "7x5=35" and a salamander, but that's probably a logo.

I think \boxed{5} is reasonable.

So I'll go with that.