Maya Numerals Worksheet - Solve equations using ancient Maya number symbols.

Let's solve the Maya numeral problems step by step using the provided chart.

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Understanding Maya Numerals

The Maya used a vigesimal (base-20) number system with three symbols:

- Dot (•) = 1
- Bar (—) = 5
- Shell (○) = 0

Numbers are written vertically, with each position representing increasing powers of 20. The bottom position is units (20⁰), then 20¹, 20², etc.

But in this worksheet, we're dealing with simple numbers from 0 to 19, so we only need the bottom row of the chart.

From the chart:
- 0 = shell (○)
- 1 = one dot (•)
- 2 = two dots (••)
- 3 = three dots (•••)
- 4 = four dots (••••)
- 5 = one bar (—)
- 6 = bar + one dot (—•)
- 7 = bar + two dots (—••)
- 8 = bar + three dots (—•••)
- 9 = bar + four dots (—••••)
- 10 = two bars (=)
- 11 = two bars + one dot (=•)
- 12 = two bars + two dots (=••)
- 13 = two bars + three dots (=•••)
- 14 = two bars + four dots (=••••)
- 15 = three bars (===)
- 16 = three bars + one dot (===•)
- 17 = three bars + two dots (===••)
- 18 = three bars + three dots (===•••)
- 19 = three bars + four dots (===••••)

Now let’s solve each problem.

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Problem 1: •• + — = ?

- •• = 2
- — = 5
- 2 + 5 = 7

Answer: 7 → Maya numeral: —••

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Problem 2: == + •••• = ?

- == = 10
- •••• = 4
- 10 + 4 = 14

Answer: 14 → Maya numeral: =••••

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Problem 3: — + •••• = ?

- — = 5
- •••• = 4
- 5 + 4 = 9

Answer: 9 → Maya numeral: —••••

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Problem 4: •• + — = ?

- •• = 2
- — = 5
- 2 + 5 = 7

Answer: 7 → Maya numeral: —••

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Problem 5: — + •••• = ?

- — = 5
- •••• = 4
- 5 + 4 = 9

Answer: 9 → Maya numeral: —••••

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Problem 6: = + ••• = ?

- = = 10
- ••• = 3
- 10 + 3 = 13

Answer: 13 → Maya numeral: =•••

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Problem 7: = + ○ + •• = ?

- = = 10
- ○ = 0
- •• = 2
- 10 + 0 + 2 = 12

Answer: 12 → Maya numeral: =••

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Problem 8: ••• + — - = = ?

- ••• = 3
- — = 5
- = = 10
- So: 3 + 5 - 10 = 8 - 10 = -2

Wait! Negative numbers? But Maya numerals don’t have negative signs.

Let’s double-check the expression:
It says: `••• + — - =`
So: 3 + 5 - 10 = -2

But since Maya didn’t use negative numbers, and this is likely a simple arithmetic exercise, maybe it's meant to be interpreted as absolute value or there's a typo?

Alternatively, perhaps the minus sign is just subtraction.

But -2 can't be represented in standard Maya numerals.

Wait — let's check if the problem might be misread.

Is it possible that the equation is:

`••• + — - =` → 3 + 5 - 10 = -2

But no valid Maya symbol for negative numbers.

Alternatively, could it be a typo? Or perhaps it's asking for the result in Arabic numerals?

Looking at other problems, they all result in positive numbers.

Maybe it's 3 + 5 - 10 = -2, but since we can’t represent negatives, perhaps the answer is not expressible in Maya numerals?

But that seems unlikely for a grade-level worksheet.

Wait — maybe I misread the symbols.

Let me recheck:

- ••• = 3
- — = 5
- = = 10

Yes.

So: 3 + 5 = 8; 8 - 10 = -2

No Maya representation.

But perhaps the problem is meant to be:

`••• + — - =` → 3 + 5 - 10 = -2 → Answer: -2 (in Arabic numerals)

But since the instructions say "use the chart", and the chart only has 0–19, maybe we leave it as -2, or assume it's an error.

Alternatively, maybe the order is different?

Wait — could it be `••• + — - =` meaning: (3 + 5) - 10 = -2

Still same.

Perhaps it's 3 + 5 = 8, and then subtracting 10 gives -2.

But no Maya numeral for negative.

So unless the problem allows writing "-2" in Arabic numerals, we must conclude that the result cannot be expressed in Maya numerals.

But let's see what the expected format is.

Given that all other answers are Maya numerals, and this one isn't possible, perhaps it's a trick question?

Alternatively, maybe it's ••• + — = 8, then minus = (10) → 8 - 10 = -2

Still.

But let's move on and come back.

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Problem 9: = + •• × ••• + ○ = ?

This has multiplication and addition.

Order of operations: multiplication first.

- = = 10
- •• = 2
- ••• = 3
- ○ = 0

So:

First: •• × ••• = 2 × 3 = 6

Then: = + 6 + ○ = 10 + 6 + 0 = 16

Answer: 16 → Maya numeral: ===•

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Problem 10: = + •••• × •• ÷ — = ?

Again, order of operations: multiplication and division before addition.

- = = 10
- •••• = 4
- •• = 2
- — = 5

So:

First: •••• × •• = 4 × 2 = 8

Then: 8 ÷ — = 8 ÷ 5 = 1.6

Wait — division?

But Maya numerals are integers. 8 ÷ 5 = 1.6 → not integer.

But maybe we do integer division? 8 ÷ 5 = 1 remainder 3 → 1?

But let's check:

If we follow standard math: 8 ÷ 5 = 1.6

But since Maya numbers are whole numbers, and the chart shows only integers, perhaps we need to interpret as integer division?

Or maybe it's meant to be exact?

But 8 ÷ 5 is not a whole number.

Wait — could it be (= + ••••) × •• ÷ —?

No — the expression is:

`= + •••• × •• ÷ —`

So: = + (•••• × ••) ÷ —
= 10 + (4 × 2) ÷ 5
= 10 + 8 ÷ 5
= 10 + 1.6 = 11.6

Not an integer.

But again, Maya numerals only go up to 19 and are whole numbers.

So unless it's meant to be 11.6, which can't be shown, or perhaps we round?

But that seems unlikely.

Wait — maybe the operation is left to right?

But standard order is PEMDAS.

Multiplication and division from left to right.

So: •••• × •• = 8
Then 8 ÷ — = 8 ÷ 5 = 1.6

Then 10 + 1.6 = 11.6

Still not an integer.

But perhaps it's meant to be:

`(= + ••••) × •• ÷ —` → (10 + 4) × 2 ÷ 5 = 14 × 2 = 28 ÷ 5 = 5.6

Still not integer.

Alternatively, maybe it's = + (•••• × ••) ÷ —

Same thing.

Unless we’re supposed to use whole number division: 8 ÷ 5 = 1 (quotient)

Then 10 + 1 = 11

Answer: 11 → Maya numeral: =•

That might be intended.

But it's ambiguous.

Alternatively, perhaps the expression is:

`•••• × •• = 8`, then `8 ÷ — = 8 ÷ 5 = 1.6` — not valid.

So likely, this problem may have a typo, or we assume integer division.

Let’s assume integer division (floor division):

8 ÷ 5 = 1

Then 10 + 1 = 11

Answer: 11 → Maya numeral: =•

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Now Revisit Problem 8

`••• + — - =` = 3 + 5 - 10 = -2

Can't be represented.

But maybe it's a typo and should be `••• + — + =` → 3 + 5 + 10 = 18 → ===•••?

Or maybe it's `••• + — = 8`, and then subtract something else?

But as written: `••• + — - =` → 3 + 5 - 10 = -2

Since Maya numerals don't represent negatives, perhaps the answer is not applicable, or we write -2.

But given that it's a worksheet, maybe it's expecting 8 - 10 = -2, and we just write -2 in Arabic numerals.

Alternatively, perhaps the bar is being used differently?

Wait — no.

Another idea: maybe the minus sign is not subtraction, but part of the numeral?

But no — it's clearly an operator.

Let’s look at the image again.

In problem 8: `••• + — - =`

So: three dots, plus a bar, minus two bars.

Yes.

So: 3 + 5 - 10 = -2

We can’t represent negative numbers in Maya numerals.

So likely, this is an error, or the problem expects -2 as the answer.

But since the instruction says "use the chart above", and the chart doesn't have negative numbers, we might just write -2.

Alternatively, perhaps the order is wrong?

Wait — could it be `••• + — = 8`, and then subtracting 10? That would be -2.

But no way around it.

So for now, I'll note that problem 8 results in -2, which cannot be expressed in Maya numerals.

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Final Answers:

Let’s list them clearly:

1. •• + — = 2 + 5 = 7 → —••
2. == + •••• = 10 + 4 = 14 → =••••
3. — + •••• = 5 + 4 = 9 → —••••
4. •• + — = 2 + 5 = 7 → —••
5. — + •••• = 5 + 4 = 9 → —••••
6. = + ••• = 10 + 3 = 13 → =•••
7. = + ○ + •• = 10 + 0 + 2 = 12 → =••
8. ••• + — - = = 3 + 5 - 10 = -2 → cannot be represented (or write -2)
9. = + •• × ••• + ○ = 10 + (2×3) + 0 = 10 + 6 + 0 = 16 → ===•
10. = + •••• × •• ÷ — = 10 + (4×2) ÷ 5 = 10 + 8 ÷ 5 = 10 + 1.6 = 11.6 → not integer

But for #10, if we use integer division: 8 ÷ 5 = 1 → 10 + 1 = 11 → =•

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Likely Intended Answers (assuming integer division):

| Problem | Expression | Calculation | Answer (Maya) |
|--------|------------|-------------|----------------|
| 1 | •• + — | 2 + 5 = 7 | —•• |
| 2 | == + •••• | 10 + 4 = 14 | =•••• |
| 3 | — + •••• | 5 + 4 = 9 | —•••• |
| 4 | •• + — | 2 + 5 = 7 | —•• |
| 5 | — + •••• | 5 + 4 = 9 | —•••• |
| 6 | = + ••• | 10 + 3 = 13 | =••• |
| 7 | = + ○ + •• | 10 + 0 + 2 = 12 | =•• |
| 8 | ••• + — - = | 3 + 5 - 10 = -2 | -2 (not representable) |
| 9 | = + •• × ••• + ○ | 10 + (2×3) + 0 = 16 | ===• |
| 10 | = + •••• × •• ÷ — | 10 + (4×2) ÷ 5 = 10 + 8÷5 ≈ 10 + 1 = 11 | =• |

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Final Answer Summary:

1. —••
2. =••••
3. —••••
4. —••
5. —••••
6. =•••
7. =••
8. -2 (cannot be represented in Maya numerals)
9. ===•
10. =• (assuming integer division)

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Explanation:

- We used the Maya numeral chart to convert dots and bars into values.
- Addition and subtraction were done in base 10.
- For multiplication and division, we followed order of operations.
- Problems involving non-integers or negatives couldn't be represented in Maya numerals, so we noted them accordingly.

✔ Most answers are valid Maya numerals.

⚠️ Problems 8 and 10 require assumptions due to negative or fractional results.

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Note: If you have access to the original image, please verify if the expressions are correctly interpreted. Some operators might be misread.