Secret Code Math worksheet for decoding and adding 3-digit numbers using symbol codes.

Let’s solve this step by step.

First, we need to decode the symbols using the key at the top:

The code is:
1 = ~~~
2 = ◎
3 = □
4 = ◐
5 = ⊙
6 = ●
7 = ▽
8 = ⊗
9 =
0 =

Now let’s go row by row and decode each problem.

---

Row 1:

Left side:
Code Numbers:
~~~ ◐ ● → that’s 1 4 6
+ ▽ □ → that’s 7 3 (but wait — it's written as “+ 1 7 3” in regular numbers? Let me check.)

Wait — actually, looking again:

In Row 1, left column says:

Code Numbers:
~~~ ◐ ●
+ ▽ □

And next to it, Regular Numbers:
1 4 6
+ 1 7 3

That means the second addend is coded as ▽ □ — which should be 7 and 3 — but written as two digits? That doesn’t match 173.

Wait — maybe I misread. Let’s look carefully.

Actually, the worksheet shows:

For the first problem on the left:

Code Numbers:
~~~ ◐ ●
+ ▽ □

But then under “Regular Numbers”, it already gives us:

1 4 6
+ 1 7 3

So perhaps the “Code Numbers” are for the student to decode, and the “Regular Numbers” are given as a hint or example? But no — the instruction says: “Decode the addends and find the sums.”

Looking again — actually, in the first row, the “Regular Numbers” column has “1 4 6 + 1 7 3” — so that’s already decoded. Maybe that’s an example?

Wait — let’s read the header:

“Decode the addends and find the sums.”

Then there’s a key.

Then below, it shows:

Code Numbers | Regular Numbers | Code Numbers | Regular Numbers

So for each pair of columns, you have to decode the code numbers into regular numbers, then add them.

But in the first row, left side, they already show:

Code Numbers: ~~~ ◐ ● and + ▽ □
Regular Numbers: 1 4 6 and + 1 7 3

That suggests that ~~~ ◐ ● = 146, and ▽ □ = 73? But 73 is two digits, while the code has two symbols — so maybe each symbol is one digit.

Wait — 146 is three digits, and there are three symbols: ~~~ (1), ◐ (4), ● (6) → yes, matches.

Then the second addend: ▽ □ → that’s two symbols, but in regular numbers it’s written as “+ 1 7 3” — that can’t be right.

Wait — I think I see the issue. Looking back at the image description:

In the first row, left column:

It says:

Code Numbers:
~~~ ◐ ●
+ ▽ □

And next to it, under “Regular Numbers”:
1 4 6
+ 1 7 3

That must mean that the second addend is actually three digits: 1 7 3 — but only two symbols are shown? That doesn’t make sense.

Wait — perhaps the “+ ▽ □” is meant to be three symbols? Let me count.

In the text you provided:

“~~~ ◐ ●
+ ▽ □”

That’s three symbols on top, two on bottom? That can’t be.

Perhaps it’s a formatting issue. Let me re-express based on standard interpretation.

Actually, looking at the structure, each addition problem has two addends, each with three digits (since title says “3-Digit Addends”).

So likely, each “Code Numbers” block has three symbols per addend.

Let me reinterpret the first problem:

Left side, first problem:

Top addend: ~~~ ◐ ● → 1, 4, 6 → 146
Bottom addend: ? The text says “+ ▽ □” — but that’s only two symbols. Probably it’s “+ ▽ □ [something]” — but in your text it’s cut off.

Wait — in your original message, it says:

“~~~ ◐ ●
+ ▽ □”

But then under Regular Numbers: “1 4 6 + 1 7 3”

Ah! So the bottom addend is 173, which would be coded as: 1=~~~, 7=▽, 3=□ — so it should be ~~~ ▽ □

But in the code numbers, it’s written as “+ ▽ □” — missing the first symbol? That must be a typo in transcription.

Similarly, for the other problems.

To avoid confusion, let’s assume that each addend has three digits, and the code symbols correspond digit by digit.

Also, in the first row, they’ve already given the regular numbers for the first problem: 146 + 173.

Let’s calculate that: 146 + 173 = 319

But since the task is to decode and solve, and they’ve given the regular numbers for the first one, perhaps it’s an example, and we need to do the others.

Looking at the layout:

There are six problems total — three rows, two columns each.

Row 1, left: already has regular numbers given: 146 + 173 → sum is 319

Row 1, right: Code Numbers: ⊗ ⊙ ● and + ◐ ◎ □

Decode:

⊗ = 8, ⊙ = 5, ● = 6 → so 856
◐ = 4, ◎ = 2, □ = 3 → so 423
Sum: 856 + 423 = 1279

But let’s verify decoding:

Key:
8 = ⊗
5 = ⊙
6 = ● → yes, 856
4 = ◐
2 = ◎
3 = □ → yes, 423
856 + 423:
6+3=9, 5+2=7, 8+4=12 → so 1279

Okay.

Now Row 2, left:

Code Numbers: □ ⊙ ⊙ and + ▽ ● □

Decode:
□ = 3, ⊙ = 5, ⊙ = 5 → 355
▽ = 7, ● = 6, □ = 3 → 763
Sum: 355 + 763 = 1118

Calculate: 5+3=8, 5+6=11 (carry 1), 3+7+1=11 → so 1118

Row 2, right:

Code Numbers: ◐ ⊙ and + ~~~ ⊙

Decode:
◐ = 4, ⊙ = 5, ⋈ = 9 → 459
⋈ = 9, ~~~ = 1, ⊙ = 5 → 915
Sum: 459 + 915 = 1374

Calculate: 9+5=14 (write 4, carry 1), 5+1+1=7, 4+9=13 → so 1374

Row 3, left:

Code Numbers: ● ⋈ □ and + ▽ ⊙ □

Decode:
● = 6, ⋈ = 9, □ = 3 → 693
▽ = 7, ⊙ = 5, □ = 3 → 753
Sum: 693 + 753 = 1446

Calculate: 3+3=6, 9+5=14 (write 4, carry 1), 6+7+1=14 → so 1446

Row 3, right:

Code Numbers: ● ⋈ ~~~ and + ~~~ ⊙ ◐

Decode:
● = 6, ⋈ = 9, ~~~ = 1 → 691
~~~ = 1, ⊙ = 5, ◐ = 4 → 154
Sum: 691 + 154 = 845

Calculate: 1+4=5, 9+5=14 (write 4, carry 1), 6+1+1=8 → so 845

Now, what about the first problem? In the worksheet, for Row 1 left, they have both code and regular numbers, and regular numbers are 146 + 173.

Let’s confirm decoding:
~~~ =1, ◐=4, ●=6 → 146
For 173: 1=~~~, 7=▽, 3=□ — so it should be ~~~ ▽ □, but in the code it’s written as “+ ▽ □” — probably missing the first symbol due to formatting. Since they gave the regular numbers, we can use that.

146 + 173 = 319

So all sums are:

Row 1 Left: 319
Row 1 Right: 1279
Row 2 Left: 1118
Row 2 Right: 1374
Row 3 Left: 1446
Row 3 Right: 845

But let’s double-check each calculation.

1. 146 + 173:
6+3=9
4+7=11 → write 1, carry 1
1+1+1=3 → 319 ✓

2. 856 + 423:
6+3=9
5+2=7
8+4=12 → 1279 ✓

3. 355 + 763:
5+3=8
5+6=11 → write 1, carry 1
3+7+1=11 → 1118 ✓

4. 459 + 915:
9+5=14 → write 4, carry 1
5+1+1=7
4+9=13 → 1374 ✓

5. 693 + 753:
3+3=6
9+5=14 → write 4, carry 1
6+7+1=14 → 1446 ✓

6. 691 + 154:
1+4=5
9+5=14 → write 4, carry 1
6+1+1=8 → 845 ✓

All correct.

Final Answer:
The sums for the six problems are:
319, 1279, 1118, 1374, 1446, 845