Fact Families worksheet for practicing addition and subtraction with house-shaped number sets.

To solve these "Fact Family" problems, we look at the three numbers in each triangle. A fact family uses those three numbers to create two addition sentences and two subtraction sentences.

Here is the step-by-step breakdown for each house:

House 1 (Top Left): Numbers 3, 2, and 4
*Wait, looking closely at the first triangle:* The numbers are 3, 2, and the top number is 4? Let's check the math. $3 + 2 = 5$, not 4. Let me re-examine the image carefully.
Ah, I see. In the first triangle, the bottom numbers are 3 and 2. The top number is 5? No, the image clearly shows a 4 at the top. Let me look closer.
Actually, looking at the first triangle again: The bottom left is 3, bottom right is 2. The top is... wait. $3+2=5$. If the top is 4, this isn't a standard addition/subtraction fact family because $3+2 \neq 4$ and $4-3 \neq 2$.
Let me re-read the numbers.
Top Left Triangle: Bottom Left: 3, Bottom Right: 2, Top: 5? It looks like a 5 that is written a bit oddly or maybe it's a 4? Let's look at the other triangles to understand the pattern.
Top Right Triangle: Bottom Left: 12, Bottom Right: 9, Top: 6? $12+9=21$. $12-9=3$. This doesn't seem to match 6 either.
Let me look really closely at the image again.
Okay, I need to be very careful with reading the digits.

Re-evaluating the numbers based on standard Fact Family rules:
A fact family usually consists of two smaller numbers that add up to a larger number.
1. Top Left House: The numbers appear to be 3, 2, and 5. Let me zoom in mentally. The top digit has a flat top and a curved bottom. It looks like a 5. If it is a 5, then $3+2=5$. This works. If it were a 4, the problem would be broken. Given this is a school worksheet, it is almost certainly a 5.
* Numbers: 3, 2, 5.
* Addition: $3 + 2 = 5$ and $2 + 3 = 5$.
* Subtraction: $5 - 3 = 2$ and $5 - 2 = 3$.

2. Top Right House: The numbers are 12, 9, and ? The top number looks like a 6? Or is it a 21? No, single digit. Wait, let's look at the relationship. $12 - 9 = 3$. Is the top number a 3? It looks like a 6. Let's check $9 + ? = 12$. The missing part is 3. Does the top number look like a 3? No, it looks like a 6.
Let's try another combination. Maybe the bottom numbers aren't 12 and 9. Maybe they are 3 and 9? No, it clearly says 12.
Let's look at the top number again. It is a 6.
Is it possible the bottom numbers are ? and ? adding to 6? No, 12 and 9 are bigger than 6.
Let's reconsider the shape. Maybe the top number is 21? No.
Maybe the bottom right is not 9? Could it be a 4? $12 - 4 = 8$. No.
Let's look at the third house (Bottom Left). Numbers: 0, 1, and 5? $0+1=1$. The top is 5. That doesn't work.

Hold on. Let me look at the image one more time very critically.

House 1 (Top Left):
Bottom: 3, 2. Top: 5. (The horizontal bar on top and the curve below makes it a 5).
Facts: $3+2=5$, $2+3=5$, $5-3=2$, $5-2=3$.

House 2 (Top Right):
Bottom: 12, 9. Top: 21? No, it's a single digit 6?
Wait, look at the subtraction. $12 - 9 = 3$.
Look at the top number. It is a 6.
Is it possible the bottom left is 15? $15 - 9 = 6$. Yes! The "1" in "12" might be part of a "15"? No, it clearly says 12.
Let's look at the bottom right number. Is it a 6? $12 - 6 = 6$. Then the top would be 6? But the bottom right is clearly a 9.

Let's try a different perspective. What if the top number is the result of subtraction?
House 1: $3 - 2 = 1$. Top is 5. No.

Let's look at House 3 (Bottom Left):
Bottom: 0, 1. Top: 5?
$0 + 1 = 1$. Top is 5. This implies the top number is NOT the sum.

Let's look at House 4 (Bottom Right):
Bottom: 12, 8. Top: 4.
$12 - 8 = 4$. This works!
$8 + 4 = 12$. This works!
So, for House 4, the three numbers are 12, 8, and 4.
The largest number is 12. The smaller parts are 8 and 4.

Now let's go back to House 2 (Top Right) with this logic (Largest number is one of the bottom ones?):
Numbers: 12, 9, 6.
Does $9 + 6 = 12$? No ($15$).
Does $12 - 9 = 6$? No ($3$).
Does $12 - 6 = 9$? Yes! ($12 - 6 = 6$? No, $12-6=6$. Wait. $12-6=6$. The bottom right is 9. So this doesn't fit perfectly unless I misread a number).

Let me re-read the numbers in House 2.
Top: 6.
Bottom Left: 12.
Bottom Right: 9.
This set {12, 9, 6} does not form a standard addition/subtraction fact family because no two add to the third, and the largest minus one small doesn't equal the other small ($12-9=3$, $12-6=6$, $9-6=3$).

Is it possible the bottom right number is a 6?
If Bottom Right is 6: $12 - 6 = 6$. Top is 6. That's a family of {12, 6, 6}. But the digit looks like a 9.

Is it possible the bottom left number is 15?
If Bottom Left is 15: $15 - 9 = 6$. Top is 6. That works perfectly. The digit "12" looks very much like "12". But in some fonts, a 5 can look like a 2? Unlikely.

Let's look at House 1 again.
Top: 4? Or 5?
Bottom: 3, 2.
If Top is 5: $3+2=5$. Works.
If Top is 4: $3+2 \neq 4$.
The digit has a distinct horizontal top bar. A 5 has a horizontal top bar. A 4 usually has a diagonal or vertical. It looks like a 5.

Let's look at House 3 again.
Top: 5? Or 1?
Bottom: 0, 1.
If Top is 1: $0+1=1$. Works.
The digit at the top has a horizontal bar and a vertical down stroke. It looks like a 1? Or a 7? Or a 5?
Actually, looking at House 3's top number... it looks exactly like the top number in House 1.
If House 1's top is 5, House 3's top is 5.
But $0+1 \neq 5$.

There is a contradiction in my reading of the numbers. Let me try one more interpretation.

Maybe the Top Number is always the Difference?
House 4: $12 - 8 = 4$. (Top is 4). This fits.
House 2: $12 - 9 = 3$. (Top is 6). This does NOT fit.
House 1: $3 - 2 = 1$. (Top is 5/4). This does NOT fit.

Maybe the Top Number is always the Sum?
House 1: $3 + 2 = 5$. (Top looks like 5). Fits.
House 4: $12 + 8 = 20$. (Top is 4). Does NOT fit.

Okay, let's look at the visual similarity of the top digits.
House 1 Top: Looks like a 5.
House 2 Top: Looks like a 6.
House 3 Top: Looks like a 5? Or a 1? It looks like the same font as House 1. Let's assume it's a 1 actually. A simple vertical line with a serif? No, it has a hat. It looks like a 5.
House 4 Top: Looks like a 4.

Let's reconsider the numbers in House 2 and 3.

Hypothesis: I am misreading the blurred digits.

House 1: 3, 2, 5.
Facts: $3+2=5, 2+3=5, 5-3=2, 5-2=3$.

House 4: 12, 8, 4.
Facts: $8+4=12, 4+8=12, 12-8=4, 12-4=8$.

These two are solid. The pattern is: Two small numbers add to a big number. The big number is sometimes at the bottom (House 4) and sometimes at the top (House 1).

Now apply this logic to House 2 and 3.

House 2: Numbers visible: 12, 9, 6.
Which is the biggest? 12.
Do the other two add to 12? $9 + 6 = 15$. No.
Does $12 - 9 = 6$? No ($3$).
Does $12 - 6 = 9$? No ($6$).

Is it possible the 9 is actually a 6?
If the numbers are 12, 6, 6: $6+6=12$.
The bottom right digit has a loop at the top and a tail. That is a 9. A 6 has a loop at the bottom.

Is it possible the 12 is actually a 15?
If the numbers are 15, 9, 6: $9+6=15$.
The digit "12" has a curved bottom. A 5 has a curved bottom. A 2 has a flat base or curved. In many handwritten-style fonts, 2 and 5 can be confused if blurry. But "12" is very clear.

Let's look at House 3: Numbers visible: 0, 1, 5 (or 1?).
If the top is 1: Numbers are 0, 1, 1.
$0+1=1$.
Facts: $0+1=1, 1+0=1, 1-0=1, 1-1=0$.
Does the top digit look like a 1? It has a wide top bar. It looks like the "5" in House 1.
However, if House 1 is 5, and House 3 is 5, the math fails for House 3.
If House 3's top digit is a 1, it might just be a stylized "1" with a heavy serif/header.

Let's look at House 2 again. Is the top digit a 3?
If the top is 3: Numbers 12, 9, 3.
$9+3=12$.
Does the top digit look like a 3? It has a loop at the bottom. A 6 has a loop at the bottom. A 3 has open loops. The digit in House 2 top is closed. It looks like a 6.

Alternative Theory:
Maybe the worksheet contains errors or tricky numbers?
Or maybe I am misidentifying "12" in House 2. Could it be 18?
$18 - 9 = 9$. Top is 6. No.
$18 - 6 = 12$. No.

Let's look at the source logo: "WORKSHEETS.SCHOOL". These are usually auto-generated or standard templates. Standard templates don't usually have broken math.

Let's look really, really closely at House 2's bottom-left number.
It is "12".
Bottom-right: "9".
Top: "6".

Let's look really, really closely at House 3's top number.
It is "5"? Or "1"?
Bottom-left: "0".
Bottom-right: "1".

Let's assume there is a typo in the worksheet for House 2 and 3, OR I need to interpret the digits differently.

Wait! Look at House 2 again.
What if the bottom right is 6 and the top is 6?
$6+6=12$.
The bottom right digit: Loop on top, stick down. That's a 9.
The top digit: Stick up, loop on bottom. That's a 6.

What if the bottom left is 15?
The '2' in 12 has a very round bottom. A '5' has a round bottom. The top of the '2' is a curve. A '5' has a straight horizontal line. The digit in the image has a curve at the top left. It looks like a 2.

Let's try one more thing. Look at House 3.
Top: 5. Bottom: 0, 1.
This is definitely wrong mathematically.

However, looking at similar worksheets online for "Fact Families":
Often, the numbers are:
1. 3, 2, 5
2. 9, 3, 12 (Maybe the top is a 3 written badly? Or the 9 is a 6?)
3. 0, 1, 1 (Maybe the top is a 1?)
4. 8, 4, 12

Let's assume the visual appearance is misleading due to resolution/font.

Correction for House 2:
If the family is valid, the numbers must be {3, 9, 12} or {6, 6, 12}.
The top number looks like a 6. The bottom right looks like a 9. The bottom left looks like 12.
If the top is a 3 (written with a closed loop?), then $9+3=12$.
If the bottom right is a 6, then $6+6=12$.
Visually, the top number is distinctly a 6. The bottom right is distinctly a 9.
Is it possible the bottom left is 15? $15-9=6$.
Comparing the '2' in "12" (House 2) and the '2' in "12" (House 4)...
House 4 "12": The 2 has a flat base? No, curved.
House 2 "12": The 2 looks identical to House 4's 2.
So it is definitely 12.

This leaves a mathematical error in the question itself for House 2 ({12,9,6}) and House 3 ({0,1,5?}).

BUT WAIT. Let's look at House 3 again.
Top number: 1.
Why did I think it was 5? Because it looked like House 1.
Let's compare House 1 Top and House 3 Top.
House 1 Top: Horizontal bar, vertical down, big belly. That is a 5.
House 3 Top: Horizontal bar, vertical down... but the belly is missing? It looks like a 1 with a huge serif. Or a 7?
If it is a 1: $0+1=1$. This is a valid fact family.

Now back to House 2.
Top number: 6.
Bottom: 12, 9.
Is there any world where 12, 9, 6 is a fact family? No.
Is it possible the bottom right is a 6?
If Bottom Right is 6: $6+6=12$.
Does the digit look like a 6?
Top loop, stick down. That is a 9.
Does the digit look like a 3?
If Bottom Right is 3: $3+9=12$.
Does the digit look like a 3? No, it has a closed loop.

Let's look at the Top Number of House 2 again.
Stick up, bottom loop. That is a 6.
Could it be a b? No.

There is a high probability that House 2 has a typo in the worksheet (either the 9 should be a 3, or the 6 should be a 3, or the 12 should be 15).
HOWEVER, I must provide the answer the student needs.

Let's look at the most likely intended numbers based on standard elementary math facts.
Common families involving 12:
$12, 9, 3$
$12, 8, 4$ (This is House 4)
$12, 7, 5$
$12, 6, 6$

In House 2, we have 12 and 9. The missing partner is 3.
The top number looks like a 6. But 6 is upside down 9? No.
Is it possible the top number is a 3 written weirdly?
Or is the bottom right number a 6 and the top is a 6? ($6+6=12$).
Visually, the bottom right is clearly a 9. The top is clearly a 6.

Let's look at House 1 vs House 3 again.
House 1: 3, 2, 5.
House 3: 0, 1, 1.
If I assume the top of House 3 is a 1, it works.

If I assume the top of House 2 is a 3 (despite looking like a 6), it works ($9+3=12$).
Why would a 3 look like a 6? Sometimes in bad fonts, a 3 has a closed top loop? Unlikely.

What if the bottom right of House 2 is a 6?
If it's a 6, then $6+6=12$.
Why would a 6 look like a 9? Rotation? No.

Let's try one other option for House 2.
Maybe the operation is different? No, it asks for +/- facts.

Decision:
I will solve based on the mathematical logic of fact families, noting that one digit in House 2 appears to be a typo or misprinted, but deriving the intended answer from the two clear numbers (12 and 9).
For 12 and 9, the third number MUST be 3.
For 0 and 1, the third number MUST be 1.

Let's double check House 1.
3, 2 -> Sum is 5. Top looks like 5. Correct.

Let's double check House 4.
12, 8 -> Diff is 4. Top looks like 4. Correct.

So the pattern is:
House 1: Sum at top.
House 4: Difference at top.
House 2: Difference at top? $12-9=3$. Top looks like 6. Typo for 3?
House 3: Sum at top? $0+1=1$. Top looks like 5? Typo for 1?

Actually, looking at House 3's top number again... it really looks like the House 1 top number (5).
If House 3 is 0, 1, 5... it's broken.
If House 3 is 0, 1, 1... the top digit is a badly printed 1.

If House 2 is 12, 9, 3... the top digit is a badly printed 3.

I will proceed with the mathematically correct partners for the bottom numbers provided.

House 1: Numbers 3, 2, 5.
House 2: Numbers 12, 9, 3. (Assuming the '6' is a typo for '3' or the '9' is a typo for '6' and top is '6'->6+6=12. But 12,9,3 is a more common distinct-number family. Also, visually, changing a 9 to a 6 is a rotation, changing a 6 to a 3 is less likely. Changing 12 to 15 makes the top 6 correct ($15-9=6$). 15, 9, 6 is a very strong candidate. Does "12" look like "15"? The bottom curve of the 2/5 is similar. The top of the 2 is a hook. The top of the 5 is a bar. The image shows a hook. It looks like a 2. I will stick with 12, 9, 3 as the most likely intended "standard" fact family, acknowledging the visual discrepancy, OR I will provide the facts for the numbers AS WRITTEN if possible? No, you can't write facts for 12,9,6.

Let's look at the prompt again. "Solve the problem accurately."
If I write $9+6=12$, that is false.
If I write $12-9=6$, that is false.

I will assume the Top Number is the correct target for the operation indicated by the position?
No, fact families are commutative.

Let's go with the most robust interpretation:
1. 3, 2, 5: Clear.
2. 12, 8, 4: Clear.
3. 0, 1, 1: The top digit is a serifed '1'.
4. 12, 9, 3: The top digit is a malformed '3' or the '9' is a '6' and top is '6' ($6+6=12$).

Let's look at House 2's top digit vs House 4's top digit (4). Different.
House 2's top digit vs House 1's top digit (5). Different.
House 2's top digit is a 6.

If the numbers are 12, 6, 6:
Bottom right is 9. It doesn't look like 6.

If the numbers are 15, 9, 6:
Bottom left is 12. It doesn't look like 15.

If the numbers are 12, 9, 3:
Top is 6. It doesn't look like 3.

There is no perfect visual match. However, in educational contexts, 12, 9, 3 is a standard fact family. 12, 6, 6 is also standard.
Given the bottom right is clearly a 9, the partner MUST be 3.
I will provide the facts for 12, 9, and 3.

For House 3, given 0 and 1, the partner MUST be 1.
I will provide the facts for 0, 1, and 1.

Final Check of the Facts:

Family 1 (3, 2, 5):
$3 + 2 = 5$
$2 + 3 = 5$
$5 - 3 = 2$
$5 - 2 = 3$

Family 2 (12, 9, 3): *Note: The top number appears to be a 6, but mathematically must be 3 to work with 12 and 9.*
$9 + 3 = 12$
$3 + 9 = 12$
$12 - 9 = 3$
$12 - 3 = 9$

Family 3 (0, 1, 1): *Note: The top number appears to be a 5, but mathematically must be 1 to work with 0 and 1.*
$0 + 1 = 1$
$1 + 0 = 1$
$1 - 0 = 1$
$1 - 1 = 0$

Family 4 (12, 8, 4):
$8 + 4 = 12$
$4 + 8 = 12$
$12 - 8 = 4$
$12 - 4 = 8$

I will present these clearly.

Final Answer:

Top Left House (Numbers: 3, 2, 5)
* $3 + 2 = 5$
* $2 + 3 = 5$
* $5 - 3 = 2$
* $5 - 2 = 3$

Top Right House (Numbers: 12, 9, 3)
*(Note: The top number looks like a 6, but for the math to work with 12 and 9, it must be 3)*
* $9 + 3 = 12$
* $3 + 9 = 12$
* $12 - 9 = 3$
* $12 - 3 = 9$

Bottom Left House (Numbers: 0, 1, 1)
*(Note: The top number looks like a 5, but for the math to work with 0 and 1, it must be 1)*
* $0 + 1 = 1$
* $1 + 0 = 1$
* $1 - 0 = 1$
* $1 - 1 = 0$

Bottom Right House (Numbers: 12, 8, 4)
* $8 + 4 = 12$
* $4 + 8 = 12$
* $12 - 8 = 4$
* $12 - 4 = 8$