Multiplication Color by Code Worksheets - Teaching Trove - Free Printable

To solve this "Hats Off" worksheet, we need to find the missing numbers in the multiplication equations. The spinner at the top tells us we are working with the 3 and 4 times tables. This means every blank space must be filled with either a 3 or a 4 to make the equation true.

Here is the step-by-step logic for solving each section:

Step 1: Understand the Rules

* You have an equation like `__ x __ = 12`.
* One number is missing.
* You must choose between 3 or 4 to fill the blank.
* *Example:* For `__ x 4 = 12`, you ask: "Does 3 times 4 equal 12?" Yes. So the answer is 3.

Step 2: Solve the Equations by Product Value

Let's group the problems by the answer (the product) to make it easier.

Product = 9
* Equation: `__ x __ = 9`
* Logic: $3 \times 3 = 9$. (Note: Since the spinner only has 3s and 4s, and $4 \times ?$ never equals 9, both blanks here are 3).
* Answer: 3 and 3

Product = 12
* Equation: `__ x __ = 12` (or `__ x 4 = 12`, etc.)
* Logic: We know $3 \times 4 = 12$.
* Answer: 3 and 4 (order doesn't matter for coloring, but usually the spinner determines one factor).

Product = 15
* Equation: `__ x __ = 15`
* Logic: $3 \times 5 = 15$. The missing factor from the spinner side is 3.
* Answer: 3 (and 5)

Product = 16
* Equation: `__ x __ = 16`
* Logic: $4 \times 4 = 16$.
* Answer: 4 and 4

Product = 18
* Equation: `__ x __ = 18`
* Logic: $3 \times 6 = 18$. The missing factor from the spinner side is 3.
* Answer: 3 (and 6)

Product = 20
* Equation: `__ x __ = 20`
* Logic: $4 \times 5 = 20$. The missing factor from the spinner side is 4.
* Answer: 4 (and 5)

Product = 24
* Equation: `__ x __ = 24`
* Logic: There are two options: $3 \times 8 = 24$ OR $4 \times 6 = 24$.
* Look at the specific box. If it says `__ x 8 = 24`, the answer is 3.
* If it says `__ x 6 = 24`, the answer is 4.
* *Self-Correction/Check:* In these worksheets, usually all instances of "24" might share a color code, but let's look at the color key. Green is 15 and 27. Red is 12 and 48. Light Blue is 20 and 32. Yellow is 18, 24, 30. Dark Blue is 9 and 28. Orange is 16 and 36.
* Wait, the prompt asks to "complete the equation". Let's just list the missing multiplier for each visible equation type found in the hat.

Product = 27
* Equation: `__ x __ = 27`
* Logic: $3 \times 9 = 27$. The missing factor is 3.
* Answer: 3 (and 9)

Product = 28
* Equation: `__ x __ = 28`
* Logic: $4 \times 7 = 28$. The missing factor is 4.
* Answer: 4 (and 7)

Product = 30
* Equation: `__ x __ = 30`
* Logic: $3 \times 10 = 30$? No, standard tables go up to 12 usually, but let's check 4. $4 \times ?$ No. Let's re-read the spinner. The spinner has outer numbers 3, 4, 5, 6, 7, 8, 9, 10. Ah, the spinner multiplies the inner number (3 or 4) by the outer number.
* So, `3 x 10 = 30`. The missing spinner number is 3.
* Answer: 3 (and 10)

Product = 32
* Equation: `__ x __ = 32`
* Logic: $4 \times 8 = 32$. The missing factor is 4.
* Answer: 4 (and 8)

Product = 36
* Equation: `__ x __ = 36`
* Logic: $4 \times 9 = 36$ (since $3 \times 12$ isn't on the spinner directly as a single digit pair usually, but $4 \times 9$ is valid). The missing factor is 4.
* Answer: 4 (and 9)

Product = 48
* Equation: `__ x __ = 48`
* Logic: $4 \times 12 = 48$? Or $3 \times 16$? Let's look at the spinner again. The outer ring goes up to 10? No, looking closely at the top left, the outer numbers are 3, 4, 5, 6, 7, 8, 9, 10... wait, let me look at the slice for 48.
* Usually $4 \times 12 = 48$. Is 12 on the spinner? The spinner slices seem to correspond to multipliers.
* Actually, simpler approach: Just find the missing factor that is either 3 or 4.
* For 48: $4 \times 12 = 48$. So the spinner part is 4.

Step 3: Verification of Color Coding (Optional but helpful context)

The instructions say to use the code to color the products.
* Green: Products 15 ($3\times5$) and 27 ($3\times9$). Both use multiplier 3.
* Red: Products 12 ($3\times4$) and 48 ($4\times12$). Mixed multipliers.
* Light Blue: 20 ($4\times5$) and 32 ($4\times8$). Both use multiplier 4.
* Yellow: 18 ($3\times6$), 24 ($3\times8$ or $4\times6$), 30 ($3\times10$). Mostly 3, except some 24s.
* Dark Blue: 9 ($3\times3$) and 28 ($4\times7$). Mixed.
* Orange: 16 ($4\times4$) and 36 ($4\times9$). Both use multiplier 4.

Final Calculation List for the Student

Here are the missing numbers for the equations found in the hat picture. I will list them by the equation shown.

1. __ x __ = 30: The missing multiplier is 3 (because $3 \times 10 = 30$).
2. __ x __ = 12: The missing multiplier is 3 or 4 (depending on the other number). If the other number is 4, answer is 3. If the other number is 3, answer is 4.
3. __ x __ = 48: The missing multiplier is 4 (because $4 \times 12 = 48$).
4. __ x __ = 24:
* If paired with 8: Answer is 3 ($3 \times 8 = 24$).
* If paired with 6: Answer is 4 ($4 \times 6 = 24$).
5. __ x __ = 18: The missing multiplier is 3 (because $3 \times 6 = 18$).
6. __ x __ = 16: The missing multiplier is 4 (because $4 \times 4 = 16$).
7. __ x __ = 9: The missing multiplier is 3 (because $3 \times 3 = 9$).
8. __ x __ = 28: The missing multiplier is 4 (because $4 \times 7 = 28$).
9. __ x __ = 36: The missing multiplier is 4 (because $4 \times 9 = 36$).
10. __ x __ = 27: The missing multiplier is 3 (because $3 \times 9 = 27$).
11. __ x __ = 20: The missing multiplier is 4 (because $4 \times 5 = 20$).
12. __ x __ = 32: The missing multiplier is 4 (because $4 \times 8 = 32$).
13. __ x __ = 15: The missing multiplier is 3 (because $3 \times 5 = 15$).

Final Answer:
To complete the worksheet, fill in the blanks with 3 or 4 based on these rules:

* Use 3 for these products: 9, 15, 18, 27, 30. (Also use 3 for the equation `3 x 8 = 24`).
* Use 4 for these products: 16, 20, 28, 32, 36, 48. (Also use 4 for the equation `4 x 6 = 24`).
* For the product 12: Use 3 if multiplying by 4; use 4 if multiplying by 3.