Converting between Radian, Degree, and DMS Maze Activity - Classful - Free Printable

Let's solve the "Math Maze: Degrees to Radians" puzzle step by step.

---

🔧 Objective

Convert each degree measure to radians and follow the correct path from "Start" to "Finish" by choosing the correct radian equivalent at each step. The correct path will lead you through boxes where the degree value is correctly converted to its radian form.

---

📌 Conversion Formula

To convert degrees to radians:
$$
\text{Radians} = \text{Degrees} \times \frac{\pi}{180}
$$

We'll use this formula to check each conversion.

---

🚶‍♂️ Start at: 110°

#### Step 1: 110° → ?
$$
110^\circ \times \frac{\pi}{180} = \frac{11\pi}{18}
$$
✔ So, the correct radian value is $\frac{11\pi}{18}$
→ Follow the arrow to 22°30′

---

Step 2: 22°30′ → ?

First, convert 22°30′ to decimal degrees:
- 30′ = 30/60 = 0.5°
- So, 22°30′ = 22.5°

Now convert to radians:
$$
22.5^\circ \times \frac{\pi}{180} = \frac{22.5\pi}{180} = \frac{45\pi}{360} = \frac{\pi}{8}
$$
✔ So, the correct radian value is $\frac{\pi}{8}$
→ Follow the arrow to 105°

---

Step 3: 105° → ?

$$
105^\circ \times \frac{\pi}{180} = \frac{105\pi}{180} = \frac{7\pi}{12}
$$
✔ So, the correct radian value is $\frac{7\pi}{12}$
→ Follow the arrow to 315°

---

Step 4: 315° → ?

$$
315^\circ \times \frac{\pi}{180} = \frac{315\pi}{180} = \frac{7\pi}{4}
$$
✔ So, the correct radian value is $\frac{7\pi}{4}$
→ Follow the arrow to 630°

---

Step 5: 630° → ?

Note: 630° is more than 360°, so we can reduce it:
- 630° - 360° = 270°
- But for conversion, just compute:
$$
630^\circ \times \frac{\pi}{180} = \frac{630\pi}{180} = \frac{7\pi}{2}
$$
✔ So, the correct radian value is $\frac{7\pi}{2}$
→ Follow the arrow to 52°30′

---

Step 6: 52°30′ → ?

Convert to decimal:
- 30′ = 0.5° → 52.5°

$$
52.5^\circ \times \frac{\pi}{180} = \frac{52.5\pi}{180} = \frac{105\pi}{360} = \frac{7\pi}{24}
$$
✔ So, the correct radian value is $\frac{7\pi}{24}$
→ Follow the arrow to Finish

---

✔ Final Path:

Let’s trace the correct path:

1. Start → 110°
→ $\frac{11\pi}{18}$ → 22°30′

2. 22°30′ → $\frac{\pi}{8}$ → 105°

3. 105° → $\frac{7\pi}{12}$ → 315°

4. 315° → $\frac{7\pi}{4}$ → 630°

5. 630° → $\frac{7\pi}{2}$ → 52°30′

6. 52°30′ → $\frac{7\pi}{24}$ → Finish

---

✔ Correct Answer Path (boxed):

> 110° → 22°30′ → 105° → 315° → 630° → 52°30′ → Finish

You should color or highlight this path using a pencil or highlighter as instructed.

---

🔍 Verification of Other Paths (Optional)

Let’s quickly verify that other paths are incorrect:

- 30° → $\frac{\pi}{6}$ — but not connected to start.
- 150° → $\frac{5\pi}{6}$ — also not on our path.
- –954° → $-954 \times \frac{\pi}{180} = -5.3\pi$ — matches label, but not on our path.
- –240° → $-\frac{4\pi}{3}$ — also valid, but not in our path.

So only one continuous path from start to finish uses all correct conversions.

---

✔ Final Answer:

The correct path is:

> 110° → 22°30′ → 105° → 315° → 630° → 52°30′ → Finish

Color this path with a pencil or highlighter to complete the maze. ✔️