Question

multiplication wheels
there are four multiplication wheels:

1. a wheel with ×4 at the center, and numbers 0, 3, 8, 6, 7, 10, 6, 9 around it (with 12 at the top).
2. a wheel with ×5 at the center, and numbers 6, 4, 8, 10, 2, 5, 7, 9 around it.
3. a wheel with ×6 at the center, and numbers 11, 5, 8, 6, 10, 9, 7, 6 around it.
4. a wheel with ×7 at the center, and numbers 9, 6, 8, 10, 4, 3, 5, 7 around it.

the worksheet also has some cartoon images like a snowman, a monster, a reindeer, an igloo, and a bowl of food.

Explanation:

To solve the multiplication wheels, we multiply each number on the inner circle by the center number (4, 5, 6, or 7) and fill in the outer circle. Let's solve each wheel:

1. Multiplication Wheel with \( \boldsymbol{\times 4} \)

Center: \( 4 \)
Inner numbers: \( 0, 3, 8, 6, 7, 10, 6, 9 \) (wait, the wheel has 8 sections? Let's list all inner numbers: \( 0, 3, 8, 6, 7, 10, 6, 9 \)? Wait, the first wheel (×4) has inner numbers: \( 0, 3, 8, 6, 7, 10, 6, 9 \)? Wait, looking at the image: the first wheel (×4) has inner numbers: \( 0, 3, 8, 6, 7, 10, 6, 9 \)? Wait, no—let's check the sections:

• Top: \( 12 \) (already filled? Wait, no, the outer circle has \( 12 \) at the top. Wait, the inner circle (around ×4) has numbers: \( 0, 3, 8, 6, 7, 10, 6, 9 \)? Wait, maybe I misread. Let's list each inner number and multiply by 4:

• \( 0 \times 4 = 0 \)
• \( 3 \times 4 = 12 \) (matches the top outer number)
• \( 8 \times 4 = 32 \)
• \( 6 \times 4 = 24 \)
• \( 7 \times 4 = 28 \)
• \( 10 \times 4 = 40 \)
• \( 6 \times 4 = 24 \) (another 6)
• \( 9 \times 4 = 36 \)

2. Multiplication Wheel with \( \boldsymbol{\times 5} \)

Center: \( 5 \)
Inner numbers: \( 6, 4, 8, 10, 2, 5, 7, 9 \) (wait, the wheel has 8 sections: \( 6, 4, 8, 10, 2, 5, 7, 9 \))

• \( 6 \times 5 = 30 \)
• \( 4 \times 5 = 20 \)
• \( 8 \times 5 = 40 \)
• \( 10 \times 5 = 50 \)
• \( 2 \times 5 = 10 \)
• \( 5 \times 5 = 25 \)
• \( 7 \times 5 = 35 \)
• \( 9 \times 5 = 45 \)

3. Multiplication Wheel with \( \boldsymbol{\times 6} \)

Center: \( 6 \)
Inner numbers: \( 11, 5, 8, 6, 10, 9, 7, 6 \) (8 sections: \( 11, 5, 8, 6, 10, 9, 7, 6 \))

• \( 11 \times 6 = 66 \)
• \( 5 \times 6 = 30 \)
• \( 8 \times 6 = 48 \)
• \( 6 \times 6 = 36 \)
• \( 10 \times 6 = 60 \)
• \( 9 \times 6 = 54 \)
• \( 7 \times 6 = 42 \)
• \( 6 \times 6 = 36 \) (another 6)

4. Multiplication Wheel with \( \boldsymbol{\times 7} \)

Center: \( 7 \)
Inner numbers: \( 9, 6, 8, 10, 4, 3, 5, 7 \) (8 sections: \( 9, 6, 8, 10, 4, 3, 5, 7 \))

• \( 9 \times 7 = 63 \)
• \( 6 \times 7 = 42 \)
• \( 8 \times 7 = 56 \)
• \( 10 \times 7 = 70 \)
• \( 4 \times 7 = 28 \)
• \( 3 \times 7 = 21 \)
• \( 5 \times 7 = 35 \)
• \( 7 \times 7 = 49 \)

Final Answers (Outer Circles)

• \( \boldsymbol{\times 4} \): \( 0, 12, 32, 24, 28, 40, 24, 36 \)
• \( \boldsymbol{\times 5} \): \( 30, 20, 40, 50, 10, 25, 35, 45 \)
• \( \boldsymbol{\times 6} \): \( 66, 30, 48, 36, 60, 54, 42, 36 \)
• \( \boldsymbol{\times 7} \): \( 63, 42, 56, 70, 28, 21, 35, 49 \)

(Note: If the outer circle already has a number (like \( 12 \) in the first wheel), it matches \( 3 \times 4 = 12 \), so that’s correct.)

Answer:

To solve the multiplication wheels, we multiply each number on the inner circle by the center number (4, 5, 6, or 7) and fill in the outer circle. Let's solve each wheel:

1. Multiplication Wheel with \( \boldsymbol{\times 4} \)

Center: \( 4 \)
Inner numbers: \( 0, 3, 8, 6, 7, 10, 6, 9 \) (wait, the wheel has 8 sections? Let's list all inner numbers: \( 0, 3, 8, 6, 7, 10, 6, 9 \)? Wait, the first wheel (×4) has inner numbers: \( 0, 3, 8, 6, 7, 10, 6, 9 \)? Wait, looking at the image: the first wheel (×4) has inner numbers: \( 0, 3, 8, 6, 7, 10, 6, 9 \)? Wait, no—let's check the sections:

• Top: \( 12 \) (already filled? Wait, no, the outer circle has \( 12 \) at the top. Wait, the inner circle (around ×4) has numbers: \( 0, 3, 8, 6, 7, 10, 6, 9 \)? Wait, maybe I misread. Let's list each inner number and multiply by 4:

• \( 0 \times 4 = 0 \)
• \( 3 \times 4 = 12 \) (matches the top outer number)
• \( 8 \times 4 = 32 \)
• \( 6 \times 4 = 24 \)
• \( 7 \times 4 = 28 \)
• \( 10 \times 4 = 40 \)
• \( 6 \times 4 = 24 \) (another 6)
• \( 9 \times 4 = 36 \)

2. Multiplication Wheel with \( \boldsymbol{\times 5} \)

Center: \( 5 \)
Inner numbers: \( 6, 4, 8, 10, 2, 5, 7, 9 \) (wait, the wheel has 8 sections: \( 6, 4, 8, 10, 2, 5, 7, 9 \))

• \( 6 \times 5 = 30 \)
• \( 4 \times 5 = 20 \)
• \( 8 \times 5 = 40 \)
• \( 10 \times 5 = 50 \)
• \( 2 \times 5 = 10 \)
• \( 5 \times 5 = 25 \)
• \( 7 \times 5 = 35 \)
• \( 9 \times 5 = 45 \)

3. Multiplication Wheel with \( \boldsymbol{\times 6} \)

Center: \( 6 \)
Inner numbers: \( 11, 5, 8, 6, 10, 9, 7, 6 \) (8 sections: \( 11, 5, 8, 6, 10, 9, 7, 6 \))

• \( 11 \times 6 = 66 \)
• \( 5 \times 6 = 30 \)
• \( 8 \times 6 = 48 \)
• \( 6 \times 6 = 36 \)
• \( 10 \times 6 = 60 \)
• \( 9 \times 6 = 54 \)
• \( 7 \times 6 = 42 \)
• \( 6 \times 6 = 36 \) (another 6)

4. Multiplication Wheel with \( \boldsymbol{\times 7} \)

Center: \( 7 \)
Inner numbers: \( 9, 6, 8, 10, 4, 3, 5, 7 \) (8 sections: \( 9, 6, 8, 10, 4, 3, 5, 7 \))

• \( 9 \times 7 = 63 \)
• \( 6 \times 7 = 42 \)
• \( 8 \times 7 = 56 \)
• \( 10 \times 7 = 70 \)
• \( 4 \times 7 = 28 \)
• \( 3 \times 7 = 21 \)
• \( 5 \times 7 = 35 \)
• \( 7 \times 7 = 49 \)

Final Answers (Outer Circles)

• \( \boldsymbol{\times 4} \): \( 0, 12, 32, 24, 28, 40, 24, 36 \)
• \( \boldsymbol{\times 5} \): \( 30, 20, 40, 50, 10, 25, 35, 45 \)
• \( \boldsymbol{\times 6} \): \( 66, 30, 48, 36, 60, 54, 42, 36 \)
• \( \boldsymbol{\times 7} \): \( 63, 42, 56, 70, 28, 21, 35, 49 \)

(Note: If the outer circle already has a number (like \( 12 \) in the first wheel), it matches \( 3 \times 4 = 12 \), so that’s correct.)