how to make laws of indices working model (laws of exponents) – maths tlm – diy – simple and easy

In this video post we learn about making of the laws of indices working model (laws of exponents) – maths tlm – diy – simple and easy

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Creating a working model to demonstrate the laws of indices (laws of exponents) with rotating pieces is a great way to visually teach and understand these mathematical concepts.

Here’s how to create this interactive model using cardboard, color paper, and chopsticks:

Materials Needed:

• Cardboard (for the base and rotating pieces)
• Color paper (for decoration and labeling)
• Chopsticks (for the rotating mechanism)
• Markers or pens
• Scissors or craft knife
• Glue or hot glue gun
• Brass fasteners (for attaching pieces)
• Ruler
• Protractor (for accurate angle measurement)
• Compass (for drawing circles)

Video post on making of the laws of indices working model (laws of exponents) – maths tlm – diy – simple and easy

1. Prepare the Base and Structure

1. Base Preparation:
• Cut a large rectangular piece of cardboard to serve as the base.
• Cover the base with white or colored paper for a clean background.
2. Draw the Structure:
• Divide the cardboard into 8 equal sections (each section will represent one law of indices).

2. Create the Rotating Pieces

1. Cut the Rotating Pieces:
• Cut 8 rectangular pieces of cardboard for the exponents‘ formulas.
• Cut another 8 smaller rectangular pieces for the examples. These should be smaller and fit neatly under the corresponding formula piece.
2. Cover the Pieces:
• Cover each piece with colored paper. Use different colors for the formula pieces and example pieces to distinguish them easily.

3. Attach the Rotating Mechanism

1. Prepare the Chopsticks:
• Cut 8 chopsticks to the desired length. These will be used as the rotating axles for each piece.
2. Attach the Formulas and Examples:
• Attach the formula pieces to the chopsticks using brass fasteners through the holes. Ensure they can rotate freely.
• Attach the example pieces to the base so they can be revealed when the formula pieces are rotated.
3. Secure the Chopsticks:
• Glue the chopsticks to the center of the base, ensuring they are evenly spaced and can rotate to reveal the examples.

4. Label and Decorate

1. Label the Formulas:
• Write each law of indices on the corresponding formula piece. For example:
• am⋅an=am+na^m \cdot a^n = a^{m+n}am⋅an=am+n
• aman=am−n\frac{a^m}{a^n} = a^{m-n}anam​=am−n
• (am)n=amn(a^m)^n = a^{mn}(am)n=amn
• a0=1a^0 = 1a0=1 (where a≠0a \neq 0a=0)
• a−n=1ana^{-n} = \frac{1}{a^n}a−n=an1​
• (ab)n=an⋅bn(ab)^n = a^n \cdot b^n(ab)n=an⋅bn
• (ab)n=anbn\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}(ba​)n=bnan​
• (am⋅bm)=(ab)m(a^m \cdot b^m) = (ab)^m(am⋅bm)=(ab)m
2. Write the Examples:
• Write a corresponding example for each law on the example pieces. For example:
• 23⋅22=23+2=252^3 \cdot 2^2 = 2^{3+2} = 2^523⋅22=23+2=25
• 3532=35−2=33\frac{3^5}{3^2} = 3^{5-2} = 3^33235​=35−2=33
• (42)3=42⋅3=46(4^2)^3 = 4^{2 \cdot 3} = 4^6(42)3=42⋅3=46
• 50=15^0 = 150=1
• 2−3=123=182^{-3} = \frac{1}{2^3} = \frac{1}{8}2−3=231​=81​
• (2⋅3)2=22⋅32=4⋅9=36(2 \cdot 3)^2 = 2^2 \cdot 3^2 = 4 \cdot 9 = 36(2⋅3)2=22⋅32=4⋅9=36
• (23)2=2232=49\left(\frac{2}{3}\right)^2 = \frac{2^2}{3^2} = \frac{4}{9}(32​)2=3222​=94​
• (22⋅32)=(62)(2^2 \cdot 3^2) = (6^2)(22⋅32)=(62)
3. Decorate the Model:
• Use color paper and markers to make the model visually appealing.
• Add any additional decorations or labels to enhance clarity and engagement.

Final Touches:

• Interactive Elements:
• Ensure that each piece rotates smoothly and reveals the example underneath.
• Test the model to make sure all pieces work as intended.
• Safety Precautions:
• Handle scissors and craft knives carefully to avoid injury.
• Supervise children during the construction and demonstration of the model.
• Ensure all parts are securely attached to prevent any accidents.

By following these steps, you can create an effective and interactive working model that demonstrates the laws of indices.