In this post I will write about on how to make the laws of exponents – math’s working model – algebraic expressions – diy
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Creating a working model to demonstrate the laws of exponents and algebraic expressions using cardboard, color paper, and chopsticks is a great hands-on learning project.
This model will help visualize and understand the exponent rules and how they apply to algebraic expressions.
Here’s a step-by-step guide:
Materials Needed:
- Cardboard (for the base and rotating mechanism)
- Color paper (for covering and detailing)
- Chopsticks (for the rotating mechanism)
- Scissors
- Glue or double-sided tape
- Ruler
- Marker or pen
- Hot glue gun (optional, for stronger connections)
- Brass fasteners or pins (for the rotating mechanism)
Guide for making of the laws of exponents – math’s working model – algebraic expressions – diy
1. Prepare the Base and Rotating Mechanism
- Base Preparation:
- Cut a large rectangular piece of cardboard to serve as the base of your model. This should be sturdy enough to support the rotating mechanism and the algebraic expressions.
- Rotating Mechanism:
- Cut out a smaller rectangle or square from cardboard to serve as the rotating platform. Ensure it is large enough to fit eight algebraic expressions.
- Make a small hole in the center of the rotating platform and the base for the chopstick to go through.
2. Prepare the Algebraic Expressions
- Create the Expression Cards:
- Cut eight small rectangles from cardboard. These will be the cards that display the algebraic expressions.
- Cover each card with color paper and write one algebraic expression on each card using a marker. Make sure the expressions include different exponent rules, such as:
- 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
- (ab)m=am⋅bm(ab)^m = a^m \cdot b^m(ab)m=am⋅bm
- (ab)m=ambm\left(\frac{a}{b}\right)^m = \frac{a^m}{b^m}(ba)m=bmam
- a−n=1ana^{-n} = \frac{1}{a^n}a−n=an1
- (am⋅bn)p=amp⋅bnp(a^m \cdot b^n)^p = a^{mp} \cdot b^{np}(am⋅bn)p=amp⋅bnp
- Attach the Expressions to the Platform:
- Glue or tape each expression card to the rotating platform. Space them evenly around the edge of the platform.
3. Assemble the Model
- Attach the Rotating Platform:
- Insert a chopstick through the hole in the center of the rotating platform and secure it with a brass fastener or pin so that it can rotate freely.
- Push the other end of the chopstick through the hole in the base. Secure it with another brass fastener or pin under the base, allowing the platform to rotate horizontally.
- Create Stoppers (Optional):
- To ensure the platform rotates to each expression accurately, create small stoppers using pieces of cardboard and attach them at intervals around the base.
4. Decorate and Detail
- Cover the Base and Platform:
- Cover the base and the edges of the rotating platform with color paper for a neat finish.
- Use markers or colored pens to add labels or decorate the model as desired.
- Label Each Expression:
- Write or print labels for each exponent rule and attach them next to the corresponding expression cards.
5. Presentation and Explanation
- Interactive Demonstration:
- Rotate the platform to show different algebraic expressions and explain the associated exponent rules.
- Highlight how each rule is applied in simplifying expressions and solving equations.
- Discussion Points:
- Discuss the importance of the laws of exponents in algebra and how they simplify complex calculations.
- Provide examples of real-life applications of exponent rules.
By following these steps, you can create an engaging and educational working model that effectively demonstrates the laws of exponents and their application in algebraic expressions.