Creating working models for math concepts can help students understand and visualize abstract ideas. Here are 25 math working models suitable for 10th-grade students:

### Algebra and Arithmetic

**Algebraic Expression Simplifier****Materials**: Cardboard, colored paper, sliders**Description**: A model with sliders that combine like terms and simplify expressions.

**Quadratic Equation Solver****Materials**: Cardboard, graph paper, strings**Description**: A model that visualizes the solutions of a quadratic equation using a parabola graph.

**Polynomial Function Graph****Materials**: Cardboard, colored paper, strings**Description**: A visual representation of polynomial functions and their roots.

**Arithmetic Sequence and Series****Materials**: Cardboard, colored paper, beads**Description**: A model demonstrating the terms of arithmetic sequences and their sums.

**Geometric Sequence and Series****Materials**: Cardboard, colored paper, beads**Description**: A visual representation of geometric sequences and their sums.

### Geometry

**Pythagorean Theorem Proof****Materials**: Cardboard, colored paper, right-angled triangles**Description**: A model showing different proofs of the Pythagorean theorem.

**Circle Theorems****Materials**: Cardboard, compass, string**Description**: A model illustrating various circle theorems, including angles and tangents.

**3D Geometric Shapes****Materials**: Cardboard, colored paper, glue**Description**: Models of various 3D shapes like cubes, cones, and cylinders with labeled properties.

**Surface Area and Volume of Solids****Materials**: Cardboard, colored paper, small containers**Description**: Models demonstrating the calculation of surface area and volume for different solids.

**Similar Triangles****Materials**: Cardboard, colored paper, strings**Description**: A model showing properties of similar triangles and their proportional sides.

### Trigonometry

**Unit Circle****Materials**: Cardboard, colored paper, compass**Description**: A model illustrating the unit circle, radians, and trigonometric functions.

**Sine and Cosine Wave Generator****Materials**: Cardboard, strings, pins**Description**: A model showing how sine and cosine waves are generated.

**Trigonometric Ratios****Materials**: Cardboard, colored paper, right-angled triangles**Description**: A visual representation of sine, cosine, and tangent ratios.

**Trigonometric Identities****Materials**: Cardboard, colored paper, sliders**Description**: A model illustrating fundamental trigonometric identities.

**Angle of Elevation and Depression****Materials**: Cardboard, protractor, strings**Description**: A model demonstrating real-life applications of angle of elevation and depression.

### Calculus (Basics)

**Derivative Visualization****Materials**: Cardboard, graph paper, sliders**Description**: A model illustrating the concept of a derivative as the slope of a tangent.

**Integral Representation****Materials**: Cardboard, graph paper, colored paper**Description**: A model showing the area under a curve to represent definite integrals.

**Limits and Continuity****Materials**: Cardboard, graph paper, sliders**Description**: A model demonstrating the concept of limits and continuity of functions.

### Statistics and Probability

**Probability Tree****Materials**: Cardboard, colored paper, markers**Description**: A visual representation of different outcomes and their probabilities.

**Mean, Median, Mode****Materials**: Cardboard, beads, sliders**Description**: A model to calculate and display the mean, median, and mode of a dataset.

**Histogram and Bar Graphs****Materials**: Cardboard, colored paper, markers**Description**: Models showing how data is represented in histograms and bar graphs.

**Standard Deviation****Materials**: Cardboard, colored paper, beads**Description**: A model demonstrating the calculation of standard deviation in a dataset.

### Miscellaneous

**Fibonacci Sequence****Materials**: Cardboard, colored paper, beads**Description**: A model illustrating the Fibonacci sequence and its golden ratio.

**Mathematical Set Operations****Materials**: Cardboard, colored paper, Venn diagrams**Description**: A model showing various set operations like union, intersection, and difference.

**Transformation of Shapes****Materials**: Cardboard, colored paper, sliders**Description**: A model demonstrating geometric transformations like translation, rotation, and reflection.

These models provide a hands-on learning experience, helping students better understand and engage with various mathematical concepts.