• Resource ID: MATH_GEO_LOGIC
• Grade Range: 9–12
• Subject: Math

### Introduction to Logical Reasoning

This activity provides the opportunity to explore the validity of the converse, inverse, and contrapositive of statements. It also assists in recognizing the connections between biconditional statements and true conditional statements with a true converse.

• Resource ID: MATH_GEO_PROB
• Grade Range: 9–12
• Subject: Math

### Introduction to Probability

This activity provides the opportunity to explore the difference between finding the probability of independent events and dependent events. It also addresses how to use a tree diagram when calculating conditional probabilities.

• Resource ID: GM4L15b
• Grade Range: 9–12
• Subject: Math

### Making Conjectures About Quadrilaterals

Given examples of quadrilaterals and their component parts, the student will use explorations and concrete models to prove a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite sides, opposite angles, or diagonals.

• Resource ID: GM4L6
• Grade Range: 9–12
• Subject: Math

### Applying Geometric Probability

The student will find the area of polygons and circles. Then, the student will use probability to solve real-world problems.

• Resource ID: GM1L1
• Grade Range: 9–12
• Subject: Math

### Connecting Postulates, Definitions, and Theorems

The student will distinguish the difference between undefined terms, definitions, postulates, conjectures, and theorems.

• Resource ID: GM4L11
• Grade Range: 9–12
• Subject: Math

### Determining the Surface Area and Volume of Spheres

Given a problem involving spheres, the student will find the surface area and volume.

• Resource ID: GM2L3
• Grade Range: 9–12
• Subject: Math

### Generalizing Geometric Properties of Ratios in Similar Figures

Students will investigate patterns to make conjectures about geometric relationships and apply the definition of similarity, in terms of a dilation, to identify similar figures and their proportional sides and congruent corresponding angles.

• Resource ID: GM4L12
• Grade Range: 9–12
• Subject: Math

### Determining the Surface Area and Volume of Composite Figures

Given a problem involving composite figures made from prisms, pyramids, spheres, cones, and/or cylinders, the student will find the surface area and volume of the composite figure.

• Resource ID: GM4L16
• Grade Range: 9–12
• Subject: Math

### Making Conjectures About Circles and Segments

Given examples of circles and the lines that intersect them, the student will use explorations and concrete models to formulate and test conjectures about the properties and relationships among the resulting segments.

• Resource ID: GM2L8
• Grade Range: 9–12
• Subject: Math

### Applying Pythagorean Triples to Solve Problems

Given verbal and pictorial representations of problem situations, the student will apply patterns from right triangles whose sides are Pythagorean Triples to solve the problems.

• Resource ID: GM1L9
• Grade Range: 9–12
• Subject: Math

### Making and Verifying Conjectures about Polygons

Students will investigate patterns and make conjectures about geometric relationships, including interior angles of polygons.

• Resource ID: GM4L1
• Grade Range: 9–12
• Subject: Math

### Determining Area: Regular Polygons and Circles

The student will apply the formula for the area of regular polygons to solve problems.

• Resource ID: GM4L5
• Grade Range: 9–12
• Subject: Math

### Using The Pythagorean Theorem

The student will use triangle relationships to prove the Pythagorean Theorem and solve problems.

• Resource ID: GM1L10
• Grade Range: 9–12
• Subject: Math

### Making and Verifying Conjectures About Circles

Given information about the relationship(s) witnin one circle or a set of circles, the student will explore special segments and angles of circles.

• Resource ID: GM3L10
• Grade Range: 9–12
• Subject: Math

### Coordinate Geometry: Slope

Given coordinate points, the student will use slope formulas to solve problems.

• Resource ID: GM3L11
• Grade Range: 9–12
• Subject: Math

### Coordinate Geometry: Midpoint

Given coordinate points the student will use midpoint formulas to solve problems.

• Resource ID: GM3L6
• Grade Range: 9–12
• Subject: Math

### Introduction to Coordinate Geometry

The students will use multiple representations of undefined terms on a coordinate plane to solve problems.

• Resource ID: GM4L3
• Grade Range: 9–12
• Subject: Math

### Determining Area: Sectors of Circles

Students will use proportional reasoning to develop formulas to determine the area of sectors of circles. Students will then solve problems involving the area of sectors of circles.

• Resource ID: GM1L18
• Grade Range: 9–12
• Subject: Math

### Using Logical Reasoning to Prove Conjectures About Quadrilaterals

Given conjectures about quadrilaterals, the student will use deductive reasoning and counterexamples to prove or disprove the conjectures.

• Resource ID: GM5L4
• Grade Range: 9–12
• Subject: Math

### Applying Trigonometric Ratios

Given problem situations involving similar figures, the student will apply and justify triangle similarity relationships such as trigonometric ratios.