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Honors Geometry Unit 3 Notes

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Unit 3: Lengths, Area, and Volumes

Euclid said "A line is breadthless length."

1D: Length and Linear Measurement

Lesson 1: Units and Measurement in 1D

Standards: MA19.GDA.2, MA19.GDA.4

  • Objective: Students will use units and dimensional analysis to solve measurement problems in one dimension.
  • Essential Question: Why are consistent units important in problem solving?
  • Sample Tasks:
    • Convert between inches, feet, and yards in real-life contexts.
    • Calculate the length of fencing needed for a rectangular garden.
    • Rearrange the formula to solve for time or rate.

Lesson 2: Lines, Linear Equations, and Distance in the Plane

Standards: MA19.GDA.5, MA19.GDA.18

  • Objective: Students will apply the distance and midpoint formulas and verify solutions to linear equations on graphs.
  • Essential Question: How can we represent distance and location on a coordinate plane?
  • Sample Tasks:
    • Use the distance formula to calculate the side length of a polygon given its vertices.
    • Graph a line and verify that points satisfy its equation.
    • Find the midpoint between two cities on a map.

Lesson 3: Algebra in Geometry

Standards: MA19.GDA.4

  • Objective: Students will rearrange geometric formulas to isolate variables.
  • Essential Question: How does algebra help us work flexibly with geometric relationships?
  • Sample Tasks:
    • Solve for radius in the circumference formula .
    • Solve for base in the area formula .
    • Apply rearranging to real-world problems, e.g., finding required side length for a rectangular field with a given area.

2D: Area and Surface Relationships

Lesson 4: Area of Basic Polygons

Standards: MA19.GDA.18

  • Objective: Students will calculate areas of polygons using formulas and coordinates.
  • Essential Question: How can we use coordinates to find area?
  • Sample Tasks:
    • Compute the area of a triangle using its vertices.
    • Apply shoelace method for irregular polygons.
    • Solve problems involving tiling and land plots.

Lesson 5: Circles and Composite Figures

Standards: MA19.GDA.2, MA19.GDA.4

  • Objective: Students will apply circle area formulas and decompose figures to calculate composite areas.
  • Essential Question: How can we find the area of shapes that don’t have a single formula?
  • Sample Tasks:
    • Find the area of a circle sector given radius and angle.
    • Calculate the area of a playground with a semicircle attached to a rectangle.
    • Model floor plans using composite area.

Lesson 6: Patterns and Special Figures

Standards: MA19.GDA.29

  • Objective: Students will explore tessellations and fractals to find repeating area patterns.
  • Essential Question: What patterns can we discover in shapes that repeat infinitely?
  • Sample Tasks:
    • Create tessellations using triangles, squares, or hexagons.
    • Analyze fractal growth in the Sierpinski triangle.
    • Predict area/perimeter in successive iterations of a fractal.

3D: Volume and Surface Area

Lesson 7: Prisms and Cylinders

Standards: MA19.GDA.16, MA19.GDA.17

  • Objective: Students will calculate volume and surface area of right prisms and cylinders.
  • Essential Question: How do cross-sections help us understand 3D solids?
  • Sample Tasks:
    • Model volume of a water tank (cylinder).
    • Explore cross-sections of cubes and rectangular prisms.
    • Solve packaging design problems.

Lesson 8: Pyramids and Cones

Standards: MA19.GDA.17

  • Objective: Students will calculate volume and surface area of pyramids and cones.
  • Essential Question: Why do pyramids and cones have one-third in their volume formula?
  • Sample Tasks:
    • Compare volumes of a prism vs. a pyramid with the same base and height.
    • Apply cone volume to design an ice cream scoop.
    • Solve optimization problems involving storage efficiency.

Lesson 9: Spheres and Composite Solids

Standards: MA19.GDA.17

  • Objective: Students will calculate volume and surface area of spheres and composite figures.
  • Essential Question: How can we break down complex solids into manageable parts?
  • Sample Tasks:
    • Find the volume of a hemisphere.
    • Calculate volume of a capsule (cylinder with hemispherical ends).
    • Apply to sports equipment design (basketballs, footballs).

Lesson 10: Applications and Modeling Project

Standards: MA19.GDA.2, MA19.GDA.4, MA19.GDA.17, MA19.GDA.18

  • Objective: Students will synthesize understanding of perimeter, area, and volume to model a real-world scenario.
  • Essential Question: How can geometry help us design the world around us?
  • Sample Tasks:
    • Design a mini-world (park, aquarium, sports complex, museum).
    • Calculate fencing, flooring, paint, and water storage needs.
    • Present solutions and justify calculations.
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