ISEE Upper Level Quantitative Reasoning

A comprehensive course to master the mathematical reasoning skills needed for success on the ISEE Upper Level exam.

Numbers, Operations, and Number PropertiesAlgebraic Thinking and ExpressionsFractions, Decimals, and Percents
Ratios, Proportions, and RatesSolving Word Problems and Quantitative ComparisonsGeometry: Shapes, Area, and Volume
Using Math in Everyday LifeInterpreting Data and GraphsBudgeting and Managing Money
Time Management During the TestElimination and Smart Guessing
Numbers, Operations,...Algebraic Thinking a...Fractions, Decimals,...Ratios, Proportions,...Solving Word Problem...Geometry: Shapes, Ar...Using Math in Everyd...Interpreting Data an...Budgeting and Managi...Time Management Duri...Elimination and Smar...
Advanced Topics

Geometry: Shapes, Area, and Volume

Getting to Know Shapes and Space

Geometry is all about shapes, sizes, and how much space they take up. You use these ideas when building, drawing, or even wrapping gifts!

2D Shapes

  • Triangles, rectangles, circles, and more
  • Perimeter: The distance around a shape (\( P = 2l + 2w \) for rectangles)
  • Area: The space inside a shape (\( A = lw \) for rectangles, \( A = \pi r^2 \) for circles)

3D Shapes

  • Cubes, rectangular prisms, cylinders, spheres
  • Volume: The space inside a solid (\( V = lwh \) for rectangular prisms)

Why It’s Useful

Geometry helps you design spaces, pack boxes, and find how much paint you need!

Examples

  • Finding the area of a rectangular garden to buy enough soil.

  • Calculating the volume of a box to see if your toys will fit.

In a Nutshell

Calculate perimeter, area, and volume of common shapes for real-world tasks.

Key Terms

Perimeter
The distance around a two-dimensional shape.
Area
The amount of space inside a flat shape.
Volume
The space inside a three-dimensional object.
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Using Math in Everyday Life