Field notes

Keep the useful ideas close.

Sixteen connected concepts, worked examples, and guided paths through the tools.

Start with geometry

Build from lengths to shapes.

  1. Right triangles
  2. Area and perimeter
  3. Explore regular polygons
  4. Try a discovery challenge

Make sense of trigonometry

Connect a turning point to a wave.

  1. Angles and radians
  2. The unit circle
  3. Sine, cosine, tangent
  4. Shape a trig graph

Explore the coordinate plane

Describe position, distance, and movement.

  1. Distance and midpoint
  2. Slope and lines
  3. Transform a triangle
  4. Similarity and scale

Every concept, in one place

FIELD NOTE

The Pythagorean theorem

The relationship that holds every right triangle together.

Formula · example · common mistake
FIELD NOTE

The law of cosines

Pythagoras, extended to every triangle.

Formula · example · common mistake
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The law of sines

A shared ratio between sides and their opposite angles.

Formula · example · common mistake
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Heron’s formula

Find a triangle’s area using only its three sides.

Formula · example · common mistake
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Radians & degrees

Two ways to describe the very same turn.

Formula · example · common mistake
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Sine, cosine & tangent

Three ratios. One right triangle.

Formula · example · common mistake
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Area & perimeter

The space inside is different from the distance around.

Formula · example · common mistake
FIELD NOTE

Volume & surface area

What fits inside, and what covers the outside.

Formula · example · common mistake
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Polygon angles & diagonals

A triangle-based explanation for many-sided shapes.

Formula · example · common mistake
FIELD NOTE

Distance & midpoint

Pythagoras meets the coordinate plane.

Formula · example · common mistake
FIELD NOTE

Slope & line equations

Describe a direction, then locate the line.

Formula · example · common mistake
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Arc length & sector area

Measure a slice of a circle.

Formula · example · common mistake
FIELD NOTE

Transforming sine & cosine graphs

Four parameters shape an entire wave.

Formula · example · common mistake
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Translations, rotations & reflections

Move a shape while keeping track of every vertex.

Formula · example · common mistake
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Similarity & scale factors

Why doubling the size changes more than you might expect.

Formula · example · common mistake
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Triangle medians & the centroid

Find the balance point of a triangle.

Formula · example · common mistake