📐 Geometry
One printable 40-minute plan for each of the 24 lessons. A substitute can run any lesson with the lesson's 3D video and Movie. No account needed.
Lesson 1: Definitions and basic constructions
Lesson link: books/hs-geometry · lesson 1
Big idea: Compass copies lengths; straightedge draws lines.
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“With only a compass and a straightedge, builders long ago drew perfect shapes.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 2 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- Geometry starts with undefined terms. A point is an exact location, with no size.
- A line goes on forever in both directions. Two points name it: line A B.
- A plane is a flat surface that goes on forever, like a floor without edges.
- An angle is two rays that share one endpoint, the vertex.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
A compass is used to…
- A. Copy a length or draw a circle
- B. Measure an angle in degrees
Answer (for the teacher): Copy a length or draw a circle
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
A circle is all points the same distance from…
- A. The center
- B. A line
Answer (for the teacher): The center
Leave on the board
- Definitions and basic constructions
- Big idea: Compass copies lengths; straightedge draws lines.
- Memory trick: “Compass keeps the distance.”
- Goal: 100%
Watch for this mistake
- Changing the compass width in the middle of a construction.
Students do not need accounts; progress stays on each device.
Notes for the teacher
Lesson 2: Bisectors, parallels and inscribed polygons
Lesson link: books/hs-geometry · lesson 2
Big idea: Arcs that cross show where to draw.
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“Find the exact middle of a beam, or draw a perfect hexagon, with no ruler numbers.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 3 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- Find the exact middle of a beam, segment A B, with no ruler numbers.
- Open the compass more than halfway. From A, draw arcs above and below.
- Same width from B. The arcs cross in two points.
- A line through the two crossings is the perpendicular bisector. It meets A B at its midpoint, at a right angle.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
A 70° angle is bisected. Each new angle (°)?
Answer (for the teacher): 35
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
Equilateral triangle in a circle: from the hexagon points, connect…
- A. Every other point
- B. Every point
Answer (for the teacher): Every other point
Leave on the board
- Bisectors, parallels and inscribed polygons
- Big idea: Arcs that cross show where to draw.
- Memory trick: “Radius fits 6 times around.”
- Goal: 100%
Watch for this mistake
- Drawing arcs too small to cross.
Students do not need accounts; progress stays on each device.
Notes for the teacher
Lesson 3: Transformations and congruence
Lesson link: books/hs-geometry · lesson 3
Big idea: Rigid motions keep size and shape.
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“Slide, flip, turn: the shape moves but keeps its size and shape.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 2 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- Triangle A B C. Rigid motions move it but keep its size and shape.
- Translation: slide every point 3 right and 2 down.
- Reflection over the y-axis: flip it like a page. Each point lands the same distance on the other side.
- Rotation 90 degrees counterclockwise about the origin: turn it.
- Every image is congruent to the original: same side lengths, same angles.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
Reflect (3, 5) over the x-axis. New y = ?
Answer (for the teacher): -5
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
Translate (1,4) by (x+3, y−2): new x?
Answer (for the teacher): 4
Leave on the board
- Transformations and congruence
- Big idea: Rigid motions keep size and shape.
- Memory trick: “Slide, flip, turn: still the same.”
- Goal: 100%
Watch for this mistake
- Rotating clockwise when asked counterclockwise.
Students do not need accounts; progress stays on each device.
Notes for the teacher
Lesson 4: Symmetry and rotations of polygons
Lesson link: books/hs-geometry · lesson 4
Big idea: Rotate by 360° ÷ the number of sides.
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“A pizza cut into 8 equal slices looks the same after a 45° turn.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 2 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- A square. Turn it 90 degrees about its center. It lands exactly on itself.
- 180 and 270 degrees also work. A square has turns of 90, 180 and 270 degrees.
- A regular pentagon: the smallest turn is 360 divided by 5, which is 72 degrees.
- For a regular n-gon, the smallest turn is 360 divided by n.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
Smallest rotation that maps a regular pentagon onto itself (°)?
Answer (for the teacher): 72
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
Does a 90° turn map a rectangle that is not a square onto itself?
- A. No
- B. Yes
Answer (for the teacher): No
Leave on the board
- Symmetry and rotations of polygons
- Big idea: Rotate by 360° ÷ the number of sides.
- Memory trick: “360 over n.”
- Goal: 100%
Watch for this mistake
- Using 180° ÷ n.
Students do not need accounts; progress stays on each device.
Notes for the teacher
Lesson 5: Sequences of transformations
Lesson link: books/hs-geometry · lesson 5
Big idea: Do the steps in order; order can matter.
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“Game moves: slide, then flip. The order can change where the shape ends up.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 2 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- Start with a triangle whose corner is at 1, 3.
- Move 1: translate right 2. A goes from 1, 3 to 3, 3.
- Move 2: reflect over the x-axis. 3, 3 goes to 3, negative 3.
- Any chain of rigid motions keeps the size and shape, so the final image is congruent.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
(2, 5): translate by (x − 3, y), then reflect over the y-axis. New x?
Answer (for the teacher): 1
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
A translation then a dilation by 3 gives…
- A. Similar figures
- B. Congruent figures
Answer (for the teacher): Similar figures
Leave on the board
- Sequences of transformations
- Big idea: Do the steps in order; order can matter.
- Memory trick: “One step, one point, in order.”
- Goal: 100%
Watch for this mistake
- Doing the steps in reverse order.
Students do not need accounts; progress stays on each device.
Notes for the teacher
Lesson 6: Lines, angles and parallel lines
Lesson link: books/hs-geometry · lesson 6
Big idea: Parallel lines make equal and supplementary angle pairs.
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“Railroad tracks and a road crossing them make matching angles.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 2 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- Two parallel lines, like railroad tracks, and a transversal road crossing them.
- The crossing makes 8 angles. Angle 1 is 65 degrees.
- Vertical angles, across from each other, are equal: angle 3 is also 65.
- Corresponding angles, in matching corners, are equal. Alternate interior angles, in a Z, are equal.
- Same-side interior angles add to 180: 65 plus 115.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
Parallel lines cut by a transversal: one angle is 65°. Its same-side interior partner (°)?
Answer (for the teacher): 115
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
Alternate interior angles: 3x + 10 = 70. x = ?
Answer (for the teacher): 20
Leave on the board
- Lines, angles and parallel lines
- Big idea: Parallel lines make equal and supplementary angle pairs.
- Memory trick: “Z angles match; C angles add to 180.”
- Goal: 100%
Watch for this mistake
- Calling same-side interior angles congruent.
Students do not need accounts; progress stays on each device.
Notes for the teacher
Lesson 7: Triangle congruence and proofs
Lesson link: books/hs-geometry · lesson 7
Big idea: Statement, reason, repeat.
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“A proof is a chain: each step has a reason.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 3 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- Two triangles with three pairs of equal sides: the tick marks match.
- A rigid motion, here a reflection, carries one exactly onto the other. So they are congruent.
- Shortcuts that prove congruence: S S S, S A S, A S A, A A S, and H L for right triangles.
- The three angles of any triangle add to 180 degrees: 50 plus 60 plus 70.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
Triangle angles 50° and 60°. Third angle?
Answer (for the teacher): 70
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
Isosceles triangle base angles are…
- A. Congruent
- B. Different
Answer (for the teacher): Congruent
Leave on the board
- Triangle congruence and proofs
- Big idea: Statement, reason, repeat.
- Memory trick: “No SSA, no donkey proofs.”
- Goal: 100%
Watch for this mistake
- Using SSA.
Students do not need accounts; progress stays on each device.
Notes for the teacher
Lesson 8: Midsegments and medians
Lesson link: books/hs-geometry · lesson 8
Big idea: A midsegment is parallel to the third side and half as long.
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“Connect the midpoints of a triangle's sides and you get a smaller triangle with half-length sides.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 2 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- A triangle with base 18. Mark the midpoints of the other two sides.
- Join them: the midsegment M N. It is parallel to the base.
- And it is half as long: 18 divided by 2 is 9.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
The third side is 18. Midsegment length?
Answer (for the teacher): 9
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
Interior angles of a triangle add to (°)
Answer (for the teacher): 180
Leave on the board
- Midsegments and medians
- Big idea: A midsegment is parallel to the third side and half as long.
- Memory trick: “Mid means half.”
- Goal: 100%
Watch for this mistake
- Splitting the median 1 : 1.
Students do not need accounts; progress stays on each device.
Notes for the teacher
Lesson 9: Triangle centers
Lesson link: books/hs-geometry · lesson 9
Big idea: Each center comes from three special lines crossing.
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“Where should a fountain go so it is the same distance from three classrooms? At the circumcenter.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 2 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- Three classrooms at A, B and C. Where should a fountain go so it is the same distance from all three?
- Draw the perpendicular bisector of each side.
- They meet at one point, the circumcenter.
- A circle centered there passes through all three corners. Each radius is the same distance.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
The point equally far from all three vertices:
- A. Circumcenter
- B. Incenter
Answer (for the teacher): Circumcenter
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
The circumcenter of a right triangle is at…
- A. The midpoint of the hypotenuse
- B. The right-angle vertex
Answer (for the teacher): The midpoint of the hypotenuse
Leave on the board
- Triangle centers
- Big idea: Each center comes from three special lines crossing.
- Memory trick: “Circum = corners; in = inside circle.”
- Goal: 100%
Watch for this mistake
- Mixing up the incenter and the circumcenter.
Students do not need accounts; progress stays on each device.
Notes for the teacher
Lesson 10: Parallelogram proofs
Lesson link: books/hs-geometry · lesson 10
Big idea: Opposite sides equal; diagonals bisect each other.
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“A folding gate keeps its opposite sides parallel as it moves.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 2 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- A parallelogram: both pairs of opposite sides are parallel.
- Opposite sides are congruent: the tick marks match.
- Opposite angles are equal. Consecutive angles add to 180 degrees.
- The diagonals bisect each other: they cut each other in half at the same midpoint.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
A parallelogram has a 110° angle. A consecutive angle (°)?
Answer (for the teacher): 70
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
A square is a rectangle that is also a…
- A. Rhombus
- B. Trapezoid
Answer (for the teacher): Rhombus
Leave on the board
- Parallelogram proofs
- Big idea: Opposite sides equal; diagonals bisect each other.
- Memory trick: “Opposites match; neighbors add to 180.”
- Goal: 100%
Watch for this mistake
- Assuming every parallelogram has congruent diagonals.
Students do not need accounts; progress stays on each device.
Notes for the teacher
Lesson 11: Dilations
Lesson link: books/hs-geometry · lesson 11
Big idea: Multiply distances from the center by k.
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“A phone zoom or a photo enlargement is a dilation.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 2 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- A small triangle and the center of dilation at the origin.
- Scale factor 3: multiply every coordinate by 3. The point 1, 1 goes to 3, 3, and 3, 1 goes to 9, 3.
- Every length triples, and every angle stays the same. The image is similar.
- The scale factor k is always positive. Between 0 and 1 it shrinks: k equals one half.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
Dilate (3, −2) by k = 4 about the origin. New x?
Answer (for the teacher): 12
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
The image of a line not through the center is…
- A. Parallel to it
- B. Perpendicular to it
Answer (for the teacher): Parallel to it
Leave on the board
- Dilations
- Big idea: Multiply distances from the center by k.
- Memory trick: “Multiply by k.”
- Goal: 100%
Watch for this mistake
- Adding k instead of multiplying.
Students do not need accounts; progress stays on each device.
Notes for the teacher
Lesson 12: Similar triangles
Lesson link: books/hs-geometry · lesson 12
Big idea: Same shape, proportional sides.
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“Use a shadow to measure a flagpole: similar triangles share ratios.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 2 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- A 6 foot person casts a 4 foot shadow.
- At the same moment, a flagpole casts a 20 foot shadow. The sun's rays make the same angle.
- Set up a proportion: height over shadow. 6 over 4 equals h over 20.
- h equals 6 times 20 over 4: 30 feet.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
A 5 ft person casts a 2 ft shadow; a tree casts 8 ft. Tree height (ft)?
Answer (for the teacher): 20
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
If sides scale by 2, area scales by…
Answer (for the teacher): 4
Leave on the board
- Similar triangles
- Big idea: Same shape, proportional sides.
- Memory trick: “Match the parts, cross-multiply.”
- Goal: 100%
Watch for this mistake
- Mismatching corresponding sides.
Students do not need accounts; progress stays on each device.
Notes for the teacher
Lesson 13: Similarity proofs and proportions
Lesson link: books/hs-geometry · lesson 13
Big idea: Parallel lines split sides proportionally.
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“A line parallel to one side of a triangle cuts the other two sides in the same ratio.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 2 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- A line parallel to one side of a triangle cuts the other two sides.
- It cuts them in the same ratio: 4 to 6 on one side, 6 to x on the other.
- Cross multiply: 4x equals 36, so x equals 9.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
Side splitter: 4/6 = 6/x. x = ?
Answer (for the teacher): 9
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
3/5 = x/20. x = ?
Answer (for the teacher): 12
Leave on the board
- Similarity proofs and proportions
- Big idea: Parallel lines split sides proportionally.
- Memory trick: “Match parts, then cross-multiply.”
- Goal: 100%
Watch for this mistake
- Using the whole side instead of the part.
Students do not need accounts; progress stays on each device.
Notes for the teacher
Lesson 14: Right-triangle trigonometry
Lesson link: books/hs-geometry · lesson 14
Big idea: SOH-CAH-TOA.
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“A ramp, a ladder, a kite string: trig finds missing sides and angles.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 3 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- A right triangle with legs 3 and 4 and hypotenuse 5. Stand at angle A.
- From A: the side across is opposite, 3. The side touching A is adjacent, 4. The longest side, across from the right angle, is the hypotenuse, 5.
- Sine is opposite over hypotenuse: 3 over 5. Cosine is adjacent over hypotenuse: 4 over 5. Tangent is opposite over adjacent: 3 over 4.
- The ratios depend only on the angle. A bigger triangle with the same angle has the same ratios.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
Legs 6 and 8. Hypotenuse?
Answer (for the teacher): 10
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
sin 40° = cos ?°
Answer (for the teacher): 50
Leave on the board
- Right-triangle trigonometry
- Big idea: SOH-CAH-TOA.
- Memory trick: “SOH-CAH-TOA.”
- Goal: 100%
Watch for this mistake
- Calculator in radians instead of degrees.
Students do not need accounts; progress stays on each device.
Notes for the teacher
Lesson 15: Angles of elevation and inverse trig
Lesson link: books/hs-geometry · lesson 15
Big idea: Use sin⁻¹, cos⁻¹ or tan⁻¹ to find an angle.
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“Standing 50 ft from a tree, you look up at its top. Trig finds its height.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 2 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- You stand 50 feet from a tree and look up at its top.
- The angle of elevation is measured up from the horizontal: 30 degrees.
- Height is opposite, 50 feet is adjacent: tangent. h over 50 equals tangent of 30.
- h equals 50 times tangent of 30: about 28.9 feet. This picture measures from the ground; add eye height if needed.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
A 20 ft ladder makes a 60° angle with the ground. Height it reaches (ft), to the nearest tenth?
Answer (for the teacher): 17.3
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
Hypotenuse 10, angle 30°: the opposite side?
Answer (for the teacher): 5
Leave on the board
- Angles of elevation and inverse trig
- Big idea: Use sin⁻¹, cos⁻¹ or tan⁻¹ to find an angle.
- Memory trick: “Find a side: ratio. Find an angle: inverse.”
- Goal: 100%
Watch for this mistake
- Calculator in radian mode.
Students do not need accounts; progress stays on each device.
Notes for the teacher
Lesson 16: Coordinate geometry
Lesson link: books/hs-geometry · lesson 16
Big idea: Slopes for parallel and perpendicular; distance for length.
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“Prove a shape is a parallelogram using slopes and distances.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 2 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- How far is it from 1, 2 to 4, 6?
- Run, the change in x, is 3. Rise, the change in y, is 4.
- The distance is the hypotenuse: the square root of 3 squared plus 4 squared, which is 5.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
Distance from (1, 2) to (4, 6)?
Answer (for the teacher): 5
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
Equal slopes means…
- A. Parallel
- B. Perpendicular
Answer (for the teacher): Parallel
Leave on the board
- Coordinate geometry
- Big idea: Slopes for parallel and perpendicular; distance for length.
- Memory trick: “Flip and switch for perpendicular.”
- Goal: 100%
Watch for this mistake
- Forgetting the negative in perpendicular slopes.
Students do not need accounts; progress stays on each device.
Notes for the teacher
Lesson 17: Coordinate proofs
Lesson link: books/hs-geometry · lesson 17
Big idea: Use slope, distance and midpoint as evidence.
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“Prove a shape is a rectangle using only its corner coordinates.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 2 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- A at 0, 0; B at 4, 0; C at 4, 3; D at 0, 3. Prove A B C D is a rectangle.
- Opposite sides are parallel: A B and D C have slope 0; A D and B C are vertical. So it is a parallelogram.
- Horizontal meets vertical: a right angle. A parallelogram with a right angle is a rectangle.
- Check the diagonals: A C and B D are both 5. Congruent diagonals, as a rectangle should have.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
A(0, 0), B(4, 0), C(4, 3), D(0, 3). Diagonal AC length?
Answer (for the teacher): 5
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
Diagonals with the same midpoint show the shape is a…
- A. Parallelogram
- B. Kite
Answer (for the teacher): Parallelogram
Leave on the board
- Coordinate proofs
- Big idea: Use slope, distance and midpoint as evidence.
- Memory trick: “Slope for angles, distance for sides.”
- Goal: 100%
Watch for this mistake
- Proving one pair of sides parallel and stopping.
Students do not need accounts; progress stays on each device.
Notes for the teacher
Lesson 18: Partitions, perimeter and area on the grid
Lesson link: books/hs-geometry · lesson 18
Big idea: Start plus fraction times change finds the point.
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“Place a bus stop 1/3 of the way from home to school on a map grid.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 2 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- Home is at 0, 0 and school is at 9, 6. Put a bus stop one third of the way.
- Ratio 1 to 2 means 3 equal parts in all. k is 1 over 1 plus 2: one third.
- x equals 0 plus one third of 9: 3. y equals 0 plus one third of 6: 2. The stop is at 3, 2.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
From (0, 0) to (9, 6), the point 1/3 of the way. x = ?
Answer (for the teacher): 3
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
Triangle (0,0), (6,0), (0,4): area?
Answer (for the teacher): 12
Leave on the board
- Partitions, perimeter and area on the grid
- Big idea: Start plus fraction times change finds the point.
- Memory trick: “Add the ratio parts for the denominator.”
- Goal: 100%
Watch for this mistake
- Using 1/2 for a 1 : 2 ratio.
Students do not need accounts; progress stays on each device.
Notes for the teacher
Lesson 19: Circle equations and angles
Lesson link: books/hs-geometry · lesson 19
Big idea: (x − h)² + (y − k)² = r².
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“Circles have arcs, chords, tangents and their own equation.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 2 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- The equation x minus 2, squared, plus y plus 1, squared, equals 49.
- Center h, k: here 2, negative 1. Watch the signs: plus 1 means k is negative 1.
- r squared is 49, so the radius is 7.
- Every point on the circle is exactly 7 from the center, like 2, 6 at the top.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
(x − 2)² + (y + 1)² = 49. Radius?
Answer (for the teacher): 7
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
Arc length = (θ/360) · ?
- A. 2πr
- B. πr²
Answer (for the teacher): 2πr
Leave on the board
- Circle equations and angles
- Big idea: (x − h)² + (y − k)² = r².
- Memory trick: “Inscribed is half.”
- Goal: 100%
Watch for this mistake
- Reading (y + 1) as center y = +1 (it is −1).
Students do not need accounts; progress stays on each device.
Notes for the teacher
Lesson 20: Chords, secants and tangents
Lesson link: books/hs-geometry · lesson 20
Big idea: Crossing chords: part times part equals part times part.
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“A bike chain wrapping a gear and the spokes of a wheel obey circle angle rules.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 2 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- A chord joins two points on a circle. Two chords cross at a point inside.
- One chord is cut into 3 and 8. The other into 4 and x.
- Part times part equals part times part: 3 times 8 equals 4 times x. 24 equals 4x, so x is 6.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
Two chords cross: 3 × 8 = 4 × x. x = ?
Answer (for the teacher): 6
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
An inscribed angle in a semicircle measures (°)
Answer (for the teacher): 90
Leave on the board
- Chords, secants and tangents
- Big idea: Crossing chords: part times part equals part times part.
- Memory trick: “Part times part.”
- Goal: 100%
Watch for this mistake
- Multiplying a part by the whole chord.
Students do not need accounts; progress stays on each device.
Notes for the teacher
Lesson 21: Arc length, sectors and radians
Lesson link: books/hs-geometry · lesson 21
Big idea: Use the fraction of the circle: θ/360.
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“A pizza slice is a sector; its crust is an arc.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 2 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- A pizza with radius 6. Cut a 90 degree slice: a sector.
- The crust of the slice is an arc. It is 90 over 360 of the whole circumference: one fourth of 12 pi, which is 3 pi.
- The slice's area is one fourth of pi r squared: one fourth of 36 pi, which is 9 pi.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
r = 6, θ = 90°. Arc length = ?π
Answer (for the teacher): 3
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
r = 3, θ = 120°. Sector area = ?π
Answer (for the teacher): 3
Leave on the board
- Arc length, sectors and radians
- Big idea: Use the fraction of the circle: θ/360.
- Memory trick: “Fraction of the whole circle.”
- Goal: 100%
Watch for this mistake
- Using the area formula for arc length.
Students do not need accounts; progress stays on each device.
Notes for the teacher
Lesson 22: Volume and density
Lesson link: books/hs-geometry · lesson 22
Big idea: V = Bh; cones and pyramids ⅓Bh.
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“How much water fits in a cylinder tank? Volume tells you.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 2 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- A cylinder tank with radius 3 and height 10.
- Volume is pi r squared h: pi times 9 times 10, which is 90 pi, about 282.7 cubic units.
- A cone with the same radius and height holds one third as much: 30 pi.
- Watch: three cones of water fill the cylinder.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
Cylinder r = 3, h = 10. Volume in terms of π: ?π
Answer (for the teacher): 90
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
A cone is ___ of the cylinder with the same base and height.
- A. One third
- B. Half
Answer (for the teacher): One third
Leave on the board
- Volume and density
- Big idea: V = Bh; cones and pyramids ⅓Bh.
- Memory trick: “Pointy = one third.”
- Goal: 100%
Watch for this mistake
- Using diameter as radius.
Students do not need accounts; progress stays on each device.
Notes for the teacher
Lesson 23: Cross sections and Cavalieri's principle
Lesson link: books/hs-geometry · lesson 23
Big idea: Same height and same slices mean same volume.
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“Push a stack of coins into a slant: it still has the same volume.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 2 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- Two stacks of the same 12 coins.
- Push one stack into a slant. Every slice is the same size at every height.
- So the volumes are equal. That is Cavalieri's principle.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
A right triangle spun around one leg makes a…
- A. Cone
- B. Cylinder
Answer (for the teacher): Cone
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
Every flat cross section of a sphere is a…
- A. Circle
- B. Square
Answer (for the teacher): Circle
Leave on the board
- Cross sections and Cavalieri's principle
- Big idea: Same height and same slices mean same volume.
- Memory trick: “Same slices, same volume.”
- Goal: 100%
Watch for this mistake
- Using the slant length instead of the height.
Students do not need accounts; progress stays on each device.
Notes for the teacher
Lesson 24: Geometric modeling and design
Lesson link: books/hs-geometry · lesson 24
Big idea: Pick a shape, write the formula, check the units.
Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.
“How much paint does a cylinder-shaped water tower need? Model it with shapes.”
- Open the lesson link on the board.
- Press Next to the 🎬 Watch in 3D step and press ▶ Play. Students can drag to turn the model. This lesson has 2 3D videos in a row: press Next and ▶ Play for each part.
- Press Next to the Movie step and press ▶ Play.
The video says:
- A tree trunk is close to a cylinder: radius 1 foot, height 20 feet.
- Its volume is about pi times 1 squared times 20: about 62.8 cubic feet.
- A model is close, not exact. Real trunks taper, so the true volume is a bit less.
Students open the same lesson on their own device (or work with the board). Press Next to Try it.
Try it together first:
5,000 people live on 2 square miles. People per square mile?
Answer (for the teacher): 2500
🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.
If time is left, students play the lesson's game steps (they show up between the videos and Check).
Students press Next to Check and answer the 4 questions on their own device. Goal: 100%. 95% or more is Mastered. “Not yet” means try again; students may retry.
Read this question aloud. Students write the answer on a slip of paper with no name or with a class number, and hand it in.
A wood block: 600 g and 1,000 cm³. Density (g/cm³)?
Answer (for the teacher): 0.6
Leave on the board
- Geometric modeling and design
- Big idea: Pick a shape, write the formula, check the units.
- Memory trick: “Model, compute, round sensibly.”
- Goal: 100%
Watch for this mistake
- Rounding down when you need enough material.
Students do not need accounts; progress stays on each device.