∑ Algebra II

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“No real number squares to −1, so mathematicians invented i.”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• No real number squares to negative 1. So we add a new direction: the imaginary axis, straight up.
• Multiply 1 by i and it turns 90 degrees: i points straight up.
• Multiply by i again: another quarter turn, to negative 1. So i squared equals negative 1.
• A complex number a plus b i is a point: 3 plus 2i is 3 right and 2 up.

Students open the same lesson on their own device (or work with the board). Press Next to Try it.

Try it together first:

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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.

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“Some parabolas never touch the x-axis, but their equations still have complex solutions.”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• y equals x squared plus 9 never touches the x-axis: no real solutions to x squared plus 9 equals 0.
• Solve anyway: x squared equals negative 9.
• The square root of negative 9 is 3i. So x equals plus or minus 3i: complex solutions.
• They come as a conjugate pair: 3i and negative 3i.

Students open the same lesson on their own device (or work with the board). Press Next to Try it.

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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.

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“Pythagorean triples come from an identity: (x² − y²)² + (2xy)² = (x² + y²)².”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• A big cube with side a. Its volume is a cubed.
• Take away a small corner cube with side b. What is left is a cubed minus b cubed.
• What is left splits into three blocks. Each has one side a minus b.
• Pull out a minus b: a cubed minus b cubed equals a minus b times a squared plus a b plus b squared.

Students open the same lesson on their own device (or work with the board). Press Next to Try it.

Try it together first:

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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.

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“Divide a big polynomial into smaller factors, like splitting 156 into 12 × 13.”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• Divide x squared plus 5x plus 6 by x plus 2.
• Divide: x squared over x is x. Multiply: x times x plus 2 is x squared plus 2x.
• Subtract: what is left is 3x plus 6. Bring it down.
• Divide again: 3x over x is 3. 3 times x plus 2 is 3x plus 6. Remainder 0.
• So the answer is x plus 3, and x plus 2 is a factor.

Students open the same lesson on their own device (or work with the board). Press Next to Try it.

Try it together first:

🧱 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.

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“Zeros, end behavior and multiplicity let you sketch any polynomial.”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• p of x equals x cubed minus 2x plus 5.
• Divide by x minus 2 and the remainder is 9. Now look at the graph at x equals 2: p of 2 is 9.
• Remainder theorem: the remainder of p of x divided by x minus a is p of a.
• So if p of a is 0, the remainder is 0 and x minus a is a factor: a is a zero of the graph.

Students open the same lesson on their own device (or work with the board). Press Next to Try it.

Try it together first:

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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.

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“Average cost per item = total cost ÷ number of items: a rational expression.”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• x squared minus 9, over x plus 3.
• Factor the top: x minus 3 times x plus 3. Cancel x plus 3. It looks like the line y equals x minus 3.
• But x cannot be negative 3: that would divide by zero. The graph has a hole at negative 3, negative 6.

Students open the same lesson on their own device (or work with the board). Press Next to Try it.

Try it together first:

🧱 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.

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“Two pipes fill a tank together: work problems use rational equations.”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• Solve 2 over x equals 1 over 4. Graph both sides.
• Cross multiply: x equals 8. The curves meet at x equals 8.
• Check: 2 over 8 is 1 over 4. It works.

Students open the same lesson on their own device (or work with the board). Press Next to Try it.

Try it together first:

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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.

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“A pendulum's swing time grows with the square root of its length. Radical equations undo the root.”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• Solve the square root of x plus 3 equals 5.
• Square both sides: x plus 3 equals 25, so x equals 22.
• Always check: the square root of 25 is 5. It works.

Students open the same lesson on their own device (or work with the board). Press Next to Try it.

Try it together first:

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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.

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“Three ticket types and three totals: three unknowns need three equations.”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• In 3D, each equation with x, y and z is a flat plane. x plus y plus z equals 6.
• Add x minus y equals negative 1. Two planes meet in a line.
• Add z equals 3. The third plane cuts the line at one point.
• The point 1, 2, 3 lies on all three planes. It solves the system.

Students open the same lesson on their own device (or work with the board). Press Next to Try it.

Try it together first:

🧱 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.

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“Shift a sound wave or stretch a growth curve: each is one move on the parent graph.”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• The point 1, 3 is on the graph of f. Where does it go on g of x equals f of x minus 2, plus 5?
• Inside, minus 2: move right 2. Outside, plus 5: move up 5. So 1, 3 goes to 3, 8.
• a times f of x stretches up and down. Bigger a, taller graph.
• f of negative x flips the graph over the y-axis.

Students open the same lesson on their own device (or work with the board). Press Next to Try it.

Try it together first:

🧱 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.

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“Convert Celsius to Fahrenheit and back: inverse functions undo each other.”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• f of x equals 2x plus 3. It sends 1 to 5.
• To find the inverse, swap x and y, then solve: y equals x minus 3, over 2.
• The inverse sends 5 back to 1. The two graphs are mirror images over the line y equals x.

Students open the same lesson on their own device (or work with the board). Press Next to Try it.

Try it together first:

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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.

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“log₂8 asks: 2 to what power is 8?”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• y equals 2 to the x. The point 3, 8 is on it: 2 cubed is 8.
• Its inverse, the mirror image over y equals x, is log base 2. The point flips to 8, 3.
• So log base 2 of 8 asks: 2 to what power is 8? The answer, 3, is an exponent.

Students open the same lesson on their own device (or work with the board). Press Next to Try it.

Try it together first:

🧱 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.

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“When will $1,000 at 6% grow to $2,000? Logs bring the exponent down.”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• Solve 2 to the x equals 20. Graph y equals 2 to the x and y equals 20.
• They meet between 4 and 5, since 2 to the 4 is 16 and 2 to the 5 is 32.
• Take the log of both sides. The power rule brings x down: x times log 2 equals log 20.
• x equals log 20 over log 2: about 4.32.

Students open the same lesson on their own device (or work with the board). Press Next to Try it.

Try it together first:

🧱 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.

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“$1,000 at 5% compounded monthly: A = P(1 + r/n)^(nt).”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• 1,000 dollars at 5 percent, compounded once a year, for 10 years.
• Compounded monthly, n is 12: a little more, about 1,647 dollars.
• Compounded continuously: A equals P e to the r t. About 1,648.72 dollars, the most of the three.

Students open the same lesson on their own device (or work with the board). Press Next to Try it.

Try it together first:

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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.

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“Saving $10 more each week is arithmetic; doubling is geometric.”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• Saving 3 dollars, then 4 more each week: 3, 7, 11, 15. Arithmetic: add d equals 4.
• Week 10: 3 plus 9 times 4 is 39.
• Doubling instead: 3, 6, 12, 24, 48. Geometric: multiply by r equals 2.
• A series adds the terms: 3 plus 6 plus 12 plus 24 plus 48 equals 93.

Students open the same lesson on their own device (or work with the board). Press Next to Try it.

Try it together first:

🧱 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.

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“Monthly savings deposits and loan payments add up as a geometric series.”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• Add 3 plus 6 plus 12 plus 24 plus 48. First term 3, ratio 2, 5 terms.
• The reference sheet formula: S n equals a1 minus a1 r to the n, over 1 minus r.
• Plug in: 3 minus 3 times 2 to the 5th, over 1 minus 2. 2 to the 5th is 32.
• 3 minus 96 is negative 93. Over negative 1: 93.

Students open the same lesson on their own device (or work with the board). Press Next to Try it.

Try it together first:

🧱 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.

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“As a wheel rolls, the length of rim that touches the ground measures its turn: that is the idea of a radian.”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• A circle with radius 1, centered at the origin: the unit circle.
• Lay one radius along the edge: that arc makes 1 radian, about 57.3 degrees.
• Turn 60 degrees, which is pi over 3 radians. The point on the circle is cosine, sine: one half and root 3 over 2.
• Every point on the unit circle is cosine theta, sine theta.

Students open the same lesson on their own device (or work with the board). Press Next to Try it.

Try it together first:

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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.

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“Ferris wheels and tides repeat: sine waves model them.”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• Turn around the unit circle. Track the height, the sine.
• Plot height against the angle and you get the sine wave. One full turn, 2 pi, is one period.
• It repeats forever. Tides and Ferris wheels repeat like this too.

Students open the same lesson on their own device (or work with the board). Press Next to Try it.

Try it together first:

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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.

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“On the unit circle, x² + y² = 1 turns into a famous identity.”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• On the unit circle every point is x, y with x squared plus y squared equal to 1.
• The legs of the right triangle are cosine theta and sine theta. The hypotenuse is the radius, 1.
• So by Pythagoras: sine squared theta plus cosine squared theta equals 1, for every angle.

Students open the same lesson on their own device (or work with the board). Press Next to Try it.

Try it together first:

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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.

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“A weather app shows a 30% chance of rain. Probability rules combine chances.”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• P of A is 0.5 and P of B is 0.4. Here they overlap: P of A and B is 0.2.
• P of A or B: add them, but the overlap got counted twice. Subtract it once: 0.5 plus 0.4 minus 0.2 is 0.7.
• The complement, not A or B, is everything outside: 1 minus 0.7 is 0.3.

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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.

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“Does being on a team change your chance of an A? Two-way tables test independence.”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• 200 students: on a team or not, and whether they got an A.
• Overall, 60 of 200 got an A: P of A is 0.3.
• Given team, look only at the team row: 24 of 80, also 0.3.
• Same probability either way: being on the team does not change it. A and team are independent.

Students open the same lesson on their own device (or work with the board). Press Next to Try it.

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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.

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“Adult heights form a bell shape: most are near the middle, few at the ends.”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• Adult heights in inches, with mean 70 and standard deviation 5, form a bell shape.
• About 68 percent are within 1 standard deviation of the mean: 65 to 75 inches.
• About 95 percent are within 2 standard deviations: 60 to 80.
• About 99.7 percent are within 3: 55 to 85. Almost everyone.

Students open the same lesson on their own device (or work with the board). Press Next to Try it.

Try it together first:

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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.

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“To learn what a whole city thinks, ask a random sample, not just your friends.”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• To learn what a whole city thinks, you cannot ask everyone. Each dot is one person.
• Asking only your friends, who sit together, gives a biased sample. They may think alike.
• A random sample gives every person the same chance. It spreads across the whole city.
• Survey: ask. Observational study: watch. Experiment: do, with randomly assigned treatments. Only experiments can show cause.

Students open the same lesson on their own device (or work with the board). Press Next to Try it.

Try it together first:

🧱 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.

Read this aloud (it is the lesson's hook). Students think, then tell a partner what they notice.

“A poll says 54% ± 3%. What could the true value be?”

1. Open the lesson link on the board.
2. 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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• A poll says 54 percent, plus or minus 3 percent.
• The true value is likely between 51 and 57 percent.
• 62 plus or minus 4: from 58 to 66. The highest likely value is 66 percent.

Students open the same lesson on their own device (or work with the board). Press Next to Try it.

Try it together first:

🧱 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.