➗ Math · Grade 8

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

“Some numbers never end and never repeat, like π and √2. They are called irrational, and they live on the number line too.”

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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• Rational numbers can be written as a fraction. Their decimals stop or repeat.
• Irrational numbers, like √2 and π, have decimals that never stop and never repeat.
• Careful: √9 = 3 is rational, because 9 is a perfect square.
• Every real number is either rational or irrational.

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.

“√10 is not a whole number, but you can trap it between two perfect squares: 9 and 16.”

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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• 10 is between the perfect squares 9 and 16.
• So √10 is between 3 and 4, much closer to 3: about 3.2.
• Check by squaring: 3.2 squared is 10.24, very close.

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.

“2³ × 2⁴ means (2·2·2)(2·2·2·2): seven 2s. Exponent rules are shortcuts for counting factors.”

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:

• Same base, multiply: add the exponents. 2³ · 2⁴ is seven 2s: 2⁷.
• Same base, divide: subtract the exponents. 5⁶ ÷ 5² = 5⁴.
• Power of a power: multiply the exponents. (3²)³ = 3⁶.
• Any nonzero number to the zero power is 1. A negative exponent means one over.

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 square with area 64 has side √64 = 8. A cube with volume 27 has edge ∛27 = 3.”

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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• A square with area 64. Its side is the square root: 8.
• x squared = 49 has two answers: 7 and −7.
• x cubed = 125: the cube root is 5. Only one real answer.

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.

“The Sun is about 93,000,000 miles away. Scientists write 9.3 × 10⁷. Easier to read, easier to compare.”

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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• 93,000,000: move the point 7 places left. 9.3 × 10⁷.
• Small numbers use a negative exponent: 0.00052 = 5.2 × 10⁻⁴.
• Multiply: multiply the front numbers and add the exponents. 6 × 10⁹.
• Calculators show E: 4E9 means 4 × 10⁹.

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.

“Equations are balanced scales. Whatever you do to one side, do to the other, until x stands alone.”

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:

• Start: 3(x + 2) = 2x + 11. Distribute the 3: 3x + 6 = 2x + 11.
• Subtract 2x from both sides: x + 6 = 11.
• Subtract 6 from both sides: x = 5.
• Check: 3 times 7 is 21, and 10 plus 11 is 21.

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.

“Slope is how steep a line is: how much it rises for every 1 step right. A proportional line goes through (0, 0).”

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:

• Two points on a line: (1, 3) and (3, 7).
• Rise 4 over run 2: the slope is 2.
• y = mx + b: slope 2, crossing the y-axis at 1.
• If b is 0, the line goes through the origin: proportional.

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.

Also in this lesson: 🎮 Play: Move the slope slider. Watch the dashed slope triangle: rise for a run of 1.

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 phone plans: when do they cost the same? Where two lines cross is the answer for BOTH 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:

• Two equations: y = 2x − 3 and y = −x + 6.
• Both equal y, so set them equal: 2x − 3 = −x + 6.
• 3x = 9, so x = 3. Then y = 3. The lines cross at (3, 3).
• Parallel lines never cross: no solution. The same line: infinitely many.

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.

Also in this lesson: 🎮 Play: Turn on line 2. Move the sliders until the lines are parallel, then until they cross at a whole-number point.

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 vending machine is a function: press one button, get exactly one snack. If one button gave two snacks, it would not be a function.”

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 function takes an input and gives exactly one output.
• No x repeats with a different y: a function.
• x = 2 goes to 5 and to 7: not a function.
• On a graph: if any vertical line hits it twice, it is not a function.

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 taxi charges $3 to start plus $2 per mile. $3 is the initial value; $2 per mile is the rate of change.”

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 taxi: $3 to start plus $2 per mile.
• In the table, y goes up 2 each time: the rate. At x = 0, y is 3: the start.
• y = x² is nonlinear: its rate changes, so its graph curves.

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 graph tells a story: speeding up, staying still, going back home. You can read the story without numbers.”

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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• Distance from home: up as you walk away, flat when you stop, down as you come back.
• A steeper part means a faster change.

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.

“Slide, flip, turn: the shape moves but stays the same size and shape. These rigid motions make congruent figures.”

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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• Translation: slide 3 right and 4 down. (x, y) → (x + 3, y − 4).
• Reflection over the x-axis: change the sign of y.
• Rotation 90 degrees counterclockwise about the origin: (x, y) → (−y, x).

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.

Also in this lesson: 🎮 Play: Try every move. Read the rule and the new points.

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.

“Zoom in on a photo: everything grows by the same scale factor. Angles stay the same, so the shapes are similar.”

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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• A dilation with scale factor 2 from the origin doubles each coordinate: (2, 3) → (4, 6).
• A scale factor between 0 and 1 shrinks: times 1/2.
• Similar figures: equal angles, sides in the same ratio.

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 a line crosses two parallel lines, eight angles appear, but only two different sizes.”

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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• A line crosses two parallel lines: corresponding and alternate interior angles are equal.
• Angles on a straight line add to 180: x + 115 = 180, so x = 65.
• The three angles of any triangle add to 180 degrees.
• An exterior angle equals the two far angles added: 30 + 85 = 115.

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 ladder 13 feet long leans on a wall, its foot 5 feet out. How high does it reach? Right triangles answer it.”

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:

• Legs 3 and 4: a square on each side. 9 plus 16 is 25, so the hypotenuse is 5.
• A 13-foot ladder, its foot 5 feet out: 169 minus 25 is 144, so it reaches 12 feet high.
• Is 7, 24, 25 a right triangle? 49 plus 576 is 625, which is 25 squared. Yes.

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.

Also in this lesson: 🎮 Play: Press Build it for a Pythagorean triple. Then Take it apart: the two small squares together equal the big one.

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.

“Fill a cone with water three times and pour it into a cylinder of the same base and height: it fills exactly.”

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:

• Cylinder: base area pi r squared, times height.
• Cone: one third of the cylinder with the same base and height.
• Sphere: four thirds pi r cubed.
• Cylinder with radius 3 and height 6: 54 pi, about 169.6 cubic units.

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.

Also in this lesson: 🎮 Play: Choose Cone, then press Take it apart: three cones make one cylinder.

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.

“Do students who sleep more score higher? A scatter plot shows whether two things move together.”

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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• Points rising left to right: a positive association. The lone high point is an outlier.
• A line of fit: y = 2x + 10. Slope 2 means y grows about 2 for each 1 in x.
• Associations can be negative…
• …or there may be none.

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.

“Do more 8th graders who play sports also do a club? A two-way table organizes two yes/no questions at once.”

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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• A two-way table: sports or not, club or not.
• Of 50 sports players, 30 do a club: 30 ÷ 50 = 60%.
• Of 50 non-sports students, only 10 do a club: 20%. Sports and clubs seem associated.

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.

Also in this lesson: 📘 Learn: Example

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.

“You know the math. Now show it: read carefully, use the calculator wisely, and show your work on response questions.”

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.
3. Press Next to the Movie step and press ▶ Play.

The video says:

• Two sessions, and a scientific calculator is allowed in both in Grade 8.
• Read carefully and estimate first.
• Check your answer, then explain with steps and a final sentence.
• Unsure? Flag it, move on, and come back.

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

Do the lesson's Try it step together on the board.

🧱 Build it: the lesson's short 3D build game. Let students play it after Try it. Its score never changes grades.

Also in this lesson: 📘 Learn: How the test works (NYSED); 🎮 Play: Take a 15-question practice test. Flag the hard ones, then review before finishing.

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.