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Algebra 1 9-12 / Week 10 / Loft Day
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Week 10 · Quadratic Equations

Loft Day

Loft Day: landing-time cards
// When is the height zero?
⏱ about 20 min

Loft Day: Landing-Time Cards

Saturday the whiteboard comes down to the kitchen table and the family gathers around it.

"Each card has a rocket rule," Comet says. "You find the landing time before Wren can factor it."

The first card reads h = -5t² + 30t. Someone calls out "Six!" before Wren finishes writing.

"How did you know?" Wren asks. "I noticed 30 divided by 5," comes the answer.

Nova hovers above the cards, her light a soft hint. "Would you like to check it by substitution?"

"-5 times 36 is -180, plus 180 is 0. Lands at six," Comet says.

"Next card," Wren says. "This one asks when the rocket is at 25 meters. Two answers, or one, or none?"

  1. A quadratic equation sets a squared expression equal to a number. Standard form is ax² + bx + c = 0.
  2. Four ways to solve: factoring, square roots, completing the square and the quadratic formula. All agree.
  3. The zero-product rule: if factors multiply to 0, one factor is 0.
  4. The discriminant b² - 4ac tells how many real solutions: two, one or none.
  5. Test every solution against the build. Negative seconds and negative widths are set aside.
◇ FAMILY LANDING-TIME CARDS
Write five rocket rules on cards, each h = -5t² + 5Tt for a whole number T from 2 to 8.
Deal a card. Everyone races to find the landing time by factoring out -5t. Check by substitution.
For a harder round, add a height to the card and ask when the rocket is there. Use the discriminant first.
Trade roles so everyone writes a card and everyone solves one.
For a grown-up
This is a paper activity, no launch needed. If the family wants to launch, a grown-up is present, everyone stands back and the rocket points away from people.
A wrong answer is a good moment: substitute it into the rule and see which side does not match.
The 5 in the rule is the crew's own fit to their timings, not a fact about the world.
LOFT DAY CHECK
  • Read the question.
  • Tap your answer.
The first card: -5t² + 30t = 0. What are the solutions?
When is the 6-second rocket at 25 m? Solve t² - 6t + 5 = 0.
When is the 4-second rocket at 25 m? For t² - 4t + 5 = 0, what is the discriminant?
A card reads h = -5t² + 35t. How many seconds after launch does this rocket land? Type the number.
WHY THIS EXERCISEEvery card is the same equation shape. Once you see the pattern, the landing time is the number in front of t divided by 5.
Draw two of the family cards with their rules, and mark each landing time on a small sketch of the arc.
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