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Algebra 1 9-12 / Week 12 / Loft Day
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Week 12 · Data From the Loft and Fair Day

Loft Day

Fair Day
// Scatter plots, lines of best fit and the family fair
⏱ about 20 min

Fair Day: The Loft Opens

The garage door rolls up. The ramp is set on its sawhorses, the launcher waits in the backyard and the data poster hangs on the wall.

"Three tables," Comet says. "Ramp timing, the tiles puzzle and the launch chart. Everyone gets a turn."

A visitor rolls the cart and reads the stopwatch. Wren adds the dot to the ramp plot. "What do you notice?"

"It landed right on your line," the visitor says. "Nearly," Wren says. "The residual is small."

At the tiles table, someone slides an x² square, five x strips and six unit squares into a rectangle. "x plus 2 by x plus 3!"

Nova projects the launch chart. "Would you like to predict the next flight before we launch?"

"Ten pumps," says Comet. "About 12.7 meters, by the line." The grown-up gives the go, and everyone stands back.

  1. A scatter plot shows two measurements per trial. Read its direction, tightness and shape.
  2. The least-squares line makes the squared residuals as small as possible. Say its slope and intercept with units.
  3. r, between -1 and 1, measures how tight and which way. It does not prove cause.
  4. Patterned residuals mean the wrong model. An arch calls for a quadratic, equal ratios for an exponential.
  5. From week 1 to week 12: units, equations, functions, lines, systems, exponents, polynomials, factoring, quadratics and data.
◇ RUN YOUR OWN FAIR DAY
Ramp timing table: set the ramp at five heights. Each family member times one run per height. Plot the dots, lay a line by eye and say the slope in a sentence.
Tiles puzzle: cut one big square, five strips and six small squares from colored cardboard. Challenge everyone to slide them into one rectangle and name its sides.
Launch chart: show the pumps and height plot with its line. Have everyone predict the height for a new pump count before the launch, then compare.
Close with the poster. Each person says one thing the data showed and one thing they would measure next.
For a grown-up
For the launch chart, a grown-up is present and everyone stands back behind the launch line. The rocket points up and away from people, windows and roads.
A grown-up helps lift the plank, and the cart gets a soft landing zone with nothing fragile nearby.
A prediction that misses is the best moment of the day: ask what the residual is and what might explain it.
Every number on the poster is the family's own, measured today or made up for practice. None of it is a fact about the world.
Algebra tiles as one rectangle: an x² square, five x strips and six unit squares, x + 2 by x + 3.
FAIR DAY CHECK
  • Read the question.
  • Tap your answer.
The tiles puzzle: one x² square, five x strips and six unit squares. Which rectangle do they make?
The launch chart line is y = 1.25x + 0.18. What height does it predict for 10 pumps? Round to one decimal place.
A visitor's run time dot lands close to the ramp line. What is true about its residual?
The launch chart shows pumps and height. What is its r, to two decimal places?
Using the launch chart line y = 1.25x + 0.18, what height does it predict for 12 pumps? Round to one decimal place and type the number.
WHY THIS EXERCISEA prediction before a launch is a test of the model. The flight itself is the check.
Draw your Fair Day poster: the ramp plot with its line, the tiles rectangle and the launch chart with one prediction marked.
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