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Algebra 1 9-12 / Week 01 / Loft Day
6/6
Week 01 · Quantities and the Shape of an Expression

Loft Day

Loft Day: measure the house
// Units that cancel, numbers that mean something
⏱ about 20 min

Loft Day: Measure the House

Saturday morning the family climbs into the Loft and Comet hands out tape measures. "Everything gets a unit today."

"Doorway, in centimeters," Wren calls, and someone reads it out. "Now the same doorway in meters."

"Divide by one hundred," a voice says. Wren nods. "The doorway did not shrink. Only the number changed."

Nova hovers over the whiteboard, keeping a table of every measurement. "Would you like a hint? Write the unit first."

Comet times a cousin walking the length of the Loft. "Six meters in four seconds. What is the quantity?"

"Meters per second," comes the answer, "one point five."

"What do you notice?" Wren asks. "Every number here means something because it carries a unit."

  1. A quantity is a number with a unit, and units cancel like numbers do.
  2. A conversion factor is a fraction equal to 1. Centimeters to meters divides by 100, seconds to minutes by 60.
  3. Choose the quantity that answers the question, such as centimeters per second for a cart.
  4. Report only the digits the tool can give.
  5. An expression has terms, coefficients and factors. A chunk in parentheses can be read as one thing.
◇ FAMILY MEASURING DAY
Each person measures three things at home in centimeters and writes each quantity with its unit.
Trade lists. Convert every length to meters by writing the conversion factor and canceling the unit.
Time someone walking a measured distance. Work out the speed in meters per second together.
Pick one rectangle in the house and find the distance around it two ways: 2w + 2l and 2(w + l).
For a grown-up
Tape measures snap back fast. Hold the end and let it return slowly.
Walking timings stay indoors or on level ground, with shoes on and the path clear.
If a conversion goes the wrong way, ask which unit should cancel. That question usually fixes it.
LOFT DAY CHECK
  • Read the question.
  • Tap your answer.
A cousin walked 6 meters in 4 seconds. What was the speed in meters per second?
A doorway measures 210 centimeters. How many meters is that? (100 centimeters make 1 meter.)
A table top has w = 60 and l = 90 centimeters. What is 2(w + l), the distance around it?
A hallway is 3.5 meters long. How many centimeters is that? Type the number.
WHY THIS EXERCISEThe same hallway, written in a smaller unit, needs a bigger number.
Draw a table of today's family measurements with a column for centimeters and a column for meters.
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