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Algebra 1 9-12 / Week 01 / Friday
5/6
Week 01 · Quantities and the Shape of an Expression

Friday

A chunk as one thing
// Units that cancel, numbers that mean something
⏱ about 20 min

Friday: A Chunk as One Thing

Comet writes the frame expression on the whiteboard two ways: 2w + 2l and 2(w + l). "Same frame?"

"Same frame," Wren says. "What do you notice about the parentheses?"

"They hold w + l together. One width plus one length, half the way around. Then times two."

Nova circles the (w + l) with a ring of light. "Would you like a hint? Treat the ring as one number."

"So 2 times one chunk," Comet says. "If w + l is 75, the frame is 150. I never needed w and l apart."

"Chunking," Wren says. "Seeing a piece of an expression as one thing. It will matter all year."

"Review time," Comet says, "then the weekend. What can we make on Loft Day?"

Seeing a chunk as a single quantity

2(w + l) means two copies of the chunk (w + l). The chunk is half the distance around the frame.

For the crew's frame, w + l = 30 + 45 = 75. So 2(w + l) = 150, the same as 2w + 2l.

Chunking saves work and shows structure. You do not always need every letter on its own.

Another Loft chunk: the paper-cup tower has n + 2 cups in every row, and 4 rows. Cups in all: 4(n + 2).

With n = 3, the chunk n + 2 is 5, so 4(n + 2) = 20 cups.

Quantities in everyday life

  • A recipe time of 90 seconds is 1.5 minutes. Divide by 60 because 60 seconds make a minute.
  • A walk of 1.2 kilometers is 1,200 meters. Multiply by 1,000, since 1,000 meters make a kilometer.
  • A bathroom scale that shows whole kilograms cannot honestly report 61.374 kilograms.
  • A graph of a walk needs units on both axes and a scale you can read, with the origin marked.

The week in five lines

  • A quantity is a number with a unit. Units ride along and cancel like numbers.
  • A conversion factor is a fraction equal to 1. Put the unit you want to cancel on the bottom.
  • Choose a quantity that answers the question, such as centimeters per second for a cart.
  • Report only the digits the tool can give. Round results to match.
  • An expression has terms, coefficients and factors, and a chunk in parentheses can be read as one thing.
CHUNKS AND CONVERSIONS
  • Read the question.
  • Tap your answer.
The frame chunk: if w + 5 is one chunk and w = 10, what is 2(w + 5)?
The cup tower has 4 rows of n + 2 cups. With n = 3, how many cups is 4(n + 2)?
A timer runs 90 seconds. How many minutes is that? (60 seconds make 1 minute.)
A path is 1.2 kilometers long. How many meters is that? (1,000 meters make 1 kilometer.)
MIXED REVIEW
  • Read the question.
  • Tap your answer.
Which expression is the same frame as 2w + 2l?
A different jug follows 5s + 40 after s seconds. What is its fill rate, the coefficient of s?
A stopwatch shows tenths of a second. Which is an honest report of one run?
A graph shows a cart run. What must both axes have?
StatementTrue or false?
2(w + l) and 2w + 2l give the same number for every w and l.?
In 4(n + 2), the chunk n + 2 is the number of cups in one row.?
90 ÷ 60 = 1.5?
2 × (30 + 45) = 150?
A conversion factor changes how long the plank really is.?
WHY THIS EXERCISEThese five lines are the whole week. Next week the crew turns expressions into equations and solves them.
Try it
Find a rectangle at home. Measure its width and length in centimeters.
Compute the distance around it as 2w + 2l and again as 2(w + l). Check that they match.
Draw the frame two ways: four edges labeled w, l, w, l, then two copies of the chunk (w + l).

Terrific week. You can carry units, choose a quantity, report honestly and read an expression. Tomorrow is Loft Day.

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