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Geometry and Measurement 6-8 / Week 10 / Wednesday
3/6
Week 10 · Dilations and Similar Figures

Wednesday

Build Lab: the flashlight scale
// The flashlight shadow: same shape, new size
⏱ about 20 min

Wednesday: Build Lab, The Flashlight Scale

Rocket sets the flashlight on a stack of books so the beam points at the wall. "Science time. Where does k come from?"

Raven tapes paper to the wall and stands the cutout 20 centimeters from the bulb. "Wall at 40. Trace."

Rocket traces the shadow and measures its base. "The cutout base is 4. The shadow base is 8. Two times."

"Move the wall paper," Raven says, which means moving the books. "Bulb to wall 60 now. What do you notice?"

"Shadow base 12. Three times," Rocket says. "And 60 divided by 20 is 3. The distances give the scale factor!"

Nova hovers, her light off so only the flashlight shines. "Predict 80 before you measure," she says.

Rocket grins. "Four times. Sixteen centimeters." Nova hums. "Measure twice."

Your mission

Find out what sets the scale factor of a shadow. Keep the cutout the same distance from the bulb and move the wall paper.

Predict each shadow length from the distances before you measure it. Then check with the tape measure.

  • A flashlight and a stack of books to rest it on.
  • A cardboard triangle cutout with a base you can measure, about 4 cm.
  • Paper, masking tape, a marker and a tape measure.
  • Your Blueprint Book and a pencil.
Safety first
Never shine the flashlight toward anyone's eyes, including a pet's. Point it only at the wall.
Cut the cardboard with scissors only, with a grown-up nearby. A grown-up cuts thick cardboard.
Tape loose paper down so no one slips. Shoes on in the garage.
  1. Rest the flashlight on the books so the beam points straight at the wall.
  2. Hold the cutout 20 cm from the bulb, standing upright in the beam. Measure the distance from bulb to wall.
  3. Divide bulb-to-wall by bulb-to-cutout. That is your predicted scale factor.
  4. Predict the shadow base: cutout base × scale factor. Write the prediction down.
  5. Trace the shadow and measure its base. Compare with your prediction.
  6. Move the flashlight and books farther from the wall and repeat two more times.

The crew's shadow log

These are the crew's own measurements from the garage wall, in centimeters. The cutout base was 4 cm, held 20 cm from the bulb.

Bulb to cutout (cm)Bulb to wall (cm)Scale factorShadow base (cm)
204028
2060312
2080416

The scale factor is bulb-to-wall divided by bulb-to-cutout. The bulb is the center, so distances from it set k.

Every shadow base is the cutout base times k. 4 × 2 = 8. 4 × 3 = 12. 4 × 4 = 16.

READ THE SHADOW LOG
  • Read the question.
  • Tap your answer.
The bulb is 20 cm from the cutout and 60 cm from the wall. What is the scale factor of the shadow?
The scale factor is 4 and the cutout base is 4 cm. How long is the shadow base, in cm?
The cutout base is 4 cm and its shadow base is 8 cm. What is the scale factor?
The cutout is 3 cm tall and the scale factor is 3. How tall is the shadow, in cm?
With the bulb 80 cm from the wall and 20 cm from the cutout, what is the scale factor? Type the number.
WHY THIS EXERCISEDistances from the center set the scale factor, so a shadow can be predicted before it is traced.
StatementTrue or false?
Moving the wall farther from the bulb makes the shadow bigger.?
The scale factor is bulb-to-cutout divided by bulb-to-wall.?
The shadow has the same angles as the cutout.?
WHY THIS EXERCISEKnowing what sets k lets you plan a shadow instead of guessing at it.
Draw the flashlight, the cutout and the wall from the side. Draw the two light rays that pass the cutout's ends.

Distances set the scale factor. Tomorrow the crew enlarges the whole clubhouse wall and keeps the shape similar.

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