Indirect measurement and similar-figure problems
- Four shadows, one quotient — 3 tasks
- From a paragraph to two triangles — 3 tasks
- Two triangles in one shadow — 3 tasks
- A mirror flat on the ground — 3 tasks
- Going Deeper — 6 tasks
- Practice — 27 tasks
- Summary — 2 tasks
- Cool-down — 3 tasks
Classroom activities
Things a class does rather than writes on. Each one is a finished PDF: print it, cut it up if it says so, and hand it round.
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Will This Plan Work? Indirect Measurement — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 measuring plans in words, each a scene (the sun, a mirror on the ground, a ruler held up) and three lengths someone measures to find a height. Students sort them: the plan works; one length is measured from the wrong place; or the two triangles are not similar, so no lengths will work (a lamp, a hill, two times of day, a tilted mirror).
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Eyes or the Top of the Head? Indirect Measurement — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each a scene in words with no drawing: a person and a tall object in the sun, or a mirror flat on the ground. Students draw the two triangles and find a height, a shadow or a distance. The wrong answers are the two costliest mistakes: pairing a height with a shadow, and using the full height instead of the eye height. The row of box numbers at the foot is the check.
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Which Lengths Match? Indirect Measurement — Mystery Picture 25–35 minutes · 5 sheets
25 squares, each a scene in words (the sun, a mirror on the ground, a ruler held up) and two lengths in it, with no drawing and no number. Do the two lengths match in the two similar triangles? Fill it or leave it white, and a picture appears.
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How Tall Is It? Indirect Measurement — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each a scene in words with no drawing: a person and a tall object in the sun, or a mirror flat on the ground. Students draw the two similar triangles and find the height. Pairing a height with a shadow, or using the full height instead of the eye height, lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.