Partitioning a directed segment
- Four dots, one ratio — 3 tasks
- The same ratio from each end — 3 tasks
- When counting the steps runs out — 3 tasks
- Which endpoint gets the big share — 3 tasks
- One parameter, the whole line — 3 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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Partitioning a Directed Segment: Which End Is P Nearer? — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 short descriptions of a point P on a segment: a directed ratio such as AP : PB = 1 : 4, a fraction of the way from one end, or weights such as P = 3/4 A + 1/4 B. Students compute nothing: they sort each one by the end P is nearer, or into "cannot tell" when the words name no start.
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Partitioning a Directed Segment: One Change at a Time — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page. Each gives two points and a directed ratio such as AP : PB = 3 : 4 and asks for the point P, a pair of whole numbers. The route takes each pair of points twice in a row with one change: the trip starts at the other end, or the ratio is turned round. The wrong answers are the common mistakes, and the row of box numbers at the foot is the check.
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Partitioning a Directed Segment: Which Rule Finds P? — Mystery Picture 25–35 minutes · 5 sheets
25 squares, each with a directed ratio such as AP : PB = 1 : 3 or BP : PA = 2 : 5 and one rule for the point P written with letters only, such as P = A + 1/4(B − A) or P = 3/4 · A + 1/4 · B. Students compute nothing: they check where the trip starts, how many equal steps it has, and which end gets the larger share. Fill it or leave it white, and a picture appears.
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Partitioning a Directed Segment: Find the Point — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each with two points in the coordinate plane and a directed ratio such as AP : PB = 5 : 2. Students cut the trip from A to B into equal steps and find the point P, a pair of whole numbers. Swapping the fractions, or reading 3 : 2 as 3/2, lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.