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Fraction Classroom · 2.6.0 · Student pages

Follow a grid route and repair a reversed coordinate

Build a first-quadrant route record with ordered pairs, repair a coordinate reversal and account for each horizontal or vertical leg.

Anonymous group code: __________   Date: __________

Exact route data: A (1, 2), B (5, 2), C (5, 6), D (2, 6). Coordinates are measured from (0, 0); each listed leg follows a horizontal or vertical grid line. The table supplies all positions without requiring measurement of a picture.Stopx: righty: upNext legA12right 4B52up 4C56left 3D26finish
Exact route data: A (1, 2), B (5, 2), C (5, 6), D (2, 6). Coordinates are measured from (0, 0); each listed leg follows a horizontal or vertical grid line. The table supplies all positions without requiring measurement of a picture.

Start with a diagnostic

diagnostic. From the origin, move 3 units right and 1 unit up. Write the ordered pair, then enter its first coordinate.

Build the idea

model. A grid journey visits A (1, 2), then B, then C (5, 6), then D (2, 6). Its directions are A to B: right 4; B to C: up 4; C to D: left 3. A helper records B as (2, 5). Correct B and find the total distance traveled along these three legs.

  1. Label the origin and both axes before plotting. Locate A by going right 1 from the origin and up 2. An ordered pair describes a position relative to the origin; it is not an instruction to move that amount from the previous stop.
  2. Follow the first leg from A: move right 4, so x becomes 1 + 4 = 5 and y remains 2. Write B (5, 2). Plot the helper's (2, 5) separately and ask which point actually lies four units to the right of A.
  3. Continue up 4 to C (5, 6), keeping x fixed, then left 3 to D (2, 6), keeping y fixed. Have partners read each pair aloud and check which coordinate changes on each leg.
  4. Count the intervals traveled, not the points visited: A to B is 5 - 1 = 4, B to C is 6 - 2 = 4, and C to D is 5 - 2 = 3. Add 4 + 4 + 3 = 11 units. Check the final position separately; its coordinates (2, 6) are not the total journey length.

Worked example: B is (5, 2), and the route travels 11 units: 4 + 4 + 3. Moving right from A changes x from 1 to 5 while y stays 2. The helper reversed the coordinates. The complete record is A (1, 2), B (5, 2), C (5, 6), D (2, 6).

Practise and explain

Try p1–p3 with a partner. Use a drawing and label your units. Try e1 independently before comparing responses.

p1. Support: from (0, 0), move 2 units right and 4 units up. Enter the first coordinate, then write the complete ordered pair and label x and y on your grid.

p2. Core: a route goes from (2, 1) to (7, 1), then to (7, 4), using straight horizontal and vertical legs. Enter the total distance in units and label each leg on paper.

p3. Challenge: start at (1, 5), move right 6 and then down 3. A helper writes the endpoint as (2, 7). Enter the correct second coordinate and write the corrected endpoint with an explanation.

e1. Independent check: start at P (2, 3). Travel right 6 to Q, up 4 to R and left 3 to S. Enter the total distance in units. On paper, write Q, R and S as ordered pairs, plot them on labeled one-unit axes and label all three leg lengths.

Transfer the idea

transfer. Must every horizontal-and-vertical route from the worked A (1, 2) to D (2, 6) travel 11 units? Give another route and its distance using the same one-unit grid.