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Classroom activity Grade 4 Science

The Denhollow Hill Pipe Route Challenge

A grade 4 activity where teams read an elevation grid, then lay a pipe route from the plant to the tower under token rules that charge for climbs and wet ground.

Objectives

  1. Students will use elevation numbers on a grid map to find the high ground and the creek line.
  2. Students will plan a pipe route from the plant to the water tower and count its cost in tokens.
  3. Students will compare their route with another team's and explain why one cost less.

Vocabulary

Water tower
A water tower is a big tank raised high above town that stores drinking water. Its height is what pushes water through the pipes, keeping the pressure steady even when the power goes out.

Also: elevation, grid, route, gravity

Teacher overview

Denhollow Hill is a fictional town whose treatment plant sits beside a creek at the bottom of a slope and whose water tower stands on the highest corner of the map, which means every drop has to be pushed up the hill through a pipe the town has to pay for. Teams of three work a grid where each square carries its elevation in meters, and the token rules make the concept physical: one token per square of pipe, one more for every square that climbs, and two more for the soft ground along the creek. The misconception the rules are built to expose is the assumption that the number of squares a route uses is what makes it cheap, because two routes of the same length can cost very different totals: a route that climbs on nearly every square costs more than one that crosses the flat shelf in Row D first. A second idea worth naming in the debrief is why the tower belongs on high ground at all.

Activity Directions

  1. Set up (5 min). Put students in teams of three. Give each team a printed grid map, a pile of about thirty counters, and a pencil. Tell them their job is to lay one pipe from the treatment plant at square E1 to the water tower at square A5.

  2. Read the map (7 min). Before any route is drawn, teams find the highest number on the map, the lowest row, and the line the creek follows. Ask each team to point to the high corner and say its elevation out loud before you move on, which is the check that they can read the grid.

  3. Teach the token rules with one demo route (8 min). On a projected or posted copy, walk one route square by square and count the tokens aloud. The rules are: one token for every square of pipe you lay after the plant's own square, one extra token whenever the next square's number is higher than the square you just left, and two extra tokens for any square in Row E other than the plant's own square, because that ground stays soggy. Pipes run up, down, left, or right between next-door squares and never diagonally.

  4. Teams plan and count (12 min). Each team marks a route on its map with the pencil or yarn, lays out one counter for every token the route costs, and writes the total on the map. Teams that finish early try a second route and keep the cheaper one. Circulate and ask teams to recount any route whose total looks lower than the number of squares it uses.

  5. Post and compare (8 min). Teams post their maps with the totals showing, and the class sorts them from fewest tokens to most. Ask the two cheapest teams to trace their routes, then ask the class what those two routes have in common. The activity ends when every team's route and total are posted and compared.

  6. Debrief (5 min). Ask two questions of the whole class: why the cheapest routes avoided Row E even though it is flat, and why the tower stands on square A5 instead of somewhere near the houses. Have students answer question 6 on the handout before they leave.

The Denhollow Hill Pipe Route Challenge — Grade 4 Science
Name: ____________________________ Date: ______________

Student Handout

Suppose your team works for the town of Denhollow Hill. The table shows the elevation of every square in meters. The treatment plant is at square E1. The water tower is at square A5. The creek runs along the lowest row.

Row Column 1 Column 2 Column 3 Column 4 Column 5
A 40 45 50 55 60
B 35 40 45 50 55
C 30 30 35 40 45
D 25 25 25 30 35
E 20 20 20 25 30

Token rules. One token for each square of pipe. Do not count the plant's own square. One extra token each time you move to a higher square. Two extra tokens for any square in Row E except square E1.

  1. Which square on the map is the highest ground?

  2. Which row of the map has the lowest numbers?

  3. How do the numbers show you where the creek runs?

  4. How many tokens did your team's route cost?

  5. Which route in the class cost the fewest tokens?

  6. Why would the town put its water tower on square A5 instead of square E3?

  7. Why do the rules charge two extra tokens for squares in Row E?

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key

  1. Answer: Square A5, at 60 meters.
    It holds the largest number on the grid, and the numbers rise steadily toward that corner.

  2. Answer: Row E, where the numbers run from 20 to 30 meters.
    Every number in Row E is lower than the number directly above it in Row D.

  3. Answer: The creek follows the lowest numbers, so it runs along Row E.
    Accept any answer stating that water runs downhill and that Row E holds the smallest elevations on the map.

  4. Answer: Accept the team's own total, checked against their marked route.
    Recount with the team: one token per square after the plant, one more for each climb, two more for each Row E square after the plant. Routes that stay on the flat Row D shelf and climb the last stretch cost fourteen tokens, the cheapest total the rules allow.

  5. Answer: Accept whichever posted route had the lowest total.
    The winning routes almost always use the three flat squares in Row D and avoid Row E after the plant. A route claiming fewer tokens than it has squares has miscounted somewhere.

  6. Answer: A5 is the highest ground, so water can flow downhill to the whole town.
    Accept any answer naming gravity, downhill flow, or pressure. A tower at E3 would sit lower than most of the town, so pumps would have to run constantly to push water uphill.

  7. Answer: The ground beside the creek is soft and wet, so pipe costs more to lay there.
    Accept any answer noting that Row E is the lowest ground, that it floods or stays soggy, and that a pipe there is harder to build and to repair.

Differentiation

Support

Give these students a map with one route already marked and the first three tokens already counted, so their task is to finish the count rather than plan and count at the same time. Provide a laminated rules card with a small picture beside each rule. Let them place a counter physically on each square as they trace the route with a finger.

Extension

Ask these teams to find the cheapest route the rules allow and prove no route can beat it, which requires them to argue about the climbs no route can avoid. A second challenge is to redraw the map with the tower moved to square A1 and to work out how the cheapest route changes.

ELL supports

Pre-teach elevation, route, and uphill with a side-view drawing of the same hill beside the grid, so the numbers on the flat map connect to a slope students can see. Provide the rules as three labeled pictures rather than sentences. Give sentence frames for the debrief: "Our route cost ___ tokens because ___." and "The tower goes on square ___ because the water can ___."

Extensions

Have students find their own town's water tower on a road map or a satellite view and describe the ground around it, then explain why that spot was chosen. A second follow-on is to price the same grid with a new rule that raises the Row E charge to three extra tokens per square, which forces teams to rethink every route that runs along the creek.