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Lesson plan Grade 5 Math

Havermoor's Hydrant Grid: A Grade 5 Coordinate Map Lesson

A 45-minute grade 5 lesson where students plot a fictional town's hydrants and valves as ordered pairs, then read block distances off the coordinate map.

Objectives

  1. Students will plot points in the first quadrant from ordered pairs given in a town map.
  2. Students will interpret the first and second numbers of an ordered pair as blocks east and blocks north.
  3. Students will find the distance in blocks between two points that share a coordinate.

Vocabulary

Valve
A valve is a device in a pipe that operators can open or close to control where water flows. Valves let crews shut off one street for repairs without turning off the whole town.

Also: ordered pair, coordinate, origin, hydrant

Teacher overview

Havermoor is a fictional town whose streets run in a plain grid, which is how its water department keeps track of every fire hydrant and every shutoff valve. Each piece of equipment is recorded as an ordered pair counted from the corner of Main Street and River Road: the first number gives blocks east and the second gives blocks north. Crews use that record to find a valve quickly during a main break, so the order of the two numbers matters in practice. The misconception this lesson corrects is reading an ordered pair backward, so that (2, 5) is plotted two blocks north and five blocks east and the crew is sent to the wrong intersection.

Procedure

Hook (5 min): Project a blank grid with the corner labeled Main Street and River Road. Tell the class that a hydrant in Havermoor is recorded as (3, 1) and ask two volunteers to come up and mark where they think it belongs. If the two marks disagree, leave both in place and tell the class the lesson will settle which one a crew would drive to.

Direct instruction (12 min): Establish the rule out loud and in writing: the first number counts blocks east from the corner, and the second counts blocks north. Plot (3, 1) correctly and mark the reversed point (1, 3) in a second color so the class can see two different intersections. Then plot three more pieces of Havermoor equipment together, naming each coordinate aloud as you go, and show how the crew reads a point back off the map.

Guided practice (10 min): In pairs, students plot two hydrants at (2, 4) and (7, 4) on the handout grid and count the blocks between them along the street. As a formative check, ask each pair to hold up fingers for the number of blocks. If more than a quarter of the class shows a number other than 5, count the blocks together on the projected grid before moving on.

Independent practice (13 min): Students complete handout questions 1 through 7 alone. Circulate and watch for students who count the grid lines rather than the spaces between them, which produces an answer one too large.

Closure and exit ticket (5 min): Students answer handout question 8 on the bottom of the page and turn the handout in. Scan for reversed coordinates before the next class, since that error will also appear in later work with graphs.

Havermoor's Hydrant Grid: A Grade 5 Coordinate Map Lesson — Grade 5 Math
Name: ____________________________ Date: ______________

Student Handout

Havermoor records every hydrant and valve as an ordered pair. The first number tells how many blocks east of Main Street it sits. The second number tells how many blocks north of River Road it sits. Use the town list below.

Hydrant A is at (2, 5). Hydrant B is at (6, 5). Hydrant C is at (6, 1). Hydrant D is at (3, 2). Valve V is at (4, 7).

  1. Plot and label all five points on your grid.
  2. Hydrant A is at (2, 5) and Hydrant B is at (6, 5). How many blocks apart are they?
  3. Hydrant B is at (6, 5) and Hydrant C is at (6, 1). How many blocks apart are they?
  4. Every block in Havermoor is 300 feet long. A crew lays hose in a straight line from Hydrant A to Hydrant B. How many feet of hose is that?
  5. A truck drives from Hydrant D at (3, 2) to Hydrant C at (6, 1). How many blocks east does it drive?
  6. That same truck drives from Hydrant D at (3, 2) to Hydrant C at (6, 1). How many blocks south does it drive?
  7. Valve V is at (4, 7) and Hydrant A is at (2, 5). Which one is farther north?
  8. The town adds a new hydrant 2 blocks east of Hydrant D at (3, 2). Write the ordered pair for the new hydrant.

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: Five points plotted correctly.
    The marks belong at (2, 5), (6, 5), (6, 1), (3, 2), and (4, 7). Check that each student counted east first and north second.
  2. Answer: 4 blocks.
    Both hydrants sit 5 blocks north, so only the east numbers differ: 6 minus 2 = 4 blocks.
  3. Answer: 4 blocks.
    Both hydrants sit 6 blocks east, so only the north numbers differ: 5 minus 1 = 4 blocks.
  4. Answer: 1,200 feet.
    The hydrants are 4 blocks apart, and 4 x 300 = 1,200 feet of hose.
  5. Answer: 3 blocks.
    The east numbers go from 3 to 6, and 6 minus 3 = 3 blocks east.
  6. Answer: 1 block.
    The north numbers go from 2 down to 1, and 2 minus 1 = 1 block south.
  7. Answer: Valve V.
    Valve V sits 7 blocks north while Hydrant A sits 5 blocks north, and 7 is greater than 5.
  8. Answer: (5, 2).
    Moving east changes only the first number, so 3 plus 2 = 5, and the north number stays 2.

Differentiation

Support

Give these students a grid that already has the corner labeled and the first two points plotted, and hand them a small paper arrow marked "east first" to slide along the bottom edge before they move up. Let them say each ordered pair aloud as "over, then up" while a partner watches the pencil.

Extension

Ask students to write the ordered pairs for four hydrants that form a rectangle 5 blocks wide and 3 blocks tall, then find how many blocks a crew would drive around the whole rectangle. Have them explain how they chose the four pairs without plotting first.

ELL supports

Post a two-column word bank with "east" beside a right-pointing arrow and "north" beside an up-pointing arrow, along with "hydrant," "valve," and "block" paired with simple pictures. Provide a sentence frame for question 7: "Valve V is farther north because ___ is greater than ___."

Extensions

Have students draw a grid of their own school grounds with one corner as the starting point, then mark the ordered pairs of three real features such as a drinking fountain, an outside spigot, and the main door. Ask them to trade maps with a partner and see whether the partner can find each feature using only the ordered pairs.