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Worksheet Grade 6 Math

Oxholt's Service Line Inventory: Ratios and Percents

A grade 6 worksheet on a town's inventory of 5,000 water service lines, with ratios in simplest form, percents by pipe material, and a replacement schedule.

Objectives

  1. Students will write ratios from an inventory table in simplest form.
  2. Students will find what percent of a town's service lines each pipe material makes up.
  3. Students will use a weekly replacement rate to find how long a replacement program takes.

Vocabulary

Service line
A service line is the small pipe that connects the water main under the street to the plumbing inside one home or building. It is the last leg of the trip water makes to your tap.

Also: inventory, ratio, simplest form, percent

Teacher overview

A service line is the small pipe that carries water from the main under the street into one building, and water systems now keep an inventory of what every one of those pipes is made of. The lead action level is 15 ppb, dropping to 10 ppb in 2027 under the Lead and Copper Rule Improvements, which also require systems to replace nearly all lead service lines within ten years, so the inventory decides how much work a town faces. This worksheet uses the inventory of the fictional town of Oxholt, where students write ratios in simplest form, convert each material to a percent of the whole, and turn the replacement count into a schedule.

Oxholt's Service Line Inventory: Ratios and Percents — Grade 6 Math
Name: ____________________________ Date: ______________

Student Worksheet

The fictional town of Oxholt finished its service line inventory this year. The table lists what the town found. Round any percent that does not come out even to the nearest tenth.

Pipe material Number of service lines
Lead 750
Galvanized steel 250
Copper 3,000
Plastic 1,000
Total 5,000
  1. Write the ratio of lead lines to copper lines in simplest form.
  2. Write the ratio of lead lines to all service lines in simplest form.
  3. What percent of the town's service lines are lead?
  4. What percent are copper?
  5. What percent are plastic?
  6. What percent are galvanized steel?
  7. Every galvanized steel line in Oxholt was once connected to a lead pipe, so the town must replace the lead lines and the galvanized steel lines. How many lines is that in all?
  8. What percent of all the town's service lines must be replaced?
  9. A crew replaces 25 lines each week. How many weeks will 1,000 lines take?
  10. In the first year the crew replaced 300 of those 1,000 lines. What percent of the replacement work is finished?
  11. A nearby town has 2,000 service lines, and 300 of them are lead. Which town has the greater percent of lead lines? Show the percent for each.

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: 1 to 4.
    There are 750 lead lines and 3,000 copper lines. Divide both by 750, which gives 1 to 4, so there is 1 lead line for every 4 copper lines.
  2. Answer: 3 to 20.
    There are 750 lead lines out of 5,000 lines. Divide both by 250, which gives 3 to 20.
  3. Answer: 15 percent.
    Divide the part by the whole: 750 divided by 5,000 is 0.15, which is 15 percent.
  4. Answer: 60 percent.
    Divide 3,000 by 5,000, which is 0.6, or 60 percent.
  5. Answer: 20 percent.
    Divide 1,000 by 5,000, which is 0.2, or 20 percent.
  6. Answer: 5 percent.
    Divide 250 by 5,000, which is 0.05, or 5 percent. The four percents add to 100, which checks items 3 through 6.
  7. Answer: 1,000 lines.
    Add the two materials that must go: 750 lead lines plus 250 galvanized steel lines is 1,000 lines.
  8. Answer: 20 percent.
    Divide 1,000 by 5,000, which is 0.2, or 20 percent of the town's lines.
  9. Answer: 40 weeks.
    Divide the work by the weekly rate: 1,000 divided by 25 is 40 weeks.
  10. Answer: 30 percent.
    Divide 300 by 1,000, which is 0.3, or 30 percent of the replacement work.
  11. Answer: They are the same, 15 percent each.
    In the fictional town of Oxholt, 750 divided by 5,000 is 0.15. In the nearby town, 300 divided by 2,000 is also 0.15. The nearby town has fewer lead lines yet the same share of its system is lead.

Differentiation

Support

Give these students a hundred-square grid for the fictional town, where each square stands for 50 service lines, and have them shade the lead, galvanized, copper, and plastic counts before writing any percent. Assign items 3, 4, 5, 6, and 7, and provide the division for item 3 already written as 750 divided by 5,000.

Extension

Ask these students to compare two replacement plans for the fictional town of Oxholt, one at 25 lines each week and one at 40 lines each week, and to state how many weeks each plan needs for the 1,000 lines. They should also report what percent of the work the faster plan finishes in the first 20 weeks, and write one sentence on what a town would have to arrange to run the faster plan.

ELL supports

Pre-teach service line, inventory, and simplest form with a labeled cross-section drawing of a street, a water main, and one pipe branching into a house. Provide these sentence frames: "There are ___ lead lines out of ___ lines in all." and "___ divided by ___ is ___, so ___ percent of the lines are ___."

Extensions

Have students look up whether their own water system publishes a service line inventory, and if it does, have them find the count of lines whose material is still listed as unknown. Comparing that unknown count with the fictional town's tidy table shows the class that the first task in a real replacement program is finding out what is in the ground.