Lesson plan Grade 6 Math

Halverton's Purple Pipe: Ratio Language for Recycled Water

A 45-minute grade 6 lesson where students describe a town's recycled-water deliveries with ratio language, a ratio table, and a percent of park water.

Grade: Grade 6
Subject: Math
Material: Lesson plan
Time: 45 min
Prep: Low prep
Materials: Printed student handout, Chart paper, Calculators, Two clear jars of colored water, labeled recycled and drinking

Standards

6.RP.A.1 Common Core Math

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, 'The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.'

How this material aligns: Handout items 1, 2, and 4 have students write and say ratios of recycled water to drinking water in the for-every phrasing this standard describes.

All materials for 6.RP.A.1 →

6.RP.A.3 Common Core Math

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations, including finding a percent of a quantity and converting measurement units.

How this material aligns: Item 5 scales the ball field's equivalent ratio up to a month of deliveries, and items 3, 6, and 7 find a percent of a stated total and the gallons a new percent goal would require.

All materials for 6.RP.A.3 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-09-23.

Objectives

Students will describe a recycled-water delivery with ratio language in simplest form.
Students will use an equivalent ratio to find an unknown amount of drinking water.
Students will find what percent of a town's park water is recycled water.

Vocabulary

Recycled water: Wastewater that has been cleaned and used again, often to water parks, golf courses, and crops instead of being thrown away. Purple pipes usually carry it.

Also: ratio, simplest form, equivalent ratio, percent

Teacher overview

Towns that reuse treated wastewater for irrigation run it through pipes painted purple so that nobody confuses it with drinking water, and the two supplies are then tracked separately every day. This lesson uses the fictional town of Halverton, which sends recycled water to its parks alongside drinking water from the same utility, so students can describe the mix with ratio language before converting it to a percent. The misconception this lesson addresses is that the ratio of recycled water to drinking water and the percent of park water that is recycled are the same comparison; one compares a part with a part, and the other compares a part with the whole.

Procedure

Hook (5 min): Show students two labeled jars of colored water, one marked recycled and one marked drinking, holding amounts in a 1 to 3 relationship, and ask how they would describe the mix to somebody who cannot see the jars. Accept several wordings and write them on the board without ranking them yet.

Direct instruction (12 min): Introduce the fictional town of Halverton, which delivered 45,000 gallons of recycled water and 135,000 gallons of drinking water to its parks on one July day. Write the ratio 45,000 to 135,000 on chart paper and divide both numbers by 45,000 to reach 1 to 3, saying it aloud as one gallon of recycled water for every three gallons of drinking water. Then add the two amounts to get the whole, 180,000 gallons, and write the second comparison, 45,000 to 180,000, which simplifies to 1 to 4. Point at the jars again and name which comparison each one answers.

Guided practice (12 min): Have pairs convert the 1 to 4 comparison into a percent by writing 45,000 divided by 180,000, and then have them explain in one sentence why the answer is 25 percent rather than 33 percent. Pause for a formative check: ask students to hold up one finger if 25 percent compares recycled water with drinking water and two fingers if it compares recycled water with all park water, and re-teach the part-to-part and part-to-whole distinction with the jars if more than five students hold up one finger.

Independent practice (11 min): Students complete items 1 through 6 of the handout, writing each ratio in simplest form and labeling each percent with what it is a percent of.

Closure (5 min): Students complete item 7 as an exit ticket. Read a few answers aloud and ask whether reaching the goal would mean treating more wastewater, laying more purple pipe, or both, which previews the design questions a reuse program actually faces.

Halverton's Purple Pipe: Ratio Language for Recycled Water — Grade 6 Math

Name: ____________________________ Date: ______________

Student Handout

On one July day, the fictional town of Halverton delivered 45,000 gallons of recycled water and 135,000 gallons of drinking water to its parks. Together that is 180,000 gallons of park water.

Write the ratio of recycled water to drinking water in simplest form.
Write the ratio of recycled water to all park water in simplest form.
What percent of the park water that day was recycled water?
On the ball field alone, the town used 12 gallons of recycled water for every 4 gallons of drinking water. Write that ratio in simplest form.
The ball field keeps that same ratio all summer. If 2,400 gallons of recycled water go to the field in a month, how many gallons of drinking water go with it?
The town wants recycled water to make up 40 percent of the 180,000 gallons of park water. How many gallons of recycled water would that be?
How many more gallons of recycled water each day would the goal in item 6 require than the 45,000 gallons the town delivers now?

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

Answer Key

Answer: 1 to 3.
Divide both amounts by 45,000. 45,000 divided by 45,000 is 1, and 135,000 divided by 45,000 is 3, so there is 1 gallon of recycled water for every 3 gallons of drinking water.
Answer: 1 to 4.
All park water is 45,000 plus 135,000, which is 180,000 gallons. Divide both numbers by 45,000, which gives 1 to 4.
Answer: 25 percent.
Divide the part by the whole: 45,000 divided by 180,000 is 0.25, which is 25 percent of the park water.
Answer: 3 to 1.
Divide both amounts by 4. 12 divided by 4 is 3, and 4 divided by 4 is 1, so the field uses 3 gallons of recycled water for every 1 gallon of drinking water.
Answer: 800 gallons.
The ratio 3 to 1 means the drinking water is one third of the recycled water, and 2,400 divided by 3 is 800 gallons.
Answer: 72,000 gallons.
Find 40 percent of the whole: 0.40 times 180,000 is 72,000 gallons of recycled water.
Answer: 27,000 gallons.
The goal calls for 72,000 gallons and the town delivers 45,000 gallons, and 72,000 minus 45,000 is 27,000 more gallons each day.

Differentiation

Support

Give these students a tape diagram for the fictional town with four equal boxes, one shaded for recycled water and three left blank, so the part-to-part and part-to-whole comparisons are visible before any division. Assign items 1, 2, 3, and 4, and provide the total of 180,000 gallons already written for item 2.

Extension

Ask these students to find what percent of the fictional town's park water would be recycled if the town added 18,000 gallons of recycled water each day without changing the drinking water it delivers. They should state the new total, give the percent to the nearest tenth, and explain why the percent does not climb as much as the added gallons alone might suggest, since the total rises along with the recycled share.

ELL supports

Pre-teach ratio, simplest form, and percent using the two labeled jars and a strip of paper folded into four equal parts. Provide these sentence frames: "For every ___ gallons of recycled water there are ___ gallons of drinking water." and "Recycled water is ___ percent of all park water because ___ divided by ___ is ___."

Extensions

Have students draw a map of their own school grounds and mark which uses could accept recycled water, such as the ball field, the planting beds, and the bus wash, and which could not, such as drinking fountains and the cafeteria. Totaling the gallons each marked use needs, from a rough estimate the class agrees on, gives a ratio for the school that students can compare with the fictional town's 1 to 3.