Lesson plan Grade 6 Math

Cranleigh Canal Flow Rates: A Grade 6 Hydraulics Lesson

A 45-minute grade 6 lesson where students find canal flow with area times speed, then convert cfs to gpm, using the fictional Cranleigh canal and clean numbers.

Grade: Grade 6
Subject: Math
Material: Lesson plan
Time: 45 min
Prep: Low prep
Materials: Printed student handout, Calculators

Standards

6.RP.A.2 Common Core Math

Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to 0, and use rate language in the context of a ratio relationship.

How this material aligns: Handout items 1, 3, and 4 have students read flow as a per-second rate found by multiplying area and speed, the unit-rate reasoning in context that this standard defines.

All materials for 6.RP.A.2 →

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: Handout item 2 converts a flow from cfs to gpm using the rate 448.8 gpm per cfs, the measurement-unit conversion this standard names among its problem types.

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 2026-07-23.

Objectives

Students will calculate flow in cfs by multiplying a cross-section area by a water speed.
Students will convert a flow from cfs to gpm using a unit rate.

Vocabulary

Key words: flow, cfs, gpm, cross-section

Teacher overview

Water flow is how much water passes a point each second, and it depends on two things: how wide the opening is and how fast the water moves. The rule is flow equals area times speed, written Q = A x V. This lesson uses the fictional Cranleigh canal, with a flow of 18 cfs, to teach that rule and then convert the answer into gallons per minute. A common misconception this lesson addresses is that flow depends on width alone; handout item 4 shows that speed matters just as much, because doubling the speed doubles the flow.

Procedure

Hook (5 min): Ask students to picture two pipes carrying water: a narrow one and a wide one, both moving water at the same speed. Ask which carries more, and why. Collect a few answers, then tell them they will use a rule to settle the question with numbers.

Direct instruction (12 min): Introduce the rule flow equals area times speed, Q = A x V. Explain that area is measured in square feet, speed in feet per second, and the flow that results in cubic feet per second, written cfs. Stress that both the area and the speed must be used; using only one leaves out half of the picture. Then introduce the conversion 448.8 gpm for every 1 cfs, which turns a flow into gallons per minute.

Worked example (10 min): Use the fictional Cranleigh canal. Its opening has an area of 6 square feet, and the water moves at 3 feet per second. Show Q = 6 x 3 = 18 cfs. Then convert: 18 cfs x 448.8 gpm per cfs = 8,078.4 gpm. Write each step on the board and label the units at every stage.

Guided and independent practice (13 min): Hand out the student handout. Complete item 1 together, then have students finish items 2 through 4 in pairs while you circulate. As a formative check, confirm that at least 80 percent of pairs multiply both the area and the speed on item 3 rather than using a single number; pause to reteach if more than a few pairs miss it.

Closure and exit ticket (5 min): Have each student answer handout item 5 on a slip of paper as an exit ticket. Scan the slips to check that students connect a larger area to a larger flow at the same speed.

Cranleigh Canal Flow Rates: A Grade 6 Hydraulics Lesson — Grade 6 Math

Name: ____________________________ Date: ______________

Student Handout

These practice channels are all fictional examples. Use the rule flow equals area times speed, and the conversion 448.8 gpm for every 1 cfs.

A pipe has a cross-section area of 4 square feet. The water moves at 2 feet per second. Find the flow in cfs.
Convert your answer from item 1 to gpm, using 448.8 gpm per cfs.
A wider channel has an area of 10 square feet and a speed of 3 feet per second. Find the flow in cfs.
A canal keeps its area at 6 square feet, but the speed doubles from 3 to 6 feet per second. What happens to the flow, and what is the new flow in cfs?
Explain why a wider pipe can carry more water than a narrow pipe even when the water moves at the same speed.

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: 8 cfs.
Q = area x speed = 4 x 2 = 8 cfs.
Answer: 3,590.4 gpm.
8 cfs x 448.8 gpm per cfs = 3,590.4 gpm.
Answer: 30 cfs.
Q = 10 x 3 = 30 cfs. Both the area and the speed are used.
Answer: 36 cfs.
The flow doubles. New flow = 6 x 6 = 36 cfs, which is twice the old 18 cfs.
Answer: A wider pipe has more area.
Flow equals area times speed, so a larger area gives a larger flow at the same speed, which is why a wider pipe carries more water.

Differentiation

Support

Give students the rule Q = A x V printed at the top of the handout with the units labeled, and complete item 1's setup (4 x 2) for them so they can focus on the pattern in items 3 and 4.

Extension

Ask students to imagine a canal that must carry exactly 60 cfs with a speed of 3 feet per second. Have them work backward to find the area it needs, then explain how they used the rule in reverse.

ELL supports

Provide a labeled cross-section diagram showing area (the opening), speed (an arrow), and flow (water leaving). Pair each of the words "area," "speed," and "flow" with the matching part of the picture before students begin.

Extensions

Have students measure the width and depth of a spare section of rain gutter or a small model channel, estimate its area in square feet, and use an assumed speed to predict its flow, then discuss how real crews measure speed in the field.