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Math problem set Grade 6 Math

Ketterby Dam's Fish Ladder: Rate and Percent Problems

A grade 6 problem set on a dam's fish ladder, covering the climb height, a fish's rate per pool, the share of river flow the ladder takes, and a counting rate.

Objectives

  1. Students will find a unit rate from a count taken over a stated number of minutes or hours.
  2. Students will find what percent of a river's flow is sent down a fish ladder.
  3. Students will find what percent a rise in fish counts is of the first season's count.

Vocabulary

Fish ladder
A series of water steps built beside a dam so migrating fish, like salmon, can swim past it. Fish leap or swim from pool to pool to reach the river above.

Also: pool, flow, unit rate, percent

Teacher overview

A fish ladder is a staircase of small pools beside a dam, and fish climb it by swimming from one pool up into the next until they reach the water above the dam. This set uses the fictional Ketterby Dam on the fictional Zennor River, where a ladder of 24 pools runs alongside the powerhouse and a counter watches fish pass a viewing window. The misconception this set corrects is dividing by the wrong whole when finding a percent of flow. Students often compare the ladder's water with the turbines' water, which is a part compared with a part, when the question asks for the ladder's share of the river's whole flow.

Ketterby Dam's Fish Ladder: Rate and Percent Problems — Grade 6 Math
Name: ____________________________ Date: ______________

Problems

Use these facts about the fictional Ketterby Dam for every problem.

  • The fish ladder has 24 pools, and each pool lifts the water 0.75 foot.
  • The river carries 9,000 gallons each minute past the dam.
  • The ladder takes 1,800 gallons each minute, and the turbines take the rest.
  1. The ladder has 24 pools and each pool lifts the water 0.75 foot. How high is the whole climb, from the river below the dam to the water above it?
  2. A tagged salmon moves up 3 pools every 10 minutes. What is its rate in pools for each minute?
  3. At that rate, how many minutes does the salmon need to climb all 24 pools?
  4. The river carries 9,000 gallons each minute, and the ladder takes 1,800 of them. What percent of the river's flow goes down the ladder?
  5. How many gallons each minute reach the turbines?
  6. Counters watched the viewing window for 5 hours and counted 420 fish. What is the counting rate in fish for each hour?
  7. Suppose fish keep passing at that rate all day. How many fish would pass in 24 hours?
  8. Last season the counters recorded 1,800 fish in the first week. This season they recorded 2,700 in the first week. The count rose by 900 fish. What percent of last season's 1,800 fish is that rise?
  9. A state rule says the ladder must always get at least 15 percent of the river's flow. In August the river drops to 6,000 gallons each minute. How many gallons each minute must the ladder get then?
  10. In August the ladder still gets its usual 1,800 gallons each minute. What percent of the river's 6,000 gallons each minute is that?

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: 18 feet.
    Multiply the number of pools by the lift of each one: 24 times 0.75 is 18 feet.
  2. Answer: 0.3 pool per minute.
    Divide the pools by the minutes: 3 divided by 10 is 0.3 pool each minute.
  3. Answer: 80 minutes.
    Divide the pools by the rate: 24 divided by 0.3 is 80 minutes. Checking, 0.3 times 80 is 24 pools.
  4. Answer: 20 percent.
    Divide the ladder's flow by the river's whole flow: 1,800 divided by 9,000 is 0.2, which is 20 percent.
  5. Answer: 7,200 gallons each minute.
    Subtract the ladder's share from the river's flow: 9,000 minus 1,800 is 7,200 gallons each minute.
  6. Answer: 84 fish per hour.
    Divide the count by the hours: 420 divided by 5 is 84 fish each hour.
  7. Answer: 2,016 fish.
    Multiply the hourly rate by the hours: 84 times 24 is 2,016 fish.
  8. Answer: 50 percent.
    The rise is 2,700 minus 1,800, which is 900 fish. Divide the rise by the first season's count: 900 divided by 1,800 is 0.5, which is 50 percent.
  9. Answer: 900 gallons each minute.
    Find 15 percent of the August flow: 0.15 times 6,000 is 900 gallons each minute.
  10. Answer: 30 percent.
    Divide the ladder's flow by the smaller river flow: 1,800 divided by 6,000 is 0.3, which is 30 percent. The ladder's share rises in August even though its gallons never changed.

Differentiation

Support

Give these students a double number line for the fictional dam with the river's 9,000 gallons each minute marked at 100 percent and 4,500 marked at 50 percent, so problem 4 can be placed on the line before any division. Assign problems 1, 2, 4, 5, and 6, and provide problem 4 with the division already written as 1,800 divided by 9,000.

Extension

Ask these students to find how many gallons each minute the fictional ladder would need to carry 25 percent of the river's flow in both seasons, at 9,000 gallons each minute and at 6,000 gallons each minute. They should then explain why a rule written as a percent asks for different amounts of water in different months, and what that means for the turbines.

ELL supports

Pre-teach fish ladder, pool, and flow with a side-view sketch of stepped pools climbing beside a dam, with an arrow for the water and an arrow for the fish. Provide these sentence frames: "Each pool lifts the water ___ foot, and there are ___ pools, so the climb is ___ feet." and "The ladder gets ___ gallons out of ___ gallons, which is ___ percent."

Extensions

Have students look up whether the nearest dam or milldam on a local river has a fish passage of any kind, and what fish it was built for. Comparing the fictional Ketterby ladder's 24 pools with a real structure, or with a river where the dam has simply been removed, gives the class a reason to ask what a percent of flow costs a power plant and who decides that trade.