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Worksheet Grade 6 Math

Feltingham's Biosolids Load: Dividing Fractions on the Farm

A grade 6 worksheet where students divide mixed numbers and fractions to find how many acres a biosolids truckload covers and how many loads a farm needs.

Objectives

  1. Students will divide a mixed number by a fraction to find how many acres one load covers.
  2. Students will multiply a fraction by a whole number to find the tons a field needs.
  3. Students will explain why dividing by a number less than one gives a larger quotient.

Vocabulary

Biosolids
Biosolids are the nutrient-rich solid material left over after sewage sludge has been treated and made safe. Many farms use treated biosolids as fertilizer for their fields.

Also: mixed number, quotient, acre

Teacher overview

After a treatment plant cleans wastewater, the solids it removes are treated again, dried, and often spread on farm fields as fertilizer, which turns a disposal problem into a nutrient supply. This worksheet uses the fictional Feltingham Water Reclamation Plant, which sends dried biosolids to the fictional Upwell Farm in truckloads, so students divide mixed numbers by fractions to find how far one load goes. The misconception this worksheet addresses is that dividing always makes a number smaller; because each acre takes less than a full ton, the number of acres one load covers is larger than the number of tons it holds.

Feltingham's Biosolids Load: Dividing Fractions on the Farm — Grade 6 Math
Name: ____________________________ Date: ______________

Student Worksheet

The fictional Feltingham Water Reclamation Plant hauls dried biosolids to the fictional Upwell Farm. Use these facts for every item.

  • A spreader truck holds 4 1/2 tons.
  • Each acre of the farm gets 3/4 of a ton.
  • The farm has 45 acres to cover.
  • The plant makes 2 1/4 tons of dried biosolids each day.
  1. How many acres can one full truckload cover?
  2. How many tons does the whole 45-acre farm need?
  3. How many truckloads does the farm's total in item 2 take?
  4. A smaller spreader holds 1 1/2 tons and puts down 3/8 of a ton on each acre. How many acres does one of its loads cover?
  5. The plant makes 2 1/4 tons each day. How many days does it take to fill one 4 1/2-ton truck?
  6. How many tons does the plant make in a 30-day month?
  7. The farm takes the tons from item 2 during that month. What percent of the month's production is that?
  8. The rest of the month's production goes to a compost yard. How many tons go there?
  9. The compost yard pays 18 dollars for each ton. What does the yard pay for the tons in item 8?
  10. One field on the farm is 7 1/2 acres. How many tons does that field need at 3/4 of a ton for each acre?
  11. Dividing 4 1/2 by 3/4 gives an answer larger than 4 1/2. Explain why that happens here.

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: 6 acres.
    Divide the load by the rate for each acre: 4 1/2 divided by 3/4 is 9/2 times 4/3, which is 36/6, or 6 acres.
  2. Answer: 33 3/4 tons.
    Multiply the acres by the rate: 45 times 3/4 is 135/4, which is 33 3/4 tons.
  3. Answer: 7 1/2 truckloads.
    Divide the tons by the truck's capacity: 33 3/4 divided by 4 1/2 is 135/4 times 2/9, which is 270/36, or 7 1/2 loads. The farm would schedule 8 trips, with the last one only half full.
  4. Answer: 4 acres.
    Divide the smaller load by its rate: 1 1/2 divided by 3/8 is 3/2 times 8/3, which is 24/6, or 4 acres.
  5. Answer: 2 days.
    Divide the truck's capacity by the daily production: 4 1/2 divided by 2 1/4 is 9/2 times 4/9, which is 36/18, or 2 days.
  6. Answer: 67 1/2 tons.
    Multiply the daily production by the days: 2 1/4 times 30 is 9/4 times 30, which is 270/4, or 67 1/2 tons.
  7. Answer: 50 percent.
    Divide the farm's share by the month's production: 33 3/4 divided by 67 1/2 is 0.5, which is 50 percent.
  8. Answer: 33 3/4 tons.
    Subtract the farm's share from the month's production: 67 1/2 minus 33 3/4 is 33 3/4 tons, the same amount the farm took.
  9. Answer: 607.50 dollars.
    Multiply the tons by the price: 33.75 times 18 is 607.50 dollars.
  10. Answer: 5 5/8 tons.
    Multiply the acres by the rate: 7 1/2 times 3/4 is 15/2 times 3/4, which is 45/8, or 5 5/8 tons.
  11. Answer: Because each acre takes less than one whole ton.
    A quotient counts how many times the divisor fits into the dividend. Since 3/4 of a ton is less than a ton, it fits into 4 1/2 tons more than 4 1/2 times, so the answer is 6 rather than something smaller.

Differentiation

Support

Give these students a strip diagram for the fictional farm showing 4 1/2 tons cut into three-quarter-ton pieces, so item 1 can be answered by counting pieces before any algorithm is used. Assign items 1, 4, 5, and 10, and provide the keep-change-flip step already written for item 1.

Extension

Ask these students to plan the hauling schedule for the fictional Upwell Farm if the plant switches to a truck that holds 6 tons and the farm raises its rate to 1 ton for each acre. They should state the acres one load covers, the loads the 45 acres need, and whether the plant's 2 1/4 tons a day can keep that schedule supplied.

ELL supports

Pre-teach biosolids, load, and acre with a simple drawing of a truck, a field divided into squares, and an arrow from one to the other. Provide these sentence frames: "One load holds ___ tons, and each acre takes ___ of a ton." and "___ divided by ___ is ___, so one load covers ___ acres."

Extensions

Have students compare the fictional plant's fertilizer with a bag of lawn fertilizer from a hardware store by reading the coverage line on the bag, which is usually written in square feet for each bag. Converting that coverage into tons for each acre, using 43,560 square feet in an acre, gives the class a second application rate to hold beside the 3/4 ton this worksheet uses.