Water for Schools
Menu

Math problem set Grade 5 Math

Corrowdale Reclamation Plant Solids Log: A Grade 5 Decimal Set

A grade 5 problem set adding, subtracting, multiplying, and dividing decimals using a fictional water reclamation plant's weekly log of dried solids.

Objectives

  1. Students will add and subtract decimals to hundredths from a plant log.
  2. Students will multiply and divide decimals to solve problems about hauling solids.
  3. Students will explain why decimal points must be aligned before adding.

Vocabulary

Key words: decimal, hundredths, ton, reclamation, digester

Teacher overview

Corrowdale Water Reclamation Plant is a fictional facility that cleans the used water from a small city and returns it to a creek. Tiny living things called microbes eat the waste in large tanks, and what is left behind is dried into solids that a truck hauls away for use on farm fields. Operators weigh those solids every day and record the weight in tons, using two decimal places. This set works through one week of that log, and it targets the misconception that a decimal with more digits is automatically larger, which leads students to claim that 0.95 ton weighs more than 1.4 tons.

Corrowdale Reclamation Plant Solids Log: A Grade 5 Decimal Set — Grade 5 Math
Name: ____________________________ Date: ______________

Problems

The Corrowdale plant recorded these weights of dried solids for one week.

  • Monday 1.25 tons, Tuesday 0.80 ton, Wednesday 1.40 tons, Thursday 0.95 ton, Friday 1.20 tons.
  1. How many tons of solids did the plant produce on Monday and Tuesday together?
  2. How many more tons did the plant produce on Wednesday than on Thursday?
  3. Find the total weight of solids for the five days.
  4. The hauling truck carries 2.50 tons on each trip. It made two full trips this week. Using your total from problem 3, how many tons are still waiting at the plant?
  5. The crew divided Friday's 1.20 tons evenly into 4 bins. How much went into each bin?
  6. A second digester makes 0.35 ton of solids each day. How much does it make in 6 days?
  7. The crew loaded the week's 5.60 tons evenly into 4 containers. How much went into each container?
  8. A smaller plant nearby produces 0.75 times as much as Corrowdale's 5.60 tons for the week. How many tons is that?
  9. Explain why the decimal points must line up before you add the five daily weights.

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: 2.05 tons. Stack the decimal points and add: 1.25 + 0.80 = 2.05 tons.
  2. Answer: 0.45 ton. Stack the decimal points and subtract: 1.40 - 0.95 = 0.45 ton.
  3. Answer: 5.60 tons. Add in order: 1.25 + 0.80 = 2.05; 2.05 + 1.40 = 3.45; 3.45 + 0.95 = 4.40; 4.40 + 1.20 = 5.60 tons.
  4. Answer: 0.60 ton. Two trips carry 2.50 + 2.50 = 5.00 tons. Then 5.60 - 5.00 = 0.60 ton still at the plant.
  5. Answer: 0.30 ton. 1.20 divided by 4 = 0.30 ton in each bin, because 120 hundredths divided by 4 is 30 hundredths.
  6. Answer: 2.10 tons. 0.35 x 6 = 2.10 tons, because 35 hundredths times 6 is 210 hundredths.
  7. Answer: 1.40 tons. 5.60 divided by 4 = 1.40 tons in each container, because 560 hundredths divided by 4 is 140 hundredths.
  8. Answer: 4.20 tons. 0.75 x 5.60 = 4.20 tons. One way to see it: 5.60 divided by 4 = 1.40, and 1.40 x 3 = 4.20 tons, since 0.75 is three fourths.
  9. Answer: Lining up the decimal points lines up the place values, so tenths add to tenths and hundredths add to hundredths. If Tuesday's weight were written as 0.8 and lined up at the right end with 1.25, the 8 would land in the hundredths place and be added as though it were 0.08.

Differentiation

Support

Give students grid paper with a bold vertical line for the decimal point so each daily weight is written in a fixed column. Complete problem 1 together, then have students write all five weights in the grid before attempting problem 3. Allow a calculator for problems 6 through 8 once the setup is correct.

Extension

Ask students to plan a hauling schedule for a second week in which the plant produces 6.75 tons and the truck still carries 2.50 tons per trip. They should state how many full trips are needed, how much is left for the last trip, and show the subtraction that supports each step.

ELL supports

Provide a place-value chart labeled ones, tenths, and hundredths, and read the weights aloud as "one and twenty-five hundredths" rather than "one point two five" so the value of each digit is audible. Offer a sentence frame for problem 9: "The decimal points must line up because ___."

Extensions

Have students research what happens to dried solids after they leave a treatment plant in their own region, then write two new decimal problems about a week of hauling. Ask them to trade problems with a partner and check each other's arithmetic against the original log.