Water for Schools
Menu

Lesson plan Grade 5 Math

Trestlebank Dam Gauge Log: A Grade 5 Decimal Division Lesson

A 50-minute grade 5 lesson using a fictional dam's daily staff-gauge readings to subtract decimals to hundredths and divide a total drop over equal days.

Objectives

  1. Students will subtract decimals written to hundredths by lining up the decimal points.
  2. Students will divide a decimal total by a whole number to find an equal daily amount.
  3. Students will explain why the answer to a decimal division keeps a decimal point in the quotient.

Vocabulary

Reservoir
A human-made lake, usually created by a dam, that stores water for later. Reservoirs supply cities and farms and help control floods.
Spillway
A dam's overflow channel, giving extra water a safe path around or over the dam when the reservoir gets too full. It protects the dam from being damaged in floods.

Also: staff gauge, decimal point, quotient

Teacher overview

Trestlebank Dam is a fictional structure that holds back Gadwall Creek to form a small reservoir for the valley below it. A painted ruler called a staff gauge stands in the water beside the dam, and every morning the tender writes down how high the water sits on the gauge, measured from the gauge's zero mark, in feet and hundredths of a foot. Those readings tell the crew whether the reservoir is filling or falling, and comparing one morning's reading with the next takes careful decimal subtraction. The misconception this lesson corrects is the habit of lining up the right-hand digits instead of the decimal points, which gives an answer with the wrong place value when one reading is written as 8.6 instead of 8.60, along with the related habit of dropping the decimal point from a quotient so that 0.80 divided by 4 is written as 2 instead of 0.20.

Procedure

Hook (5 min): Stand a yardstick upright in a bucket or against the wall and tell the class it is the staff gauge at Trestlebank Dam. Write Monday's reading, 8.60 feet, and Tuesday's reading, 8.45 feet, on the board. Ask students whether the reservoir rose or fell and by how much, and record two or three student answers without saying which is right.

Direct instruction (13 min): Work Monday to Tuesday together, writing the two readings one above the other with the decimal points aligned, and show that 8.60 minus 8.45 = 0.15 feet. Beside it, write Monday's reading as 8.6 and line up its last digit with the last digit of 8.45, so students can see that misaligned digits give a wrong answer; then write the zero back in to show why 8.60 lines up correctly. Then model the second skill: the reservoir fell 0.60 feet over 3 nights at the same amount each night, so 0.60 divided by 3 = 0.20 feet. Say aloud why the quotient keeps two decimal places, since twenty hundredths, not two whole feet, is what fits three times into sixty hundredths.

Guided practice (10 min): Pairs work one subtraction and one division with you circulating. The reading falls from 7.40 feet to 7.16 feet, a drop of 0.24 feet, and a separate 0.72-foot drop spread evenly over 6 nights gives 0.12 feet a night. As a formative check, ask each pair to hold up a card showing the second answer. If more than a quarter of the class shows a number other than 0.12, work another division together before the handout.

Independent practice (15 min): Students complete handout questions 1 through 6 alone. Circulate and watch for two errors: subtracting without aligning the decimal points, and writing a whole number where the quotient should be less than one.

Closure and exit ticket (7 min): Students answer handout question 7 on an index card and hand it in as they leave. Sort the cards before the next class so you know which students still need place-value support.

Trestlebank Dam Gauge Log: A Grade 5 Decimal Division Lesson — Grade 5 Math
Name: ____________________________ Date: ______________

Student Handout

The tender at Trestlebank Dam writes down the water level every morning. Each reading tells how many feet the water sits above the gauge's zero mark. Here is one week of readings.

Monday 8.60 feet. Tuesday 8.45 feet. Wednesday 8.27 feet. Thursday 8.06 feet. Friday 7.80 feet.

  1. How much did the water level fall from Monday to Tuesday?
  2. How much did the water level fall from Tuesday to Wednesday?
  3. How much did the water level fall from Monday all the way to Friday?
  4. The level fell 0.80 feet over the 4 nights from Monday to Friday. If it fell the same amount each night, how much did it fall each night?
  5. The next week the level fell 1.26 feet over 6 nights. If it fell the same amount each night, how much did it fall each night?
  6. The tender expects the level to keep falling 0.21 feet each day for 5 more days. How much will it fall in those 5 days?
  7. In a dry month the level fell 0.96 feet over 8 nights. If it fell the same amount each night, how much did it fall each night?

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: 0.15 feet.
    Line up the decimal points and subtract: 8.60 minus 8.45 = 0.15 feet.
  2. Answer: 0.18 feet.
    Line up the decimal points and subtract: 8.45 minus 8.27 = 0.18 feet.
  3. Answer: 0.80 feet.
    Subtract Friday from Monday: 8.60 minus 7.80 = 0.80 feet. Adding the four nightly drops of 0.15, 0.18, 0.21, and 0.26 gives the same total.
  4. Answer: 0.20 feet.
    Eighty hundredths divided by 4 is twenty hundredths, so 0.80 divided by 4 = 0.20 feet each night. An answer of 2 feet has lost the decimal point.
  5. Answer: 0.21 feet.
    One hundred twenty-six hundredths divided by 6 is twenty-one hundredths, so 1.26 divided by 6 = 0.21 feet each night.
  6. Answer: 1.05 feet.
    Multiply the daily drop by the number of days: 0.21 x 5 = 1.05 feet.
  7. Answer: 0.12 feet.
    Ninety-six hundredths divided by 8 is twelve hundredths, so 0.96 divided by 8 = 0.12 feet each night.

Differentiation

Support

Give these students grid paper with a bold vertical line down one column so the decimal points have a place to sit, and let them write each reading with the point on that line before subtracting. For the division questions, provide a place-value chart and have students read the dividend aloud as hundredths before they divide, which keeps the quotient in the right place.

Extension

Ask students to build a five-day gauge log of their own in which the level falls a total of 1.00 foot, with a different drop each night and every reading written to hundredths. Have them exchange logs with a partner, who checks that the nightly drops add to the stated total.

ELL supports

Post a labeled drawing of a dam, a spillway, and a staff gauge with the words written in English and, where possible, in students' home languages. Pre-teach "fall," "level," and "each night," and provide a sentence frame for question 4: "The level fell ___ feet in all, so it fell ___ feet each night."

Extensions

Have students keep a five-day rain or snow record for their own town using a school rain gauge, writing each reading to hundredths of an inch. Ask them to find the total for the week and the amount that would have fallen each day if the total had been spread evenly, then compare that even amount with what actually happened on the wettest day.