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Lesson plan Grade 4 Math

Pellwater Reservoir's Dry Summer: Reading the Gauge as Decimals

A grade 4 lesson where students rewrite a fictional reservoir's gauge readings as tenths and hundredths, then compare two drops written as decimals.

Objectives

  1. Students will write a reservoir gauge reading given in tenths or hundredths of a foot using decimal notation.
  2. Students will compare two decimal readings and tell which one is larger.
  3. Students will locate a hundredths reading between two tenths marks on a number line.

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.

Also: gauge, tenth, hundredth, decimal

Teacher overview

Pellwater Reservoir supplies the fictional town of Mendlow, and a tall marked post called a staff gauge stands in the shallow water near the dam. During a dry summer the reservoir operator reads that gauge every morning and records how far the water sits below the full mark, using tenths and hundredths of a foot. The misconception this lesson is built to correct is treating the digits after the decimal point as an ordinary whole number, so that a student decides 0.35 foot is a bigger drop than 0.4 foot because 35 looks larger than 4. Working from a 10-by-10 grid, where four full columns are visibly more than thirty-five small squares, gives students a picture they can return to whenever the comparison feels backwards.

Procedure

Hook (5 min): Project or draw a tall post marked from 0 at the top down to 1 foot, with the space divided into ten equal parts. Ask students how they would write down a water level that has fallen part way between the top mark and the first tenth mark. Explain that the operator at Pellwater Reservoir faces this every morning and writes the answer as a decimal.

Direct instruction (12 min): Hand each pair a 10-by-10 grid square and explain that the whole square stands for one foot. Shade four full columns and write both 4/10 and 0.4 beside it. Then shade thirty-five small squares on a second grid and write both 35/100 and 0.35. Place the two grids side by side and ask which shows more shading. Record on chart paper that 0.4 is greater than 0.35 even though 35 is greater than 4, and label the tenths place and hundredths place on both numbers.

Guided practice (10 min): As a class, move in the other direction. Write 0.7 on the board and have students name it as 7/10, then write 6/10 and have them rename it as 60/100 by splitting each tenth into ten smaller parts on the grid. Ask one student to explain aloud why 6/10 and 60/100 shade the same amount of the square.

Independent practice (13 min): Students complete the eight questions on the student handout using their grid squares and a number line marked in tenths. Circulate and ask students working on question 7 to point at both neighboring tenths marks before they write.

Closure / exit ticket (5 min): On an index card, students answer one question: which is the larger drop, 0.6 foot or 0.55 foot, and how do they know? Collect the cards and count how many chose 0.6 foot. If fewer than three-quarters chose correctly, begin the next lesson with the two shaded grids again.

Pellwater Reservoir's Dry Summer: Reading the Gauge as Decimals — Grade 4 Math
Name: ____________________________ Date: ______________

Student Handout

At Pellwater Reservoir, the operator records how far the water sits below the full mark. Answer each question using the numbers given in that question.

  1. On Monday the gauge showed the water was 4/10 foot below the full mark. Write that reading as a decimal.

  2. On Tuesday the gauge showed the water was 35/100 foot below the full mark. Write that reading as a decimal.

  3. On Wednesday the operator wrote 0.7 foot. Write that reading as a fraction with a denominator of 10.

  4. On Thursday the operator wrote 6/10 foot. Write that same reading as a fraction with a denominator of 100.

  5. Monday's drop was 0.4 foot and Tuesday's drop was 0.35 foot. Which day had the larger drop?

  6. The water fell 2/10 foot on one day and 3/10 foot on the next day. How far did it fall over those two days in all?

  7. A number line runs from 0 to 1 and is marked at every tenth. Between which two marks does 0.45 sit?

  8. Explain in one or two sentences why the operator writes 0.35 foot instead of writing "a little more than a third of a foot."

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: 0.4 foot.
    The fraction 4/10 has a denominator of 10, so the 4 belongs in the tenths place, one place to the right of the decimal point. The reading is 0.4 foot.

  2. Answer: 0.35 foot.
    The fraction 35/100 has a denominator of 100, so the digits fill the tenths and hundredths places. Three tenths and five hundredths are written 0.35 foot.

  3. Answer: 7/10 foot.
    The digit 7 sits in the tenths place, which means seven of the ten equal parts of one foot. As a fraction that is 7/10 foot.

  4. Answer: 60/100 foot.
    Each tenth can be split into ten hundredths, so 6 tenths is the same shaded amount as 60 hundredths. On the grid, six full columns cover sixty small squares.

  5. Answer: Monday, with a drop of 0.4 foot.
    Compare the tenths place first: 0.4 has 4 tenths while 0.35 has only 3 tenths. Since 4 tenths is more than 3 tenths, 0.4 foot is greater, even though 35 is a larger whole number than 4.

  6. Answer: 5/10 foot.
    Both drops are written in tenths, so add the numerators and keep the denominator: 2/10 plus 3/10 equals 5/10 foot. Written as a decimal that is 0.5 foot.

  7. Answer: Between 0.4 and 0.5.
    The number 0.45 has 4 tenths and 5 hundredths, so it sits past the 0.4 mark but has not reached the 0.5 mark. On a number line marked only in tenths, it falls halfway between those two marks.

  8. Answer: A decimal gives an exact reading.
    Accept any explanation stating that 0.35 foot names a precise position on the gauge that anyone reading the log can find again, while a phrase such as "a little more than a third" cannot be compared with the next day's reading or added to it.

Differentiation

Support (below grade level)

Give these students grid squares with the tenths columns already outlined in bold, and let them shade every reading before writing it. Provide a place-value chart with the tenths and hundredths columns labeled so each digit can be written into a named column rather than counted out from the decimal point. Reduce the assignment to questions 1, 2, 3, and 5.

Extension (above grade level)

Ask students to build a seven-day gauge log for the fictional town of Mendlow in which the water falls a little further each day, every reading is written both as a fraction and as a decimal, and at least two readings use hundredths. Students then order the seven readings from smallest drop to largest and explain the rule they used to compare a tenths reading against a hundredths reading.

ELL supports

Pre-teach "gauge," "below," and "drop" with a labeled drawing of a marked post standing in water, with an arrow showing the distance from the full mark down to the current surface. Provide sentence frames for questions 5 and 8: "___ had the larger drop because ___ tenths is more than ___ tenths," and "The operator writes a decimal because ___." Allow oral rehearsal with a partner before writing.

Extensions

Have students keep a two-week classroom log of a measurable depth, such as water in a clear tub left uncovered on a windowsill, reading it to the nearest tenth of a centimeter and recording each reading as both a fraction and a decimal. They can then compare their own log with the Pellwater Reservoir scenario and describe what a steady decline looks like in a table of decimals.