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Lesson plan Grade 4 Math

Coldwick Hatchery Raceways: Adding Eighths of a Foot of Water

A grade 4 lesson at a fictional fish hatchery where students add and subtract eighths of a foot to keep four concrete raceways at their correct water depth.

Objectives

  1. Students will add and subtract mixed numbers written in eighths of a foot to find a new water depth.
  2. Students will regroup eight eighths into one whole foot when a sum passes a whole number.
  3. Students will explain why the denominator stays the same when depths measured in eighths are combined.

Vocabulary

Key words: raceway, hatchery, depth, mixed number, denominator

Teacher overview

The fictional Coldwick Hatchery sits beside Trentmoor Creek and raises young trout in four long concrete channels called raceways. Creek water flows in at one end and out at the other, and a hatchery technician raises or lowers the depth in each raceway by small amounts, reading a wall gauge marked in eighths of a foot. The misconception this lesson is designed to correct is the belief that adding fractions means adding the bottom numbers, so that a student writes 5/8 plus 2/8 as 7/16 and reports a depth that is smaller than the one they started with. A second error to watch for is failing to regroup: when eighths add up past 8/8, students often write an improper answer such as 1 9/8 feet and stop there.

Procedure

Hook (5 min): Hold a yardstick upright in an empty tub or bucket and mark a depth line with tape. Ask the class how they would describe a depth that sits between the 1-foot and 2-foot marks. Introduce the wall gauge at Coldwick Hatchery, which is marked in eighths of a foot so a technician can read a depth such as 1 5/8 feet exactly.

Direct instruction (12 min): Explain why depth matters at a hatchery: the fish need enough water to swim in, and the flow through the raceway carries away waste. Model 1 5/8 plus 2/8 on chart paper using a number line marked in eighths, moving two eighth-steps to the right and landing on 1 7/8. Say aloud that the denominator names the size of the step and does not change when steps are counted. Then model 1 5/8 plus 4/8 on the same number line and stop deliberately at 1 9/8, asking students what is wrong with that way of writing it before regrouping to 2 1/8.

Guided practice (10 min): Work one subtraction problem together. A raceway reads 2 3/8 feet, and the technician lets out 5/8 foot. Guide students to rename 2 3/8 as 19/8, subtract 5/8 to get 14/8, and rewrite that as 1 6/8 feet. Ask two students to explain the renaming step in their own words before moving on.

Independent practice (13 min): Students complete the seven questions on the student handout using fraction strips or the printed number line as needed. Circulate and check that answers with more than eight eighths have been regrouped into whole feet.

Closure / exit ticket (5 min): On an index card, each student answers one question: a raceway holds water 1 3/8 feet deep and the technician adds 6/8 foot, so what is the new depth? Collect the cards and sort them into three piles, correct at 2 1/8 feet, correct sum but not regrouped, and denominator changed. Use the piles to plan the next day's warm-up.

Coldwick Hatchery Raceways: Adding Eighths of a Foot of Water — Grade 4 Math
Name: ____________________________ Date: ______________

Student Handout

Coldwick Hatchery reads every raceway depth in eighths of a foot. The morning readings are shown below.

Raceway Morning depth
A 1 5/8 feet
B 2 3/8 feet
C 1 1/8 feet
D 2 7/8 feet

  1. Raceway A reads 1 5/8 feet. The technician adds 2/8 foot of water. What is the new depth of Raceway A?

  2. Raceway B reads 2 3/8 feet. The technician lets out 5/8 foot of water. What is the new depth of Raceway B?

  3. Raceway C reads 1 1/8 feet in the morning and 1 7/8 feet at night. How much did the depth in Raceway C rise during the day?

  4. Raceway A reads 1 5/8 feet. The technician adds 1/8 foot every hour for 4 hours. What is the depth of Raceway A after those 4 hours?

  5. The morning depths are 1 5/8 feet in Raceway A, 2 3/8 feet in Raceway B, and 1 1/8 feet in Raceway C. What is the total of those three depths?

  6. Raceway D reads 2 7/8 feet, and it must be brought down to 2 4/8 feet. How much water must the technician let out?

  7. In question 5 you added three depths that were all written in eighths. Explain in one or two sentences why the bottom number stayed 8 in your answer.

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: 1 7/8 feet.
    Add the eighths and keep the whole foot: 5/8 plus 2/8 equals 7/8, so the depth is 1 7/8 feet. The denominator stays 8 because every step on the gauge is one eighth of a foot.

  2. Answer: 1 6/8 feet.
    Rename 2 3/8 feet as 19/8 feet, since two whole feet are 16/8. Then 19/8 minus 5/8 equals 14/8, which is 1 whole foot and 6/8 of a foot, or 1 6/8 feet. Accept 1 3/4 feet as an equivalent answer.

  3. Answer: 6/8 foot.
    Subtract the morning depth from the night depth: 1 7/8 minus 1 1/8. The whole feet cancel, and 7/8 minus 1/8 equals 6/8 foot. Accept 3/4 foot as an equivalent answer.

  4. Answer: 2 1/8 feet.
    Four hours at 1/8 foot each hour adds 4/8 foot. Then 1 5/8 plus 4/8 equals 1 9/8 feet. Regroup 8/8 into one whole foot, which gives 2 1/8 feet.

  5. Answer: 5 1/8 feet.
    Add the whole feet first: 1 plus 2 plus 1 equals 4 feet. Then add the eighths: 5/8 plus 3/8 plus 1/8 equals 9/8. Regroup 8/8 into one more whole foot, so the total is 4 plus 1 plus 1/8, or 5 1/8 feet.

  6. Answer: 3/8 foot.
    Subtract the target depth from the current depth: 2 7/8 minus 2 4/8. The whole feet cancel, and 7/8 minus 4/8 equals 3/8 foot.

  7. Answer: The denominator names the size of each step.
    Accept any explanation stating that every depth was measured in the same unit, one eighth of a foot, so the answer counts eighths as well. Adding the bottom numbers would change the size of the step instead of counting more steps.

Differentiation

Support (below grade level)

Give these students fraction strips already cut into eighths and a printed number line running from 0 to 3 feet with every eighth marked and labeled. Let them build each depth physically before writing anything. For question 2, provide the renaming step already written, so 2 3/8 appears as 19/8 on the page and the student only performs the subtraction. Reduce the assignment to questions 1, 2, 3, and 6.

Extension (above grade level)

Ask students to write a weekly log for Raceway D at the fictional Coldwick Hatchery in which the depth starts at 2 4/8 feet and changes by an eighth or two each day for five days, ending exactly at 2 7/8 feet. They should record each day's change, show the running depth, and then prove with addition and subtraction that their log lands on the required final depth.

ELL supports

Pre-teach "raceway," "depth," and "let out" using a labeled side-view drawing of a concrete channel with water in it and an arrow showing water leaving through a gate. Post the drawing during independent practice. Provide sentence frames for questions 3 and 7: "The depth rose by ___ of a foot," and "The bottom number stayed 8 because ___." Allow students to answer question 7 orally before writing it.

Extensions

Have students research, using materials the teacher supplies rather than open searching, how a hatchery technician measures water depth and why fish need a steady level. Students can then rewrite the fictional Coldwick log using sixteenths of a foot instead of eighths and explain what changes about the arithmetic and what stays the same.