Lesson plan Grade 5 Math
Pennythorn School Garden Soaker Hoses: A Grade 5 Fraction Lesson
A 45-minute grade 5 lesson multiplying fractions and whole numbers to find how much water a fictional school garden's soaker hoses deliver in a watering.
Objectives
- Students will multiply a whole number by a fraction to find a total flow.
- Students will multiply a fraction by a fraction and interpret the smaller product.
- Students will explain why multiplying by a fraction less than one gives a smaller result.
Vocabulary
Key words: soaker hose, fraction, product, gallon, watering
Teacher overview
Pennythorn Elementary is a fictional school whose garden club waters six raised beds with soaker hoses, which are hoses that weep water slowly along their whole length instead of spraying it. Each hose section puts out a fraction of a gallon every minute, so the club cannot plan a watering without multiplying fractions. This lesson moves from multiplying a whole number by a fraction, which students usually accept, to multiplying a fraction by a fraction, which they often resist. The misconception it addresses directly is the belief that multiplication always makes a number larger, so a student who finds that half of three fourths of a gallon comes to three eighths of a gallon may assume the answer is wrong.
Procedure
Hook (5 min): Hold up a one-gallon jug and a marker. Tell the class that one section of soaker hose in the Pennythorn garden lets out three fourths of a gallon each minute, and ask a volunteer to mark on the jug where the water would stand after one minute. Then ask what the mark would be after two minutes, and let students argue briefly before recording their predictions on chart paper.
Direct instruction (12 min): Model multiplying a whole number by a fraction with fraction strips. Lay out four sets of three fourths and combine them: 4 x 3/4 = 12/4 = 3 gallons each minute from four sections. Write the multiplication and the fraction-strip picture side by side. Then model a fraction times a fraction using a rectangle divided into fourths one way and halves the other: one half of three fourths shades three of the eight parts, so 1/2 x 3/4 = 3/8. Say plainly that the product is smaller because taking half of something leaves less than the whole.
Guided practice (12 min): In pairs, students work two problems with fraction strips on the table. First, six hose sections each putting out 3/4 gallon per minute, which comes to 6 x 3/4 = 18/4 = 4 1/2 gallons per minute. Second, two thirds of a half-gallon watering can, which comes to 2/3 x 1/2 = 2/6 = 1/3 gallon. As a formative check, ask pairs to signal thumbs up or thumbs down on the statement "multiplying always makes a bigger number." If more than five students signal thumbs up, return to the shaded rectangle before moving on.
Independent practice (11 min): Distribute the student handout and have students complete questions 1 through 5 alone, showing the multiplication for each. Circulate and look for students who add the fractions instead of multiplying, which shows up as an answer of 6 3/4 on question 1.
Closure and exit ticket (5 min): Students answer handout question 6 on an index card and turn it in. Read the cards before the next class and group students who wrote 3/4 gallon, the flow for one minute, or 4 3/4 gallons, since those answers point to a misread of the question or to adding instead of multiplying rather than a computation error.
Student Handout
The Pennythorn Elementary garden club waters six raised beds with soaker hoses. Show the multiplication for each question.
- One hose section puts out 3/4 gallon of water each minute. How much water do 6 sections put out in one minute?
- One hose section puts out 3/4 gallon each minute. How much water does it put out in 8 minutes?
- A short hose section puts out one half of 3/4 gallon each minute. How much water is that?
- Six hose sections together put out 4 1/2 gallons each minute. The club waters for 10 minutes. How many gallons do the six sections put out in all?
- The club uses 2/5 of a 20-gallon rain barrel on the tomato bed. How many gallons is that?
- One hose section puts out 3/4 gallon each minute. How much water does it put out in 4 minutes?
From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.
Answer Key
- Answer: 4 1/2 gallons. 6 x 3/4 = 18/4, and 18/4 = 4 2/4, which simplifies to 4 1/2 gallons.
- Answer: 6 gallons. 8 x 3/4 = 24/4 = 6 gallons.
- Answer: 3/8 gallon. 1/2 x 3/4 = 3/8 gallon, which is less than 3/4 because only half of that amount is counted.
- Answer: 45 gallons. 4 1/2 x 10 = 45 gallons, because 4 x 10 = 40 and 1/2 x 10 = 5, and 40 + 5 = 45.
- Answer: 8 gallons. 2/5 x 20 = 40/5 = 8 gallons.
- Answer: 3 gallons. 4 x 3/4 = 12/4 = 3 gallons.
Differentiation
Support
Provide fraction strips for every question and let students build each product before writing it. For question 1, give them six pre-cut three-fourths strips so the combining step is physical. Accept a drawing with a matching number sentence in place of written work while students are still building fluency.
Extension
Ask students to plan a watering that delivers exactly 30 gallons to the garden using the six sections at 4 1/2 gallons per minute, including any leftover fraction of a minute, and then explain how the club could adjust the plan if one section were shut off for repair.
ELL supports
Label a real soaker hose or a photograph of one with the words "hose," "section," "drip," and "per minute" in English and, where possible, in students' home languages. Provide a sentence frame for question 3: "One half of three fourths is ___ because ___."
Extensions
Have students measure how much water a classroom faucet releases in 15 seconds, write that amount as a fraction of a gallon, and then calculate the amount for a full minute and for five minutes. Ask them to compare that flow with a single soaker hose section and say which one would water a garden bed more gently.