Lesson plan Grade 5 Math
Sandy Bluff Well Samples: A Grade 5 Fraction Division Lesson
A 50-minute grade 5 lesson where students divide unit fractions by whole numbers and whole numbers by unit fractions using a fictional well's sampling routine.
Objectives
- Students will divide a unit fraction by a whole number to split a sample.
- Students will divide a whole number by a unit fraction to count equal portions.
Vocabulary
Key words: unit fraction, divide, portion, tracer
Teacher overview
Sandy Bluff is a fictional well field where workers measure out tracer dye before a groundwater tracing test, in which dye is added to one well and water samples from nearby wells are checked for the dye. Splitting a fraction of a gallon of dye into several jars is a natural setting for dividing a unit fraction by a whole number, and counting how many small scoops fill a container is a setting for dividing a whole number by a unit fraction. A common student error is multiplying when the problem calls for division, so the lesson keeps students tied to a drawing or a fraction strip for every problem.
Procedure
Hook (5 min): Hold up a half-gallon jug of colored water and ask how much would go into each jar if it were poured equally into 4 jars. Take a few guesses and write them on the board without saying which is correct.
Direct instruction (12 min): Show that 1/2 gallon shared among 4 jars is 1/2 divided by 4. Draw a half-gallon bar, cut it into 4 equal parts, and label each part 1/8. Then reverse the idea: draw 3 whole cups and cut each into thirds to show that 3 divided by 1/3 gives 9 one-third scoops. State the two patterns: dividing a unit fraction by a whole number makes smaller pieces, and dividing a whole number by a unit fraction counts many small pieces.
Guided practice (10 min): Work handout items 1 and 3 together, one of each type, using fraction strips so students can see the pieces. Pause after each to ask a check question.
Formative check (5 min): Ask every student to hold up fingers for the answer to "How many 1/2-liter bottles fill 4 liters?" Look for the class to show 8. If more than a few miss it, redraw the 4 whole liters cut into halves before moving on.
Independent practice (13 min): Students complete the remaining handout items on their own while you circulate. Encourage a drawing beside each answer.
Closure and exit ticket (5 min): Students answer one question on a card: "A worker splits 1/4 gallon of dye equally into 2 jars. How much goes in each jar?" Collect and scan for the answer 1/8 gallon before dismissal.
Student Handout
Solve each problem. Draw a picture or use a fraction strip to show your thinking.
- A well test uses 1/2 gallon of tracer dye poured equally into 4 jars. How much dye goes in each jar?
- A worker splits 1/3 cup of powder equally into 2 scoops. How much powder is in each scoop?
- How many 1/4-cup scoops can be filled from 3 cups of treatment powder?
- How many 1/2-liter bottles can be filled from 4 liters of water?
- A worker pours 1/4 gallon of dye equally into 3 jars. How much dye goes in each jar?
- Explain in one or two sentences why 3 divided by 1/4 gives an answer greater than 3.
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: 1/8 gallon. 1/2 divided by 4 = 1/8 gallon in each jar.
- Answer: 1/6 cup. 1/3 divided by 2 = 1/6 cup in each scoop.
- Answer: 12 scoops. 3 divided by 1/4 = 12 quarter-cup scoops.
- Answer: 8 bottles. 4 divided by 1/2 = 8 half-liter bottles.
- Answer: 1/12 gallon. 1/4 divided by 3 = 1/12 gallon in each jar.
- Answer: Dividing 3 by 1/4 gives more than 3 because you are counting how many small quarter-cup pieces fit in 3 whole cups, and many small pieces fit.
- Exit ticket answer: 1/8 gallon. 1/4 divided by 2 = 1/8 gallon in each jar.
Differentiation
Support
Provide pre-cut fraction strips for halves, thirds, and quarters so students can build each problem with their hands before writing the answer. Keep the guided example on display during independent work.
Extension
Ask students to write one problem of each type, one that divides a unit fraction by a whole number and one that divides a whole number by a unit fraction, then solve both and explain how the answers differ in size.
ELL supports
Pre-teach "portion," "scoop," "split," and "equally" with a demonstration of pouring water into jars. Provide sentence frames for item 6: "The answer is greater than 3 because ___."