Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
Measurement Topic
This standard is reported on the report card in these quarters as follows:
5th Grade Students Learning 5th Grade Standards
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Report Card Measurement Topic:Demonstrates understanding of multiplication and division of different number types.
4th Grade Students Learning 5th Grade Standards
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Report Card Measurement Topic:Demonstrates understanding of division.
Learning Targets (I can)
Explain division of a unit fraction by a whole number using physical models and diagrams.
Explain division of a whole number by a unit fraction using physical models and diagrams.
Divide a unit fraction by a whole number.
Divide a whole number by a unit fraction.
Create story contexts for problems involving division of a unit fraction by a whole number and a whole number by a unit fraction.
Solve problems involving division of a unit fraction by a whole number and a whole number by a unit fraction.
About the Math
Students may need a great deal of practice seeing the connection between the visual representation and the more abstract equations.
Progression of Standard within Grade 5
This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.
Progression Throughout Year
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Explain division of a unit fraction by a whole number using physical models and diagrams.
Explain division of a whole number by a unit fraction using physical models and diagrams.
Divide a unit fraction by a whole number.
Divide a whole number by a unit fraction.
Create story contexts for problems involving division of a unit fraction by a whole number and a whole number by a unit fraction.
Solve problems involving division of a unit fraction by a whole number and a whole number by a unit fraction.
These tasks can be used with small group or whole group instruction.
Begin the lesson by asking students to describe the two different types of division (partitive and quotative). Ask students to explain the meaning of the expression 24 ÷ 3. Students might share the following statements: "24 is being split evenly into 3 groups and I need to find out how many are in each group" or "I need to find out how many groups of 3 are in 24." Ask students to use their knowledge of division to explain the meaning of the expression 1÷ 1/2 using quotative division ("I am trying to find how many 1/2 pieces are in 1 whole"). Continue defining expressions from additional number strings (1÷ 1/3, 1÷ 1/4, 1÷ 1/6, 1÷ 1/8, 4 ÷ 1/2, 3 ÷ 1/3).
Students will participate in a discussion about a set of expressions in a number string. Present students with the expression 2 ÷ 1/2 and ask students to define the meaning of the expression (Determine how many 1/2 are in 2 wholes). The next expression in the number string is 1/2 ÷ 2. Ask students to predict if both expressions will have the same quotient. A short discussion of the commutative property and division should help students explain that the quotients will be different. Ask students to define the meaning of the expression and point out that partitive division should be used in this situation (If 1/2 is separated into 2 group, how many are in each group?) Continue defining expressions from additional number strings.
Use fraction manipulatives (fraction tiles, Cuisenaire rods, pattern blocks) and the recoding sheetLinks to an external site. to help students develop a solid understanding of whole number ÷ fraction and fraction ÷ whole number expressions. Encourage students to work in partners to show all different representations of a given expression.
What is the relationship between (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
Compare and contrast the following, using visual models/drawings: ⅕ ÷ 3 and 3 ÷ ⅕
How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
Use a visual model to show ⅖ ÷ 3 and 3 ÷ ⅖. Which quotient is larger and why does that result make sense?
Why does 5 divided by ⅕ result in a quotient greater than 5 and ⅕?
Maya is making cookies for her school bake sale. To make one batch of cookies she needs ¾ cup sugar. Her mom has 4 cups of sugar in the bin. How many full batches of cookies will Maya be able to make?
Everyday, Mark’s dog needs 1 ¾ cups of dry food and 2 ¼ cups of wet food. Mark picks up one bag of dry dog food that contains 16 cups and a large container of wet dog food that has contains 12 cups. How many days will Mark be able to feed his dog the specified diet?
SLIDE-BASED TASKS
These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first(often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.
These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.
These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.