5.NF.7 - About the Math, Learning Targets, and Rigor

Full Standard

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

1. 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.
2. 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.
3. 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?

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 4 G/T

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

TASKS

These tasks can be used with small group or whole group instruction.

• 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.

Additional Tasks 

  These links provide instructional ideas connected to this standard. 

• How many servings of oatmeal? Links to an external site. (Illustrative Mathematics)
• Dividing by One-Half Links to an external site.  (Links to an external site.) (Illustrative Mathematics)
• Banana Pudding Links to an external site. (Illustrative Mathematics)
• Origami Stars Links to an external site. (Illustrative Mathematics)
• How many marbles? Links to an external site.  (Links to an external site.)  (Illustrative Mathematics)
• Standing in Line Links to an external site. (Illustrative Mathematics)
• Painting a room Links to an external site.  (Links to an external site.) (Illustrative Mathematics)
• Salad Dressing Links to an external site.  (Links to an external site.) (Illustrative Mathematics)
• Dividing With Unit Fractions Links to an external site. (Georgia Department of Education, pg. 133-138)
• Adjusting Recipes Links to an external site. (Georgia Department of Education, pg. 139-146)
• Designing a Textbook Download Designing a Textbook
  (HCPSS UDL lesson and resources)
• Planning a Picnic Download Planning a Picnic (HCPSS UDL lesson and resources)

Tasks From Print Resources

  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. 

Print Resources

Book Thumbnail	Book Title	Grade	Pages
	Teaching Student-Centered Mathematics	3-5	Sharing Camels, Activity 5.6, Page 144
	Hands-On Standards, Common Core Fractions	5	56-62 Lessons 6 and 7
	Hands-On Standards	5-6	50 "Lesson 16 Divide W/ Fractions"
	Read It, Draw It, Solve It	4-5	146

Learning Targets

• 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.

Learning targets identify what students should be able to do.  This rubric can be applied to tasks and observations for assessment and/or grading. 

Rubric for Tasks Links to an external site.