5.NF.4. - About the Math, Learning Targets, and Rigor

Full Standard

Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

1. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
2. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

 

Learning Targets (I can)

• Represent multiplication of a fraction by a whole number.
• Represent multiplication of a fraction by a fraction.
• Estimate the product of a fraction by a whole number.
• Estimate the product of a fraction by a fraction.
• Multiply a fraction by a whole number.
• Multiply a fraction by a fraction.
• Create story contexts for problems involving multiplication of fractions and whole numbers or multiplication of two fractions.
• Multiply fractional side lengths to find areas of rectangles.

 

About the Math

• Represent multiplication of a fraction by a whole number.
• Represent multiplication of a fraction by a fraction.

Multiplication with fractions should feature diverse representations. Area models are good for making meaning of the concept. But students should also work with other representations. Fractions of a set may be especially useful for a 

• Estimate the product of a fraction by a whole number.
• Estimate the product of a fraction by a fraction.

Estimating products helps us determine if our answers are reasonable. Students should be consistently asked to estimate their products before finding the actual product. After doing so, they should be asked to compare their estimates to the actuals.

• Multiply a fraction by a whole number.
• Multiply a fraction by a fraction.

Students should connect the equations/symbols to their representations. As students show understanding, they should begin to work with associated procedures. Students who use procedures to multiply fractions must be able to explain what is happening and what the product means in relation to the factors. 

• Create story contexts for problems involving multiplication of fractions and whole numbers or multiplication of two fractions.
• Multiply fractional side lengths to find areas of rectangles.

Connecting area to the multiplication of fractions is very natural. It may be the best place to introduce fractions times fractions. 

 

 

 Math In Minutes:  The video below highlights multiplying whole numbers with fractions.

  The Illustrative Mathematics Project task below demonstrates expectation for this standard.

• Connor and Makayla Discuss Multiplication Links to an external site.
• Folding Strips of Paper Links to an external site.

 

 

 

 

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
	Represent multiplication of a fraction by a whole number. Represent multiplication of a fraction by a fraction. Estimate the product of a fraction by a whole number. Estimate the product of a fraction by a fraction. Multiply a fraction by a whole number. Multiply a fraction by a fraction. Create story contexts for problems involving multiplication of fractions and whole numbers or multiplication of two fractions. Multiply fractional side lengths to find areas of rectangles.

 

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.

Progression Across Grades

Grade 4	Grade 6
Multiply a fraction by a whole number (4.NF.4)	Solve real-world problems by solving equations (6.EE.7) Find the area of triangles and special quadrilaterals (6.G.1)

 

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TASKS

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

• Provide students with colored tiles and prompts on the Colored Tiles Links to an external site. slides. Allow students to work though the prompt before providing direct instruction.
• Use fraction manipulatives (fraction tiles, Cuisenaire rods, pattern blocks) and the recoding sheet Links to an external site. to help students develop a solid understanding of whole number × fraction, fraction × whole number, and fraction × fraction. Encourage students to work in partners to show all different representations of a given expression.
• Use the number line to model 6 x ⅔ (6 groups of ⅔)and then use a different number line to model ⅔ x 6 (⅔ of 6). How are these similar and different?
• Draw a model to show ⅔ x ⅗.
• Draw a model to show the area of a rectangle that measures 2 ¼ inches x 1 ½ inches.
• What are two fractions with a product close to ⅗?
• What are two fractions with a product a bit less than ½?
• What are two fractions with a product close to one whole?

 

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. 

• Connor and Makayla Discuss Multiplication Links to an external site.  (Links to an external site. (Illustrative Mathematics)
• Cornbread Fundraiser Links to an external site. (Illustrative Mathematics) 
• Painting a Wall (Links to an external site.)  Links to an external site. (Illustrative Mathematics)
• Folding Strips of Paper (Links to an external site.) Links to an external site. (Illustrative Mathematics)
• Cross Country Training Links to an external site. (Illustrative Mathematics)
• Distance Around a Track or Mrs. Gray's HW Assignment Links to an external site. (Illustrative Mathematics) 
• Bathroom Tiles Links to an external site. (Illustrative Mathematics) 
• Find Areas with Fractional Lengths Links to an external site.(MSDE Lesson)
• The Hiking Trail Links to an external site. (Georgia Department of Education, pg. 48-52)
• Reasoning With Fractions Links to an external site. (Georgia Department of Education, pg. 115-122)
• Comparing MP3 Players Links to an external site. (Georgia Department of Education, pg. 95-106)
• Measuring For a Pillow Links to an external site. (Georgia Department of Education, pg. 107-114)
• Getting a Feel For Fractions Download Getting a Feel For Fractions (HCPSS UDL lesson and resources)
• Multiplication of Fractions Links to an external site. (MSDE Lesson)

 

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	6-8	Water, Walking, and Wheels, Activity 8.18, Page 130 Quilting Pieces, Activity 8.19, Page 132 Playground Problem, Activity 8.20, Page 132
	Hands-On Standards, Common Core Fractions	5	38-42 "Lessons 2 and 3"
	Fundamentals	5	48 "Fraction Target"
	Hands-On Standards	5-6	46 "Lesson 14"
	Read It, Draw It, Solve It	4-5	146
	Math In Practice Teaching Fifth-Grade Math	5	Module 9

 

 

 

 

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Centers

  These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

 

• Fraction Feast Download Fraction Feast
  (HCPSS-adapted print resource)
• Using Rectangles to Multiply Fractions Download Using Rectangles to Multiply Fractions
  (HCPSS-adapted print resource
• Multiplying a Fraction by a Whole Number with Problems Download Multiplying a Fraction by a Whole Number with Problems
• Multiplying Fractions by Whole Numbers - Template Download Multiplying Fractions by Whole Numbers - Template

 

 

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

  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.

• Multiply Fractions by Whole Numbers Links to an external site.
• Multiply Whole Numbers or Fractions by Fractions Links to an external site.
• Multiply Fractions by Fractions no mixed a Links to an external site.
• Multiply Fractions by Fractions no mixed b Links to an external site.
• Multiply Fractions by Fractions b Links to an external site.
• Multiply Fractions by Fractions c Links to an external site.
• Whole x Fraction: Represent as a Visual Model and a Story Problem Links to an external site.
• Fraction x Fraction: Solve and Represent as a Story Problem A Links to an external site.
• Fraction x Fraction: Solve and Represent as a Story Problem B Links to an external site.
• Fraction x Fraction: Solve and Represent as a Visual Model Links to an external site.
• Fraction x Fraction: Solve and Represent as a Visual Model_2 Links to an external site.
• Mixed x Mixed: Reasoning About Rectangular Areas Links to an external site.

 

 

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Learning Targets

• Represent multiplication of a fraction by a whole number.
• Represent multiplication of a fraction by a fraction.
• Estimate the product of a fraction by a whole number.
• Estimate the product of a fraction by a fraction.
• Multiply a fraction by a whole number.
• Multiply a fraction by a fraction.
• Create story contexts for problems involving multiplication of fractions and whole numbers or multiplication of two fractions.
• Multiply fractional side lengths to find areas of rectangles.

 

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.

 

 

 

 

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