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

Full Standard

Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

 

About the Math

This standard is critical for understanding the relationship between fractions and decimals. Denominators of 10 and 100 have obvious connections to decimals (tenths and hundredths). Understanding the fraction equivalents enables students to work with decimal equivalents. This understanding is the applied to comparing and computing with decimals.

 

The Illustrative Mathematics Project tasks Adding Tenths and Hundredths Links to an external site. and Fraction Equivalence Links to an external site. demonstrate the expectation of this standard. Essential vocabulary for this standard includes tenths, hundredths, sum, and addend. Visit the online dictionary Links to an external site., multilingual dictionary Links to an external site. for vocabulary support.

 

Learning Targets

• Write a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100.
• Represent addition of fractions with denominators of 10 and 100.
• Add two fractions with denominators 10 and 100.

 

 

 

 

Progression of Standard within Grade 4

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

Quarter 1	Quarter 2	Quarter 3	Quarter 4
		Write a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100. Represent addition of fractions with denominators of 10 and 100. Add two fractions with denominators 10 and 100.	continue if needed

 

 

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.

Grade 3	Grade 5
Understand unit fractions (3.NF.1) Explain and generate equivalant fractions and compare fractions by reasoning about their size (3.NF.3)	Understand the place value system (5.NBT.1)

 

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Preferred Tasks

These links provide ideas for lessons connected to this standard. They may support small group instruction or whole group collaborative investigations. They are intended to serve as a starting point for planning.

 

Add fractions with denominators of 10 and 100:

• Expanded Fractions and Decimals Links to an external site.(Illustrative Math)
• Dimes and Pennies Links to an external site. (Illustrative Math)
• Fraction Equivalence Links to an external site. (Illustrative Math)
• How Many Tenths and Hundredths? Links to an external site. (Illustrative Math)
• Adding Tenths and Hundredths Links to an external site. (Illustrative Math)

 

Lesson Seeds (Prompts for Rigor)

Rigorous mathematics instruction balances the teaching and learning of conceptual understanding, procedural understanding, and the application of mathematics standards. Below are prompts for applying rigor in your classroom. They may support small group instruction or whole group collaborative investigations. They are intended to serve as a starting point for planning. See the Increasing Rigor page for more information.

 

• How does your knowledge of multiples help you find equivalent fractions with denominators of 10 or 100?
• How can understanding 3/10 is equivalent to 30/100 help when adding and fractions? Give an example of how this can be used.
• How does your knowledge of place value help you prove that 4/10 + 5/100 = 45/100?
• Write a fraction addition number sentence where one addend has a denominator of 10 and the other addend has a denominator of 100 and the sum of 90/100. Is there another possibility?
• Do 6/10 and 60/100 occupy the same point on a number line? Justify why or why not.
• Look at these four items: 5/10 ½ 0.5 5/100. Write an argument for which one does not belong.

 

 

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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. 

 

Book Thumbnail	Book Title	Grade	Pages
	Teaching Student-Centered Mathematics	3-5
	Math Intervention: Building Number Power	3-5	162-165
	Brain-Compatible Activities for Mathematics	4-5	51-56, 63-65
	Math In Practice Teaching Fourth-Grade Math	4	Module 10

 

Additional Tasks and Lesson Seeds

These links provide ideas for lessons connected to this standard. They may support small group instruction or whole group collaborative investigations. They are intended to serve as a starting point for planning.

 

• Flag Fractions Download Flag Fractions
  (Georgia Dept. of Ed, pg. 43)***
• Dismissal Duty Download Dismissal Duty
  (Georgia Dept. of Ed, pg. 49)***
• Decimal Designs Download Decimal Designs
  (Georgia Dept. of Ed, pg. 33)***
• App for That Download App for That
  (Utah Core Academy lesson)
• Tile Download Tile
  (Utah Core Academy Lesson)

*** These lessons are all contained in the same file. ***

 

 

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Student-Facing Centers

These links provide online and print resources to engage students during independent or center time. These resources could also be used as lesson seeds.

 

• Equal to 1 Download Equal to 1
  (HCPSS-adapted print resource)
• Flats & Units: Making Decimals and Fractions Download Flats & Units: Making Decimals and Fractions
  (HCPSS-adapted print resource)
• Flats, Longs, & Units: Making Decimals and Fractions Download Flats, Longs, & Units: Making Decimals and Fractions
  (HCPSS-adapted print resource)
• Decimal Fraction Cards Download Decimal Fraction Cards
   (print resource)

 

Independent Practice

These resource sheets can be used for independent practice or homework. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

 

• Adding 10ths and 100ths Links to an external site.

 

 

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Learning Targets

• Write a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100.
• Represent addition of fractions with denominators of 10 and 100.
• Add two fractions with denominators 10 and 100.

 

Learning targets identify what students should be able to do. The resources below can be used to measure student understanding of the standard. The recording sheet can be used to collect data. The rubric can be applied to any task.  Select the preview icon to preview the task before downloading.

 

 Recording Sheet Download Recording Sheet

(docx)

 Rubric Download Rubric

(docx)

 

Assessment Tasks

These tasks align with the learning targets for the standard. They can be combined with other tasks for extended assessment opportunities. Teachers/students are not expected to complete all these tasks.

 

• Reason About Models of Fractions with Denominators of 10 and 100 Links to an external site.
• Addition of Fractions with Denominators of 10 and 100 Links to an external site.
• Addition of Fractions with Denominators of 10 and 100_2 Links to an external site.
• Addition of Fractions with Denominators of 10 and 100_3 Links to an external site.
• Reason About Addition of Fractions with Denominators of 10 and 100 Links to an external site.

 

 

PARCC Released Items

These items are PARCC released items. They can be used for assessment or instruction. See notes at the bottom of each slide for more information.

 

• PARCC Task 1 Download PARCC Task 1

 

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