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.

Measurement Topic

This standard is reported on the report card in these quarters as follows:

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.

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.

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.

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.

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. 

• Using the tenth and hundredth square from the 10 by 10 grid resources on Canvas, students should explore fractions with denominators of 10 as equivalent to fractions with denominators of 100. Begin by having students shade in 4/10 and 40/100 encourage students to explain what they notice about both representations. Continue the activity with fractions such as 8/10, 8/100, and 80/100.
• 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

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. 

• 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)
• 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. ***

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
	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

Centers

  These print resources can be used 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/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.

• Equivalent Fractions with Denominators of 10 and 100 Links to an external site.
• Add Fractions with Denominators of 10 and 100 Links to an external site.

• 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.

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. This rubric can be applied to tasks and observations for assessment and/or grading. 

Rubric for Tasks Links to an external site.

Visit the SBIR (Standards Based Instruction and Reporting) tab in Course Essentials for more information and clarification. There you will find the measurement topic crosswalk, report card comments, links to professional learning/resources and guidance.