4.NF.1 - About the Math, Learning Targets, and Rigor

Grade 4 Fractions

4.NF.1

Full Standard

Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Note: Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

 

Measurement Topic

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

4th Grade Students Learning 4th Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

 

 

Report Card Measurement Topic: Demonstrates understanding of number, fraction, and decimal concepts.

 
3rd Grade Students Learning 4th Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

 

 

Report Card Measurement Topic: Demonstrates understanding of number and fraction concepts.

 

Learning Targets

  • Represent equivalent fractions with color tiles, pattern blocks, Cuisenaire rods, fraction bars, fraction circles, and number lines. 
  • Explain why fractions are equivalent.
  • Generate equivalent fractions.
  • Recognize equivalence to 1/2 quickly.

 

About the Math

  • Represent equivalent fractions with color tiles, pattern blocks, Cuisenaire rods, fraction bars, fraction circles, and number lines. 
  • Explain why fractions are equivalent.

Understanding equivalent fractions is an important concept when comparing fractions, ordering fractions, and adding and subtracting fractions. Equivalent fractions are fractions that represent equal value. They are numerals that name the same fractional number. When we say that fractions are equivalent there is an underlying assumption that the wholes are the same size. Students need to understand this concept. A focus question should be “Are the wholes the same size?” Students should explore, using fraction strips, fraction squares or circles, pattern blocks, and number lines to discover which fractions are equivalent before moving to a procedure to find equivalent fractions. When students discover the numerical process of multiplying (or dividing) the numerator and denominator by the same number, they should understand how that connects to the identity property of multiplication and division. "Simplify" is not a term or concept taught in elementary mathematics. "Reducing" should not be used as it implies something getting smaller, which is not the case with equivalent fractions as they represent the same value. 

  • Generate equivalent fractions.

Understanding why two or more fractions are equivalent is followed by asking students to generate equivalent fractions. Students should generate and justify why their generations are equivalent. Students should use representations in their justifications. As students show understanding of the concept, they can connect it to a procedure for finding or generating equivalent fractions. Students who use a procedure must be able to explain why the procedure works.

  • Recognize equivalence to 1/2 quickly.

Fluency extends beyond basic facts. Over time, students should begin to develop fluency with some fraction concepts. Recognizing fractions equivalent to 1/2 is a worthwhile fluency pursuit. Students should work within the denominators included in the grade-level standards but can be extended to other fractions as appropriate. 

 Students should understand essential vocabulary for this standard includes equivalent and equivalent fractions.


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 Throughout Year
Quarter 1 Quarter 2 Quarter 3 Quarter 4
  • Represent equivalent fractions with color tiles, pattern blocks, Cuisenaire rods, fraction bars, fraction circles, and number lines. 
  • Explain why fractions are equivalent.
  • Generate equivalent fractions.
  • Recognize equivalence to 1/2 quickly.
  • Represent equivalent fractions with color tiles, pattern blocks, Cuisenaire rods, fraction bars, fraction circles, and number lines. 
  • Explain why fractions are equivalent.
  • Generate equivalent fractions.
  • Recognize equivalence to 1/2 quickly.
 

 

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 3 Grade 5
  • Explain and generate equivalent fractions and compare fractions by reasoning about their size (3.NF.3)
  • Add/subtract fractions with unlike denominators (5.NF.1)
  • Interpret multiplication as scaling (resizing) (5.NF.5) 

 

 

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TASKS

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

  • Distribute fraction manipulatives to each student. You can use circles, rectangles or square materials. Explain that two students each have a pizza that is the same size. One student cuts their pizza in 4 equal pieces and the other students cuts their pizza into 8 equal pieces. Ask students to use the materials to show the two pizzas. Now explain that each of the students ate half of their pizza? What pieces in their model could show this? What is the fraction that represents the eaten pizza? Have a discussion about equivalent fractions and establish that 1/2=2/4=4/8. This can be difficult because students see different numbers, but yet the different fractions represent the same value. Repeat with different equivalencies.
  • Distribute fraction manipulatives to each student. Ask students to work in pairs to find all ways to show 2/3. Discuss all found solutions, including justification of why 4/6 is the same as 2/3, etc. Record equivalent fractions on the board/chart paper as they are discussed. Repeat with other fractions. In looking at the list of equivalent fractions, ask students discuss any patterns they see. Students may notice the "multiplying the numerator and denominator by the same" type thing. This opens the door to discuss you are actually multiplying by 1 as 2/2, 3/3, etc are equivalent to one. This is the application of the Identity of Multiplication Property, when multiplying by 1, we get the same value. So, 2/3 multiplied by 2/2 results in 4/6, which makes sense because 2/3=4/6 and represent the same value.
  • Use Cuisenaire Rods to find equivalent fractions on a number line. Find the Beyond Pizzas & Pies book in your building and see activity page numbers below on this tab.
  • What are 3 fractions equivalent to 3/4?
  • How can 4/5 and 8/10 be equivalent if the numerator and denominator in each is different?
  • Represent the value of 1 ½ in 3 different ways.
  • Andy, Lee, and Val each ate ½ of pizza. The pizzas were the same size, but Andy ate one piece, Lee ate three slices, and Val ate four slices. How is this possible? (Andy cut his in halves, Lee cut his in sixths, and Val cut her pizza into eighths.)
  • Show how 5/15 is equivalent to 1/3 rather than 1/5.
  • Write the statement 10/12 is twice as large as 5/6 on the board. Ask students if they agree or disagree with the statement. Can they use a model to defend their answer?
  • Why is 3/5 the same as 6/10 when the two fractions have different numbers?

 

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. [NOTE: NCTM membership required for access to Illuminations lessons.] 

 

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

Mixed-Number Names, Activity 5.4, Page 140
Calculator Fraction Counting, Activity 5.5, Page 141
Zero, One-Half, or One, Activity 5.7, Page 145
Close Fractions, Activity 5.8, Page 145
About How Much?, Activity 5.9, Page 145
Different Fillers, Activity 5.14, Page 152
Dot Paper Equivalencies, Activity 5.15, Page 152
Group the Counters, Find the Numbers, Activity 5.16, Page 153
Divide and Divide Again, Activity 5.17, Page 154
Missing-Number Equivalencies, Activity 5.18, Page 155
Slicing Squares, Activity 5.19, Page 155
Hands-On Standards, Common Core 4 10-40 (Lessons 1 and 2)

Beyond Pizzas and Pies  

Activity: Connecting Cuisenaire Measurements to the Number Line, pg 56-58

Activity: Equivalent Expression Matchup, pg 59-61
Hands-On Standards 3-4 52-53 (Mixed Numbers)

50-51 (Comparing and Ordering Fractions)
Nimble With Numbers 4-5 108
Math Intervention: Building Number Power 3-5 153-158

166-172
NumberSense

4-6

 59-61, 92-93, 99-101

20 Thinking Questions for Pattern Blocks

 

 3-6 72
Brain-Compatible Activities for Mathematics  4-5 47-50

Super Source Color Tiles

Super Source, Snap Cubes

Super Source: Cuisenaire Rods

3-4

3-4

3-4

46

62

26
Fractions with Pattern Blocks   72

Math In Practice

Teaching Fourth-Grade Math

 4 Module 7

 

 

 

 

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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.

 

 

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.

 

 

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Learning Targets

rubric

  • Represent equivalent fractions with color tiles, pattern blocks, Cuisenaire rods, fraction bars, fraction circles, and number lines. 
  • Explain why fractions are equivalent.
  • Generate equivalent fractions.
  • Recognize equivalence to 1/2 quickly.

 

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

 

 

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.

 

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 This course content is offered under a CC Attribution Non-Commercial Share Alike Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.