5.NF.2 - About the Math, Learning Targets, and Rigor

Grade 4 G/T Fractions

5.NF.2

About the Math

Full Standard

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators (e.g., by using visual fraction models or equations to represent the problem). Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

 

Learning Targets (I can)

  • Represent problems using physical models, drawings, and equations.
  • Explain why addition or subtraction is needed to solve a problem.
  • Add and subtract to solve word problems.
  • Write an equation to solve a word problem.
  • Connect written equations to components of the word problem.
  • Estimate to determine the reasonableness of a solution.

 

About the Math 

  • Represent problems using physical models, drawings, and equations.

As students represent problems with pictures, models, and/or equations they must connect them back to the problem. Using bar diagrams to make sense of a problem is worthwhile. However, other representations are needed to make sense of the computation.

  • Explain why addition or subtraction is needed to solve a problem.

Students should work with addition and subtraction problems of all problem types including result unknown, change unknown, and start unknown. Students should explain which operation is needed to solve the problem and why. Students should be able to connect the problem to their equation.

  • Add and subtract to solve word problems.

Students use their understanding of addition and subtraction of fractions to solve problems. It is important to note that students do not have to show procedural understanding of addition and subtraction of fractions to work with problems. Instead, problems should be used to introduce and reinforce these concepts as they provide a context for understanding.

  • Write an equation to solve a word problem.
  • Connect written equations to components of the word problem.

As noted throughout elementary mathematics, students must be able to write equations to represent problems. Students should write equations that align to the problem and the problem type. 

  • Estimate to determine the reasonableness of a solution.

Estimating results of computations with whole numbers or fractions cannot be overemphasized. It develops understanding and the ability to determine if solutions to problems and calculations are reasonable. Students should estimate sums and differences of fractions using benchmarks and other strategies. For example, students should be able to explain that 3/4 + 2/3 is more than one whole because both fractions are more than one-half.

 

 

 

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 Throughout Year
Quarter 1 Quarter 2 Quarter 3 Quarter 4
  • Represent problems using physical models, drawings, and equations.
  • Explain why addition or subtraction is needed to solve a problem.
  • Add and subtract to solve word problems.
  • Write an equation to solve a word problem.
  • Connect written equations to components of the word problem.
  • Estimate to determine the reasonableness of a solution.

 

    

 

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
  • Equivalent fractions (4.NF.1)
  • Decomposing fractions/adding and subtracting fractions (4.NF.3)
  • Recognizing statistical questions (6.SP.1) 
  • Distribution of data (6.SP.2)
  • Display data in plots on number lines, dot plots, histograms, and box plots (6.SP.4)
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Instructional Tasks

TASKS

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

  • Write a word problem that can be solved with ⅔ - ⅗?
  • Is the sum of 4/5 and 7/8 under or over one? Explain how you know.
  • There is ⅘ of the pepperoni pizza left over, and ¾ of the Hawaiian pizza left over. Sydney says that there are 1 ½ total pizzas left. Do you agree? Explain why or why not.
  • Write a subtraction problem that has the same difference as ¾ - ⅛.
  • Why doesn't 2/6 - 1/4 = 1/2?
  • Why can you use mental computation to solve 5 - 3 1/2?
  • Is 3 ¾ + 2 ⅙ greater or less than 6? Explain.

 

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.

Module 3 • Adding and Subtracting Fractions

Solve Problems that Add and Subtract Fractions with Unlike Denominators (no mixed numbers):

Solve Problems that Add and Subtract Mixed Numbers with Unlike Denominators:

 

 

Additional Tasks 

These links provide instructional ideas connected to this standard. 

 

CC Indicates colleague created HCPSS instructional tasks. These tasks are provided in Google slides. When selected, a copy of the file is added to your drive for classroom use.

 

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

 

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
Ordering Unit Fractions, Activity 5.10, Page 146
Choose, Explain Test, Activity 5.11, Page 148
Line 'Em Up, Activity 5.12, Page 148 

Hands-On Standards, Common Core Fractions

5 28, Lesson 5
Read It, Draw It, Solve It 4-5 67, 141

 

 

 

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Independent Work

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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Assessment

Learning Targets

rubric

  • Represent problems using physical models, drawings, and equations.
  • Explain why addition or subtraction is needed to solve a problem.
  • Add and subtract to solve word problems.
  • Write an equation to solve a word problem.
  • Connect written equations to components of the word problem.
  • Estimate to determine the reasonableness of a solution.

 

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

 

 

 

 

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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.