4.NF.3 - About the Math, Learning Targets, and Rigor

Grade 4 Fractions

4.NF.3

Full Standard

Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

  1. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
  2. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions (e.g., by using a visual fraction model). Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
  3. Add and subtract mixed numbers with like denominators (e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction).
  4. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators (e.g., by using visual fraction models and equations to represent the problem).

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 addition and subtraction of whole numbers and fractions. (A, B, and C part of the standard)

Report Card Measurement Topic: Demonstrates understanding of patterns, expressions, equations, and algebraic thinking. (D part of the standard)

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

 

 

Report Card Measurement Topic: Demonstrates understanding of addition and subtraction. (A, B, and C part of the standard)

Report Card Measurement Topic: Solves one and two-step word problems with any operation.  (D part of the standard)

 

Learning Targets

  • Compose and decompose a fraction (i.e. 7/12 = 4/12 + 1/12 + 1/12 + 1/12).
  • Describe that adding and subtracting of fractions must refer to the same size whole and having like denominators.
  • Represent addition of fractions with varied models (including a number line).
  • Represent subtraction of fractions with varied models (including a number line).
  • Represent addition of mixed numbers with varied models.
  • Represent subtraction of mixed numbers with varied models. 
  • Add and subtract fractions and mixed numbers with varied strategies.
  • Solve word problems with adding and subtracting fractions and mixed numbers.

 

About the Math

Addition and subtraction of fractions with like denominators can be solved using an algorithm of adding or subtracting the numerators and keeping the same denominator. However, prior to this, students need instruction on the conceptual understanding of adding and subtracting fractions and what a reasonable answer looks like. Questions such as "will the answer when you add 7/8 + 3/8 be more or less than a whole and why?" should be part of instruction. Concrete materials should be used to introduce addition and subtraction prior to moving to the algorithm.

  • Compose and decompose a fraction (i.e. 7/12 = 4/12 + 1/12 + 1/12 + 1/12).

Students need to see that a fraction can be decomposed just like whole numbers. There are many different ways to decompose a fraction. Understanding this helps students see the value of fractions and enhances their fraction sense. 7/10 = 1/10 + 1/10 +1/10 + 1/10 +1/10 + 1/10 + 1/10 or 3/10 + 3/10 + 1/10 or 5/10 + 2/10 or 4/10 + 2/10 + 1/10.

  • Describe that adding and subtracting of fractions must refer to the same size whole and having like denominators.

When adding or subtracting fractions, the values must refer to the same-size whole with the same number of partitions. This is also thought of as common denominators. In fourth grade, students only work with addition and subtraction of fractions with like denominators. 

  • Represent addition of fractions with varied models (including a number line).
  • Represent subtraction of fractions with varied models (including a number line).

Addition and subtraction of fractions can be represented by a variety of models. Students should also represent addition and subtraction of fractions on a number line. Students should justify their sums and differences with models and connect that work to their equations. In time, students can work solely with the symbols/equations.

  • Represent addition of mixed numbers with varied models.
  • Represent subtraction of mixed numbers with varied models. 
  • Add and subtract fractions and mixed numbers with varied strategies.

A mixed number is a whole number and a fraction. Students need to see that 3 ¼ is the same as 3 + ¼. This can be connected to the previous standard of decomposing fractions. This understanding can be reinforced through the representations students use to add and subtract mixed numbers. Like other understandings, students should work with varied models including pattern blocks, Cuisenaire rods, and fraction tiles. 

  • Solve word problems with adding and subtracting fractions and mixed numbers.

Students should represent problems with diagrams or drawings before attempting to solve. Bar diagrams or part-to-whole models are good for reinforcing this understanding. Students can then use tools to represent the computation with fractions as needed. Students should not rely on key words for finding the solution to these problems. 

Essential vocabulary for this standard includes unit fraction, fraction, numerator, and denominator

 

 

 

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


 

  • Compose and decompose a fraction (i.e. 7/12 = 4/12 + 1/12 + 1/12 + 1/12).
  • Describe that adding and subtracting of fractions must refer to the same size whole and having like denominators.
  • Represent addition of fractions with varied models (including a number line).
  • Represent subtraction of fractions with varied models (including a number line).
  • Represent addition of mixed numbers with varied models.
  • Represent subtraction of mixed numbers with varied models. 
  • Add fractions and mixed numbers with varied strategies.
  • Solve word problems with adding and subtracting fractions and mixed numbers.
  • Describe that adding and subtracting of fractions must refer to the same size whole and having like denominators.
  • Represent addition and subtraction of fractions with varied models (including a number line).
  • Represent addition and subtraction of mixed numbers with varied models.
  • Add and subtract fractions and mixed numbers with varied strategies.
  • Solve word problems with adding and subtracting fractions and mixed numbers.

 

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
  • Understand unit fractions (3.NF.1)
  • Understand fractions as a number and represent fractions on a number line ( 3.NF.2
  • Add/subtract fractions with unlike denominators (5.NF.1

 

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