Author:
Mark Freed
Subject:
Mathematics
Material Type:
Teaching/Learning Strategy
Level:
Upper Primary
Tags:
License:
Creative Commons Attribution
Language:
English

Education Standards

OREGON MATH STANDARDS (2021): [4.NF]

OREGON MATH STANDARDS (2021): [4.NF]

Overview

The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards. 

Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.

2021 Oregon Math Guidance: 4.NF.A.1

ODE and Oregon Math Project Logo

Cluster: 4.NF.A - Extend understanding of fraction equivalence and ordering.

STANDARD: 4.NF.A.1

 Standards Statement (2021):

Use visual fraction representations to recognize, generate, and explain relationships between equivalent fractions.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

3.NF.A.3

4.NF.A.2, 4.NF.B.3, 4.NF.C.5, 5.NF.A.1, 5.NF.B.5

4.OA.A.2

4.NF.A.1

4.NF.A Crosswalk

 Standards Guidance:

Clarifications

  • Students should be able to describe how the number and size of the parts differ even though the fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
  • Students should be able to explain fraction equivalence as a multiplicative relationship, not additive.
  • Students should be able to explain why 𝑎𝑏 = (𝑛 × 𝑎)(𝑛 ×𝑏) is a true mathematical statement, whereas 𝑎𝑏 = (𝑛+𝑎)(𝑛+𝑏) is NOT a true mathematical statement.

Boundaries

  • Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.
  • This expectation includes fractions greater than 1.
  • Fractions should be limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Teaching Strategies 

  • Concrete materials may include fraction circles, fraction strips, pattern blocks.
  • Students may represent their problems and explain their reasoning with drawing and number lines.
  • Students should be able to discover, explain, and generalize the relationship between the identity property of multiplication and equivalent fractions (i.e., paper folding activities, number lines, etc.).

Progressions

  • Students can use area models and number line diagrams to reason about equivalence. They see that the numerical process of multiplying the numerator and demonimator of a fraction by the same number, n, corresponds physically to partitioning each unit fraction piece into n smaller equal pieces. The whole is then partitioned into n times as many pieces, and there are ntimes as many smaller unit fraction pieces as in the original fraction. (Please reference page 6 in the Progression document).

Examples

2021 Oregon Math Guidance: 4.NF.A.2

 ODE and Oregon Math Project Logo

Cluster: 4.NF.A - Extend understanding of fraction equivalence and ordering.

STANDARD: 4.NF.A.2

 Standards Statement (2021):

Compare two fractions with different numerators and/or different denominators, record the results with the symbols >, =, or <, and justify the conclusions.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

4.NF.A.1

4.NF.C.7, 5.NF.A.2

4.OA.A.2

4.NF.A.2

4.NF.A Crosswalk

 Standards Guidance:

Clarifications

  • Students should be able to recognize that comparisons are valid only when the two fractions refer to the same whole.
  • Students should record the results of comparisons with symbols >, =, or <, and justify the conclusions.

Boundaries

  • Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.
  •  Students should be given fractions with common numerators to compare.

Teaching Strategies

  • MP3 - Justify using conceptual and procedural strategies. Conceptual strategies should include using visual models; comparing benchmark fractions such as 0, ½, 1; and attending to the size of the piece for the like numerators or number of pieces for like denominators. Procedural strategies should include finding a common denominator to directly compare the number of pieces.

Progressions

  • Grade 4 students use their understanding of equivalent fractions to compare fractions with different numerators and different denominators. For example, to compare 5/8 and 7/12 [students] rewrite both fractions as 60/96 (= 12x5/12x8) and 56/96 (= 7x8/12x8). Because 60/96 and 56/96 have the same denominator, students can compare them using Grade 3 methods and see that 56/96 is smaller, so 7/12 < 5/8. (Please reference page 6  in the Progression document)

Examples

  • Jamie and Kendra each had the same grid to color using any pattern they wished. Jamie colored 23 of the yellow grid pattern and Kendra colored 25 of the green grid pattern. Who colored more?

  • Jamie colored more because thirds are bigger than fifths, so 23 thirds is more than 25 fifths. 

2021 Oregon Math Guidance: 4.NF.B.3

 ODE and Oregon Math Project Logo

Cluster: 4.NF.B - Build fractions from unit fractions.

STANDARD: 4.NF.B.3

 Standards Statement (2021):

Understand a fraction (a/b) as the sum (a) of fractions of the same denominator (1/b).  Solve problems in authentic contexts involving addition and subtraction of fractions referring to the same whole and having like denominators.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

3.NF.A.1, 3.NF.A.2, 4.NF.A.1

4.NF.C.5, 5.NF.A.1, 5.NF.B.3

2.OA.A.1, 4.GM.B.5

4.NF.B.3

4.NF.B Crosswalk

 Standards Guidance:

Clarifications

  • Students should be able to break apart (decompose) whole numbers and fractions as the sum of unit fractions.
  • Break apart (decompose) a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation.

Content Boundaries

  • Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100. 
  • Extend understanding addition and subtraction to include fractions.
  • Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
  • Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation.
  • Add and subtract mixed numbers with like denominators.

Teaching Strategies 

  • Students should be able to add and subtract fractions and mixed numbers with the same (like) denominators by joining and separating parts referring to the same whole while solving contextual, mathematical problems.
  • Tools include fraction concrete materials, such as Cuisenaire rods, drawings, and number lines.
  • Students should be flexible in their choice of strategy when subtracting fractions. Reasoning about the sizes of the fractions and their relationships is the expectation here rather than memorizing regrouping procedures.
  • Students can justify their work using a visual fraction representation.

Examples

  • MP2 - Decompose and recompose 3/8 as 1/8 + 1/8 + 1/8 or 1/8 + 2/8 and 2 1/8 as 1 + 1 + 1/8 or 8/8 + 8/8 + 1/8.
  • MP4 - Use visual fraction models and equations to represent problems.
  • MP7 - Replace mixed numbers with equivalent fractions and/or use properties of operations and the relationship between addition and subtraction to solve problems.
  • Alex has a whole pizza. How can it be cut so that it can be shared with (4, 6, 8, 12) people? What fraction of the whole pizza will each person get?
  • Express 1 in the form 1 = 44 (1 whole is equal to four fourths 14+ 14+ 14+ 14= 44 = 1) recognize that additional wholes cut into fourths can also be written as the sum of
  • Locate 44 and 1 at the same point of a number line diagram.

  • A piece of ribbon was cut into eighths for a classroom art project. Three pieces were left at the end of the day. Show a mathematical representation of the ribbon that is left.
    • Possible student response: 38 = 18 + 18 + 18 ; 38 = 18 + 28

  • Three pans of brownies were cut into eighths to sell at a school function. 78 of one pan were sold. How many eighths are left to sell? Show a mathematical representation of the ribbon that is left.
    • Possible student response: 2 18 = 1 + 1 + 18 = 88 + 88 + 18

Example (4.4.6)

  • Luisa needs to know how much bigger her 214 inch piece of cardstock is than her 134 inch piece of cardstock in order to finish her project. o Possible student response: The 214 inch piece is 24 inch bigger than the 134 inch piece.

2021 Oregon Math Guidance: 4.NF.B.4

 ODE and Oregon Math Project Logo

Cluster: 4.NF.B - Build fractions from unit fractions.

STANDARD: 4.NF.B.4

 Standards Statement (2021):

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.  Represent and solve problems in authentic contexts involving multiplication of a fraction by a whole number.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

3.NF.A.1

5.NF.B.3, 5.NF.B.4, 5.NF.B.7

3.OA.A.3, 4.OA.A.2, 4.GM.B.5

4.NF.B.4

4.NF.B Crosswalk

 Standards Guidance:

Clarifications

  • Extend understanding multiplication to include fractions.
    • Understand a fraction a/b as a multiple of 1/b.
    • Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.

Boundaries

  • Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Examples

2021 Oregon Math Guidance: 4.NF.C.5

 ODE and Oregon Math Project Logo

Cluster: 4.NF.C - Understand decimal notation for fractions, and compare decimal fractions.

STANDARD: 4.NF.C.5

 Standards Statement (2021):

Demonstrate and explain the concept of equivalent fractions with denominators of 10 and 100, using concrete materials and visual models. Add two fractions with denominators of 10 and 100.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

4.NF.A.1, 4.NF.B.3

4.NF.C.6, 5.NF.A.2, 5.NF.B.5

4.GM.B.5, 5.NBT.A.1

4.NF.C.5

4.NF.C Crosswalk

 Standards Guidance:

Clarifications

  • Students should also use mixed numbers and fractions greater than 1.
  • Students should express fractions such as 310 as 30100, and add fractions such as 310 + 4100 = 34100.

Boundaries

  • Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12 and 100.
  • Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.

Teaching Strategies 

  • Students should be able to solve contextual, mathematical problems involving the addition of two fractions with denominators of 10 and 100.
  • Students should be given multiple opportunities to use visual models to develop part-whole reasoning when building an understanding of equivalent fractions.

Progressions

  • Grade 4 students learn to add decimal fractions by converting them to fractions with the same denominator, in preparation for general fraction addition in Grade 5. (Please reference page 9 in the Progression document)

Examples

  • Colin wants to use 5/10 of a board for a project. He is wondering how he can cut his whole board into pieces that are equivalent to 5/10. What fraction(s) of the whole board can Colin cut the board that are equivalent to 5/10 ? Possible student response: the board could be divided into 10ths (e.g. 5/10) or 100ths (e.g. 50/100).

2021 Oregon Math Guidance: 4.NF.C.6

  ODE and Oregon Math Project Logo

Cluster: 4.NF.C - Understand decimal notation for fractions, and compare decimal fractions.

STANDARD: 4.NF.C.6

 Standards Statement (2021):

Use and interpret decimal notation for fractions with denominators 10 or 100.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

4.NF.C.5

4.NF.C.7

4.GM.B.5, 5.NBT.A.1

4.NF.C.6

4.NF.C Crosswalk

 Standards Guidance:

Clarifications

  • Represent decimal number values on a place value chart.

Boundaries

  • Students are not expected to write word names of decimal numbers at this grade level.
  • To the hundredths place

Teaching Strategies 

  • Concrete materials could include base ten block where the “flat” or hundred square is considered one whole or a ten frame where the whole frame is considered one whole.

Examples

  • Rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
    • Eric overpaid his medical bill by $0.62. When businesses write refund checks, they often write the cents as a fraction. What fraction will the doctor’s office use to represent the $0.62 on the check?
    • Possible student response: I wrote 62 cents ($0.62) as 62100 because $0.62 is sixty-two hundredths of a dollar. If I place $0.62 on a number line, it would be between $0.50 and $0.75.

2021 Oregon Math Guidance: 4.NF.C.7

  ODE and Oregon Math Project Logo

Cluster: 4.NF.C - Understand decimal notation for fractions, and compare decimal fractions.

STANDARD: 4.NF.C.7

 Standards Statement (2021):

Use decimal notation for fractions with denominators 10 or 100. Compare two decimals to hundredths place by reasoning about their size, and record the comparison using the symbols >, =, or <.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

4.NF.A.2, 4.NF.C.6

5.NBT.A.3

5.NBT.A.1

4.NF.C.7

4.NF.C Crosswalk

 Standards Guidance:

Clarifications

  • Recognize that comparisons are valid only when the two decimal numbers refer to the same whole.
  • Students should be able to order up to 5 whole numbers less than 1,000,000 through the hundred-thousands place.

Boundaries

  • Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12 and 100.
  • Students are not expected to use more than two inequality symbols when recording comparisons (< or >) to the hundredths place.

Teaching Strategies 

  • Decimal quantities should be presented within a context.
  • Students should be given multiple opportunities to use visual models to develop part-whole reasoning when comparing decimal numbers.
  • Students should be able to determine and explain, through investigation, the relationship between decimal numbers, using a variety of tools (e.g., concrete materials, drawings, number lines) and strategies.

Progressions

  • Students compare decimals using the meaning of a decimal as a fraction, making sure to compare fractions with the same denominator. For example, to compare 0.2 and 0.09, students think of them as 0.20 and 0.09 and see that 0.20 > 0.09 because 20/100 > 9/100. (Please reference page 10 in the Progression document).

Examples

  • What do you notice about the fractions 2/10 and 10/100? Write a comparison statement about the two fractions and use visual models to support your reasoning.
    • Possible student response: I know that 2-10ths is greater than 10-100ths because 2-10ths takes up more space in the decimal squares to the right. So, 2-10ths>10-100ths.