5.NF.1 - About the Math, Learning Targets, and Rigor
Grade 5 Fractions
5.NF.1
About the Math
Full Standard
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
Measurement Topic
This standard is reported on the report card in these quarters as follows:
Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 |
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Report Card Measurement Topic: Demonstrates understanding of addition and subtraction of different number types. |
Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 |
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Report Card Measurement Topic: Demonstrates understanding of addition and subtraction of whole numbers and fractions. |
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Learning Targets (I can)
- Generate common denominators of fractions and mixed numbers using representations and computation.
- Explain how common denominators are generated.
- Generate equivalent fractions with common denominators.
- Represent addition of fractions and mixed numbers with varied representations including Cuisenaire rods, pattern blocks, fraction tiles, drawings, number lines, and other tools.
- Represent subtraction of fractions and mixed numbers with varied representations including Cuisenaire rods, pattern blocks, fraction tiles, drawings, number lines, and other tools.
- Connect representations of addition and subtraction of fractions and mixed numbers to equations.
- Add fractions and mixed numbers using equations.
- Subtract fractions and mixed numbers using equations.
About the Math
- Generate common denominators of fractions and mixed numbers using presentations and computation.
Two fractions must have like denominators to be added or subtracted. Equivalent fractions for two different fractions can be used to find common denominators.
- Explain how common denominators are generated.
Finding common denominators is more than simply applying a procedure. Students should be able to represent and explain how common denominators are found using various representations including Cuisenaire rods, pattern blocks, or fraction tiles.
- Generate equivalent fractions with common denominators.
Once demonstrating an understanding of how common denominators are generated students should use number/fraction sense, reasoning, and/or procedure for finding common denominators. Keep in mind that students do not have to find least common denominators. For example, 5/6 and 9/10 have a least common denominator of 30. However, students may overlook 30 and instead rely on 60ths. This is completely acceptable. it is possible to over-emphasize the importance of simplifying fractions. There is no mathematical reason why fractions must be written in simplified form, although it may be convenient to do so in some cases. Also note that we do not reduce fractions. We find equivalent fractions.
- Represent addition of fractions and mixed numbers with varied representations including Cuisenaire rods, pattern blocks, fraction tiles, drawings, number lines, and other tools.
Addition of fractions must be represented in a variety of ways. Students should explain how their representations connect to the problem. Students should then be able to apply this understanding to mixed numbers. Keep in mind that students do not have to convert mixed numbers to improper fractions to add. Instead, students can decompose and find partial sums. For example, 3 4/5 + 7 1/8 can be thought of as 3 + 7 + 4/5 + 1/8.
- Represent subtraction of fractions and mixed numbers with varied representations including Cuisenaire rods, pattern blocks, fraction tiles, drawings, number lines, and other tools.
As mentioned above, students should use a variety of representations for subtraction of fractions. Students can add up or count back to find the difference between two fractions.
- Connect representations of addition and subtraction of fractions and mixed numbers to equations.
As with whole numbers, addition and subtraction of fractions is related. This is most notable when one adds up to find the difference. Students should be able to explain this relationship in various ways using physical models, number lines, and equations.
- Add fractions and mixed numbers using equations.
As with whole numbers, students should estimate their sum before adding fractions. Fractions can be added in a variety of ways. Though students must be able to explain their thinking, student understanding should evolve to symbolic approaches that leverage reasoning, operational strategies (partial sums) and eventually procedure.
- Subtract fractions and mixed numbers using equations.
Subtraction of fractions should be approached in parallel ways as addition with fractions. When working with mixed numbers, students do not have to convert to improper fractions. Students will need to identify when amounts will need regrouped. For example, 3 1/2 - 1 3/4 one could think about 3 - 1 and 1/2 - 3/4. However, the latter is problematic. Another whole must be decomposed to completed the calculation.
Essential vocabulary for this standard includes: mixed numbers, improper fraction, equivalent fraction, addend, sum, difference, numerator, and denominator. Visit the online dictionary Links to an external site., visual math dictionary Links to an external site. for vocabulary support.
Progression of Standard within Grade 5
This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.
Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 |
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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.
Grade 4 | Grade 6 |
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Instructional Tasks
TASKS
These tasks can be used with small group or whole group instruction.
- When adding 7/12 + 3/12, why do you add the numerators but keep the denominator the same?
- The difference of two fractions is ¾. What could the fractions be?
- Two fractions less than 1 result in a sum of 1 ⅔. What could the fractions be?
- How do you know that 2 1/2 + 3 2/3 > 6?
- Emily says the answer to 7/9 - 2/6 is 5/3. Is Emily correct? If not, help her understand her mistake?
- Use the digits 2, 3, 4, 5, 8, and 9 to form two different mixed numbers with a difference between 1 and 2.
- Show the sum of ⅔ + ⅚ using a number line?
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 5 • Adding and Subtracting Fractions
Bridging from Like Denominators to Adding and Subtracting Unlike Denominators:
Additional Tasks
These links provide instructional ideas connected to this standard.
- Fractions on a Line Plots Links to an external site. (Illustrative Mathematics)
- Egyptian Fractions (Links to an external site.) Links to an external site. (Illustrative Mathematics)
- Making S'Mores (Links to an external site.) Links to an external site. (Illustrative Mathematics)
- Finding Common Denominators to Add (Links to an external site.) Links to an external site. (Illustrative Mathematics)
- Finding Common Denominators to Subtract (Links to an external site. Links to an external site. (Illustrative Mathematics)
- Mixed Numbers with Unlike Denominators (Links to an external site.) Links to an external site. (Illustrative Mathematics)
- Cookie Calculations
Download Cookie Calculations (HCPSS UDL Lesson zip includes lesson, HW, and assessment)
- The Black Box Links to an external site. (Georgia Dept. of Education, pg. 53-60)
- Make Equivalent Fractions with Sums of Fractions Download Make Equivalent Fractions with Sums of Fractions (EngageNY Lesson 2 in a series)
- Add Fractions with Unlike Units Download Add Fractions with Unlike Units (EngageNY Lesson 3 in a series)
- Add Fractions With Sums Between 1 and 2 Download Add Fractions With Sums Between 1 and 2 (EngageNY Lesson 4 in a series)
- Subtract Fractions With Unlike Units_L5 Download Subtract Fractions With Unlike Units_L5 (EngageNY Lesson Plan)
- Subtract Fractions from Numbers Between 1 and 2 Download Subtract Fractions from Numbers Between 1 and 2 (EngageNY Lesson Plan)
- Add/Subtract Fractions From Whole Numbers Download Add/Subtract Fractions From Whole Numbers (EngageNY Lesson Plan)
- Add Fractions Making like Units Numerically Download Add Fractions Making like Units Numerically (EngageNY Lesson Plan)
- Add Fractions with Sums Greater than 1 Download Add Fractions with Sums Greater than 1 (EngageNY Lesson Plan)
- Subtract Fractions Making like Units Numerically Download Subtract Fractions Making like Units Numerically (EngageNY Lesson Plan)
- Use Fraction Benchmark Numbers Download Use Fraction Benchmark Numbers (Engage NY Lesson Plan)
- Explore Part to Whole Relationships Download Explore Part to Whole Relationships (EngageNY Lesson Plan)
- Domino Fractions Links to an external site. (OER Commons Lesson Plan)
- Stuffed Pizza (Unit) Download Stuffed Pizza (Unit) (NYC Dept of Ed)
- Unlike Denominators Links to an external site.(MSDE Lesson)
- Finding Equivalent Fractions Links to an external site. (MSDE Lesson)
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.
Book Thumbnail | Book Title | Grade | Pages |
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Teaching Student-Centered Mathematics |
6-8 |
Common Multiple Flash Cards, Activity 8.17, Page 128
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Hands-On Standards, Common Core Fractions |
5 | 10-26 Lessons 1-4 | |
Nimble With Numbers | 4-5 | 110-111 "Fraction Tic-Tac-Toe" 112-113 "Fifteen and a Half" |
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Nimble With Numbers | 5-6 | 74-75 "Target Fractions" 85-86 "Fraction Arrangements" 89 "Digits to Fractions I" |
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Groundworks: Reasoning with Numbers | 5 | 24-31 "Fraction Distraction" 72-79 "Fraction Squares" |
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Hands-On Standards | 5-6 | 40 "Lesson 11- Add Fractions with Unlike Denominators" 42 "Lesson 12 - Subtract Fractions with Unlike Denominators" |
Math In Practice Teaching Fifth-Grade Math |
5 | Module 7 |
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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.
- Using Equivalent Fractions to Subtract Download Using Equivalent Fractions to Subtract (HCPSS-adapted print resource)
- The Sum Is Download The Sum Is (HCPSS-adapted print resource)
- The Difference Is Download The Difference Is (HCPSS-adapted print resource)
- Kakooma basic 4 (Greg Tang) Links to an external site. (print resource)
- Kakooma basic 5 (Greg Tang) Links to an external site. (print resource)
- Kakooma moderate 6 (Greg Tang) Links to an external site.(print resource)
- Kakooma moderate 7 (Greg Tang) Links to an external site.(print resource)
- Kakooma advanced 9 (Greg Tang) Links to an external site.(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.
+/– Like Denominators: Fractions & Mixed Numbers:
- Addition Practice A Links to an external site.
- Addition Practice B Links to an external site. (using a number line)
- Subtraction Practice A Links to an external site.
- Subtraction Practice B Links to an external site. (using a number line)
+/– Unlike Denominators: Fractions:
- Addition Practice A Links to an external site.
- Addition Practice B Links to an external site.
- Reasoning About Fraction Addition Links to an external site.
- Add Fractions with Unlike Denominators Links to an external site.
- Subtraction Practice A Links to an external site.
- Subtract Fractions with Unlike Denominators Links to an external site.
- Add and Subtract Fractions with Unlike Denominators a Links to an external site.
- Add and Subtract Fractions with Unlike Denominators b Links to an external site.
- Add and Subtract Fractions with Unlike Denominators c Links to an external site.
- Add and Subtract Fractions with Unlike Denominators d Links to an external site.
- Add and Subtract Fractions with Unlike Denominators e Links to an external site.
+/– Unlike Denominators: Fractions & Mixed Numbers:
- Addition Practice A Links to an external site.
- Addition Practice B Links to an external site. (using a number line)
- Subtraction Practice A Links to an external site.
- Subtraction Practice B Links to an external site. (using a number line)
- Add and Subtraction Practice A Links to an external site.
- Add and Subtraction Practice B Links to an external site.
- Add and Subtract Mixed Numbers with Unlike Denominators Links to an external site.
- Add and Subtract Mixed Numbers with Unlike Denominators_2 Links to an external site.
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Assessment
Learning Targets
- Generate common denominators of fractions and mixed numbers using presentations and computation.
- Explain how common denominators are generated.
- Generate equivalent fractions with common denominators.
- Represent addition of fractions and mixed numbers with varied representations including Cuisenaire rods, pattern blocks, fraction tiles, drawings, number lines, and other tools.
- Represent subtraction of fractions and mixed numbers with varied representations including Cuisenaire rods, pattern blocks, fraction tiles, drawings, number lines, and other tools.
- Connect representations of addition and subtraction of fractions and mixed numbers to equations.
- Add fractions and mixed numbers using equations.
- Subtract fractions and mixed numbers using equations.
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.
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Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.