Word (.docx)
Acrobat (.pdf)
Examples
The difference
can be expressed as 9 fifths minus 4 fifths which is 5 fifths, or one.
Clarifications
Clarification 1: Instruction includes the use of word form, manipulatives, drawings, the properties of operations or number lines.Clarification 2: Within this benchmark, the expectation is not to simplify or use lowest terms.
Clarification 3: Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, 16 and 100.
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Equation
- Expression
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is for students to build upon their decomposition of fractions to develop an accurate, reliable method for adding and subtracting fractions with like denominators (including mixed numbers and fractions greater than one) that aligns with their understanding and learning style. Procedural reliability in addition and subtraction of fractions with unlike denominators is expected in grade 5.- Clarification 1 states that instruction should include word form (to build vocabulary), manipulatives, and drawings (to model), and the properties of operations. Using properties of operations (e.g., commutative property of addition, associative property of addition) allows students to connect prior knowledge about whole number addition and subtraction to fractions. Properties of operations also allow for students to add and subtract fractions flexibly (e.g., students may add by rewriting the expression 1 + 4 as 1 + 4 + + using the associative property of addition).
- Students need to have experience regrouping a fraction equivalent to 1 as a whole number
for addition and subtraction.
- For example, + = = + = 1 .
- This benchmark should be taught with MA.4.AR.1.2 for students to solve real-world problems while adding and subtracting fractions.
Common Misconceptions or Errors
- Some students may have difficulty understanding that when adding or subtracting fractions with like denominators, the denominator does not change. To help students understand why this happens, addition and subtraction should be accompanied by models to justify solutions.
Strategies to Support Tiered Instruction
- Instruction includes models and drawings demonstrating how when adding and subtracting with like denominators, we are adding and subtracting pieces of the whole. This learning connects to the understanding that fractions can be decomposed into smaller fractions from MA.4.FR.2.1.
- For example, using a number line, the teacher models solving by adding on the number line with guided questioning. Students explain how to use the number line as a model to solve the expression + = ?.
- Instruction includes the use of fraction bars or fraction strips to model solving expressions with explicit instruction and guided questioning.
- For example, students explain how to use fraction bars or fraction strips as a model to solve expressions.
Instructional Tasks
Instructional Task 1 (MTR.3.1, MTR.4.1)
Find the sum or difference and explain your method.
Instructional Items
Instructional Item 1
The point on a number line shows the value of the sum of two fractions.
Related Courses
Related Access Points
Related Resources
Formative Assessments
Image/Photograph
Lesson Plans
Perspectives Video: Expert
Perspectives Video: Teaching Ideas
Problem-Solving Tasks
Tutorials
Virtual Manipulative
MFAS Formative Assessments
Students are given pairs of mixed numbers to either add or subtract.
Students are asked to solve a word problem that involves subtracting fractions with like denominators. Students then analyze a word problem involving subtraction of unlike unit quantities.
Student Resources
Problem-Solving Tasks
This task provides a context where it is appropriate for students to subtract fractions with a common denominator; it could be used for either assessment or instructional purposes. For this particular task, teachers should anticipate two types of solution approaches: one where students subtract the whole numbers and the fractions separately and one where students convert the mixed numbers to improper fractions and then proceed to subtract.
Type: Problem-Solving Task
The purpose of this task is to have students add mixed numbers with like denominators. This task illustrates the different kinds of solution approaches students might take to such a task. Two general approaches should be anticipated: one where students calculate exactly how many buckets of blocks the boys have to determine an answer, and one where students compare the given numbers to benchmark numbers.
Type: Problem-Solving Task
Tutorials
This Khan Academy video uses authentic pictures to present addition of two fractions with common denominators.
Type: Tutorial
This Khan Academy video solves two word problems using visual fraction models.
Type: Tutorial
Virtual Manipulative
This virtual manipulative allows individual students to work with fraction relationships. (There is also a link to a two-player version.)
Type: Virtual Manipulative
Parent Resources
Image/Photograph
Illustrations that can be used for teaching and demonstrating fractions. Fractional representations are modeled in wedges of circles ("pieces of pie") and parts of polygons. There are also clipart images of numerical fractions, both proper and improper, from halves to twelfths. Fraction charts and fraction strips found in this collection can be used as manipulatives and are ready to print for classroom use.
Type: Image/Photograph
Problem-Solving Tasks
This task provides a context where it is appropriate for students to subtract fractions with a common denominator; it could be used for either assessment or instructional purposes. For this particular task, teachers should anticipate two types of solution approaches: one where students subtract the whole numbers and the fractions separately and one where students convert the mixed numbers to improper fractions and then proceed to subtract.
Type: Problem-Solving Task
The purpose of this task is to have students add mixed numbers with like denominators. This task illustrates the different kinds of solution approaches students might take to such a task. Two general approaches should be anticipated: one where students calculate exactly how many buckets of blocks the boys have to determine an answer, and one where students compare the given numbers to benchmark numbers.
Type: Problem-Solving Task
