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.)
Students are able to…
- Use a variety of visual representations (pictures, fraction strips, pattern blocks, etc) to understand the need for common denominators when adding and subtracting fractions and mixed numbers.
- Explain their reasoning as they find like denominators for any given addends.
- Apply their understanding of equivalent fractions to change given fractions in an addition or subtraction example to fractions with like denominators.
- Use reasoning to determine if their answer makes sense.
Students are able to…because teachers:
- Provide students with opportunities to add fractions with unlike denominators using concrete models (manipulatives), progressing to picture models, and making explicit connections to writing it with numerals. Begin with examples in which one denominator is a multiple of the other ( 2/4 + 1/8 ).
- Facilitate discussions in which students explain why they need to find like denominators to add fractions and their strategies for finding like denominators.
- Before using any algorithm, give students ample opportunities to work with visual models to see and explain how like denominators are related. Once they have a deep understanding of the need for like denominators when adding or subtracting, they can apply their understanding to the algorithm.
- Expect students to justify their thinking as they use efficient strategies to add and subtract fractions.
[divider] [/divider] Questions to ask students:
- Ask students why we need like denominators in order to add/subtract fractions.
- Sample answer that indicates understanding: Both fractions need to have the same size parts in order for us to add or subtract the number of parts represented.
- Sample answer that indicates an incomplete understanding or misconception: if we don’t make the denominators the same, the answer will be wrong.
- Ask students why we do not add/subtract the denominators.
- Sample answer that indicates understanding: The denominator indicates the size of the parts that are being added/subtracted. We only need to add/subtract the amount being represented, which is the numerator.
- Ask students how they can use models to help them subtract fractions that do not have the same denominator.
- Ask students to explain two methods for finding a common denominator for two fractions.
- Ask students to explain how estimation could be helpful when adding/subtracting fractions with unlike denominators.
[divider] [/divider] FSA Notes
Cognitive Complexity Level: Level 2- Basic Application of Skills & Concepts
Achievement Level Descriptors:
Level 2: adds/subtracts fractions with unlike denominators, where one denominator is a multiple of the other denominator
Level 3: adds and subtracts fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions to produce an equivalent sum or difference of fractions with like denominators
Level 4: adds or subtracts three fractions with unlike denominators
Level 5: solves for an unknown numerator or denominator in an addition or subtraction problem given the sum or difference
Assessment Limits:
- Fractions greater than 1 and mixed numbers may be included.
- Expressions may have up to three terms.
- Least common denominator is not necessary to calculate sums or differences of fractions.
- Items may not use the terms “simplify” or “lowest terms.”
- For given fractions in items, denominators are limited to 1‐20.
- Items may require the use of equivalent fractions to find a missing term or part of a term.
Context: No Context
[divider] [/divider] Additional Resources:
Additional in depth content knowledge:
Video: Adding fractions with unlike denominators
[divider] [/divider] Sample Tasks:
Tim added 3/6 and 1/2 and wrote an answer of 4/12.
Is Tim’s solution correct? Explain why or why not using picture, numbers of words.
Jenn subtracted 2 fractions with different denominators and came up with a difference of 1/5.
What could the 2 fractions have been? Explain your work using pictures, numbers, and/or words.
A pitcher contains pints of orange juice. After you pour of a pint into a glass, How much is left in the pitcher?
[divider] [/divider]Resources/Tasks to Help Your Child at Home
Find various recipes that contain fractions and mixed number measurements. Pose addition and subtraction types of questions using the recipes.