Looking for resources to help your students practice decomposing fractions? This set of task cards and printables provides everything you need in one “print-and-go” package. The 32 task cards, 2 graphic reference sheets, and 4 assessment activities are the perfect resource for building and evaluating your students’ understanding of fractional relationships.
This set of resources is available in a money-saving bundle with two other products that focus on decomposing fractions. The bundle contains the Break It Down!
task cards and printables, as well as Decompose It!
, a set of I Have...Who Has?
cards & self-checking puzzles, and Dinosaur Decomposers
, a set of games and number line-based resource materials. Purchase the bundle here
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Common Core State Standards for Mathematics addressed:
Numbers and Operations – Fractions (4.NF)
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
• 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. (4.NF.3b)
Decomposition is a major concept in the Common Core. From first through fourth grades, students are expected to be able to break wholes down into parts, recognizing that wholes can be broken down in a variety of ways and that the parts can always be recombined to make the whole. Students who have the flexibility to decompose numbers in a variety of ways are often more efficient with their computation, able to mentally solve problems that other students might have to labor over the algorithm to solve.
Typically, students have been taught to decompose numbers in a certain way, to use the places of a number to record the number in expanded form. Common Core expands decomposition, requiring students to be able to decompose shapes, angles, and fractions. When I first had to teach fraction decomposition, I realized that there were very few resources to help students practice this concept, so I designed these resources to meet that need.
• 2 graphic reference sheets
• 32 task cards
• 8 self-checking “answer cards”
• task card answer sheet and key
• 4 assessment activities and key/scoring guide
Introducing the Concept
Included among the printables are two graphic reference sheets, perfect for introducing and reinforcing the concept of fraction decomposition. These sheets, as well as the cards themselves, use the visual of a rock being broken with a hammer because I thought this would be an ideal metaphor to help reinforce the meaning of "decomposition".
The first of the two graphic reference sheets is full-page size and presents the terms decompose
and unit fraction
, connecting whole number decomposition to fractional decomposition. The second reference sheet is half-page size and shows how both proper and improper fractions can be decomposed, and also demonstrating how a decomposed improper fraction can be used to help identify the equivalent mixed number. Before you have your students complete the cards, you can have them glue the reference sheets in their journals. Your students can use them as guides while they work on the cards, as well as when they complete other tasks that relate decomposing fractions.
Practicing the Concept
Each card presents students with a specific fraction and asks them to identify the expression (or expressions) that represent how that fraction could be decomposed. The denominators on these cards are limited to the ones identified by the Common Core Standards for Grade 4 as “limiters”: 2, 3, 4, 5, 6, 8, and 12. One advantage of using only these denominators is that these fractional units are commonly used on commercially-made fraction bars, fraction circles, and fraction squares. This allows for easy differentiation within the math class. If you have students that are still building an understanding of fractional sizes and relationships, you may choose to give them a set of fraction manipulatives with which to complete the cards. Your students who already have a strong understanding of fractional sizes can complete the cards without the concrete representation.
The first 16 cards use proper fractions and the second 16 cards (cards 17-32) use improper fractions. I found from my own experience with teaching fraction decomposition that students who can proficiently decompose proper fractions do not automatically transfer over that skill to improper fractions, so I wanted these cards to reinforce the similarities between proper fractions and improper fractions. However, I separated the proper and improper fractions to allow these cards to be implemented in whatever way will best meet the needs of your students. You may choose to have all of the students complete the first 16 cards in one session and then the second 16 cards in a different session. You may have some of your students complete the cards with the proper fractions while other students complete the cards with the improper fractions. You can even have your students alternate between the two halves (for instance, completing #1, then #17, then #2, then #18, and so on) if you want to build your students’ flexibility with different types of fractions.
Each card has four answer choices, and there is more than one correct expression on most cards. The grammar of the cards (“which expression(s)”) are one indication that there may be more than one correct answer, and the directions on the task card answer sheet tell the students that there may be more than one correct answer. If your students are not used to working with activities that have multiple possible answers, they may need some explicit directions before working with the cards so they will know to look for more than one answer.
There are lots of ways in which you can implement the task cards. You can have the students work on them independently, working through the task cards on their own. The students can work on them in pairs or small groups, completing all the task cards in one session. You can use them in centers, having the students complete 6-8 task cards a day over the course of the week. You can even use them as a variation of “problem of the day”, giving each student 1 sheet of 4 cards to glue in their journals and solve, one sheet per day for eight days.
Assessing Student Understanding
The four provided activity sheets can be used to evaluate student understanding of fraction decomposition. Two of the activity pages are relatively straightforward, while the other two activity sheets are designed to address a student’s reasoning about fraction decomposition. You can use these activity pages in a variety of ways – independent assessment, guided practice, paired work, homework, center assignments, or any other purpose that fits your teaching style or classroom routines.
For more practice with fractions, please check out the other related resources I have available –
Fraction Matchin’ equivalent fractions task cards + printables (set a)
Fraction Matchin’ equivalent fractions task cards + printables (set b)
Froggy Fractions - adding/subtracting like denominators task cards + printables
Monkey Mania & Jumping Giraffes equivalent fractions games + task cards bundle
Flipping for Fractions activity card set
FREE self-checking mixed numeral/improper fraction puzzle set
I hope your students enjoy these resources and are able to build their proficiency with fractions.