This bundle of activity cards and printables will help your students become masters of fraction decomposition. The I Have…Who Has
cards, task cards, game, reference sheets, and assessment activities will keep your kids active and engaged as they explore with the different ways that fractions can be decomposed.
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.
The materials in this bundle are available separately: Break It Down!
, Dinosaur Decomposers
, and Decompose It!
• 32 I Have…Who Has?
• 3 self-checking puzzles (with answer keys)
• 5 graphic reference sheets
• 32 task cards
• 8 self-checking “answer cards”
• task card answer sheet and key
• 4 assessment activities and key/scoring guide
• 4 gameboards/spinners and student directions
• recording sheet for game
Decompose It! Activity cards and printables
There is a full set of 32 “I Have, Who Has?” cards, two smaller, 16-card “half-sets” that use the same questions and answers as the full 32-card sets, and a master list of the questions and answer on the cards. The cards use a mix of proper and improper fractions. While none of the fractions themselves repeat there are some fractions that are equivalent. For example, one card uses the fraction 8/12 while another uses 2/3. When using the cards, you will have to let the students know that the matching cards always use the same denominator. For instance, if someone reads, “Who has an expression with a value of 4/4?”, the matching card will have an expression that uses fourths. There is no specific starting card as the 32 cards loop around. Any student can begin, and since none of the questions or answers are repeated, the cycle will eventually lead back to whatever student began the activity.
This set is versatile and is designed to accommodate both large and small groups. There are 32 cards in the full-set to accommodate large classes. You can still use the entire set even if you don’t have 32 students by having some students hold two cards at once. However, if you much fewer than 32 students and you want to get more use out of each set, I have included a pair of “half-sets” for each set of 32 cards. These half-sets contain 16 cards and are identified as Set A1 and Set A2. They have the exact same numbers and expressions from the original sets of 32, but they are split into two groups and have their “ending” cards altered so that the 16th card loops back to the 1st card and the 32nd card loops back to the 17th card. If you have a class size closer to 16, you can use a half-set, such as Set A1, doubling up cards or kids as needed if you don’t have exactly 16 kids, and use the half-set with your class one day, saving the other half-set for a different day.
In order to allow for easier separation and sorting of the cards, each full set and each half-set has its own dinosaur icon in the upper right corner. The full set has a Tyrannosaurus Rex, while the 16-card half-sets have different dinosaurs, with the first half-set (Set A1) featuring a triceratops and the second half-set (Set A2) featuring an apatosaurus. The cards are also labeled in the bottom right corner as an additional indication of what set the card belongs to – Set A, Set A1, and Set A2.
Follow-up the cards with any of the three self-checking puzzles that focus on fraction decomposition. Use these riddles as classwork, partner practice, center work, homework assignments – any way that suits your class’s needs!
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Break It Down! task cards and printables
Each of the 32 cards in this set 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. The first 16 cards use proper fractions and the second 16 cards (cards 17-32) use improper fractions.
All of the cards have 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.
The printables consist of two graphic reference sheets and four different one-page worksheets. 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. Your students can use the journal inserts as guides while they work on the cards, as well as when they complete other tasks that relate decomposing fractions.
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. The two pairs of assessment activities are formatted similarly, and have similar types of questions, though the numbers on each are different. I designed them this way so they could be easily used as a pre/post assessment. However, you can use these activity pages in a variety of ways – guided practice, paired work, homework, center assignments, or any other purpose that fits your teaching style or classroom routines.
You can find a fuller description and preview of this product here!
Dinosaur Decomposers game & printables
The game Dinosaur Decomposers is simple, with easy-to-understand directions and requiring little in terms of materials. Students begin with 12 chips or tokens (though any colored math manipulative, such as Unifix cubes or color tiles, can work as well), and their goal is to get rid off all their chips by placing them on the board. A player spins a spinner to get a whole and then has to identify two or three fractions on the board into which the whole can be decomposed. Players alternate turns, placing exactly two or three fractions each time. The first player to put all his or her chips on the board wins.
There are four different gameboards and spinners. While the gameboards and spinners both feature color graphics, the amount of graphics is limited and lend these games to printing in either color or black & white. The denominators on the boards ands spinners are limited to the ones identified by the Common Core Standards for Grade 4 as “limiters”: 3, 4, 5, 6, 8, 10, and 12. Each board and spinner pair features three different fractional units.
: fourths, eighths, twelfths
: fifths, sixths, tenths
: thirds, sixths, twelfths
: thirds, fourths, twelfths
To support your students as they play, there are a number of reference materials provided. The one-page sheet titled “Decomposing Fractions: A Number Line Model” defines decomposition and gives examples of how twelfths, sixths, and thirds can be decomposed into smaller sections. The second one-page sheet, titled “Number Lines: Twelfths, Thirds, Fifths, and More!”, provides eight labeled number lines that are divided into each of the fractional units used on the gameboards: twelfths, sixths, thirds, fourths, eighths, fifths, and tenths. As students play, they can use this pictorial representation to help them determine the combination of fractions into which the whole can be decomposed. In addition to the two number line-based reference sheets, there is also a half-sheet reference (provided in color and grayscale) that defines and describes the concept of “composing” and “decomposing” fractions. It uses an image of puzzle pieces to help give students a visual of what it means to compose and decompose. Have your students glue these sheets in their math journal/math notebook, and they will be a handy reference throughout your work with fractions!
You can find a fuller description and preview of this product here
For practice with other fraction concepts, please check out the other related resources I have available –
Fraction Matchin’ equivalent fractions task cards + printables (set a)
Monkey Mania & Jumping Giraffes equivalent fractions games + task cards bundle
Froggy Fractions - adding/subtracting like denominators task cards + printables
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.