This set of games and printables will help you bring some dinosaur-sized fun to your math class and help build your students’ understanding of fraction decomposition as well! Differentiation is a snap with the four gameboards & spinners, and the three graphic reference sheets - ideal for your students’ math notebooks or journals – are the perfect resources for developing and maintaining your students’ proficiency with fractional relationships.
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)
• 3 graphic reference sheets
• student directions
• 4 gameboards/spinners
• recording sheet
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 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.
Gameboard/Spinner A: fourths, eighths, twelfths
Gameboard/Spinner B: fifths, sixths, tenths
Gameboard/Spinner C: thirds, sixths, twelfths
Gameboard/Spinner D: thirds, fourths, twelfths
I limited the fractional units on each of the gameboards to help build students’ familiarity with given units. By only looking for combinations of fourths, eighths, or twelfths, for instance, students will start to use the same combinations repeatedly. This repetition will allow your students to start to internalize combinations that create specific fractions, making those combinations more automatic for the kids.
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!
If you have students who are still developing their understanding of fractional relationships, they may need more support than simply the pictorial models on the reference sheet. In this case, you can break out some fraction manipulatives. The denominators featured in the games are the same ones commonly used on commercially-made fraction bars, fraction circles, and fraction squares. 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 play the game Your students who already have a strong understanding of fractional sizes can play the game without the concrete representation, using just the number line reference sheet or no reference at all. Differentiate for the varied needs within your class by having some students use fraction bars, others use the number lines, and still others draw their own models to show how they are decomposing the wholes.
Looking for more resources to build your students’ proficiency with decomposing fractions? Then check out Break It Down!
, a set of task cards, assessment activities, and other printables, all focused on fraction decomposition, and Decompose It!
, a set of I Have...Who Has?
cards and self-checking puzzles.
All three of these products are available in one, money-saving bundle: Decomposing Fractions
. Buy this bundle and save nearly 25% off the cost of the individual products!
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)
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. – Dennis McDonald