Unequal Parts - reasoning about fractions task cards & printables set

Unequal Parts - reasoning about fractions task cards & printables set
Unequal Parts - reasoning about fractions task cards & printables set
Unequal Parts - reasoning about fractions task cards & printables set
Unequal Parts - reasoning about fractions task cards & printables set
Unequal Parts - reasoning about fractions task cards & printables set
Unequal Parts - reasoning about fractions task cards & printables set
Unequal Parts - reasoning about fractions task cards & printables set
Unequal Parts - reasoning about fractions task cards & printables set
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17 MB|22 pages
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Challenge your students and expand their understanding of fraction/whole relationships with this set of task cards & printables. The 32 task cards will push your students to think about fractions and wholes in new ways. Extend your students’ practice (or assess their level of mastery) with the four included assessment activities. With this set of print-and-go resources, your students will grow stronger in their understanding of fractions.

• 2 graphic reference sheets
• 32 task cards
• 8 self-checking “answer cards”
• task card answer sheet and key
• 4 assessment activities and keys

About the Cards

I designed this set after working with a group of students on a task that presented a rectangle divided into twelve pieces, all of different sizes. While the sizes of the pieces were different, they related to each other and to the whole in ways that made it possible to identify what fraction of the rectangle each piece was (e.g., one of the pieces was three times the size of another piece, and the larger pieces was one-fourth of the whole). When I asked the students if they could name any fraction that named a piece of the rectangle, the students agreed that there were no fractions that named the rectangle's parts because, in the words of one student, "You only have fractions if the whole is divided into all equal pieces. If the pieces aren't the same size, they're just called 'pieces' not 'fractions'." I realized that the students were developing a very rigid idea of what a fraction was and needed to expand their understanding of fraction/whole relationships.

These cards present shapes as wholes (with the majority of the wholes being rectangles or circles) as well as number lines with endpoints of 0 and 1, and the fractions used on the cards are limited to the denominators 2, 3, 4, 5, 6, 8, 10, and 12. The shapes and number lines are divided into irregularly sized pieces or segments and have one piece or point labeled with a letter. The students have to figure out the fraction of the whole represented by the labeled piece or point. While the pieces and segments are irregular, their sizes are related in way that allows students to reason about size of the piece or segment in question. For instance, a square might be cut into two unequal pieces, but the larger piece can be cut into three pieces that are congruent to the smaller piece, creating four equally sized pieces.

The cards are structured so that similar cards are grouped together. In addition, the cards progress in difficulty, allowing for you to more easily scaffold for student success:

Cards 1-8: unit fractions, shapes as wholes
Cards 9-16: unit fractions, number lines with endpoints 0 and 1
Cards 17-24: non-unit fractions, shapes as wholes
Cards 25-32: non-unit fractions, number lines with endpoints 0 and 1

There are two versions of the answer sheet: one version with blanks for the numeric answer, and a second one that is multiple choice and requires students to choose one of four fractions as the correct answer. You can choose which of the sheets you would like your students to use.

Using the Cards

Because of the way the shapes and number lines are partitioned on the cards, I have found that students are most successful when they can actually write on the cards, dividing up the larger sections into smaller sections to help see how the pieces relate to each other and to the whole. One option is to laminate the cards and provide the students with dry erase markers and an eraser so they can write on the cards and then erase what they wrote when they are done. Another option is to provide sheet protectors for students to slip the cards into when they work on them.

The organization of the problem types allow for scaffolded practice. Since each set of eight cards (1-8, 9-16, etc.) is similar, you can take advantage of this structure to meet varied student needs. Decide which set of four cards you want your student to work with and then differentiate based on your students’ levels of proficiency with the target concept. You may:

1) have your students work through all eight at a time while you circulate and provide guided support;
2) work through the first couple card together and then have students use the other six as paired or independent practice.;
3) have your more able students complete the cards on their own while you provide guidance to a small group; or,
4) have students work in pairs to complete the first two and then complete the other six on their own.

As your kids work on the cards, you can take advantage of the progressive difficulty level and adjust their work based on the degree of proficiency they are showing. For instance, if a student is working quickly and accurately through cards in the first set of eight cards, with shapes and unit fractions, skip them ahead to Cards 9-16 that have number lines and unit fractions or to Cards 17-24 that have shapes and non-unit fractions.

Beyond the suggestions above, 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.

Reinforcing and Assessing Understanding

The printables consist of two graphic reference sheets and four different one-page assessment activities. The graphic reference sheets lays the groundwork for the kind of thinking students will have to do as they work through the cards. The first sheet is full-page in size and presents images of shapes and number lines cut into all equal parts and ones that are cut into unequal parts. The second sheet is half-page in size and is designed as a springboard for a classroom discussion of fractions and wholes. It presents an image of a partitioned circle and the reasoning of three hypothetical students about the circle, and your students will have to critique their reasoning.

The four provided assessment activities can be used to evaluate student understanding of evaluating a shape or number line to determine the fraction represented by a section or point. The first two assessment activities (A & B) have partitioned shapes and number lines and the correct answers are all unit fractions; the other two activities (C & D) focus on non-unit fractions.

Each assessment activity provides an opportunity for students to explain their thinking about fractions in writing. A rubric is included to help evaluate the students' written responses.

The assessment activities are formatted similarly, and have similar types of questions, though the fractions on each are different. You can use these activity pages in a variety of ways. You could give one or two as a pre-test, then teach your lesson and allow students to practice with the task cards, and then give another (or both of the others) as an independent post-test. You could also have the students work on the task cards, then complete one of the activities sheets as guided practice with yourself, a partner, or a small group, and then another activity sheet as an independent assessment.

While these activity sheets can be used as assessments, you can use them in any number of ways – homework, paired practice, 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:

Self-Checking Number Line Riddles: Fractions on a Number Line (set a)

Marina Mix-Up mixed number & improper fraction relationships task cards & printables

Panda Power - Fraction/Whole Number relationships task card, game, and printables bundle

Fraction Matchin' - equivalent eractions task cards & printables set (set a)

Fraction Matchin' - equivalent eractions task cards & printables set (set a)

I hope your students enjoy these resources and are able to build their proficiency with fractions!
Total Pages
22 pages
Answer Key
Included with rubric
Teaching Duration
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