Help your students build their proficiency with recognizing fractional names for whole numbers with this set of panda-themed task cards and printables. The 32 task cards, graphic reference sheet, and 4 assessment activities are the perfect tools for building and assessing your students’ understanding of the relationship between whole numbers and fractions.
Common Core State Standards for Mathematics addressed:
Numbers and Operations – Fractions
Develop understanding of fractions as numbers.
• Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. (3.NF.3c)
Fraction concepts are a major focus of the Common Core State Standards for Math in intermediate grades. Significant instruction with fractions begins in third grade, and by fifth grade, students are expected to be able to multiply and divide fractions. One major fraction concept is equivalence, and as part of this, students are expected to recognize and express fractions as whole numbers (and vice versa). Building a student’s flexibility with fraction and whole number names lays the foundation for later work with mixed numbers. Students who know that twelve-fourths equals three wholes will be more likely to quickly recognize that thirteen-fourths equals three and one-fourth without the work of a multi-step procedure. Later on, in fifth grade, students will be primed to understand fraction as division if they have a firm understanding of fractional names for whole numbers.
• graphic reference sheet (color and grayscale)
• 32 task cards
• task card answer sheet and key
• 8 self-checking “answer cards”
• 4 assessment activities (with scoring guides)
Introducing the Concept
Included among the printables is a kids-friendly graphic reference sheet, perfect for introducing and reinforcing the concept of fraction/whole number relationships. The graphic reference sheet is full-page size and uses a circle model to show a variety of whole numbers and the equivalent fractional names. Before you have your students complete the cards, you can have them glue the reference sheet in their journals. Your students can then use this journal insert as guides while they work on the cards, as well as when they complete other tasks that relate to whole number/fraction relationships. The open-ended questions featured on the reference sheet also make this resource the perfect springboard for a rich classroom discussion about number patterns evident in whole numbers and their fractional names.
Practicing the Concept
Each card presents a question and four answer choices. The questions on the cards vary, and there are four to five different types of questions on the cards. Some of the cards have one answer and others have more than one answer. The grammar of the cards (“Identify all of the fractions that…” or “Name the fraction that…”) 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 fractions used on the cards are limited to those with denominators 1, 2, 3, 4, 5, 6, and 8. I chose to limit the numbers in this way in the hopes that the repeated exposures to the same fraction/whole number pairs would build my students’ automaticity with recognizing common fractional names for whole numbers. Another benefit to using just these denominators is that they match the fractional pieces used in most commercially-sold fraction manipulatives, such as fractions bars and fractions circles. This allows you to have your students use a concrete representation of the fractions on the cards when they work through the questions.
In addition, none of the whole numbers used on the cards are larger than 10, and the majority of the whole numbers represented by the fractions are 8 or less. This makes it easier to use manipulatives, as less pieces will be necessary to construct the fractions displayed on the cards. The size of the whole numbers also means that no complicated multiplication or division is required to solve the cards; knowledge of basic facts is sufficient to work through the cards.
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. They’re perfect for math centers – have the students complete 6-8 task cards a day over the course of the week, allowing them to use the “answer cards” to check themselves (and lessen your own workload!). 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. You could even use the cards for a game of Scoot. Whatever your own teaching style or classroom routines, these cards can meet your needs!
Assessing Student Understanding
The four provided activity sheets can be used to evaluate student understanding of fraction decomposition. Two of the assessment activities are relatively straightforward, while the other two activity sheets are designed to address a student’s reasoning about fraction/whole number relationships. Like the cards, the first two assessment activities use a variety of questions types and include some questions that have more than one answer.
The second pair of assessment pages is designed to address both the Common Standard for fraction/whole number relationships and the Standards for Mathematical Practice. Each page focuses on reasoning, presenting the incorrect work of another hypothetical student and asking your own students to critique the flawed reasoning. Both of these activities require your students to communicate their thinking in writing, and will hopefully push them to more deeply consider fraction decomposition. Because of the nature of these activities, you may choose to use these in a more guided manner, discussing the situation and prompts as a class so your students have an opportunity to unpack their thinking before showing their understanding of the concepts assessed.
The two assessment activities in each pair 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.
Reinforcing and Extending Student Understanding
For more practice with whole number/fraction relationships, you may find these other products helpful –
Whole-y Fractions – fraction & whole number equivalence task cards + printables
Panda Pathways - fraction & whole number equivalence games and printables set
The Panda Pathways
game and Whole-y Fractions
task card and printables set address the same concept as this set but do not have any repeat pages or resources. The materials in each of those resources are unique from the ones included with this set.
I designed the Whole-y Fractions
task card set as a beginner set to use when first introducing students to fraction/whole number relationships. All of the cards and assessment materials in that set use visual models, presenting students with four different pictorial representations of whole numbers and improper fractions. Students will have to examine the model and identify the whole number and fraction represented by the model. The Whole-y Fractions
may be useful before you use the Bamboo-zled
materials, or as a supplement to help those students who are struggling with the concept.
The boards & spinners, as well as the assessment activities, in the Panda Pathways
game use numeric representations, though a reference sheet showing fractions and whole numbers on number lines is included to aid your students understanding.
For more practice with fractions, please check out the other related resources I have available –
Monkey Mania & Jumping Giraffes equivalent fractions games + task cards bundle
Fraction Matchin’ equivalent fractions task cards + printables (set a)
Fraction Matchin’ equivalent fractions task cards + printables (set b)
Break It Down! decomposing fractions task cards & printables set
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. – Dennis McDonald