Introduce your students to fractional names for whole numbers with this set of task cards and printables. The 32 task cards, 2 graphic reference sheets, and 2 assessment activities in this set present visual models of improper fractions and whole numbers, making them the perfect starting point 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.
• 2 graphic reference sheets
• 32 task cards
• task card answer sheet and key
• 8 self-checking “answer cards”
• 2 assessment activities (with scoring guides)
Introducing the Concept
Included among the printables are two graphic reference sheets. The first graphic reference sheet is half-page size and defines the terms “proper fraction” and “improper fraction”, presenting examples and models of each type. The other reference is two pages in length and uses four different models to illustrate the relationship between whole numbers and their fractional names. There are four models used: circles, squares, bars (rectangles), and number lines. This handy reference presents students with models of whole numbers 1 through 4, divided into eights, fifths, fourths, and wholes. The variety of models on these sheets will help your students develop a fuller understanding of what fractions can look like. Before you have your students complete the cards, review you can have them glue the reference sheets in their journals. 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 to whole number/fraction relationships.
Practicing the Concept
Each card presents the students with a visual model of a given number – the same models used on the reference sheets. The students are asked to identify a whole number and equivalent fraction represented by the model. On the recording sheet, student will fill in an equation to show the relationship between the two numbers. By presenting a variety of pictorial models rather than just a numeric representation, your students are more likely to develop a firmly-grounded conceptual understanding of fraction/whole number relationships. With this foundation, they will be better able to handle the more abstract work required later on in their fraction instruction.
The fractions used on the cards are limited to those with denominators 1, 2, 3, 4, 5, 6, and 8, and a number of the fractions are used on multiple cards, just with different models. 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. 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. With manageable whole numbers, your students should more easily complete the cards as well as be more likely to notice how multiplication and division can be used to describe the relationship between a whole number and the numerator and denominator in the number’s fractional names.
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!
Included in this set are eight “answer cards” that can serve as a resource if you use a self-paced structure for implementing the task cards. Often, I would have kids work in pairs on cards while I circulated to spot check and give feedback to pairs of students. Naturally, I would get backed up and not be able to reach as many kids until after they had already made many mistakes. I designed these answer cards so that the students could check themselves: catching errors, figuring out for themselves what they did wrong, and (hopefully) avoiding the same mistake on later cards. These answer cards have turned out to be huge time-saver for me, and have helped put my kids in the driver’s seat of their own learning.
Assessing Student Understanding
The two provided assessment activities can be used to evaluate student understanding of fraction/whole number relationships. Your students will have to identify whole number and improper fractions represented by a given model (the same models used on the cards), and then they will have to create their own models of specific whole number/fraction pairs. These activity sheets 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.
Extending Student Understanding
For more practice with whole number/fraction relationships, you may find these other products helpful –
Panda Pathways - fraction & whole number equivalence games and printables set
Bamboo-zled - fraction & whole number equivalence task cards and printables set
The Panda Pathways
game and Bamboo-zled
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 Bamboo-zled
task card set to provide the next level of challenge to students studying fraction/whole number relationships. The cards and assessment materials do not use visual models, presenting only numeric representations.
The boards & spinners, as well as the assessment activities, in the Panda Pathways
game also use numeric representations, though a reference sheet showing fractions and whole numbers on number lines is included to aid your students understanding.
I have a wide variety of fraction-based resources available. Please check them out!
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