Help build your students’ proficiency with dividing whole numbers with this set of task cards and printables that focus on both the area model for division and the partial quotient division method. The 32 task cards will provide your students with the necessary practice to build their skills with whole number division. Extend your students’ practice (or assess their level of mastery) with the 12 included assessment activities. With these resources, your students will grow stronger in their understanding of division concepts.
Common Core State Standards for Mathematics addressed:
Numbers and Operations in Base Ten (NBT)
Use place value understanding and properties of operations to perform multi-digit arithmetic.
• Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. (4.NBT.6)
• 2 graphic reference sheets
• 32 task cards (provided in color and grayscale)
• 8 self-checking “answer cards”
• task card answer sheet and key
• 12 assessment activities and key/scoring guide
About the Set
The 32 cards in this set present students with division expressions and ask the student to find the quotients. The division expressions are organized based on the size of the dividend and whether or not the expression results in a quotient with a remainder. Cards 1 through 16 use 3-digit dividends while cards 17-32 use four-digit dividends. In addition, the odd-numbered problems result in a quotient with no remainder and the even-numbered problems result in a quotient with a remainder.
The cards themselves simply present students with division expressions without requiring them to use any speciific strategy. The reference materials and some of the assessment activities are based on two methods of division – the area model of division and the partial quotient division strategy. You can have your students use these cards regardless of the strategies that you have instructed. However, the set as a whole makes an excellent, comprehensive resource for introducing, reinforcing, and assessing your students’ understanding of the area model of division and partial quotient division.
Practicing the Concept
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.
This organizational structure of the cards allows you to more easily differentiate for the needs of your students. You can have some of your students work on the cards with 3-digit dividends (cards 1-16) while others work on cards 17-32. You can have some of your students work on the odd-numbered cards, which have expressions that result in a quotient with no remainder, while others alternate between the odd and even-numbered cards. You might choose to do odd-numbered cards one day and save the even-numbered cards for another day. You might even have some students do just even-numbered cards, assign just odd-numbered cards to other students, and have some students do all the cards.
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.
The answer cards present the solution to the even-numbered cards in two forms – as a whole number quotient and reminder (ex: 43 r 1) as well as a mixed number (43 1/5). While the fourth grade Common Core Math Standards do not require students to write the reminder in the form of a fraction, I used these cards with my above grade level fourth graders. Since the fifth grade Common Core Math Standards do
require students to record quotients as fractions or mixed numbers, I used these cards as an opporunity to practice that skill with three- and four-digit dividends and one-digit divisors. If your students are working with the fourth grade standards, you may have them record their remainders as whole numbers rather than as a mixed number. However, if your students are working with the fifth grade standards, you can have them record their quotients as mixed numbers (or in both forms!).
Reinforcing the Concept
Included among the printables are two handy reference sheets, perfect for your students’ math notbooks. The reference sheets illustrate how the area model and the partial quotient division methods can be used to divide a three-digit number by a one-digit number. I have found that there are many different ways to represent or describe the area model and partial quotient method, and each of these references shows just one way to use the chosen method. If you taught either of these methods to your students, you may have used a different format or slightly different language. If so, I hope one or both of these resources are still of use to your students while they work on the cards, as well as when they complete other tasks that relate to dividing whole numbers.
The odd/even structure of the cards , with odd-numbered cards resulting in a quotient with no remainder and even-numbered cards resulting in a remainder, can be of use in terms of the method that you have your students use when completing the cards. I have found that the area model is easier to use when the dividend is divisible by the divisor since students can find a complete area equal to the dividend and not have to worry about having an “extra piece” left over. The partial quotient method, on the other hand, doesn’t require the dividend to fit into a rectangular area, and so having a remainder does not cause the same difficulty. If you want your students to use both the area model and the partial quotient division method, you may choose to have them alternate between them – using the area model for the odd-numbered cards and the partial quotient method for the even-numbered problems. You might also choose to share the area model reference sheet, have your students complete only the odd-numbered cards, and then share the partial quotient division reference sheet and have your students complete the even-numbered cards. There are lots of options for you to chosoe from when using these resources!
Assessing Student Understanding
The twelve provided activity sheets can be used to evaluate student understanding of whole number division. There are four one-page activity pages, each with four division problems for students to solve and space in which to show their thinking. The first two activity sheets use three-digit dividends and the second pair use four-digit dividends. All four activity sheets have two problems that result in a quotient with a remainder and two that result in a quotient without a remainder. A key and suggested scoring guide is provided for these activity pages.
Also included are eight half-page “exit ticket”-style assessments that focus on error analysis, perfect for integrating Common Core Math Standards and the Standards for Mathematical Practice (MP) – specifically MP3, “Construct viable arguments and critique the reasoning of others”. Each activity presents students with the work of another, hypothetical student who had to solve a division problem. The student’s work has an error, and your students have to identify the error that the student made. The first four exit tickets (exit tickets a through d
) show the work of students who used the partial quotient method while the other four exit tickets (e through h
) show the work of students who used the area model. Rubrics are included for all of the exit tickets.
The four full-page activity sheets and the eight half-page exit tickets are formatted similarly so that they could easily be used as pre/post assessments. You may choose to give your students one of the full-page activity sheets and two of the exit tickets before your instruction in division, and then give them a different set of activities as a post-assessment after your instruction. You needn’t use the activities solely as assessments, however. The activity pages could also be given as homework, center assignments, paired practice, or any other purpose that fits your teaching style or classroom routines.
For more practice with division concepts, please check out the other related resources I have available –
Hit the Slopes: mental division of large numbers task cards & printables (set a)
Snow Bonds: x and ÷ with multiples of 10 task cards & printables (set b)
Falling for Remainders – fall-themed division math game
I hope your students enjoy these resources and are able to build their proficiency with division. – Dennis McDonald