Hit the Slopes: mental division of large numbers task cards & printables (set a)

Grade Levels
4th, 5th, 6th
Common Core Standards
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Do your students have a knee-jerk reaction to seeing division problems with big numbers, always wanting to use long division even when it isn’t efficient? This set of task cards and printables are the perfect resource for building your students ability to mentally solve division problems using number and operation relationships. The 32 task cards, 4 journal inserts, and 4 assessment activities in this product are everything you need to help your students become more flexible with their computation.

Common Core State Standards for Mathematics addressed:

Number and Operations in Base Ten
Use place value understanding and properties of operations to perform multi-digit arithmetic.
• Find whole-number quotients, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. (4.NBT.6, 5.NBT.6)

Division is a part of the Grades 3, 4, and 5 Common Core Standards for Numbers and Operations in Base Ten. However, the standards for these grades do not require students to use the standard algorithm for division. Instead, use of the division algorithm is not required until grade 6. In the upper elementary grades, the expectation is that students explore with a variety of strategies to divide numbers, including the properties of operations and the relationship between multiplication and division. These materials were designed to help students see how number relationships can be used to help divide numbers that might seem at first glance to require the use of long division.

Each card presents the students with a division equation with a variable (this term is not used on the cards, rather the word “unknown” is used) to represent an unknown dividend, divisor, or quotient. Students are asked to identify which of the four answer choices is the value of the unknown. None of the cards use dividends that are larger than three digits, and each equation has a divisor or quotient that is a single-digit number. The majority of the number sets used in the equations involve numbers that are multiples of 10 (i.e., 150 ÷ 30 = 5 or 240 ÷ 6 = 40), though all the numbers were chosen to allow the unknown to be found mentally.

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 printables consist of three graphic reference sheets and four different one-page assessment activities. The first two graphic reference sheets are half-page size and focus on division concepts, using division vocabulary (such as “dividend”, “divisor”, and “quotient”) and demonstrating patterns when dividing with multiples of ten. The third reference sheet is full-page size and shows the relationship between multiplication and division, introducing and explaining the term “inverse operation”. Before you have your students complete the cards, you can have them glue the reference sheet in their journals. Your students can use the journal insert as a guide while they work on the cards, as well as when they complete other tasks that relate to division.

The four assessment activities can be used to evaluate student proficiency with mentally dividing large numbers, as well as their understanding of the relationship between multiplication and division. The four activity pages were designed in pairs, with the first two using fill-in-blank questions to assess student understanding, while the second pair focuses on student reasoning and communication. The pairs of worksheets are formatted similarly, and have similar types of questions, though the numbers on each are different, and there are answer keys and rubrics for all four. You can use these activity pages in a variety of ways. You could give one as a pre-test, then teach your lesson and allow students to practice with the task cards, and then give the second worksheet as an independent post-test. You could also have the students work on the task cards, then complete one of the worksheet as guided practice with yourself, a partner, or a small group, and then give the second worksheet as an independent assessment. The worksheets could also be given as homework, center assignments, or any other purpose that fits your teaching style or classroom routines.

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.

Looking for more practice with number and operations in base ten? Try these resources –

It's All Relative – multiplication and division number relationships game

Snow Bonds: x and ÷ with multiples of 10 task cards & printables (set b)

Rounding the World - rounding whole numbers task cards & printables (set a)

Placing the Value - task cards + printables set

Super Powers of Ten - task cards + printables (set a)

I hope your students enjoy these resources and grow stronger in their understanding of number relationships! – Dennis McDonald
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Hit the Slopes: mental division of large numbers task card
Hit the Slopes: mental division of large numbers task card
Hit the Slopes: mental division of large numbers task card
Hit the Slopes: mental division of large numbers task card
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