Digit Puzzlers: Multiplication reasoning about multiplication task card set

Grade Levels
4th, 5th, 6th
Common Core Standards
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8.73 MB   |   23 pages


Looking for a fun, engaging way for your students to practice multi-digit multiplication, either with the standard algorithm or with some other strategy? Ditch the worksheets and have your students dive into the challenge of these task cards, designed to build reasoning about number and operations. The task cards, reference sheet, and assessment activities in this set are the perfect “print-and-go” resources for helping your students become more proficient in their multiplication of multi-digit whole numbers.


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.
• Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. (4.NBT.4)

Use place value understanding and properties of operations to perform multi-digit arithmetic.
• Fluently multiply multi-digit whole numbers using the standard algorithm. (5.NBT.5)

• reference sheet
• 32 task cards
• task card answer sheet, rubric, and key
• 6 assessment activities
• rubric and key for assessment activities

These cards were designed to give students an opportunity to practice multiplication of multi-digit numbers – whether using the standard algorithm, the area model, or some other method – in a context that allows them to reason about numbers and number relationships and provides a challenge.

About the Cards

Each card requires student to use particular digits to create factors that multiply to make one or two specified factors. Students can use a simple guess-and-check method to try out different combinations of digits or they can use their knowledge of rounding and estimation to arrange the digits into a combination that might reasonably result in a product of a given size.

The organization of the cards was designed to provide scaffolding for students and allow you to more easily differentiate for varied student needs in your classroom. Each set of four cards features similar problems. The list below details the specifics of each set of four cards:

Cards 1-4: “sample cards” featuring one of each type of problem on the rest of the cards
Cards 5-12: three-digit by one-digit multiplication
Cards 13-20: four-digit by one-digit multiplication
Cards 21-24: two-digit by two-digit multiplication
Cards 25-28: three-digit by one-digit multiplication
Cards 29-32: “challenge cards” featuring all types of problems found on the other cards

Using the Cards

The first four cards were designed to help students understand how the cards work, providing questions with all four types of factors pairs. Students are given one completed problem and are asked to rearrange the digits in the two given factors to create another pair of factors that make a different, specified product. You can use these cards to help students understand what they will be doing on the other cards. You may have them work through all of cards 1 through 4 and then work on the rest of the cards, starting with card 5. Alternately, you can have your students simply work on the one that matches factor sizes (e.g., three digit by one digit) that they will be working with. For instance, you may have students complete card 1 (three-by-one) and then work on cards 5-12, which also feature three-by-one multiplication. They can then complete card 2 (four-by-one), and move on to working on cards 13 through 20.

You can have all of your students work through the cards in one of the orders described above, or you can use the organizations structure of the cards to differentiate for your students. If you have some students who need to practice with three-by-one multiplication and others with four-by-one, have the first set of students work with cards 5-12 and the others with cards 13-20. Have some of your students mastered multiplying a multi-digit number by a one-digit factor? Those students can work on cards 21 through 32, which require students to multiply two-digit and three-digit numbers by a two-digit factor.

You could also have some students work through all the cards in order while other students simply complete the odd cards or the even cards, allowing them to have the benefit of the scaffolded nature of the cards without having to complete every single card. You might first have all your students work through the first 8 odd-numbered cards (1, 3, 5, 7, 9, 11, 13, and 15), and then allow those students who performed well to move on to cards 17-24 while those students who struggled can go back and do the first 8 even-numbered cards. You could also have slower workers only complete the odd-numbered cards and faster workers complete all the cards.

Reinforcing and Assessing Understanding

One of the printables is a reference sheet that focuses on using rounding to estimate the products of pairs of factors. There are multiple open-ended questions on the reference sheet, which allows you to use this sheet as the springboard to a rich mathematical discussion about rounding and estimation. 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 rounding to estimate products.

The six assessment activities feature problems similar to those on the task cards, making them the perfect complement to the cards in the set. You can use these activity pages in a variety of ways. You could give one or more as a pre-test, then teach your lesson and allow students to practice with the task cards, and then give one or more of the other assessments as an independent post-test. You could also have the students work on the task cards, then complete one or more of the assessments as guided practice with yourself, a partner, or a small group, and then give one or more of the other activities as an independent assessment. The activity sheets could also be given as homework, center assignments, or any other purpose that fits your teaching style or classroom routines.

Please check out the preview to see all of the materials up close!


For more practice with rounding or multiplication, please check out these other resources I have available –

Box It Up! multiplying with the area model task cards + printables (set a)

Box It Up! multiply 2-digit numbers with the area model task cards + printables (set b)

What's the Error? multiplication error analysis task cards + printables set

Bumblebee Paths, Frog Pond Frenzy - factors & multiples math games bundle

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

Self-Checking Math Riddles – Rounding to the Nearest 10 and 100


I hope your students enjoy these resources and are able to build their proficiency with multiplication.
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Digit Puzzlers: Multiplication reasoning about multiplicat
Digit Puzzlers: Multiplication reasoning about multiplicat
Digit Puzzlers: Multiplication reasoning about multiplicat
Digit Puzzlers: Multiplication reasoning about multiplicat
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