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Common Core Standards

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Do you have students who still are struggling to accurately subtract with regrouping, even after months (or years) of practice! Ditch the same old practice - which just reinforces the same old habits that your students have developed - for this set of task cards that focus on error analysis. The task cards, reference sheet, and assessment activities in this set are the perfect “print-and-go” resources for helping your students become more analytical about their application of the subtraction algorithm.

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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.*

• Fluently subtract multi-digit whole numbers using the standard algorithm. (4.NBT.4)

____________________________________________________________________

Included:

• reference sheet

• 32 task cards

• task card answer sheet, rubric, and key

• 8 assessment activities

• rubric and key for assessment activities

Every year, I see a significant number of students coming up to fourth grade lacking proficiency with subtraction with regrouping. Often, these students show some understanding of the procedures (for instance, they know that they are supposed to cross out certain numbers and put other numbers on top of them) but make errors that show some misunderstanding of what is actually happening when they are regrouping. When kids make errors when subtracting with regrouping, often their errors are dismissed as simply the result of carelessness, and so kids are simply given more problems to practice and told to be more careful. However, I have noticed over the years that there are a set of standard errors that students make (such as subtracting the top number from the bottom number rather than regrouping or making all the zeros in the minuend into 9s), and when these errors are done consistently, it’s not generally because of carelessness but because the student thinks that they are doing the right thing. After repeatedly making the same mistake, the student has developed a habit that takes some work to undo. Giving students more problems to practice without taking the time to help them think about what they are doing is simply going to result in the habit become more and more ingrained.

These cards were designed to help children be more reflective about the subtraction algorithm. Rather than having children simply solve a series of subtraction problems, the students are asked to analyze completed subtraction problems and identify the error in each problem. The errors featured on the problems are the ones that my own students have made on a regular basis. As your students think critically about the problems on these cars, they will start to think more critically about their own work when subtracting. One student, when examining an incorrect problem on one of the cards, actually exclaimed, “That’s the same mistake I made last week!” I was so excited to hear her say this. I knew that she was on her way to no longer mindlessly crossing off and subtracting digits, but actually thinking about the procedures she was employing.

**About the Cards**

The cards all use three-digit and four-digit numbers, and the problems and tasks presented on the cards are ordered by difficulty. The first 16 cards present the work of two hypothetical students who solved the same subtraction problem. One of the student’s work is identified as correctly done while the other’s is identified as incorrectly done. The students have to compare the students’ work and then describe the error in writing. Within this group of cards, 8 of the cards present problems using three-digit numbers and 8 of the cards present problems with four-digit numbers.

Cards 17-24 also present two problems, one solved correctly and one solved incorrectly. These cards are more difficult that the first sixteen because the problems are not identified as correctly or incorrectly done. The students need to examine the work presented, figure out which student made a mistake, and then describe the mistake the student made. Within this group of cards, 4 cards use three-digit numbers and 4 cards use four-digit numbers.

Cards 25-32 up the difficulty level even further. These cards present three different subtraction problems solved by a hypothetical student. Two of the problems are correctly solved and one has an error. The students have to identify the problem that is solved incorrectly and then correctly solve that problem. Within this group of cards, 4 cards use three-digit numbers and 4 cards use four-digit numbers.

**Using the Cards**

The organization of the cards provides scaffolding for your students, slowly building their skills. You may choose to have all of your students complete the cards in order. Once they reach Card 17, their work with the first sixteen cards will make it more likely that they will be able to quickly identify which of the two problems has an error. After working through Cards 17-24 to distinguish which of two problems has an error, examining three problems (on Cards 25-32) should be a breeze!

The varied difficulty levels also provide opportunities to differentiate for your students. You may have some of your students work on the cards with three-digit numbers (Cards 1-8, 17-20, and 25-28), while others work on the cards that feature four-digit numbers. Perhaps one group of students will start with Card 1 while students who have a higher level of proficiency with subtraction could begin with Card 17. You could 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.

Beyond the suggestions above, 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.

Because of the nature of the cards, the answer sheets provided are different than those included with my other task card sets. The first answer sheet has space for a student’s name and the date, and sets of lines for students to respond to four cards. The next answer sheet also features lines for four cards, and you can copy as many of these as you need, depending on the number of cards your students will use. For the final eight cards, the answer sheet provides a fill-in-the-blank sentence and space in which students can solve the given problem. If you prefer, you can save copies by having your students simply use notebook paper (or their journals) to write their answers to each card.

The provided answer key gives a full description of the error on each card as well as two suggestions for how the students’ work can be scored.

**Reinforcing the Concept**

One of the printables includes a reference sheet that I designed for my students to glue in their math notebooks. The reference sheet shows three common errors that students make when subtracting with regrouping, with a description of the error, an explanation of what should have been done, and then a demonstration of the correct procedure. When I use reference sheets of this size, I have the students fold the sheet from the bottom to the top, not quite halfway, creasing the paper so that the title of the sheet is visible. When the students glue the folded sheet in their journals, the title is then visible so that students can more easily find it when they need to refer to the information on the sheet. You can have your students use this reference sheet as they work on the cards since the written descriptions on the reference sheet are models of how the students might use precise vocabulary to describe the errors on the cards they are examining.

**Assessing Understanding**

The eight provided activity sheets can be used to evaluate student understanding of the algorithm for subtracting with regrouping. There are six half-sheet “exit ticket”-style assessments, each of which presents two completed subtraction problems. Your students need to decide which of the two problems was solved incorrectly, describe the error, and then explain how the problem should have been solved. The first three exit tickets use three-digit numbers and the second three use four-digit numbers. The final two assessment activities are full-page in length and feature twelve completed subtraction problems, presented in four rows of three. In each row, one of the problems is solved incorrectly. The students have to identify the incorrectly solved problem in each row and use the space provided to correctly solve those problems. The exit tickets and the two full-page activities are formatted similarly, and have similar types of questions, though the numbers on each are different, making them ideal for pre/post assessing. However, you could use these activities in any way that suits your classroom routine or meets your students’ needs - homework, center assignments, paired practice, the list goes on.

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

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If you have students working on multi-digit multiplication, try**What's the Error? multiplication error analysis task cards + printables set**.

++++++++++++++++++++++++++++++++++++++++++++++++++++++++

++++++++++++++++++++++++++++++++++++++++++++++++++++++++

For more practice with whole number computation, please check out the other related resources I have available –

**Equine Quotients - dividing whole numbers task cards & printables (set a)**

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)

Snow Bonds: +, –, x, and ÷ number relationships task cards & printables (set a)

I hope your students enjoy these resources and are able to build their proficiency with subtraction with regrouping.

____________________________________________________________________

Common Core State Standards for Mathematics addressed:

• Fluently subtract multi-digit whole numbers using the standard algorithm. (4.NBT.4)

____________________________________________________________________

Included:

• reference sheet

• 32 task cards

• task card answer sheet, rubric, and key

• 8 assessment activities

• rubric and key for assessment activities

Every year, I see a significant number of students coming up to fourth grade lacking proficiency with subtraction with regrouping. Often, these students show some understanding of the procedures (for instance, they know that they are supposed to cross out certain numbers and put other numbers on top of them) but make errors that show some misunderstanding of what is actually happening when they are regrouping. When kids make errors when subtracting with regrouping, often their errors are dismissed as simply the result of carelessness, and so kids are simply given more problems to practice and told to be more careful. However, I have noticed over the years that there are a set of standard errors that students make (such as subtracting the top number from the bottom number rather than regrouping or making all the zeros in the minuend into 9s), and when these errors are done consistently, it’s not generally because of carelessness but because the student thinks that they are doing the right thing. After repeatedly making the same mistake, the student has developed a habit that takes some work to undo. Giving students more problems to practice without taking the time to help them think about what they are doing is simply going to result in the habit become more and more ingrained.

These cards were designed to help children be more reflective about the subtraction algorithm. Rather than having children simply solve a series of subtraction problems, the students are asked to analyze completed subtraction problems and identify the error in each problem. The errors featured on the problems are the ones that my own students have made on a regular basis. As your students think critically about the problems on these cars, they will start to think more critically about their own work when subtracting. One student, when examining an incorrect problem on one of the cards, actually exclaimed, “That’s the same mistake I made last week!” I was so excited to hear her say this. I knew that she was on her way to no longer mindlessly crossing off and subtracting digits, but actually thinking about the procedures she was employing.

The cards all use three-digit and four-digit numbers, and the problems and tasks presented on the cards are ordered by difficulty. The first 16 cards present the work of two hypothetical students who solved the same subtraction problem. One of the student’s work is identified as correctly done while the other’s is identified as incorrectly done. The students have to compare the students’ work and then describe the error in writing. Within this group of cards, 8 of the cards present problems using three-digit numbers and 8 of the cards present problems with four-digit numbers.

Cards 17-24 also present two problems, one solved correctly and one solved incorrectly. These cards are more difficult that the first sixteen because the problems are not identified as correctly or incorrectly done. The students need to examine the work presented, figure out which student made a mistake, and then describe the mistake the student made. Within this group of cards, 4 cards use three-digit numbers and 4 cards use four-digit numbers.

Cards 25-32 up the difficulty level even further. These cards present three different subtraction problems solved by a hypothetical student. Two of the problems are correctly solved and one has an error. The students have to identify the problem that is solved incorrectly and then correctly solve that problem. Within this group of cards, 4 cards use three-digit numbers and 4 cards use four-digit numbers.

The organization of the cards provides scaffolding for your students, slowly building their skills. You may choose to have all of your students complete the cards in order. Once they reach Card 17, their work with the first sixteen cards will make it more likely that they will be able to quickly identify which of the two problems has an error. After working through Cards 17-24 to distinguish which of two problems has an error, examining three problems (on Cards 25-32) should be a breeze!

The varied difficulty levels also provide opportunities to differentiate for your students. You may have some of your students work on the cards with three-digit numbers (Cards 1-8, 17-20, and 25-28), while others work on the cards that feature four-digit numbers. Perhaps one group of students will start with Card 1 while students who have a higher level of proficiency with subtraction could begin with Card 17. You could 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.

Beyond the suggestions above, 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.

Because of the nature of the cards, the answer sheets provided are different than those included with my other task card sets. The first answer sheet has space for a student’s name and the date, and sets of lines for students to respond to four cards. The next answer sheet also features lines for four cards, and you can copy as many of these as you need, depending on the number of cards your students will use. For the final eight cards, the answer sheet provides a fill-in-the-blank sentence and space in which students can solve the given problem. If you prefer, you can save copies by having your students simply use notebook paper (or their journals) to write their answers to each card.

The provided answer key gives a full description of the error on each card as well as two suggestions for how the students’ work can be scored.

One of the printables includes a reference sheet that I designed for my students to glue in their math notebooks. The reference sheet shows three common errors that students make when subtracting with regrouping, with a description of the error, an explanation of what should have been done, and then a demonstration of the correct procedure. When I use reference sheets of this size, I have the students fold the sheet from the bottom to the top, not quite halfway, creasing the paper so that the title of the sheet is visible. When the students glue the folded sheet in their journals, the title is then visible so that students can more easily find it when they need to refer to the information on the sheet. You can have your students use this reference sheet as they work on the cards since the written descriptions on the reference sheet are models of how the students might use precise vocabulary to describe the errors on the cards they are examining.

The eight provided activity sheets can be used to evaluate student understanding of the algorithm for subtracting with regrouping. There are six half-sheet “exit ticket”-style assessments, each of which presents two completed subtraction problems. Your students need to decide which of the two problems was solved incorrectly, describe the error, and then explain how the problem should have been solved. The first three exit tickets use three-digit numbers and the second three use four-digit numbers. The final two assessment activities are full-page in length and feature twelve completed subtraction problems, presented in four rows of three. In each row, one of the problems is solved incorrectly. The students have to identify the incorrectly solved problem in each row and use the space provided to correctly solve those problems. The exit tickets and the two full-page activities are formatted similarly, and have similar types of questions, though the numbers on each are different, making them ideal for pre/post assessing. However, you could use these activities in any way that suits your classroom routine or meets your students’ needs - homework, center assignments, paired practice, the list goes on.

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

++++++++++++++++++++++++++++++++++++++++++++++++++++++++

++++++++++++++++++++++++++++++++++++++++++++++++++++++++

If you have students working on multi-digit multiplication, try

++++++++++++++++++++++++++++++++++++++++++++++++++++++++

++++++++++++++++++++++++++++++++++++++++++++++++++++++++

For more practice with whole number computation, 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)

Snow Bonds: +, –, x, and ÷ number relationships task cards & printables (set a)

I hope your students enjoy these resources and are able to build their proficiency with subtraction with regrouping.

Total Pages

28 pages

Answer Key

Included with rubric

Teaching Duration

N/A

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