Do you have students who still are struggling to accurately multiply multi-digit numbers with the standard algorithm, even after weeks (or months) 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 multiplication algorithm.
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 multiply multi-digit whole numbers using the standard algorithm. (5.NBT.5)
• reference sheet
• 36 task cards
• task card answer sheet, rubric, and key
• 10 assessment activities
• rubric and key for assessment activities
These cards were designed to help children be more reflective about the multiplication algorithm. Rather than having children simply solve a series of multiplication problems, the students are asked to analyze completed multiplication problems and identify errors in certain problems. The errors featured on the problems are ones that students commonly make when working through the multiplication algorithm. As your students think critically about the problems on these cards, they will start to think more critically about their own work when multiplying.
About the Cards
The problems on the cards are ordered by difficulty, allowing for you to more easily scaffold for student success. There are three categories of multiplication problem presented on the cards:
: three-digit by one-digit multiplication
: four-digit by one-digit multiplication
: two-digit by two-digit and three-digit by two-digit multiplication
Within each category of problem, the cards are organized in progressive difficulty, requiring successively more work on the part of the student. The first 4 cards in each set of 12 present two identical problems, one solved correctly and one incorrectly. The incorrectly solved problem is identified, and students have to identify and describe how to correct the error. The next 4 cards are similar, but the incorrectly solved problem is not identified and so students have to first figure out which problem is incorrect before describing the error and the fix. The third set of 4 cards present three different problems, one of which is incorrectly solved, and students have to figure out which problem is incorrectly solve and solve it correctly.
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 the third set of four cards in each group of twelve, their work with the first eight cards will make it more likely that they will be able to quickly identify which of the two problems has an error.
The varied difficulty levels also provide opportunities to differentiate for your students. You may have some of your students work on the cards with 3 x 1 problems (Cards 1-12), while others work on the cards that feature 4 x 1 or 2 x 2 and 3 x 2 problems. Perhaps one group of students will start with Cards 1, 13, or 25 while students who have a higher level of proficiency with multiplication could begin with Card 9, 21, or 33. 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 6 odd-numbered cards (1, 3, 5, 7, 9, and 11), 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 is a reference sheet that shows four common errors that students make when multiplying, 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 ten provided activity sheets can be used to evaluate student understanding of the multiplication algorithm. There are eight half-sheet “exit ticket”-style assessments, each of which presents two completed multiplication 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. There are two exit tickets for each category of multiplication featured on the cards: 3 x 1, 4 x 1, 2 x 2 and 3 x 2. The final two assessment activities are full-page in length and feature twelve completed multiplication problems, presented in four rows of three. In each row, one problem 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.
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.
Please check out the preview to see all of the materials up close!
For more practice with upper elementary number standards, please check out these other resources I have available –
Brainy Birds - x and ÷ with powers of ten task cards and printables (set a)
Hit the Slopes: mental division of large numbers task cards & printables (set a)
Calc Trouble reasoning about decimal multiplication task cards + printables
Box It Up! multiplying with the area model task cards + printables (set a)
I hope your students enjoy these resources and are able to build their proficiency with multiplication.