Build your students’ proficiency with multi-digit multiplication with this set of task cards and resource materials that focus on the area model of multiplication. Your students will be challenged to reason about number relationships as analyze the area models presented on the 32 task cards in this set. Evaluate their understanding (or extend their practice!) with the four included assessment activities. With this “print-and-go” resource, you’ll have everything you need to develop, strengthen, and assess your students’ understanding of multi-digit multiplication and the area model.
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, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (4.NBT.5)
• reference sheet
• 32 task cards
• task card answer sheet and key
• 4 assessment activities
• rubric and answer key for assessment activities
This set is designed to build students’ proficiency with the area model, one of the models of multiplication referenced in the Common Core Standards for Mathematics and a stepping stone towards the standard algorithm. I created this set of task cards and resource materials to provide a degree of challenge for my students as they practiced using this method. As my students worked with the area model, I didn’t want them to simply rotely multiply and add, but to think about how the area model works and why a given model represents a particular equation. My goal was to use the area model as the springboard for some genuine reasoning about number relationships, building not just proficient multipliers, but proficient thinkers.
About the Cards
The cards present complete and partially complete area models for students to analyze and ask them to figure out the factors represented by the model, as well as the product of those factors. The models on the cards represent one-digit by three-digit and one-digit by four-digit multiplication equations, and the cards are organized by difficulty level.
The first eight cards present a complete area model and students need to write an equation showing the two original factors on which the model is based, as well as the product of those factors. The second eight cards (cards 9-16) present area models that are nearly complete. All of the numbers are filled in except for one of the partial products. The students still need to write an equation to match the factors and product represented by the model. However, in order to find the product, they also need to figure out the missing partial product. The third set of eight cards (cards 17-24) feature area models that are missing both one of the partial products as well as part of one of the factors, requiring students to figure out those unknown elements before they are able to identify the original factors and their product. The final set of eight cards (cards 25-32) feature area models that have three unknown values. Within each set of eight cards, the first four use one-digit and three-digit factors, while the second four use one-digit and four-digit factors.
Please check out the preview to see all of the cards and other resources up close!
Using the Cards
The order of the problems, as well as the similar formatting on each set of 8 cards, was designed to provide a level of scaffolding for your students, allowing them some repeated practice with a given level of difficulty before it is increased. You can also take advantage of the organizational structure and formatting of the cards to help differentiate for the varied student needs in your classroom.
If you have some students who are more proficient with their facts, with multiplying by multiples of 10, 100, and 1,000, and/or with the area model in general, you might have them complete only the cards that use four-digit factors (cards 5-8, 13-16, 21-24, and 29-32) while the other students work through all the cards. You might choose to have some of your more able students complete only the odd-numbered or even-numbered cards, allowing them the benefit of the scaffolding provided by the cards’ order, while others complete all the cards.
Looking to help support your students who are struggling with the area model? You might have some of your class work on their own or in pairs while you provide guidance to a small group. Work together with them on the first two cards in each set of four, have the students work with a partner on the third one, and then complete the fourth one on their own. Repeat this process with each set of four cards. Perhaps you might work with these students on all the cards that use three-digit factors (cards 1-4, 9-12, 17-20, and 25-28) first, and then go back and work through the cards that feature four-digit factors.
Are you unsure of your students’ levels of proficiency? Have them all work through just the odd-numbered cards or just one card in each set of four (such as cards 4, 8, 12, 16, 20, 24, 28, and 32), and then use their performance on those cards to determine which students need to complete the even-numbered cards and which would benefit from enrichment and extension. There are many possibilities for how you might support your students’ success as they work through these cards!
Beyond the suggestions above, there are lots of ways in which you can utilize these 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.
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 provides a general overview of the area model and walks the students through the process of using the area model to find the product of a one-digit factor and a three-digit factor. Some of the vocabulary used on the cards, such as “partial product”, is used on the reference sheet, and a sidebar on the sheet defines this and other terms associated with multiplication and the area model. 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 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 multiplying multi-digit numbers using the area model.
Assessing Student Understanding
The four assessment activities can be used to evaluate student understanding of the area model – or even as additional instructional resources. The first pair of activities are similar to the cards, presenting complete and incomplete area models and requiring students to identify unknown values and then write a multiplication equation to show the factors and product represented by the area model. [When having your students complete these activities, it may be helpful to give them extra paper on which to perform any necessary calculations since the activity sheet itself does not have much empty space.] The second pair of activities are more open-ended, with multiple correct answers and providing an opportunity for students to explain their thinking in writing. Each two pair of 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.
For more practice with whole number computation and multiplication concepts, 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)
Comparison Conundrums math story problems task cards + printables (set a)
Snow Bonds: +, –, x, and ÷ number relationships task cards & printables (set a)
Comparison Conundrums math logic problems task cards + printables (set c)
I hope your students enjoy these resources and are able to build their proficiency with multiplication and the area model.