Build your students’ proficiency with multi-digit multiplication with this set of task cards and resource materials that focus on using the area model of multiplication to multiply two two-digit numbers. 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 two two-digit numbers, 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 a follow-up to Set A of my Box It Up!
task cards and printables. That set is a beginner’s set, focusing on the use of the area model to multiply a one-digit number by three-digit and four-digit numbers. If your students are just building their understanding of the area model, check out Box It Up! (Set A)
About the Cards
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. It focuses on the multiplication of two two-digit factors. 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.
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 two-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 (the tens value or the ones value), 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 – one partial products and two parts of each factor.
Please check out the preview to see all of the materials 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, and/or with the area model in general, you might have them complete only the cards that have multiple unknown quantities (cards 17-32) 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.
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 eight (such as cards 8, 16, 24, 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!
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 examples of the area model used to find the product of two similar sets of factors, one-digit by two-digit and two-digit by two-digit. The students are then presented with an open-ended question, asking them to compare how the area model was used in the two situations. You might have your students discuss their responses in pairs or in tables, have them share out as a class, and/or respond in writing in their journals. The intention was to show the students how the area model that they are already familiar with can be expanded to accommodate a larger product and to stimulate a rich mathematical discussions about the use of, and relationship between, models. 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. The pairs of worksheets 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 that fits your teaching style or classroom routines.
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. – Dennis McDonald