Summary

Using the area model for double digit multiplication is a great way for students to deepen their understanding of multiplication. Learn a few strategies for how to use the area model in your math classroom!

Effective Ways to Teach Area Model Double Digit Multiplication

Area model double digit multiplication worksheets sit on top of a grey table. — Using the area model allows students to break down larger numbers into smaller, easier multiples.

Before we dive in, if you’re looking for a grab-and-go effective way to teach the area model for double-digit multiplication, check these out! Read on to learn the why below, or grab these and start teaching and differentiating double-digit multiplication!

Area model double-digit multiplication can be controversial and overwhelming. “I don’t get that common core math these days, why can’t they just teach it the old way?” This is a common complaint in the households of children learning multiplication. The area model may seem like “complicated new-fangled math”. It helps improve overall number sense and logical thinking when working with multiplication.

Before we get to the effective ways to teach area model double-digit multiplication, we need to understand what the area model is and why it is important.

Text above multiplication work sheets reads: using the area model improves number sense. — The area model is the transitional stage, where students are moving from concrete models to more abstract thinking of multiplication

What is the Area Model in Math?

What is the area model in math? It takes the math concept of area (how large is a given surface) to show the gravity of multiplication. If you built an area of 2 x 4, you’d have 2 groups of 4 but if that array increased to 6 x 4, you’d have 6 groups of 4. The area model is a way to show this grouping without having to draw the area. Additionally, using the area model allows students to break down larger numbers into smaller, easier multiples. These area model worksheets walk students step-by-step through the area model and encourage deeper understanding through word problems and math tasks.

An area model broken into place value sits under text that reads: breaking down numbers makes double digit multiplication more accessible. — When you break down the area model, like done here, students can access the math knowledge and work through the multiplication while improving their overall fluency.

Thinking about the development of math skills through the stages of representation (Bruner and Kenny, 1965), the area model is the transitional stage. Students are moving from concrete models (array models or drawings) to more abstract thinking of multiplication (i.e. standard algorithm).

Using Area Model to Multiply

Using the area model for multiplication is a great way for students to understand the distributive property as well as the size of their numbers. It can be helpful to draw the model and split the area according to the size of the numbers. For example, if you had 34 x 6, you would split 34 into 30 and 4. The rectangle with a side of 30 should be much larger than the rectangle with a side of 4 because 30 is much larger. Breaking down numbers to multiply helps improve overall fluency when multiplying numbers.

Teaching Area Model Double Digit Multiplication

Before teaching area model multiplication students should have a basic understanding of multiplication and the idea that you are putting groups together. Many students will have mastered their basic facts and will be able to solve single-digit multiplication without the use of an array model. Check out these area model double-digit multiplication worksheets to streamline your teaching while differentiating to meet the needs of individual students. With introductory activities, games, and deep-thinking math tasks these worksheets can stand alone in your teaching.

A white hand draws green circles neatly in rows and columns. Text above reads: the area model bridges the gap between abstract and concrete mathematical representations. — When you break down the area model, like done here, students can access the math knowledge and work through the multiplication while improving their overall fluency.

Once students have been taught the relationship between the array model and the area model, you can begin showing two-digit by one-digit equations using the area model. It can be helpful to explore the relationship of multiplying by 10 before introducing double-digit multiplication.

Using the area model to teach double-digit multiplication allows students to break down larger numbers into their place value to easily multiply the numbers. This can be a student’s first exposure to the distributive property, as all factors must multiply each number. These steps of double-digit multiplication help students understand the meaning of the numbers they are using and the size of the operation of multiplication.

Differentiating Teaching the Area Model

As with any topic in teaching, differentiating the content will allow you to reach more students at their level. You can learn easy ways to differentiate any subject, or topic, here. To differentiate when using the area model you can pre-draw the model and choose factors of 1, 2, and 5, as those tend to be more easily mastered. These area model double-digit multiplication worksheets are differentiated into three different levels so you can do more teaching, and less prepping. With pre-drawn models and thoughtful factors, with these worksheets, you will be able to scaffold your students’ mastery of double-digit multiplication.

Benefits of Breaking Down Multiplication

A huge benefit of using the area model is it visually helps the students understand the role of place value and magnitude when finding the product. Using the area model to break down double-digit multiplication helps students understand 1) why the standard algorithm works when you choose to teach it and 2) it makes the larger numbers more accessible. While the equation 43 x 27 might seem very overwhelming to students, equations like 40 x 20 and 3 x 7 are more accessible and opens the door for student participation. Using thoughtful, purposeful equations is a great way to differentiate students’ ability to solve double-digit multiplication. These print-and-go area model double-digit multiplication worksheets are leveled with equations to support students’ fluency while still participating in the work.

Using the Area Model to Visualize

The area model is key as students move through the representation phases when learning double-digit multiplication. Concrete representations, such as arrays, become challenging as numbers become larger. Sure, you can draw 4 groups of 7 and keep track fairly easily but imagine drawing and counting 39 groups of 16?! As the area increases, the quantities become harder to keep track of opening students to both increased frustration and error. Help your students bridge the gap between concrete and abstract representations with these area model double-digit multiplication worksheets. They’ll walk through the area model step by step and gain an understanding of partial products. Featuring word problems and math tasks, students will apply their multiplication knowledge to grow their thinking.

The visual representation of the area model helps students bridge the gap between drawing arrays and using the standard algorithm. When first introduced, attempting to draw the models proportional helps the students understand how the numbers are breaking down and the difference between 30 x 40 and 3 x 4.

Area model multiplication game cards sit on a white desk. Text above reads: multiplication games are a great way to deepen thinking. — Games are a great way to encourage analytical thinking about mathematical concepts.

Area Model Multiplication Games

Area model multiplication games are a great way to practice double-digit multiplication! Grab this area model double-digit multiplication pack and get games, lessons, worksheets, and more! Games require students to think analytically and make connections across mathematical concepts. This matching game asks students to find the area model sequence for a given equation. Working in pairs or groups, students have important mathematical conversations to match the partial products to their final answer.

Area Model of Multiplication Worksheet

Worksheets can be a great way to progress monitor students’ mastery of double-digit multiplication. Using differentiated worksheets allows teachers to quickly meet the needs of individual students. In this area model double digit multiplication worksheet set, teachers have the choice of step-by-step area model or simple equations. It also features deep-thinking math tasks to help students deepen their understanding of double-digit multiplication.

A worksheet shows each step of the area model for double digit multiplication. Text above reads: using the area model creates access points for all students. — The area model is a great way to differentiate multiplication.

Multiplication Fluency

Multiplication fluency is achieved when students can quickly solve basic facts and apply that knowledge to larger problems. Fluency can look different for everyone. Some may need to quickly jot down an area model, while others’ standard algorithms may be more efficient. To be fluent, students need an effective method to solve the given problem. Effective looks like accuracy, speed, and minimal cognitive load. As students work with and manipulate numbers, their fluency will increase. These are a great way to practice double-digit multiplication and increase students’ multiplication fluency through application.