Multi Digit Multiplication Graphic Organizer

How it works

This multi digit multiplication graphic organizer puts three methods for the same problem next to each other. When all three give one product, students can see that the standard algorithm adds up the same parts the area model shows.

Read the full guide

A multiplication graphic organizer for grades 4 and 5

In the Common Core standards, 4th grade students multiply up to four digits by one digit and two digits by two digits, and explain the calculation with equations, rectangular arrays or area models. In 5th grade they multiply multi-digit whole numbers fluently with the standard algorithm.

How the three ways are related

An area model, also called the box or grid method, splits each factor by place value and keeps the multiplying apart from the adding. Partial products is the same calculation written without the box. The standard algorithm, long multiplication, splits only one of the factors.

Estimate before multiplying: 34 × 26 is close to 30 × 30, so a product far from 900 needs a second look.
Squared paper keeps the digits of the standard algorithm in their columns.

Questions and answers

What is the standard algorithm for multiplication?

It is long multiplication: stack the factors, multiply the top number by each digit of the bottom number in turn, and add the rows. For 34 × 26 the rows are 204 and 680, which add up to 884.

What is the area model for multiplication?

A box split by place value. For 34 × 26 the sides are 30 and 4, and 20 and 6, which makes four parts: 600, 180, 80 and 24. Adding them gives 884.

What are partial products?

The small products you get when each place of one factor is multiplied by each place of the other. Two digits by two digits gives four partial products, and their sum is the answer.

All 10 organizers

Three ways 3

Exit slips: one problem, two ways Two half sheets with a cut line between them: one problem worked two ways and the product.
Multi digit multiplication graphic organizer: one problem three ways Three open boxes side by side for the same problem: an area model, partial products and the standard algorithm. The line at the foot is for checking that all three agree.
Three ways compared A row for each way, with a box for how it works and a box for when you would choose it.

One way at a time 5

Area model boxes: three digits by two digits Two area models to a page with six boxes each, for hundreds, tens and ones across the top.
Area model boxes: two digits by two digits Two area models to a page. Write the parts of one factor across the top and of the other down the side, fill the four boxes, then add them.
Area model strips: four digits by one digit Two strips to a page with a box each for the thousands, hundreds, tens and ones of the larger factor.
Partial products chart: two digits by two digits The four small multiplications named down the side, with a box for the work and a box for each partial product. Two charts to a page.
Standard algorithm in four steps Four open boxes joined by arrows: estimate, multiply by the ones digit, multiply by the tens digit, add.

Filled-in samples 2

Sample area model, filled in: 34 × 26 = 884 The four boxes of the area model for the same problem: 600, 180, 80 and 24, which add up to 884.
Sample, filled in: 34 × 26 three ways One problem worked as the parts of an area model, as partial products and by the standard algorithm, with the same product each time.