What is an area model in 4th grade math? A parent's guide to box multiplication

By 15Q20M Editorial · Last updated September 19, 2026

An area model is a rectangle that turns one hard multiplication into a few easy ones. Your child splits each number by place value, so 35 × 24 becomes 30 + 5 and 20 + 4, multiplies the four pairs, and adds the results. The column method you learned uses the same four products and combines them into two rows.

What is an area model in 4th grade math?

The area of a rectangle is its length times its width. An area model uses that fact in reverse: to multiply two numbers, draw a rectangle with those numbers as its sides and find the area in pieces. For 35 × 24, break 35 into 30 + 5 down the left side and 24 into 20 + 4 across the top. The lines between them cut the rectangle into four smaller ones. Each is a simpler multiplication, and in this problem all four can be done mentally.

The idea starts a year earlier. A 3rd grade standard has students use area models with small numbers, for example showing that a 7 by 12 rectangle has the same area as a 7 by 10 rectangle plus a 7 by 2 rectangle. Teachers call this the distributive property, and it is the reason the method works: splitting a number into parts and multiplying each part gives the same total as multiplying the whole.

How to do area model multiplication: 35 × 24

This problem comes from Day 22 of our Grade 4 book, where a teacher sets up 35 rows of 24 chairs.

1. Split both numbers by place value. 35 is 30 + 5. 24 is 20 + 4.
2. Draw a rectangle and cut it into a 2 by 2 grid. On the left side, write 30 next to the top row and 5 next to the bottom row. Across the top, write 20 over the left column and 4 over the right column. The drawing does not need to be to scale.
3. Fill in each box by multiplying its row label by its column label. Top left: 30 × 20 = 600. Top right: 30 × 4 = 120. Bottom left: 5 × 20 = 100. Bottom right: 5 × 4 = 20.
4. Add the four boxes. 600 + 120 + 100 + 20 = 840 chairs.

When one factor has a single digit, the grid is one strip of boxes. 6 × 53 needs two: 6 × 50 = 300 and 6 × 3 = 18, for 318. For 4 × 306 your child can draw three: 4 × 300, 4 × 0, and 4 × 6, which is 1,200 + 0 + 24 = 1,224. The zero box is worth drawing. It is a reminder that 306 has no tens, so the number does not get worked as 36.

Area model vs partial products vs box method

These names come home on different nights and sound like three methods. They share the same arithmetic.

Maine, one of the states that uses these standards, describes the order this way in its guidance for teachers: "The area model leads nicely into the partial product strategy." It adds that students learn to use partial products without the drawing, and may go back to the area model when the numbers get longer.

Area model vs standard algorithm: where the four boxes go

Work 35 × 24 the way you learned it. First you multiply 35 by 4 and write 140. Then you put a zero in the ones place, multiply 35 by the 2, and write 700. Add the rows and you get 840.

Now look at the boxes again. The first row, 140, is two of them added together: 30 × 4 = 120 and 5 × 4 = 20. The second row, 700, is the other two: 30 × 20 = 600 and 5 × 20 = 100. The column method combines the four boxes into two rows. The small carried digits handle the regrouping inside each row, and the zero at the end of the second row handles the place value.

One detail is worth checking with your child. That zero in the second row is there because the 2 in 24 stands for 20. A question in our Grade 4 book asks this directly: in 46 × 27, what does the second row, 46 × 2, mean? The answer is 46 × 20. The boxes make that easier to talk about, because the 20 is written on the drawing. If your child knows the steps and cannot say why the zero is there, ask what the 2 in 27 is worth.

Why use area model multiplication instead of the way you learned?

The 4th grade standard does not name one required method. It has students multiply up to four digits by one digit, and two digits by two digits, "using strategies based on place value and the properties of operations." Its next sentence reads: "Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models." An area model is one of three accepted ways to show the work, and it keeps each place value written on the drawing. The words "standard algorithm" are not in that standard. They appear for multiplication one year later, in 5th grade: "Fluently multiply multi-digit whole numbers using the standard algorithm."

So the column method is still coming. Maine's guidance says mastery of it "is not expected until grade 5," and that students "will begin practicing the standard algorithm alongside other strategies much earlier than grade 5." Your child's class may already be using both.

Mistakes to look for in area model homework

The boxes make errors easier to find than a single wrong answer does. These are the ones to look for in the written work. A single slip does not prove a gap, so look for the same mistake showing up across several problems.

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How to help when you learned it a different way

Ask your child to teach you one problem. Explaining the calculation is part of the standard, and you will hear quickly whether the boxes mean something or are a routine being followed.

Let your child finish the problem with the boxes first. Then write the column method next to it and ask where 140 and 700 come from. Connecting the boxes to the rows can help your child see the place value behind the column method.

Estimate before multiplying. Round each number to the nearest ten: 35 × 24 is close to 40 × 20, which is 800. An answer of 8,400 then looks wrong before anyone checks the arithmetic, and 620 looks low enough to check.

If the homework directions are unclear about which method to use, ask the teacher. The standard accepts equations, rectangular arrays, or area models as ways to explain the calculation, and a teacher or curriculum may ask for a particular one on a given assignment.

A mistake that repeats shows up across daily pages sooner than it would in one long weekend session. Our books are built on that routine: a fixed set of 15 mixed problems on paper, answers entered in the free app, and an explanation for anything missed.

Try a free sample day (the sample is one Grade 5 session, scored in the app)

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