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Features

Area models that split both factors by place value into six parts
Partial products in columns, each labelled with what was multiplied
The standard algorithm with small boxes for regrouped digits
4-digit by 2-digit, 3-digit by 3-digit, and zeros in a factor
Estimate by rounding each factor, then multiply and compare
One- and two-step story problems
Every page in color and in black and white
Answer keys included

Skills Covered

Multiply 3- and 4-digit numbers by 2-digit numbers
Use area models and partial products
Multiply with the standard algorithm

Place the 0 when multiplying by the tens
Multiply with zeros in a factor and by 3-digit numbers
Estimate products to check that an answer makes sense

How to Use This Pack

Five pages that move from pictures to the standard algorithm. Page 1 splits both factors by place value in an area model: 346 × 27 becomes 300, 40 and 6 across and 20 and 7 down, six parts to multiply; adding each row gives 346 × 20 and 346 × 7, which are the two rows of the standard algorithm. Page 2 writes the same parts as partial products in a column, each one labelled with what was multiplied, for 3-digit and 4-digit numbers. Page 3 is the standard algorithm for 3 digits by 2 digits, with small boxes for regrouped digits and the 0 that holds the ones place in the second row. Page 4 has larger factors: 4-digit numbers, numbers with zeros such as 6,040 × 38, and a 3-digit number times a 3-digit number. Page 5 rounds each factor to estimate before multiplying, then has one- and two-step stories. Every page starts with a worked example.

In the Classroom

Put 346 × 27 on the board and solve it three ways side by side: an area model, partial products and the standard algorithm. Ask students to find the same numbers in all three (the area model's row for 20 adds up to 6,920, the second row of the standard algorithm). On page 3, ask why the second row starts with a 0, and what goes wrong without it: estimate 300 × 30 = 9,000 and compare.

At Home

Multiply with real numbers from around the house: 24 cans in a case and 15 cases, 365 days in a year and 12 years. Before multiplying, round each number and guess the answer. After, compare: is the answer close to the guess?

Tips for Success

Multiply by the ones first, then by the tens, then add the rows
When you multiply by the tens, write a 0 in the ones place first
Write regrouped digits small, above the top number, and add them after you multiply
A 0 in the top number still gets multiplied: it gives 0, plus any regrouped digit
Round each factor to estimate first, then check that the product is close

Common Core Standards Alignment

This pack supports the following Common Core State Standards for Mathematics:

4.OA.A.3 Solve multi-step story problems with whole numbers and all four operations, deciding what remainders mean, writing equations with a letter, and checking by estimating.
5.NBT.B.5 Multiply whole numbers with many digits fluently, using the standard written method.

Multiplying by 2-Digit Numbers

5th Grade

Multiplying 3- and 4-digit numbers by 2-digit numbers, from area models and partial products to the standard algorithm. Students split both factors by place value, write every partial product, multiply by the ones and then the tens, work with zeros and 3-digit factors, estimate to check, and solve one- and two-step stories.

Download PDF

What’s Included

5 worksheets in color and in black and white, with answer keys (15 pages)
Area models and partial products for 3- and 4-digit numbers
The standard algorithm with regrouping, zeros and 3-digit factors
Estimating to check, and one- and two-step story problems

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Free to print and share

This worksheet is free to download, print, copy, and hand out in your classroom or at home. You do not need to create an account, and there are no watermarks on the PDF.