Multiplication and Division – Mastery

This is the final post in our series of blog posts on teaching Multiplication and Division from 2nd through 5th grade. In this post, we discuss the final ingredients needed to master multiplication and division.

In fifth grade, we extend our understanding of whole number multiplication and division to general numbers (up to 4-digits), and master the 4 basic operations. Specifically, we want to make sure students can:

  • Multiply by tens, hundreds and thousands,
  • Multiply a 4-digit number with a 2-digit number,
  • Divide by tens, hundreds and thousands,
  • Divide a 4-digit number by a 2-digit number,
  • Combine operations involving the 4 basic operations, understand and apply the order of operations, and
  • Solve word problems involving the 4 operations.

Multiply by tens, hundreds and thousands

Students should have no problem with this if they have a good understanding of their place values, e.g.

Multiply by tens, hundreds and thousands

Multiply a 4-digit number with a 2-digit number

It might be easier to start with multiplying 2-digit numbers with 2-digit numbers, and review the techniques we learned in earlier grades, e.g. place values and distributive property:

Multiply a 4-digit number with a 2-digit number

Once we’re comfortable with 2-digit numbers, extend the same techniques to 4-digit numbers, e.g. 2,312×53.

Divide by tens, hundreds and thousands

Instead of starting with “rules” right away (e.g. remove zeros), we can start with conceptual understanding, e.g. if we have 1,800 and we want to divide into 10 equal parts, how much must each part have? 180. What if we want to divide into 100 equal parts? 18.  Then we can introduce “rules” such as adding/dropping zeros.

Divide by tens, hundreds and thousands

Divide a 4-digit number by a 2-digit number

This is sometimes tricky for students. They have to first have a good understanding of dividing by tens, hundreds and thousands, and be clear about why e.g. 360÷60 yields the same answer as 36÷6. We can use examples with remainders too, i.e.

division with remainder

When we’re ready, we start with dividing 2-digit numbers by 2-digit numbers usually with remainder, e.g.

dividing 2-digit numbers by 2-digit numbers

Finally, we’ll extend the same concepts to 4-digit numbers.

Combine operations involving the 4 basic operations

To fully master multiplication and division, we want to be familiar with the order of operations for the 4 operations:

order of operations

Here, we want to emphasize on three points:

First, basic order is from Left to Right:

order of operations left to right

Next, parentheses:

order of operations left to right parenthesis

Finally, the order of operations:

order of operations

Students actually learned some of these rules informally in earlier grades, e.g. when using the distributive property for multiplication in second grade in the example above.

Solve word problems involving the 4 operations

We’re now ready to solve general word problems involving all 4 operations, using bar modeling, and truly master multiplication and division e.g.

Hannah and Francine have $120. Hannah and Peter have $230. Peter has 6 times as much money as Francine. How much money does Hannah have?

word problems involving the 4 operations

Related Resources

Video explanation and lesson plan (member’s resource)

Common Core Standards

  • A1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
  • A2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation ‘add 8 and 7, then multiply by 2’ as 2 x (8 + 7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
  • B5 Fluently multiply multi-digit whole numbers using the standard algorithm.
  • B6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Suggested Workbook Series

  • Math in Focus workbook (5A) Chapter 2 – Whole Number Multiplication and Division (pages 27 to 78)
  • Primary Mathematics workbook (Common Core Edition) (5A) Chapter 1 – Numbers to 10, 000 (pages 18 to 61)

 

Related Resources

For more related resources, please refer to our Multiplication and Division page.

Leave a Comment

Your email address will not be published.

Scroll to Top