Multiplication and Division for Higher Order Numbers

In fourth grade, we extend our understanding of multiplication and division concepts to higher order whole numbers. Specifically, multiplication and division for higher order numbers can be divided into:

  • Multiply up to 4 digits by 1 digit, e.g. 7,032×8
  • Multiply up to 3 digits by 2 digits, e.g. 603×26
  • Divide up to 4-digits by 1 digit, e.g. 2,312÷2
  • Word problems

Multiply up to 4 digits by 1 digit

We start with multiplying 3 digits by 1 digit, and then extend to more cases involving 4-digit numbers. For each case, we can let students work with three methods:

Method 1 uses place values in a line by line format:

multiplication using place values in a line by line format

Method 2 organizes the place values into a vertical format:

multiplication using place values in a vertical format

Finally, we’ll use the standard algorithm we’re all familiar with:

multiplication using standard algorithm

Multiply up to 3 digits by 2 digits

Here, we start with multiples of ten, e.g. if 22×4 is 88, what is 22×40?

multiply 2 digits

When students are comfortable with multiples of 10, we can move on to the standard algorithm for multiplying by 2-digit numbers, starting with multiplying 2-digits by 2-digits, using place values to help us.

multiply 2 digits using standard algorithm

Once we’re comfortable, we can extend to multiplying 3-digits with 2-digits.

Divide up to 4-digits by 1 digit

We start by reviewing division with regrouping:

division with regrouping

Then we’ll work on dividing 3-digit numbers by 1-digit numbers, e.g. 468÷3,

divide 3 digit by 1 digit

3-Step Word Problem Involving the 4 Operations

Now that we’re comfortable working with higher order numbers, we can work on more interesting word problems involving the 4 basic operations. Here again, we’ll use bar models to help us, e.g.

Mrs Brown had a budget of $2,000 to spend on a hat and 4 shirts. She overspent by $250. The hat costs twice as much as a shirt. How much did she spend on the hat?

three step word problem

Related Resources

Video explanation and lesson plan (member’s resource)

Common Core Standards

  • A1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
  • A2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
  • A3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
  • A1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 divided by 70 = 10 by applying concepts of place value and division.
  • B5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
  • B6 Find whole-number quotients and remainders with up to four-digit dividends and one-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 (4A) Chapter 3 – Whole Number Multiplication and Division (pages 41 to 66)
  • Primary Mathematics workbook (Common Core Edition) (4A) Chapter 2 – The Whole Operations of Whole Numbers (pages 52 to 80)


Related Resources

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

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