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:

Method 2 organizes the place values into a vertical format:

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

# 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?

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.

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:

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

# 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?**

# 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.