Unit 16: Whole-Number Arithmetic Fluency

Day 17 of 30

Divide with remainders

3-5Mathematics

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Learning Objective

Students will be able to divide with remainders.

Today's Lesson

In this lesson, we'll explore how to divide with remainders. Mathematical thinking develops logical reasoning and problem-solving abilities.

A remainder is what's left over after division when the divisor doesn't divide evenly. For example, 17 ÷ 5 = 3 remainder 2 (because 5 × 3 = 15, and 17 - 15 = 2). We write it as 3 R2 or 3 2/5. In word problems, you interpret the remainder: Sometimes you round up (e.g., how many cars needed?), sometimes ignore it (e.g., how many full groups?), or sometimes use it (e.g., what's left?). Understanding remainders helps solve real-world division problems!

As you work through today's material, pay attention to the examples and try to identify the patterns or strategies being used. This will help you apply these concepts to new problems.

Take notes on key points and make connections to what you've already learned in previous lessons.

Key Terms
Problem

A mathematical question requiring analysis and solution

Solution

The result obtained by solving a problem

Activities
Instructions
1. Review the example problems for divide with remainders. 2. Identify the steps and strategies used. 3. Work through practice problems independently. 4. Compare solutions with a partner.
Materials Needed
  • Notebook
  • Calculator (if needed)
  • Graph paper
Practice Problems
1

17 ÷ 5 = ?

Hint: 5 goes into 17 three times (15), with 2 left over.
2

23 ÷ 4 = ?

Hint: 4 × 5 = 20. How much is left?
3

You have 50 cookies and 8 friends. How many cookies per friend? How many left?

Hint: Divide 50 by 8.

Teaching Tip

For this age group: Balance direct instruction with collaborative activities. Allow students to explain their thinking and make connections to prior knowledge when exploring divide with remainders.

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