Unit 59: Advanced Algebra (Polynomials, Factoring)

Day 22 of 30

Remainder theorem

11-12Mathematics

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Learning Objective

Students will explore remainder theorem through guided practice and application.

Today's Lesson

This lesson focuses on remainder theorem. Mathematics provides tools for modeling and analyzing complex systems.

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 engage with this material, consider both the theoretical foundations and practical applications. Think critically about how this concept builds on prior knowledge and where you might apply it beyond the classroom.

Challenge yourself to go beyond memorization—seek to understand the "why" behind the processes and principles.

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 remainder theorem. 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 advanced learners: Encourage deeper analysis and real-world connections. Consider extension activities that allow students to apply remainder theorem to novel situations.

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