Exploring Multiplication

Objective

Students will understand multiplication through arrays and learn to represent multiplication in three different ways.

Curriculum Area

• Subject: Mathematics
• Grade Level: 3
• California Common Core Standards:
  • 3.OA.A.1: Interpret products of whole numbers.
  • 3.OA.A.3: Use multiplication within 100 to solve word problems.

Overview

This 45-minute lesson will introduce students to multiplication using arrays, repeated addition, and number lines. By building on their understanding of addition, students will see how multiplication can be represented in different formats.

Materials Needed

• Whiteboard and markers
• Projector for displaying sample problems
• Chart paper and markers
• Array cards (pre-prepared)
• Small counters or cubes
• Student notebooks
• Pencils

Lesson Plan

Introduction (10 minutes)

• Engage: Start with a brief discussion about what multiplication means. Ask students if they remember times when they have grouped items together (e.g., sharing candies in equal groups).
• Connect to Prior Knowledge: Discuss how multiplication is similar to repeated addition.

Direct Instruction (10 minutes)

• Explaining Arrays: Show an array on the board, such as 3 rows of 4 objects. Explain that an array is a way to organise objects into equal rows and columns.
• Write Multiplication Sentence: Demonstrate how the array translates into a multiplication sentence (3 rows of 4 equals 3 x 4 = 12).
• Describe the Concept: Explain that the number of rows and columns forms the factors in a multiplication problem, and the total number gives the product.

Guided Practice (15 minutes)

• Activity 1: Array Cards

  • Pass out pre-prepared array cards. Have students work in pairs to interpret the arrays.
  • Ask them to write a multiplication sentence for the array and use repeated addition to confirm their answer.

• Activity 2: Create Your Own Array

  • Give each student a piece of chart paper and some markers.
  • Have students create their own arrays using the counters or cubes to form a 4 x 3 or 2 x 6 configuration.
  • They will draw their array on paper and write the corresponding multiplication sentence and addition sentence.

Independent Practice (5 minutes)

• Notebook Work: Have students solve a few multiplication problems using either arrays, repeated addition, or a number line to show their understanding. Problems can include:
  • 2 x 5
  • 4 x 3
  • 5 x 2

Conclusion (5 minutes)

• Recap: Review what was learned about representing multiplication. Highlight the connection between arrays, multiplication sentences, and repeated addition.
• Q&A Session: Allow students to ask questions for any concepts they found challenging.

Assessment

• Informal Assessment: Observe students during guided and independent practice to assess their understanding.
• Exit Ticket: Ask students to draw a quick array for "3 x 4" and list the multiplication and addition sentences.

Extension

• Encourage students to find real-life examples of arrays at home or in their surroundings. Ask them to draw or bring in photos to share in the next class.

Reflective Notes for Teacher

• Note which students grasped the concept quickly and which may need additional support.
• Reflect on the effectiveness of the activities and adjust future lessons to better suit the class dynamics.
• Consider incorporating technology for a follow-up lesson that uses interactive array games or virtual manipulatives if resources allow.