Lesson Plan Template: Finding Common Ground – Exploring Common Multiples and Least Common Multiples (LCM)

Learning Objectives:

• Students will determine common multiples of whole numbers using multiplication strategies and visual representations. (Focuses on problem-solving, connections, and representations)
• Students will collaboratively identify the least common multiple (LCM) of two or three whole numbers using a technology-based application. (Focuses on mathematical communication, collaboration, and technology)

Guiding Learning Theory: Sociocultural Theory

Rationale for Sociocultural Theory:

This lesson plan is based on Sociocultural Theory because it emphasizes the importance of social interaction and collaboration in learning. Students will work together in pairs and small groups to solve problems, share strategies, and build upon each other’s understanding of common multiples and LCM. The collaborative activities allow for guided discovery and peer learning, which are key tenets of Sociocultural Theory.

Learning Activities:

Objective 1: Finding Common Multiples

Hands-On Activity: Multiplication Arrays

• Materials: Grid paper, markers, crayons
• Instructions:
  1. Divide students into pairs and provide them with grid paper and markers/crayons.
  2. Ask each pair to choose two whole numbers (e.g., 4 and 6).
  3. Instruct students to create separate multiplication arrays for each of their chosen numbers on the grid paper.
  4. Students should then identify and mark the common multiples (numbers that appear in both arrays) on the grids.
  5. Facilitate a class discussion where pairs share their multiplication arrays and identified common multiples. Encourage students to explain their reasoning and explore different strategies for finding common multiples.

Technology-Based Activity: Online Matching Game

• Website: https://www.mathplayground.com/factortrees.html (or other similar educational game websites)
• Instructions:
  1. Students will access the online matching game focused on identifying common multiples.
  2. The game presents students with two numbers and requires them to identify the common multiples from a list of options.
  3. Students can work individually or in pairs to complete the matching game.
  4. After completing the game, have a group discussion about the strategies used to identify common multiples and how the game reinforced the concept.

Justification for Sociocultural Learning:

• The multiplication array activity encourages collaboration and communication as students work in pairs to create the arrays and identify common multiples. They can discuss their thought processes and learn from each other’s strategies.
• The online matching game allows for individual practice while still fostering a sense of social learning. Students can compare their strategies after completing the game and learn from each other’s approaches.

Objective 2: Finding the Least Common Multiple (LCM)

Hands-On Activity: Number Line Challenge

• Materials: Number lines (homemade or pre-made), markers
• Instructions:
  1. Divide students into small groups and provide each group with a number line and markers.
  2. Assign each group two or three whole numbers (e.g., 8, 12, and 16).
  3. Instruct students to mark each multiple of their assigned numbers on the number line.
  4. Challenge students to identify the least common multiple (LCM) by finding the number that appears on all three number lines.
  5. Encourage groups to discuss their reasoning and explain how they identified the LCM using the number line.

Technology-Based Activity: LCM Calculator App

• App: Several educational apps calculate the LCM (e.g., Socratic by Google, Mathway)
• Instructions:
  1. Students will explore an app that can calculate the least common multiple.
  2. In pairs, students will input different sets of two or three whole numbers into the app to find the LCM.
  3. Encourage students to discuss the results provided by the app and how they relate to their understanding of common multiples.
  4. Have students experiment with different sets of numbers to solidify their grasp of the concept of LCM.

Justification for Sociocultural Learning:

• The number line challenge promotes collaborative problem-solving. Students can work together to mark the multiples and discuss their reasoning to identify the LCM. This allows them to learn from each other’s perspectives and approaches.
• The LCM calculator app provides a valuable tool for students to practice finding LCM. However, the focus remains on discussion and understanding. Students should explain why the app provides a specific LCM and how it relates to the concept of common multiples. This encourages communication and reflection