Growing Patterns

Overview

In this activity, students explore growing patterns using manipulatives, drawings, and numbers. They will identify, extend, and create patterns that grow according to a rule, developing their algebraic thinking and pattern recognition skills.

Students will work with visual patterns that increase in a predictable way, identify the rule that governs the growth, and use that understanding to extend patterns and predict future terms. This foundational work with patterns helps build the groundwork for later algebraic concepts.

Learning Objectives

• Identify growing patterns in visual and numerical contexts
• Determine the rule that describes how a pattern grows
• Extend growing patterns based on the identified rule
• Create original growing patterns following a specified rule
• Make predictions about future terms in a growing pattern
• Use mathematical vocabulary to describe growing patterns

Materials

• Pattern blocks or other manipulatives (cubes, counters, etc.)
• Growing pattern cards (prepared examples)
• Student recording sheets
• Colored pencils or markers
• Grid paper
• Chart paper for class examples
• Optional: Digital pattern tool on tablets or computers

Preparation

1. Create or gather examples of growing patterns (visual and numerical)
2. Prepare pattern cards showing the first 3-4 terms of different growing patterns
3. Print student recording sheets with space for drawing and describing patterns
4. Organize manipulatives in containers for easy distribution
5. Set up a demonstration area with document camera or large chart paper

Steps

1. Introduction (5 minutes):
   • Show students a simple growing pattern (e.g., 1 triangle, 2 triangles, 3 triangles, etc.)
   • Ask students to describe what they notice about how the pattern changes
   • Introduce vocabulary: growing pattern, term, rule
   • Demonstrate how to identify and describe the rule (e.g., "Each term adds one more triangle")
2. Guided Practice (5 minutes):
   • Show a different growing pattern with the first 3 terms visible
   • Guide students to identify the pattern rule
   • Have students predict what the next 2 terms would look like
   • Reveal or create the next terms to check predictions
   • Model how to record the pattern and its rule
3. Partner Exploration (8 minutes):
   • Arrange students in pairs
   • Distribute pattern cards and manipulatives to each pair
   • Partners work together to identify the rule for their pattern
   • Partners extend the pattern by creating the next 2-3 terms
   • Partners record their work on the recording sheet
4. Pattern Creation (5 minutes):
   • Each pair creates their own growing pattern following a rule of their choice
   • Students show the first 4 terms of their pattern using manipulatives
   • Students record their pattern and describe the rule in writing
5. Sharing and Discussion (2 minutes):
   • Select 2-3 pairs to share their created patterns
   • Have the class identify the rule and predict the next term
   • Discuss different types of growing patterns observed

Differentiation

Assessment

Observe students during the activity and look for:

• Accurate identification of pattern rules
• Correct extension of patterns based on identified rules
• Ability to create original patterns that follow a consistent rule
• Use of mathematical vocabulary in describing patterns
• Reasoning skills when making predictions about future terms

Collect and review student recording sheets to assess understanding and identify any misconceptions.