Materials

  • CCB Mathematics pages 156 - 161

Standards

  • Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

  • Use functions to model relationships between quantities.

Objectives

  • Write expressions to represent patterns

  • Write equations to represent patterns

Key Concept

  • Identify, represent, and generalize patterns using expressions and equations.

Vocabulary

Tier 2 Generalize
Tier 3 Common difference
Input Variable
Numerical Pattern
Output Variable
Test Words Sequence

Before Lesson

In this lesson, students learn to identify patterns in sets of data. To determine their readiness, have students use a multiplication chart or mental math to share simple patterns of multiples, such as 2, 4, 6, 8, 10, … and 5, 10, 15, 20, 25, …

Background

Explain to students that patterns may be visual, auditory, or mathematical. Give them examples such as the beat in a song or the cycle of the moon. Have them identify and explain other patterns. Ask them how the pattern is repeated, and if they can find a rule that works for each part of the pattern.

Guided Practice

  • Write Expressions to Represent Patterns
  • Make a Table

Core Skill

Solve Real-World Arithmetic Problems: Have students read the text and complete the table. After they have confirmed that there is a common difference of 15 degrees, ask students why this is likely. (It was chance, dependent entirely on the weather.) Ask them if they can use the data in the table to predict temperatures the following week. Explain that weather can change from day to day, making it difficult, even for scientists with the most advanced tools, to predict weather accurately.

Build Lines of Reasoning: Have students read the first paragraph and discuss why it’s important to understand what makes each step in a solution process important. Help students understand that memorizing a series of steps may be useful in some cases, but the same steps can’t apply to all problems. Next, have students work with partners to complete the activity. This is the square number sequence. While students may not be familiar with squares, they may solve it by seeing that the value of the term is the location of the term times itself 1×1, 2×2, 3×3, etc.

Extension

Make Connections: Organize students into small groups and discuss real-world patterns. Offer an example of hourly wages as an example to start the conversation: For every delivery Joe makes, he earns $2.00. After his first delivery, he has $2.00; after his second delivery, he has $4.00, after his third delivery he has $6.00, and so on. Have students offer their own examples of real-world patterns, and challenge them to use those patterns to solve problems.

Construct Concept Maps: Challenge students to find real-world examples of input-output relationships, such as those that exist in computer science, mathematics, life science, and physical science. Ask students to construct concept maps to explain the relationships between inputs and outputs in the real world.