Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Identify and extend geometric and numeric patterns.
• Determine the rule for a number sequence.
• Generate number sequences from a given rule.
• Represent patterns using flow diagrams and tables.
• Solve problems using number patterns.

Lesson summary

Patterns are everywhere! From the tiles on your kitchen floor to the rhythm of a Gqom song, understanding patterns is a fundamental skill that helps us predict, analyze, and make sense of the world around us. In Grade 7, we delve into the fascinating world of patterns, sequences, and relationships, building upon what you learned in previous grades. This week, we'll focus on identifying different types of patterns, generating number sequences based on given rules, and expressing these relationships using mathematical language. This is incredibly useful in everyday life – from budgeting your pocket money to understanding how your cell phone data usage increases over time.

Lesson notes

What are Patterns? A pattern is a regular and repeated way in which something happens or is done. In mathematics, a pattern is a sequence that repeats itself, or a sequence that can be predicted by a mathematical rule. We can have patterns in numbers (number sequences), shapes (geometric patterns), and even letters!

Number Sequences: A number sequence is an ordered list of numbers. Each number in the sequence is called a term. To understand a number sequence, we need to find the rule that connects the terms.

Types of Number Sequences: Arithmetic Sequence: In an arithmetic sequence, the difference between consecutive terms is constant. This constant difference is called the common difference.

For example: 2, 4, 6, 8, 10… (common difference = 2).

Geometric Sequence: In a geometric sequence, each term is multiplied by a constant value to get the next term. This constant value is called the common ratio.

For example: 3, 6, 12, 24, 48… (common ratio = 2).

Other Sequences: Many sequences don't fit into the arithmetic or geometric categories. These often involve more complex rules or combinations of operations.

Finding the Rule: The key to working with patterns is identifying the rule that governs the sequence.

Here's how: Look for a constant difference: If you find a constant difference between terms, it’s likely an arithmetic sequence.

Look for a constant ratio: If you find a constant ratio between terms, it’s likely a geometric sequence. Try adding, subtracting, multiplying, or dividing: See if any of these operations consistently relate consecutive terms.

Look for combinations of operations: Sometimes, the rule might involve multiple operations. For example, multiply by 2 and then add

1. Representing Patterns: We can represent patterns using: Number Sequences: As we’ve already seen.

Flow Diagrams: These diagrams use arrows to show the rule that transforms one number (input) into another (output).

Tables: These tables organize the terms of a sequence in rows and columns, making it easier to see the relationship between the term number (position) and the term value.

Worked example

Example 1: Arithmetic Sequence

Sequence: 5, 8, 11, 14, …

Identify the Pattern: The difference between each term is 3 (8-5 = 3, 11-8 = 3, 14-11 = 3).

Rule: Add 3 to the previous term.

Next two terms: 14 + 3 = 17, 17 + 3 =

2

0. The next two terms are 17 and

2

0. Example 2: Geometric Sequence

Sequence: 2, 6, 18, 54, …

Identify the Pattern: Each term is multiplied by 3 to get the next term (6/2 = 3, 18/6 = 3, 54/18 = 3).

Rule: Multiply the previous term by

3. Next two terms: 54 3 = 162, 162 * 3 =

4

8

6. The next two terms are 162 and 486.