Lesson Notes By Weeks and Term v5 - Grade 5

Lesson Video

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Performance objectives

• Identify and describe number patterns.
• Extend number patterns using a rule.
• Use flow diagrams and tables to show patterns.
• Find the rule for a given pattern.
• Solve word problems with patterns.

Lesson summary

This week, we dive into the fascinating world of patterns, functions, and relationships in mathematics. Understanding patterns is like being a detective – you look for clues to predict what comes next! Recognizing patterns and understanding how things relate to each other is crucial for many aspects of life, from predicting the amount of groceries you need for the week, understanding how long it takes to travel a certain distance, to even recognizing recurring themes in stories and music.

Lesson notes

What are Patterns? A pattern is a sequence that repeats or changes in a predictable way. Patterns can be found everywhere, in numbers, shapes, and even sounds. This week, we're focusing on number patterns.

Types of Number Patterns: Increasing Patterns: These patterns get bigger as you move along the sequence. They are often formed by adding or multiplying.

Example:* 2, 4, 6, 8, 10… (Adding 2 each time)

Example:* 3, 6, 12, 24… (Multiplying by 2 each time)

Decreasing Patterns: These patterns get smaller as you move along the sequence. They are often formed by subtracting or dividing.

Example:* 20, 17, 14, 11, 8… (Subtracting 3 each time)

Example:* 64, 32, 16, 8… (Dividing by 2 each time)

Rules for Patterns: The rule is the instruction that tells you how to get from one number to the next in a pattern. Identifying the rule is key to extending the pattern.

Example: In the pattern 5, 10, 15, 20…, the rule is "Add 5".

Flow Diagrams: A flow diagram is a way to visually represent a pattern. It shows the input (the starting number), the rule (the operation to perform), and the output (the result). ``` Input --> Rule --> Output ``` Tables: Tables are another way to organize patterns. They show the relationship between two sets of numbers.

Example: | Input | Output | |-------|--------| | 1 | 4 | | 2 | 8 | | 3 | 12 | | 4 | 16 | In this table, the rule is "Multiply by 4".

Functions: A function is a relationship between two sets of numbers where each input has only one output. We can think of the rule as the function.

Worked example

Example 1: Find the next two numbers in the pattern: 1, 4, 7, 10, ___, ___.

Solution:

Identify the difference between consecutive numbers: 4 - 1 = 3, 7 - 4 = 3, 10 - 7 =

3.

The rule is "Add 3".

Extend the pattern: 10 + 3 = 13, 13 + 3 =

1

6.

The next two numbers are 13 and

1

6. Example 2: What is the rule for the following pattern? 24, 20, 16, 12…

Solution:

Identify the difference between consecutive numbers: 20 - 24 = -4, 16 - 20 = -4, 12 - 16 = -

4.

The rule is "Subtract 4".