Lesson Notes By Weeks and Term v5 - Grade 4

Lesson Video

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Performance objectives

• Identify and describe number patterns (adding/subtracting).
• Extend number patterns.
• Identify and describe geometric (shape) patterns.
• Create your own patterns.
• Use flow diagrams and tables to show patterns.

Lesson summary

Patterns and relationships are all around us! From the repeating designs on a traditional Zulu basket to the way houses line up on a street, recognizing and understanding patterns helps us make sense of the world. In mathematics, patterns help us predict what comes next, solve problems more easily, and understand how numbers are connected. This week, we'll focus on identifying, describing, and extending number patterns, as well as exploring geometric patterns. Understanding patterns builds a strong foundation for more advanced math topics later on, and helps us to appreciate the beauty and order in both mathematics and the world around us.

Lesson notes

2.1 Number Patterns A number pattern is a sequence of numbers that follow a specific rule. This rule tells us how to get from one number in the sequence to the next. Number patterns can be increasing (getting bigger) or decreasing (getting smaller). We often find these patterns involve adding or subtracting a fixed number each time.

Increasing Patterns: The numbers get larger. Usually, we are adding the same number each time.

Decreasing Patterns: The numbers get smaller. Usually, we are subtracting the same number each time.

Example 1: Increasing Pattern Consider the number pattern: 2, 4, 6, 8, ...

Rule: Add 2 to the previous number. To find the next number, add 2 to 8: 8 + 2 =

1

0. The pattern continues: 2, 4, 6, 8, 10, 12, 14, ...

Example 2: Decreasing Pattern Consider the number pattern: 20, 17, 14, 11, ...

Rule: Subtract 3 from the previous number. To find the next number, subtract 3 from 11: 11 - 3 =

8. The pattern continues: 20, 17, 14, 11, 8, 5, 2, ... 2.2 Geometric Patterns Geometric patterns are sequences of shapes or figures that follow a specific rule. The rule might involve changing the shape, size, orientation (direction it faces), or arrangement of the shapes.

Example 3: Geometric Pattern (Shape)

Consider the pattern: Circle, Square, Circle, Square, ...

Rule: The pattern repeats a circle followed by a square. The next shape in the pattern is a Circle.

Example 4: Geometric Pattern (Size)

Consider the pattern: Small Triangle, Medium Triangle, Large Triangle, Small Triangle, ...

Rule: The pattern repeats triangles of increasing size (small, medium, large). The next shape in the pattern is a Medium Triangle. 2.3 Flow Diagrams and Tables Flow diagrams and tables are ways to organize and represent number patterns.

Flow Diagram: A flow diagram shows the starting number (input), the rule, and the resulting number (output).

Example: Input -> + 5 -> Output If the input is 3, the output is 3 + 5 =

8. Table: A table organizes the input and output numbers in columns.

Example: | Input | Output | |-------|--------| | 1 | 6 | | 2 | 7 | | 3 | 8 | In this table, the rule is to add 5 to the input to get the output.

Example 5: Combination Imagine Nomsa is saving money for a new soccer ball. She starts with R10 and adds R5 each week.

Week 1: R10 Week 2: R15 Week 3: R20 This is an increasing pattern with the rule: add R

5. We can represent this in a table: | Week | Amount (R) | |---|---| | 1 | 10 | | 2 | 15 | | 3 | 20 | | 4 | 25 | | 5 | 30 | We can see that after 5 weeks, Nomsa will have R

3

0. Guided Practice (With Solutions)

Question 1: What is the next number in the pattern: 5, 10, 15, 20, ...?

Solution: Identify the rule: The pattern is increasing. The difference between each number is 5 (10-5=5, 15-10=5, 20-15=5).

Rule: Add 5 to the previous number.

Next number: 20 + 5 =

2

5. Answer: 25 Question 2: What is the missing number in the pattern: 30, 25, __, 15, 10?

Solution: Identify the rule: The pattern is decreasing. The difference between each number is 5 (30-25=5).

Rule: Subtract 5 from the previous number.

Missing number: 25 - 5 =

2

0. Answer: 20 Question 3: Draw the next two shapes in the following geometric pattern: Triangle, Square, Circle, Triangle, Square, ...

Solution: Identify the rule: The pattern repeats Triangle, Square, Circle.

Next two shapes: Circle, Triangle.

Answer: The next two shapes are a circle and a triangle.

Question 4: Complete the following flow diagram: Input -> + 7 -> Output Input: 2 -> Output: ?

Input: 5 -> Output: ?

Input: 10 -> Output: ?

Solution: Input: 2 -> Output: 2 + 7 = 9 Input: 5 -> Output: 5 + 7 = 12 Input: 10 -> Output: 10 + 7 = 17 Question 5: Complete the following table: | Input | Output | |---|---| | 1 | 3 | | 2 | 4 | | 3 | ? | | 4 | ? | Solution: Identify the rule. Looking at the first two rows, we see that Input + 2 = Output.

Apply the rule: 3 + 2 = 5. 4 + 2 =

6. Completed table: | Input | Output | |---|---| | 1 | 3 | | 2 | 4 | | 3 | 5 | | 4 | 6 | Independent Practice (Questions Only)

What is the next number in the pattern: 1, 3, 5, 7, ...?

What is the missing number in the pattern: 50, 45, 40, __, 30? What are the next two numbers in the pattern: 2, 6, 10, 14, ...?

Draw the next shape in the pattern: Star, Star, Moon, Star, Star, Moon, ...

Complete the flow diagram: Input -> - 4 -> Output (Input: 9, 12, 15)

Complete the table: | Input | Output | |-------|--------| | 2 | 8 | | 3 | 9 | | 4 | ? | | 5 | ? | Create your own increasing number pattern starting with the number 5, and write down the rule. Show at least 5 numbers in the pattern. Create your own decreasing number pattern starting with the number 30, and write down the rule. Show at least 5 numbers in the pattern.

Draw the next two shapes in this pattern: Square, Circle, Triangle, Square, Circle, Triangle,... Thando saves R2 every day. How much will she have saved after 7 days? Show this in a table.