Lesson Notes By Weeks and Term v5 - Grade 4

Lesson Video

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Performance objectives

• Identify and extend simple number patterns.
• Describe the rule for a number pattern.
• Identify and extend simple geometric patterns.
• Use a flow diagram to show a pattern.
• Solve simple problems with patterns.

Lesson summary

Patterns and relationships are fundamental to understanding the world around us. From the repeating patterns in traditional Zulu beadwork to the number of rows in a maize field, recognising and working with patterns helps us predict, organise, and make sense of our environment. This week, we will explore number patterns and geometric patterns, learning how to identify them, extend them, and describe the relationships within them. Understanding patterns will also strengthen your problem-solving skills, which are useful in many aspects of life, from planning your pocket money to figuring out how much bread to buy for your family.

Lesson notes

2.1 What are Patterns? A pattern is a sequence that repeats in a predictable way.

Patterns can be found everywhere: in numbers, shapes, colours, sounds, and even behaviours. We can describe a pattern by stating its rule, which tells us how to continue the sequence. 2.2 Number Patterns Number patterns are sequences of numbers that follow a specific rule. The rule tells us how to get from one number to the next.

Example 1: Increasing Patterns (Addition)

Consider the pattern: 2, 4, 6, 8, __, __ Step 1: Find the difference between consecutive numbers. 4 - 2 = 2 6 - 4 = 2 8 - 6 = 2 Step 2: Identify the rule. The rule is "add 2 each time".

Step 3: Extend the pattern. 8 + 2 = 10 10 + 2 = 12 Therefore, the pattern continues: 2, 4, 6, 8, 10, 12 Example 2: Decreasing Patterns (Subtraction)

Consider the pattern: 20, 17, 14, 11, __, __ Step 1: Find the difference between consecutive numbers. 17 - 20 = -3 14 - 17 = -3 11 - 14 = -3 Step 2: Identify the rule. The rule is "subtract 3 each time".

Step 3: Extend the pattern. 11 - 3 = 8 8 - 3 = 5 Therefore, the pattern continues: 20, 17, 14, 11, 8, 5 Example 3: More Complex Patterns (Combined operations)

Consider the pattern: 1, 3, 7, 15, __, __ This is not a simple addition or subtraction pattern.

Let's analyse: 3 = 1 x 2 + 1 7 = 3 x 2 + 1 15 = 7 x 2 + 1 Step 2: Identify the rule. The rule is "multiply by 2 and add 1 each time".

Step 3: Extend the pattern. 15 x 2 + 1 = 31 31 x 2 + 1 = 63 Therefore, the pattern continues: 1, 3, 7, 15, 31, 63 2.3 Geometric Patterns Geometric patterns are sequences of shapes or objects that follow a specific rule. The rule tells us how the shapes change or are arranged in each step. These shapes may also be colored, forming a more complex pattern.

Example 1: Imagine a pattern made of circles: Step 1: 1 circle Step 2: 3 circles Step 3: 5 circles Step 1: Identify the change between each step. We add 2 circles each time.

Step 2: Describe the rule. The rule is "add 2 circles to the previous step".

Step 3: Extend the pattern.

Step 4: 7 circles Step 5: 9 circles Example 2: Imagine a pattern made of triangles colored red and blue: Step 1: Red Triangle Step 2: Red Triangle, Blue Triangle Step 3: Red Triangle, Blue Triangle, Red Triangle Step 1: Identify the change between each step. We add a triangle each time, alternating between red and blue.

Step 2: Describe the rule. The rule is "add a triangle, alternating between red and blue, starting with red".

Step 3: Extend the pattern.

Step 4: Red Triangle, Blue Triangle, Red Triangle, Blue Triangle 2.4 Flow Diagrams A flow diagram is a visual way to represent a number pattern. It shows the starting number (input), the rule (operation), and the resulting number (output).

Example: Input: 3 Rule: Add 5 Output: 8 Input: 8 Rule: Add 5 Output: 13 This can be represented in a flow diagram as follows: 3 --(+5)--> 8 --(+5)--> 13 --(+5)--> ... Guided Practice (With Solutions)

Question 1: Complete the number pattern: 5, 10, 15, __, __ Solution: Step 1: Find the difference between consecutive numbers. 10 - 5 = 5 15 - 10 = 5 Step 2: Identify the rule. The rule is "add 5 each time".

Step 3: Extend the pattern. 15 + 5 = 20 20 + 5 = 25 Answer: 5, 10, 15, 20, 25 Question 2: Describe the rule for the number pattern: 30, 25, 20, 15, ...

Solution: Step 1: Find the difference between consecutive numbers. 25 - 30 = -5 20 - 25 = -5 15 - 20 = -5 Step 2: Identify the rule. The rule is "subtract 5 each time".

Answer: Subtract 5 each time.

Question 3: Consider a geometric pattern: Square, Triangle, Square, Triangle, __, __ What are the next two shapes in the pattern?

Solution: Step 1: Identify the repeating sequence. The sequence is Square, Triangle.

Step 2: Extend the pattern. The pattern repeats, so the next two shapes are Square and Triangle.

Answer: Square, Triangle Question 4: Complete the flow diagram: 2 --(+4)--> __ --(+4)--> __ Solution: Step 1: Apply the rule to the first input. 2 + 4 = 6 Step 2: Apply the rule to the next input (which is the previous output). 6 + 4 = 10 Answer: 2 --(+4)--> 6 --(+4)--> 10 Independent Practice (Questions Only)

Complete the number pattern: 12, 15, 18, __, __ Describe the rule for the number pattern: 40, 35, 30, 25, ...

Complete the number pattern: 2, 6, 10, 14, __, __ Describe the rule for the number pattern: 1, 4, 9, 16, ... (Hint: think about squares) What are the next two shapes in the pattern: Circle, Square, Circle, Square, __, __?

Complete the following flow diagram: 10 --(-2)--> __ --(-2)--> __ --(-2)--> __ If a pattern starts with 3 and the rule is "multiply by 2", what are the next three numbers in the pattern? Consider a pattern of sweets. The first row has 2 sweets, the second row has 4 sweets, and the third row has 6 sweets. How many sweets will be in the fifth row?

Draw the next shape in the pattern: Upward pointing triangle, rightward pointing triangle, downward pointing triangle, leftward pointing triangle, _________ A plant grows 2cm each week.