Lesson Notes By Weeks and Term v5 - Grade 4

Lesson Video

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Performance objectives

• Identify and describe simple number patterns.
• Extend number patterns by finding the rule.
• Create your own number patterns.
• Recognize and describe geometric (shape) patterns.
• Predict the next shape in a geometric pattern.

Lesson summary

Patterns are everywhere around us! In Mathematics, understanding patterns helps us predict what comes next, solve problems, and even create beautiful designs. This week, we will be exploring different kinds of number patterns and shape patterns. Understanding patterns is important in South Africa because it helps us understand things like the patterns in the prices of goods in the shops, the arrangement of houses in a township, or even the patterns in traditional beadwork and fabrics. Recognizing patterns can also help us predict when to plant crops based on the changing seasons.

Lesson notes

What is a Pattern? A pattern is a sequence that repeats or follows a certain rule. Patterns can be found in numbers, shapes, colours, or even sounds. In mathematics, we are interested in number patterns and geometric patterns (shape patterns). Number Patterns Number patterns are sequences of numbers that follow a specific rule. This rule tells us how to get from one number to the next. The rule can involve addition, subtraction, multiplication, or division.

Example 1: Increasing Pattern (Addition)

Consider the pattern: 2, 4, 6, 8, ____, ____ Step 1: Find the Rule: What is being added each time? 2 + ? =

4. The answer is

2. Let's check if this works for the next number: 4 + 2 =

6. Yes! 6 + 2 =

8. Yes!

Step 2: Apply the Rule: The rule is "add 2". So, to find the next number: 8 + 2 =

1

0. And the number after that: 10 + 2 =

1

2. Step 3: Complete the Pattern: 2, 4, 6, 8, 10, 12 Example 2: Increasing Pattern (Multiplication)

Consider the pattern: 3, 6, 12, 24, ____, ____ Step 1: Find the Rule: What is being multiplied each time? 3 x ? =

6. The answer is

2. Let's check: 6 x 2 =

1

2. Yes! 12 x 2 =

2

4. Yes!

Step 2: Apply the Rule: The rule is "multiply by 2". So, to find the next number: 24 x 2 =

4

8. And the number after that: 48 x 2 =

9

6. Step 3: Complete the Pattern: 3, 6, 12, 24, 48, 96 Example 3: Decreasing Pattern (Subtraction)

Consider the pattern: 20, 17, 14, 11, ____, ____ Step 1: Find the Rule: What is being subtracted each time? 20 - ? =

1

7. The answer is

3. Let's check: 17 - 3 =

1

4. Yes! 14 - 3 =

1

1. Yes!

Step 2: Apply the Rule: The rule is "subtract 3". So, to find the next number: 11 - 3 =

8. And the number after that: 8 - 3 =

5. Step 3: Complete the Pattern: 20, 17, 14, 11, 8, 5 Example 4: Decreasing Pattern (Division)

Consider the pattern: 64, 32, 16, 8, ____, ____ Step 1: Find the Rule: What is being divided each time? 64 / ? =

3

2. The answer is

2. Let's check: 32 / 2 =

1

6. Yes! 16 / 2 =

8. Yes!

Step 2: Apply the Rule: The rule is "divide by 2". So, to find the next number: 8 / 2 =

4. And the number after that: 4 / 2 =

2. Step 3: Complete the Pattern: 64, 32, 16, 8, 4, 2 Geometric Patterns (Shape Patterns) Geometric patterns are sequences of shapes or objects that follow a specific rule. The rule might involve changing the shape, the colour, the size, or the orientation of the shapes.

Example 1: Circle, Square, Circle, Square, ____, ____ Step 1: Find the Rule: The pattern alternates between a circle and a square.

Step 2: Apply the Rule: The next shape is a circle, and the shape after that is a square.

Step 3: Complete the Pattern: Circle, Square, Circle, Square, Circle, Square Example 2: Triangle, Triangle, Square, Triangle, Triangle, Square, ____, ____ Step 1: Find the Rule: Two triangles are followed by one square.

Step 2: Apply the Rule: The next two shapes are triangles.

Step 3: Complete the Pattern: Triangle, Triangle, Square, Triangle, Triangle, Square, Triangle, Triangle Guided Practice (With Solutions)

Question 1: What are the next two numbers in the pattern: 5, 10, 15, 20, ____, ____?

Solution: Step 1: Find the Rule: 5 + ? =

1

0. The answer is

5. Check: 10 + 5 =

1

5. Yes! 15 + 5 =

2

0. Yes! The rule is "add 5".

Step 2: Apply the Rule: 20 + 5 = 25. 25 + 5 =

3

0. Answer: The next two numbers are 25 and

3

0. The complete pattern is 5, 10, 15, 20, 25,

3

0. Question 2: What are the next two numbers in the pattern: 30, 25, 20, 15, ____, ____?

Solution: Step 1: Find the Rule: 30 - ? =

2

5. The answer is

5. Check: 25 - 5 =

2

0. Yes! 20 - 5 =

1

5. Yes! The rule is "subtract 5".

Step 2: Apply the Rule: 15 - 5 = 10. 10 - 5 =

5. Answer: The next two numbers are 10 and

5. The complete pattern is 30, 25, 20, 15, 10,

5. Question 3: What are the next two shapes in the pattern: Star, Moon, Star, Moon, ____, ____?

Solution: Step 1: Find the Rule: The pattern alternates between a Star and a Moon.

Step 2: Apply the Rule: After the Moon comes a Star, and then a Moon.

Answer: The next two shapes are Star and Moon. The complete pattern is Star, Moon, Star, Moon, Star, Moon.

Question 4: What are the next two numbers in the pattern: 2, 4, 8, ____, ____?

Solution: Step 1: Find the Rule: 2 x ? =

4. The answer is

2. Check: 4 x 2 =

8. Yes! The rule is "multiply by 2".

Step 2: Apply the Rule: 8 x 2 = 16. 16 x 2 =

3

2. Answer: The next two numbers are 16 and

3

2. The complete pattern is 2, 4, 8, 16,

3

2. Question 5: What are the next two numbers in the pattern: 81, 27, 9, ____, ____?

Solution: Step 1: Find the Rule: 81 / ? =

2

7. The answer is

3. Check: 27 / 3 =

9. Yes! The rule is "divide by 3".

Step 2: Apply the Rule: 9 / 3 = 3. 3 / 3 =

1. Answer: The next two numbers are 3 and

1. The complete pattern is 81, 27, 9, 3,

1. Independent Practice (Questions Only) What are the next two numbers in the pattern: 7, 14, 21, 28, ____, ____? What are the next two numbers in the pattern: 100, 90, 80, 70, ____, ____? What are the next two shapes in the pattern: Square, Circle, Triangle, Square, Circle, Triangle, ____, ____?