Lesson Notes By Weeks and Term v5 - Grade 4

Lesson Video

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Performance objectives

• Identify and extend geometric patterns.
• Describe the rule of a pattern.
• Create your own simple patterns.
• Recognize and continue number sequences.
• Determine the rule for a number sequence.

Lesson summary

Patterns and relationships are all around us, from the arrangement of tiles on a bathroom floor to the way vendors arrange fruit in a market. Understanding patterns helps us predict what comes next, solve problems, and make sense of the world. In South Africa, recognizing patterns is crucial for everyday activities like predicting bus arrival times based on schedules, understanding beadwork designs, or even anticipating changes in weather patterns based on historical data. It also builds the foundation for more advanced mathematical concepts later on. This week, we will focus on geometric patterns and number sequences, exploring how they grow and how to describe them.

Lesson notes

Geometric Patterns: Geometric patterns are created using shapes, colours, and sizes arranged in a repeating or growing sequence. The rule that governs the pattern dictates how it changes from one element to the next.

Identifying the Pattern Unit: The first step is to identify the shortest repeating sequence of shapes or colours. This is called the pattern unit.

Describing the Rule: Next, describe how the pattern unit is repeated or changed. Is it simply repeated? Is the size or colour changing? Is something being added to the pattern unit each time?

Example 1: Simple Repeating Pattern Pattern: Red Circle, Blue Square, Red Circle, Blue Square, Red Circle, Blue Square...

Pattern Unit: Red Circle, Blue Square Rule: The pattern unit "Red Circle, Blue Square" is repeated.

Example 2: Growing Pattern Pattern: 1 Triangle, 2 Triangles, 3 Triangles, 4 Triangles… Pattern Unit: Triangle Rule: One more triangle is added each time.

Number Sequences: A number sequence is a list of numbers that follow a specific rule or pattern. Understanding the relationship between consecutive numbers in the sequence is key to continuing the sequence.

Finding the Difference: Look at the difference between consecutive numbers. Is the same number being added (addition sequence) or subtracted (subtraction sequence)?

Describing the Rule: Write down the rule that describes how to get from one number to the next.

Example 3: Addition Sequence Sequence: 2, 4, 6, 8, … Difference between numbers: 4 - 2 = 2, 6 - 4 = 2, 8 - 6 = 2 Rule: Add 2 to the previous number.

Next number: 8 + 2 = 10 Complete Sequence: 2, 4, 6, 8, 10...

Example 4: Subtraction Sequence Sequence: 20, 17, 14, 11, … Difference between numbers: 17 - 20 = -3, 14 - 17 = -3, 11 - 14 = -3 Rule: Subtract 3 from the previous number.

Next number: 11 - 3 = 8 Complete Sequence: 20, 17, 14, 11, 8...

Combining Patterns: Sometimes, patterns involve a combination of geometric shapes and number sequences. For instance, the number of sides of the shape might follow a sequence.

Example 5: Combined Pattern Pattern: Triangle (3 sides), Square (4 sides), Pentagon (5 sides), Hexagon (6 sides)...

Shape: Triangle, Square, Pentagon, Hexagon Number of Sides: 3, 4, 5, 6 Rule: The number of sides increases by 1 each time. The shape gains one side at a time.

Next shape: Heptagon (7 sides) Guided Practice (With Solutions)

Question 1: Continue the following geometric pattern: Green Square, Yellow Circle, Green Square, Yellow Circle, ____, ____ Solution: Pattern Unit: Green Square, Yellow Circle Rule: The pattern unit is repeated.

Next shapes: Green Square, Yellow Circle Answer: Green Square, Yellow Circle Question 2: What are the next two numbers in the sequence: 5, 10, 15, 20, ____, ____ Solution: Difference between numbers: 10 - 5 = 5, 15 - 10 = 5, 20 - 15 = 5 Rule: Add 5 to the previous number.

Next numbers: 20 + 5 = 25, 25 + 5 = 30 Answer: 25, 30 Question 3: Draw the next shape in the pattern: Circle, Circle, Square, Circle, Circle, Square, ____ Solution: Pattern Unit: Circle, Circle, Square Rule: The pattern unit is repeated Next shape: Circle Answer: Draw a Circle Question 4: Complete the following number sequence: 30, 27, 24, ____, ____ Solution: Difference between numbers: 27 - 30 = -3, 24 - 27 = -3 Rule: Subtract 3 from the previous number.

Next numbers: 24 - 3 = 21, 21 - 3 = 18 Answer: 21, 18 Independent Practice (Questions Only)

Question 1: Draw the next two shapes: Star, Moon, Star, Moon, ____, ____ Question 2: What is the next number in the sequence: 1, 3, 5, 7, ____ Question 3: Draw the next two shapes: Triangle, Square, Triangle, Square, ____, ____ Question 4: Find the missing number: 10, ____, 30, 40, 50 Question 5: What comes next in this pattern: Blue, Blue, Red, Blue, Blue, Red, ____ Question 6: Complete the sequence: 50, 45, 40, 35, ____, ____ Question 7: Continue the pattern: Circle, Square, Triangle, Circle, Square, Triangle, ____, ____ Question 8: What is the missing number: 2, 4, ____, 8, 10 Question 9: Extend the pattern: Black bead, White bead, Black bead, White bead, ____, ____ Question 10: Complete the sequence: 12, 10, 8, 6, ____, ____