Lesson Notes By Weeks and Term v5 - Grade 5

Lesson Video

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Performance objectives

• This week, we delve deeper into the fascinating world of patterns, functions, and relationships in mathematics. Understanding patterns helps us make predictions, solve problems, and see the beauty and order in the world around us. From the repeating designs in traditional Ndebele art to the way our savings grow over time, patterns are everywhere! Learning about functions and relationships shows us how different things are connected and influence each other. This skill is crucial for understanding more complex math concepts later on and for making informed decisions in everyday life. Imagine planning a birthday party: you need to understand the relationship between the number of guests and the amount of food and drinks you need. Or, consider saving money for a new bicycle: understanding how your savings grow each month is a function of how much you deposit.
• By the end of this week, you will be able to:
• Objective 1: Identify and extend geometric patterns involving shape and size, including those found in South African art and architecture. (CAPS: Number, Operations and Relationships - Patterns, functions and algebra).
• Objective 2: Determine the rule (function) for number patterns represented in flow diagrams with one operation (addition, subtraction, multiplication, or division). (CAPS: Number, Operations and Relationships - Patterns, functions and algebra).
• Objective 3: Represent number patterns found in real-life scenarios using flow diagrams. (CAPS: Number, Operations and Relationships - Patterns, functions and algebra).

Lesson summary

This week, we delve deeper into the fascinating world of patterns, functions, and relationships in mathematics. Understanding patterns helps us make predictions, solve problems, and see the beauty and order in the world around us. From the repeating designs in traditional Ndebele art to the way our savings grow over time, patterns are everywhere! Learning about functions and relationships shows us how different things are connected and influence each other. This skill is crucial for understanding more complex math concepts later on and for making informed decisions in everyday life.

Lesson notes

What are Patterns? A pattern is a repeating arrangement of shapes, colours, numbers, or other objects. The repetition follows a specific rule. There are two main types of patterns we'll focus on: Geometric Patterns: These are patterns made up of shapes that repeat.

Number Patterns: These are patterns made up of numbers that follow a specific rule. Geometric Patterns Geometric patterns use shapes that repeat in a predictable way. The shapes can change in size, colour, or orientation, but the underlying pattern remains.

Example: Triangle, Square, Triangle, Square... What comes next? A triangle! Consider Ndebele art. The vibrant geometric patterns are not just beautiful; they are based on mathematical principles of repetition and symmetry. By studying these patterns, we can learn about geometric transformations like translation, rotation, and reflection.

Example: A row of houses, each painted with increasingly larger triangles pointing upwards. Number Patterns and Rules (Functions) Number patterns are sequences of numbers that follow a specific rule. This rule is called a function because it tells us how to get from one number to the next. We can represent these patterns using flow diagrams. A flow diagram is a visual way to represent a number pattern and the rule that governs it.

It consists of: Input: The starting number.

Rule (Function): What you do to the input number (add, subtract, multiply, or divide).

Output: The number you get after applying the rule to the input number.

Example 1: Simple Addition Input: 1, 2, 3, 4 Rule: Add 3 Output: 4, 5, 6, 7 Explanation: We start with the number 1, add 3 to it, and get

4. Then, we start with 2, add 3 to it, and get

5. And so on.

Example 2: Simple Subtraction Input: 10, 9, 8, 7 Rule: Subtract 2 Output: 8, 7, 6, 5 Explanation: We start with the number 10, subtract 2 to it, and get

8. Then, we start with 9, subtract 2 from it, and get

7. And so on.

Example 3: Simple Multiplication Input: 1, 2, 3, 4 Rule: Multiply by 5 Output: 5, 10, 15, 20 Explanation: We start with the number 1, multiply by 5, and get

5. Then, we start with 2, multiply by 5, and get

1

0. And so on.

Example 4: Simple Division Input: 20, 30, 40, 50 Rule: Divide by 10 Output: 2, 3, 4, 5 Explanation: We start with the number 20, divide by 10, and get

2. Then, we start with 30, divide by 10, and get

3. And so on. Describing the Relationship We can describe the relationship between the input and output numbers using words. For example, in Example 1, we can say: "The output number is always 3 more than the input number." In Example 3, we can say: "The output number is always five times the input number." Real-World

Example: Imagine you are selling lemonade. You charge R5 per glass.

Input (Number of glasses): 1, 2, 3, 4 Rule: Multiply by 5 (R5 per glass)

Output (Total cost in Rands): 5, 10, 15, 20 Relationship: The total cost is always five times the number of glasses sold. Guided Practice (With Solutions)

Question 1: Complete the following geometric pattern: Circle, Square, Circle, _____, _____.

Solution: Circle, Square, Circle, Square, Circle.

Commentary: The pattern alternates between a circle and a square. The next two shapes continue the alternating pattern.

Question 2: Complete the following number pattern: 2, 4, 6, _____, _____. What is the rule?

Solution: 2, 4, 6, 8,

1

0. The rule is: Add

2. Commentary: Each number is 2 more than the previous number. This is an increasing pattern.

Question 3: Complete the flow diagram: Input: 5, 10, 15, 20 Rule: Divide by 5 Output: _____, _____, _____, _____ Solution: Input: 5, 10, 15, 20 Rule: Divide by 5 Output: 1, 2, 3, 4

Commentary: We divide each input number by 5 to get the corresponding output number.

Question 4: Describe the relationship between the input and output numbers in the following flow diagram: Input: 3, 4, 5, 6 Rule: Add 7 Output: 10, 11, 12, 13 Solution: The output number is always 7 more than the input number.

Commentary: We are describing the relationship between the Input and Output, connecting them through the rule.

Question 5: Farmer Zola plants 3 rows of maize every day. Create a flow diagram showing the relationship between the number of days and the number of rows planted. Show for 4 days.

Solution: Input: 1, 2, 3, 4 (Number of Days)

Rule: Multiply by 3 (Rows per Day)

Output: 3, 6, 9, 12 (Total Rows Planted)

Commentary: The problem presents a real-world scenario that we can represent with a number pattern. This helps students understand the application of these concepts. Independent Practice (Questions Only)

Question 1: Continue the pattern: Red Bead, Blue Bead, Red Bead, Blue Bead, ____, ____.

Question 2: Complete the following number pattern: 10, 8, 6, _____, _____. What is the rule?