Lesson Notes By Weeks and Term v5 - Grade 5

Lesson Video

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Performance objectives

• Identify and describe numerical patterns.
• Find the rule for a pattern and use it to extend the pattern.
• Use flow diagrams and tables to show relationships.
• Find missing input values, output values, or rules.
• Solve number sentences.

Lesson summary

This week, we're diving deeper into the world of patterns, functions, and relationships in mathematics. Understanding patterns is crucial because it helps us make predictions, solve problems, and understand the world around us. In South Africa, recognizing patterns can help us understand things like the seasons affecting agriculture, the designs in traditional art, or even predict traffic patterns in our cities. Patterns aren't just about numbers; they're about seeing connections and order.

Functions are like machines: you put something in (an input), and it gives you something else out (an output), according to a specific rule.

Lesson notes

What is a Pattern? A pattern is a sequence that repeats in a predictable way. Patterns can be found in numbers, shapes, sounds, and many other things. In mathematics, we often deal with numerical patterns – sequences of numbers that follow a specific rule.

Types of Numerical Patterns: Growing Patterns: The numbers get larger. These patterns often involve addition or multiplication.

Shrinking Patterns: The numbers get smaller. These patterns often involve subtraction or division.

Finding the Rule: The rule is what describes how the pattern works. To find the rule, look at how the numbers change from one term to the next.

Example 1: Growing Pattern Consider the pattern: 2, 4, 6, 8, … How does each number change to get to the next? It increases by

2. Therefore, the rule is "Add 2". The next number in the pattern would be 10 (8 + 2 = 10).

Example 2: Shrinking Pattern Consider the pattern: 20, 16, 12, 8, … How does each number change to get to the next? It decreases by

4. Therefore, the rule is "Subtract 4". The next number in the pattern would be 4 (8 - 4 = 4).

Functions and Relationships: Flow Diagrams and Tables A function is like a machine that takes a number as input, applies a rule, and produces a number as output. We can represent functions using flow diagrams and tables.

Flow Diagrams: A flow diagram shows the input, the rule, and the output.

Input: The number that goes into the function machine.

Rule: What the function machine does to the input.

Output: The number that comes out of the function machine.

Example 3: Flow Diagram Input → Rule: Multiply by 3 → Output If the input is 2, then the output is 2 * 3 =

6. If the input is 5, then the output is 5 * 3 =

1

5. Tables: A table lists pairs of input and output values.

Example 4: Table | Input | Output | |-------|--------| | 1 | 5 | | 2 | 6 | | 3 | 7 | | 4 | 8 | What is the rule? The output is always 4 more than the input. (Input + 4 = Output) Solving Number Sentences A number sentence is a mathematical statement with an unknown value. We can solve number sentences by inspection (looking at the sentence and figuring out the answer) or by trial and improvement (guessing and checking until we find the correct answer).

Example 5: Solving by Inspection x + 5 = 12 What number plus 5 equals 12? The answer is 7. (x = 7)

Example 6: Solving by Trial and Improvement 2 * y = 18 Let's try y = 8: 2 * 8 = 16 (too small) Let's try y = 9: 2 * 9 = 18 (correct!) Therefore, y =

9. Guided Practice (With Solutions)

Question 1: What is the next number in the pattern: 3, 6, 9, 12, ____?

Solution: Each number increases by 3. (6-3 = 3, 9-6 = 3, 12-9 = 3) The rule is "Add 3". The next number is 12 + 3 =

1

5. Answer: 15 Question 2: Complete the following flow diagram: Input: 7 → Rule: Subtract 2 → Output: ____ Solution: The rule is "Subtract 2". We need to subtract 2 from the input, 7. 7 - 2 = 5 Answer: 5 Question 3: Find the missing number in the table: | Input | Output | |-------|--------| | 2 | 8 | | 4 | 16 | | 5 | 20 | | 8 | ? | Solution: Look for the rule. The output is always the input multiplied by 4. (24=8, 44=16, 54=20)

Apply the rule to the last input: 8 4 = 32 Answer: 32 Question 4: Solve the number sentence: p - 3 = 9 Solution: What number minus 3 equals 9?

We can think: 9 + 3 = 12 Therefore, p =

1

2. Answer: p = 12 Question 5: Complete the following flow diagram: Input: ____ → Rule: Divide by 2 → Output: 6 Solution: This is an inverse operation question. We have to do the opposite to find the input. The opposite of division is multiplication. 6 multiplied by 2 is

1

2. Answer: 12 Independent Practice (Questions Only)

What is the next number in the pattern: 5, 10, 15, 20, ____?

What is the next number in the pattern: 30, 25, 20, 15, ____?

Complete the following flow diagram: Input: 9 → Rule: Multiply by 4 → Output: ____ Complete the following flow diagram: Input: ____ → Rule: Add 7 → Output: 15 Find the missing number in the table: | Input | Output | |-------|--------| | 1 | 3 | | 3 | 9 | | 4 | 12 | | 6 | ? | Find the rule and the missing number in the table: | Input | Output | |-------|--------| | 2 | 10 | | 5 | 25 | | 8 | ? | | 10 | 50 | Solve the number sentence: a + 8 = 15 Solve the number sentence: b / 3 = 6 Create your own numerical pattern with at least 5 numbers. Describe the rule. Design a flow diagram with a rule that involves two operations (e.g., multiply by 2, then add 1). Provide 3 input/output pairs for your flow diagram.