Lesson Notes By Weeks and Term v5 - Grade 5

Lesson Video

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Performance objectives

• Identify and describe number patterns.
• Extend number patterns by finding the rule.
• Use flow diagrams and tables to show patterns.
• Find the rule in a flow diagram or table.
• Find missing numbers in patterns.

Lesson summary

Patterns, functions, and relationships are all about finding order and making predictions. This is a fundamental part of mathematics and helps us understand the world around us. From predicting when the next taxi will arrive based on its current schedule to figuring out how many bricks we need to build a wall, patterns are everywhere. In South Africa, understanding patterns can help us with budgeting our pocket money, understanding population growth, predicting the weather, and even appreciating the complex patterns found in traditional beadwork and artwork.

Lesson notes

What is a Number Pattern? A number pattern is a sequence of numbers that follow a specific rule. This rule describes how the numbers in the sequence are related to each other. The rule could involve addition, subtraction, multiplication, division, or a combination of these operations.

Identifying the Rule: The key to understanding a number pattern is to find the rule. To do this, look at the difference between consecutive numbers. Is there a constant difference (addition or subtraction)? Or, is there a constant factor (multiplication or division)? Sometimes, patterns can be more complex, involving a combination of operations.

Example 1: Consider the sequence: 2, 4, 6, 8, 10... What is the rule? Notice that each number is 2 more than the previous number.

Therefore, the rule is "+ 2".

Example 2: Consider the sequence: 3, 6, 12, 24, 48... What is the rule? Notice that each number is multiplied by 2 to get the next number.

Therefore, the rule is "x 2".

Extending the Pattern: Once you have identified the rule, you can use it to find the next numbers in the sequence.

Example: Using the sequence from Example 1 (2, 4, 6, 8, 10...), what are the next three numbers? Since the rule is "+ 2", the next three numbers are: 12, 14,

1

6. Flow Diagrams and Tables: Flow diagrams and tables are useful tools for representing number patterns and functions. A flow diagram shows the input, the rule (operation), and the output. A table shows the input and corresponding output values.

Example: Flow Diagram Input --> Rule (+3) --> Output 1 --> --> 4 2 --> --> 5 3 --> --> 6

Example: Table | Input | Output | |-------|--------| | 1 | 4 | | 2 | 5 | | 3 | 6 | In both the flow diagram and the table above, the rule is "+ 3".

Finding Missing Values: We can use flow diagrams and tables to find missing input or output values. If we know the rule and either the input or output, we can calculate the missing value.

Example 1: Finding the missing output (using the same rule +3)

Input: 5; Rule: +3; Output: ? Output = 5 + 3 = 8 Example 2: Finding the missing input (using the same rule +3)

Input: ?; Rule: +3; Output: 10 Input = 10 - 3 = 7 Combined Rules: Some rules may involve more than one step.

Example: Consider this table: | Input | Output | |-------|--------| | 1 | 5 | | 2 | 8 | | 3 | 11 | | 4 | 14 | What is the rule? Looking at the differences, we see that for every increase of 1 in the input, the output increases by

3. This suggests multiplication by

3. Let's see: If we multiply the input by 3: 1 x 3 = 3 2 x 3 = 6 3 x 3 = 9 4 x 3 = 12 But the outputs are 5, 8, 11,

1

4. To get there we add 2 to the product: 3 + 2 = 5, 6 + 2 = 8, 9 + 2 = 11, 12 + 2 =

1

4. So the rule is: Multiply by 3 and add 2 (x 3 + 2) Guided Practice (With Solutions)

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

Solution: The rule is "+ 5".

Therefore, the next two numbers are 25 and

3

0. Commentary: This is a simple addition pattern. Identifying the constant difference is the key.

Question 2: Complete the following flow diagram: Input --> Rule (x 2) --> Output 3 --> --> ? 5 --> --> ? 7 --> --> ?

Solution: 3 x 2 = 6 5 x 2 = 10 7 x 2 = 14 Input --> Rule (x 2) --> Output 3 --> --> 6 5 --> --> 10 7 --> --> 14

Commentary: This exercise reinforces multiplication and the concept of input and output.

Question 3: Complete the following table and state the rule. | Input | Output | |-------|--------| | 2 | 8 | | 3 | 12 | | 4 | 16 | | 5 | ? | Solution: Notice that the Output is always 4 times the Input. | Input | Output | |-------|--------| | 2 | 8 | | 3 | 12 | | 4 | 16 | | 5 | 20 | Rule: Multiply by 4 (x 4)

Commentary: This requires identifying a multiplication rule based on provided input and output.

Question 4: Find the missing input value in the following: Input --> Rule (-5) --> Output:

3. Solution: To find the input, we need to do the inverse operation which is +5 3 + 5 = 8 So, the Input is

8. Commentary: Focus on understanding inverse operations to find the missing input. Independent Practice (Questions Only) What is the rule for the following sequence: 1, 4, 7, 10, 13,...? What are the next three numbers?

Complete the following flow diagram: Input --> Rule (+ 7) --> Output 4 --> --> ? 9 --> --> ? 12 --> --> ? Complete the following table and state the rule. | Input | Output | |-------|--------| | 1 | 6 | | 2 | 12 | | 3 | 18 | | 4 | ? | Find the missing output: Input: 8; Rule: (-2) --> Output: ?

Find the missing input: Input: ?; Rule: (+8) --> Output: 15 Consider the pattern: 2, 6, 10,

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4. What is the rule? What will the 7th term in the pattern be?

Complete the pattern: 36, 30, 24, ____, ____, ____. What is the rule? A tuck shop sells sweets for R2 each.

Complete the table: | Number of Sweets | Cost (R) | |--------------------|----------| | 1 | | | 2 | | | 3 | | | 4 | | | 5 | | Given the rule is "x 5 - 2", find the output when the input is

4. If the output is 18 and the rule is "x 2 + 4", what is the input?