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.
• Complete flow diagrams using a rule.
• Find the rule in a flow diagram.
• Use patterns and flow diagrams for real-life situations.

Lesson summary

Patterns, functions, and relationships are all around us. Understanding them helps us to predict what will happen next, solve problems, and make sense of the world. In South Africa, recognising patterns can help us understand things like the patterns in the weather, the growth of plants, or even the increase in prices at the shops. Learning about patterns is also essential for future maths topics such as algebra and geometry. This week, we will focus on identifying, describing, and extending number patterns, using flow diagrams to represent functions, and finding rules for relationships between numbers.

Lesson notes

What are Patterns? A pattern is a sequence of numbers, objects, or events that follows a specific rule. Number patterns are ordered lists of numbers that are linked together by a mathematical rule.

Types of Patterns: Increasing Patterns: Patterns where the numbers get larger. These often involve addition or multiplication.

Decreasing Patterns: Patterns where the numbers get smaller. These often involve subtraction or division.

Repeating Patterns: Patterns where a sequence of numbers repeats itself.

Finding the Rule: The most important step is figuring out the rule that governs the pattern.

Ask yourself: "What do I need to do to one number to get to the next?" Example 1: Increasing Pattern Consider the pattern: 2, 4, 6, 8, … To get from 2 to 4, we add

2. To get from 4 to 6, we add

2. To get from 6 to 8, we add

2. Therefore, the rule is to add 2 to the previous number. The next three numbers in the pattern would be 10, 12, and

1

4. Example 2: Decreasing Pattern Consider the pattern: 20, 17, 14, 11, … To get from 20 to 17, we subtract

3. To get from 17 to 14, we subtract

3. To get from 14 to 11, we subtract

3. Therefore, the rule is to subtract 3 from the previous number. The next three numbers in the pattern would be 8, 5, and

2. Example 3: Multiplication Pattern Consider the pattern: 3, 6, 12, 24, … To get from 3 to 6, we multiply by

2. To get from 6 to 12, we multiply by

2. To get from 12 to 24, we multiply by

2. Therefore, the rule is to multiply by

2. The next three numbers would be 48, 96, and

1

9

2. Example 4: Division Pattern Consider the pattern: 100, 50, 25, … To get from 100 to 50, we divide by

2. To get from 50 to 25, we divide by

2. Therefore, the rule is to divide by

2. The next number would be 12.

5. What are Functions and Flow Diagrams? A function is a relationship between two sets of numbers: an input and an output.

Think of it like a machine: you put something in (the input), the machine does something to it (the rule or function), and something comes out (the output). A flow diagram is a visual way to represent a function. It shows the input, the rule, and the output.

Example 5: Flow Diagram Input -> Rule -> Output Let's say the rule is "Multiply by 3." If the input is 5: 5 -> Multiply by 3 -> 15 So, if you put 5 into the "multiply by 3" machine, 15 comes out.

Finding the Rule in a Flow Diagram: Sometimes you are given the input and output and need to find the rule. To do this, look for the relationship between the input and the output.

Ask yourself: "What do I need to do to the input to get the output?" Example 6: Finding the Rule Input: 2 -> Output: 8 Input: 4 -> Output: 16 Input: 6 -> Output: 24 What is the rule? We can see that each output is four times the input (2 x 4 = 8, 4 x 4 = 16, 6 x 4 = 24). So, the rule is "Multiply by 4." Example 7: Real-Life Application: Calculating the Cost of Sweets Imagine sweets cost R2 each. We can use a flow diagram to calculate the cost of buying different numbers of sweets. Input (Number of Sweets) -> Rule (Multiply by R2) -> Output (Total Cost)

Input: 3 -> Multiply by R2 -> Output: R6 Input: 5 -> Multiply by R2 -> Output: R10 Input: 8 -> Multiply by R2 -> Output: R16 Guided Practice (With Solutions)

Question 1: Identify the pattern and find the next three terms: 1, 5, 9, 13, … Solution: To get from 1 to 5, we add

4. To get from 5 to 9, we add

4. To get from 9 to 13, we add

4. The rule is to add 4 to the previous number.

The next three terms are: 17, 21,

2

5. Question 2: Identify the pattern and find the next two terms: 48, 24, 12, … Solution: To get from 48 to 24, we divide by

2. To get from 24 to 12, we divide by

2. The rule is to divide by

2. The next two terms are: 6,

3. Question 3: Complete the flow diagram: Input: 7 -> Rule: Multiply by 5 -> Output: ?

Input: 12 -> Rule: Multiply by 5 -> Output: ?

Solution: 7 x 5 =

3

5. So, Input: 7 -> Rule: Multiply by 5 -> Output: 35 12 x 5 =

6

0. So, Input: 12 -> Rule: Multiply by 5 -> Output: 60 Question 4: Determine the rule for the following flow diagram: Input: 3 -> Output: 9 Input: 5 -> Output: 15 Input: 8 -> Output: 24 Solution: Notice that each output is three times the input (3 x 3 = 9, 5 x 3 = 15, 8 x 3 = 24). So, the rule is "Multiply by 3." Independent Practice (Questions Only) Identify the pattern and find the next three terms: 3, 7, 11, 15, … Identify the pattern and find the next two terms: 81, 27, 9, … Complete the flow diagram: Input: 9 -> Rule: Subtract 6 -> Output: ?

Input: 15 -> Rule: Subtract 6 -> Output: ?

Complete the flow diagram: Input: 6 -> Rule: Divide by 3 -> Output: ?

Input: 21 -> Rule: Divide by 3 -> Output: ? Determine the rule for the following flow diagram: Input: 4 -> Output: 12 Input: 7 -> Output: 21 Input: 10 -> Output: 30 Determine the rule for the following flow diagram: Input: 20 -> Output: 5 Input: 32 -> Output: 8 Input: 44 -> Output: 11 Find the missing number in the pattern: 10, __, 30, 40,

5

0. Find the missing number in the pattern: 1, 4, __, 10, 13.