Lesson Notes By Weeks and Term v5 - Grade 6

Lesson Video

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Performance objectives

• Identify and extend geometric patterns.
• Determine the rule for a given pattern.
• Use flow diagrams and tables to represent relationships.
• Write number sentences to describe a relationship.
• Solve simple equations with a missing number.

Lesson summary

This week, we're diving into the fascinating world of patterns, functions, and simple algebraic expressions. Understanding these concepts is like learning a secret code that unlocks how things work around us. From the repeating designs in traditional Ndebele art to predicting how much airtime you'll need for the month, patterns and simple algebra help us make sense of our everyday lives. They form the foundation for more advanced mathematics and problem-solving skills that you will use throughout your schooling and beyond. Think of it as building blocks for your future!

Lesson notes

What are Patterns? A pattern is a sequence of objects, numbers, or events that repeat in a predictable way. These repetitions help us understand the relationship between different elements within the sequence. Patterns can be visual (geometric patterns), numerical (number patterns), or even involve sounds or movements.

Types of Patterns: Geometric Patterns: These patterns involve shapes or drawings that repeat or change in a predictable way. For example, a pattern could be a sequence of squares that increase in size.

Number Patterns: These patterns involve a sequence of numbers that follow a specific rule. For example, 2, 4, 6, 8… is a number pattern where you add 2 to the previous number.

Understanding the Rule: The rule is the key to understanding and continuing a pattern. It describes how each element in the sequence is related to the previous one. For example, in the number pattern 1, 3, 5, 7…, the rule is "add 2 to the previous number." Functions and Flow Diagrams: A function is a relationship between two sets of numbers called input and output. Think of it like a machine. You put something in (the input), the machine does something to it (the rule), and you get something out (the output). A flow diagram is a visual way to represent a function. It shows the input, the rule (or operation), and the output.

For example: ``` Input --> Rule: + 3 --> Output ``` If the input is 5, the output would be 8 (5 + 3 = 8). A table can also represent a function, showing pairs of input and output values.

Example: | Input | Output | |---|---| | 1 | 4 | | 2 | 5 | | 3 | 6 | In this case, the rule is "add 3 to the input." Simple Algebraic Expressions: Algebra uses letters and symbols to represent unknown numbers or quantities. We use number sentences to describe relationships or solve for missing values.

A number sentence might look like this: _x_ + 5 =

1

0. Here, _x_ represents the unknown number.

Solving for the Unknown: To solve for the unknown, we need to figure out what number makes the number sentence true.

We can use different strategies: Inspection: Sometimes, you can look at the number sentence and know the answer immediately.

Trial-and-Improvement: You can guess a number, test it, and then adjust your guess until you find the correct answer.

Working Backwards: You can use the inverse operation (the opposite operation) to find the unknown. For example, if the number sentence is _x_ + 5 = 10, you can subtract 5 from both sides to get _x_ = 5.

Worked example

Geometric Pattern: Look at this pattern: Triangle, Square, Triangle, Square, ... What comes next?

Answer: Triangle. The pattern is Triangle, Square, repeated.

Number Pattern: What is the next number in the pattern: 3, 6, 9, 12, ...?

Answer:

1

5. The rule is "add 3 to the previous number." (3 + 3 = 6, 6 + 3 = 9, 9 + 3 = 12, 12 + 3 = 15)

Function Table: Complete the following table using the rule "multiply by 2":

| Input | Output |

|---|---|

| 4 | ? |

| 7 | ? |