Lesson Notes By Weeks and Term v5 - Grade 6

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.

Performance objectives

• Identify and describe patterns in tables and flow diagrams.
• Determine the rule between input and output values.
• Use algebraic expressions to represent number patterns.
• Solve problems by finding missing elements in a sequence.

Lesson summary

This week, we're diving deeper into the fascinating world of patterns, functions, and simple algebraic expressions! Understanding these concepts is like learning a secret code that helps us predict what comes next and solve problems in a logical way. Just like knowing the patterns in a catchy gqom song helps you anticipate the beat, recognizing mathematical patterns helps you understand and solve problems in everyday life. From figuring out how much pocket money you'll save each week to understanding how a spaza shop calculates its profits, patterns and algebra are all around us. This week builds on what you learned last week.

Lesson notes

What is a Pattern? A pattern is a sequence that repeats or follows a specific rule. In mathematics, we often work with number patterns.

For example: 2, 4, 6, 8... is a pattern where we add 2 each time. What is a Function? A function is a relationship between two sets of numbers called input and output. The function tells us what to do to the input to get the output.

Think of it like a machine: you put something in (input), the machine does something to it according to a rule (function), and something comes out (output). We often represent functions using tables or flow diagrams. What are Algebraic Expressions? An algebraic expression is a mathematical phrase that can contain numbers, variables (letters representing unknown numbers), and operations (like +, -, ×, ÷). For example, `2x + 3` is an algebraic expression. `x` is the variable. We use algebraic expressions to represent patterns and functions in a concise way. Connecting Patterns, Functions, and Algebraic Expressions The real power comes when we connect these ideas. Let's say you're saving R5 every week.

We can represent this as a pattern: Week 1: R5 Week 2: R10 Week 3: R15 Week 4: R20 We can also represent this as a function: Input (Week Number): 1, 2, 3, 4 Output (Savings): R5, R10, R15, R20 Now, let's use an algebraic expression. Let `n` represent the week number. The savings can be represented by the expression `5 x n` or `5n`. This expression is the rule that links the week number to the total savings.

Example 1: Finding the Rule from a Table Consider the following table showing the cost of airtime: | Airtime (Minutes) | Cost (R) | |-------------------|-----------| | 1 | 2 | | 2 | 4 | | 3 | 6 | | 4 | 8 | What is the rule that links the airtime to the cost? What algebraic expression can represent this?

Solution: Notice that the cost is always double the airtime.

Therefore, the rule is: "Multiply the airtime (in minutes) by 2 to get the cost." Let `m` represent the airtime (in minutes). The algebraic expression is `2 x m` or `2m`.

Example 2: Using a Flow Diagram Imagine a flow diagram where the input is a number, and the rule is "Multiply by 3 and add 1".

Input: 5 Rule: x 3 + 1 Output: ? What is the output?

Solution: Following the rule, we multiply 5 by 3 and then add 1: 5 x 3 = 15 15 + 1 = 16 Therefore, the output is

1

6. Example 3: Representing a Pattern with an Algebraic Expression A vendor sells samoosas. The first day, she sells 10 samoosas. Each day after, she sells 3 more samoosas than the day before.

Day 1: 10 samoosas Day 2: 13 samoosas Day 3: 16 samoosas Day 4: 19 samoosas What algebraic expression can represent this pattern?

Solution: Let `d` represent the day number. The number of samoosas sold can be represented as: `10 + 3 x (d - 1)` Why `(d-1)`? Because the extra 3 samoosas only start from day

2. On day 1, there are no "extra" samoosas.

We can simplify this expression: `10 + 3d - 3 = 7 + 3d` So, the expression `7 + 3d` also represents the number of samoosas sold each day.

Let's test it: Day 1: 7 + 3(1) = 10 Day 2: 7 + 3(2) = 13 Day 3: 7 + 3(3) = 16 It works! Guided Practice (With Solutions)

Question 1: Complete the following table, stating the rule in words and as an algebraic expression. | Input (x) | Output (y) | |-----------|------------| | 1 | 4 | | 2 | 5 | | 3 | 6 | | 4 | | | 5 | | Solution: Pattern: Each output is 3 more than the input.

Rule in words: Add 3 to the input.

Algebraic Expression: y = x + 3 Completed Table: | Input (x) | Output (y) | |-----------|------------| | 1 | 4 | | 2 | 5 | | 3 | 6 | | 4 | 7 | | 5 | 8 | Question 2: Use the flow diagram to find the output for the following input values: Input: 7 -> Multiply by 4 -> Subtract 2 -> Output: ?

Input: 10 -> Multiply by 4 -> Subtract 2 -> Output: ?

Solution: Input: 7 7 x 4 = 28 28 - 2 = 26 Output: 26 Input: 10 10 x 4 = 40 40 - 2 = 38 Output: 38 Question 3: A taxi charges a fixed rate of R15 plus R8 per kilometre travelled. Write an algebraic expression to represent the total cost of a taxi ride. If someone travels 12 km, how much will the taxi ride cost?

Solution: Let `k` represent the number of kilometres travelled.

The algebraic expression is: `15 + 8k` If someone travels 12 km, then k =

1

2. Total cost: 15 + 8(12) = 15 + 96 = R111 Independent Practice (Questions Only)

Complete the following table: | Input (a) | Output (b) | |-----------|------------| | 1 | 6 | | 2 | 12 | | 3 | | | 4 | | | 5 | | State the rule in words and as an algebraic expression. Use the following rule to complete the table: Rule: Output = (Input x 5) - 3 | Input (x) | Output (y) | |-----------|------------| | 2 | | | 4 | | | 6 | | | 8 | | A pattern is given as: 3, 7, 11, 15, __, __. Write an algebraic expression to represent this pattern. What are the next two numbers in the pattern? A cellphone company charges R0.50 per SMS plus a fixed monthly fee of R

3

0. Write an algebraic expression to represent the total monthly cost for SMSs.