Lesson Notes By Weeks and Term v5 - Grade 6
Patterns, functions and simple algebraic expressions – Week 1 focus
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Patterns, functions and simple algebraic expressions – Week 1 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematics
Class: Grade 6
Term: 2nd Term
Week: 1
Theme: General lesson support
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This week, we're diving into the exciting world of patterns, functions, and simple algebraic expressions. These concepts are not just abstract ideas; they're fundamental tools for understanding the world around us. Whether you're figuring out how many bricks you need for a building project (pattern recognition), predicting how much money you'll save each month (functions), or solving a problem with missing information (algebra), these skills are essential for success in mathematics and in life. In South Africa, understanding patterns can help predict weather patterns for farming, manage finances, or even design beautiful traditional art.
Patterns: A pattern is a sequence of numbers, objects, or shapes that follow a specific rule. The rule tells us how the pattern is created and how it continues. Patterns can be found everywhere - in nature (sunflower seed arrangements), in art (traditional Ndebele patterns), and in mathematics.
Example: 2, 4, 6, 8, 10... The rule is "add 2 to the previous number." Number Patterns: These are patterns made up of numbers. We focus on patterns involving addition and subtraction this week.
Example 1: 5, 10, 15, 20, 25... (Adding 5 each time). This could represent the cost of buying apples at R5 each.
Example 2: 100, 90, 80, 70, 60... (Subtracting 10 each time). This could represent the amount of air left in a leaking tyre, losing 10 kPa per minute.
Functions: A function describes a relationship between two sets of numbers, called the input and the output. The function rule tells us how to change the input to get the output.
Think of it as a machine: you put something in (input), the machine does something to it according to a rule, and something different comes out (output).
Input: The number that goes into the function.
Output: The number that comes out of the function.
Rule: The operation (addition, subtraction, multiplication, division) that is performed on the input to get the output.
Example: Input: 3 Rule: Multiply by 2 Output: 6 (because 3 x 2 = 6)
Flow Diagrams: These diagrams are visual representations of functions. They show the input, the rule (often in the middle of the diagram), and the output. [Input] → [Rule] → [Output]
Example: 5 → [+ 3] → 8 12 → [- 2] → 10 Tables: Tables can also represent functions. One column shows the inputs, and another column shows the corresponding outputs.
Example: | Input | Output | |-------|--------| | 1 | 4 | | 2 | 5 | | 3 | 6 | The rule here is "+3" (each output is 3 more than its corresponding input).
Simple Algebraic Expressions: In simple terms, algebra uses letters (like x or y) to represent unknown numbers. This allows us to write number sentences that can solve problems. We will not be solving equations yet, but we will be forming number sentences.
Example: If you start with x oranges and then get 5 more, you have x + 5 oranges.
Example: The price of a taxi ride depends on the distance traveled. If d is the distance in kilometers and the price per kilometer is R10, the total price can be represented as d x 10 (or 10d). This shows how the total price depends on the distance traveled. Guided Practice (With Solutions)
Question 1: Extend the following number pattern by three terms: 7, 11, 15, 19, ...
Solution: Identify the Pattern: Find the difference between consecutive terms. 11 - 7 = 4 15 - 11 = 4 19 - 15 = 4 The pattern is adding 4 to the previous number.
Extend the Pattern: 19 + 4 = 23 23 + 4 = 27 27 + 4 = 31 Answer: The next three terms are 23, 27, and
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1. Question 2: Complete the following flow diagram: 2 → [+ 7] → ? 5 → [+ 7] → ? 8 → [+ 7] → ?
Solution: Apply the Rule: The rule is to add 7 to the input.
Calculate the Outputs: 2 + 7 = 9 5 + 7 = 12 8 + 7 = 15 Complete Flow Diagram: 2 → [+ 7] → 9 5 → [+ 7] → 12 8 → [+ 7] → 15 Question 3: Determine the rule for the following table and complete it: | Input | Output | |-------|--------| | 3 | 9 | | 4 | 12 | | 5 | ? | | 6 | ? | Solution: Find the Relationship: Compare the inputs and outputs to find the rule. 3 x ? = 9. ? = 3 4 x ? = 12. ? = 3 The rule is "multiply by 3".
Apply the Rule to complete the table: 5 x 3 = 15 6 x 3 = 18 Completed Table: | Input | Output | |-------|--------| | 3 | 9 | | 4 | 12 | | 5 | 15 | | 6 | 18 | Question 4: Write a number sentence describing the number of cookies if each of 5 learners bakes c cookies each.
Solution: The phrase "each of 5 learners" suggests multiplication. We have 5 times the number of cookies c, which is 5 x c. This is normally written as 5c Therefore, the number sentence is 5c Independent Practice (Questions Only) Extend the following number pattern by three terms: 3, 8, 13, 18, ...
What is the rule for this number pattern: 1, 4, 9, 16, 25? (Hint: think about squaring numbers).
Complete the following flow diagram: 4 → [- 3] → ? 9 → [- 3] → ? 14 → [- 3] → ? Determine the rule for the following table and complete it: | Input | Output | |-------|--------| | 2 | 10 | | 3 | 15 | | 4 | ? | | 5 | ? | If a taxi charges R8 per kilometer, write a number sentence to describe the total cost C for a journey of k kilometers. Thando earns R20 per hour.
How much does she earn if she works for: a) 3 hours? b) 5 hours? c) h hours? (Write this as an algebraic expression).
Continue this pattern: 1, 2, 4, 8, 16, ... (Hint: What are you doing to each number to get the next number?) In a tuck shop, sweets cost R2 each. Write an expression for the cost of buying s sweets. Sipho has 15 marbles and gives m marbles to his friend. How many marbles does Sipho have left? Write this as an algebraic expression. You are saving money to buy a new soccer ball. You save R5 each week.