Lesson Notes By Weeks and Term v5 - Grade 4

Lesson Video

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Performance objectives

• Find and extend number patterns.
• Describe the rule for a pattern.
• Use flow diagrams to find inputs, outputs, and rules.
• Create your own growing shape patterns.
• Solve problems using patterns.

Lesson summary

Overview This week, we continue our exciting journey into the world of patterns! Patterns are all around us in South Africa – in the geometric designs of Ndebele houses, the intricate beadwork of Zulu and Xhosa cultures, the rhythm of a djembe drum, and even in nature, like the spiral of an aloe plant. Last week, we looked at simple repeating patterns. This week, we are taking a big step forward to understand growing patterns. These are patterns that change in a predictable way. We will investigate patterns with numbers that grow or shrink, and patterns with shapes that get bigger.

Lesson notes

A. Growing Numeric Patterns A growing numeric pattern is a sequence of numbers that changes by the same amount each time. This change is called the rule or the constant difference. Patterns with Addition (Increasing Patterns) These are patterns where you add the same number each time to get to the next number in the sequence.

Example 1: Saving Pocket Money Thembi gets R10 pocket money every Friday. She decides to save it all to buy a book that costs R

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0. Let’s see how her savings grow.

Week 1: R10 Week 2: R10 + R10 = R20 Week 3: R20 + R10 = R30 The pattern is: 10, 20, 30, ... How to find the rule? Take any number in the pattern and subtract the number that came before it. 20 - 10 = 10 30 - 20 = 10 The difference is always

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0. So, the rule is "Add 10". How to extend the pattern? To find the next numbers, just keep applying the rule. 30 + 10 = 40 40 + 10 = 50 (She can buy the book in Week 5!)

The extended pattern is: 10, 20, 30, 40,

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0. Patterns with Subtraction (Decreasing Patterns) A decreasing pattern is a sequence where you subtract the same number each time.

Example 2: Sharing Sweets A teacher has a jar with 45 sweets. She gives 5 sweets to a group of learners each day.

Day 1: 45 - 5 = 40 sweets left Day 2: 40 - 5 = 35 sweets left The pattern of sweets left in the jar is: 45, 40, 35, ... How to find the rule? The numbers are getting smaller, so we know it's subtraction. The difference between 45 and 40 is

5. The rule is "Subtract 5". How to extend the pattern? 35 - 5 = 30 30 - 5 = 25 The extended pattern is: 45, 40, 35, 30,

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5. B. Growing Geometric Patterns These are patterns made of shapes or objects that grow in a regular, predictable way. To understand them, we often turn them into a number pattern.

Example: Building with Triangles Sipho is building a pattern with toothpicks.

Pattern 1: 1 triangle (uses 3 toothpicks)

Pattern 2: 2 triangles joined (uses 5 toothpicks)

Pattern 3: 3 triangles joined (uses 7 toothpicks) How to find the rule?

Look at the shapes: To get from Pattern 1 to Pattern 2, Sipho added 2 more toothpicks. To get from Pattern 2 to Pattern 3, he added another 2 toothpicks.

Look at the numbers: The number of toothpicks creates a numeric pattern: 3, 5, 7, ... The difference between 5 and 3 is

2. The difference between 7 and 5 is

2. The rule is: "Start with 3 and add 2 for each new pattern." How to extend the pattern? To find how many toothpicks are in Pattern 4, we add 2 to the number in Pattern 3: 7 + 2 =

9. So, Pattern 4 will have 9 toothpicks. C. Flow Diagrams (Function Machines) A flow diagram shows a relationship between numbers. It takes a number in (the input), applies a rule, and gives a new number out (the output). Input -> [RULE] -> Output Example 1: Finding the Output The rule is "Multiply by 4". What are the output numbers?

Input: 2 -> [x 4] -> Output: ?

Input: 5 -> [x 4] -> Output: ?

Input: 10 -> [x 4] -> Output: ?

Calculations: 2 x 4 = 8 5 x 4 = 20 10 x 4 = 40 The output numbers are 8, 20,

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0. Example 2: Finding the Input The rule is "Add 15". What were the input numbers?

Input: ? -> [+ 15] -> Output: 20 Input: ? -> [+ 15] -> Output: 25 Calculations: To find the input, we must do the opposite (inverse) operation. The opposite of adding 15 is subtracting 15. 20 - 15 = 5 25 - 15 = 10 The input numbers were 5,

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0. Example 3: Finding the Rule Look at the input and output numbers to find the missing rule.

Input: 3 -> [ ? ] -> Output: 18 Input: 5 -> [ ? ] -> Output: 30 Thinking Process: How do I get from 3 to 18? I could add 15 (3 + 15 = 18). Let's check if this rule works for the next pair. Does 5 + 15 = 30? No, 5 + 15 =

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0. So the rule is not "Add 15". Let's try multiplication. 3 x ? =

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8. I know from my times tables that 3 x 6 =

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8. Let's check if this rule works for the next pair. Does 5 x 6 = 30? Yes! The rule is "Multiply by 6". Guided Practice (With Solutions)

Question 1: Consider the number pattern: 80, 74, 68, 62, ... a) What is the rule for this pattern? b) What are the next three numbers in the pattern?

Solution: a)

Finding the rule: The numbers are getting smaller, so it is a subtraction pattern.

Let's find the difference: 80 - 74 = 6 74 - 68 = 6 The rule is "Subtract 6". b)

Extending the pattern: We apply the rule to the last number given. 62 - 6 = 56 56 - 6 = 50 50 - 6 = 44 The next three numbers are 56, 50, and

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4. Question 2: A pattern is made with squares. Pattern 1 has 1 square. Pattern 2 has 4 squares. Pattern 3 has 7 squares. a) Draw Pattern 4. b) How many squares are in Pattern 5?

Solution: a) First, let's find the numeric pattern: 1, 4, 7, ... The rule is "add 3" (4 - 1 = 3; 7 - 4 = 3). So, Pattern 4 will have 7 + 3 = 10 squares. We can draw this as a tower or block shape that has grown. (Learner's drawing should show a logical arrangement of 10 squares). b) To find the number of squares in Pattern 5, we apply the rule again to our answer for Pattern

4. Number of squares in Pattern 4 = 10 10 + 3 = 13 There will be 13 squares in Pattern 5.