Lesson Notes By Weeks and Term v5 - Grade 5

Lesson Video

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Performance objectives

• Identify and describe number patterns with addition and subtraction.
• Extend number patterns by at least three terms.
• Find the rule for a number pattern.
• Create your own number patterns.
• Solve word problems with patterns.

Lesson summary

Patterns, functions, and relationships are everywhere! From the repeating designs on your shweshwe cloth to the way your spaza shop owner calculates the cost of multiple sweets, understanding patterns helps us make sense of the world. In this week, we'll be focusing on number patterns, specifically identifying, describing, and extending them using different rules. This is important because recognizing patterns strengthens your problem-solving skills, allowing you to predict what comes next and solve more complex mathematical problems later on. Understanding patterns is crucial for managing money, understanding timetables, and even predicting weather patterns.

Lesson notes

What is a Number Pattern? A number pattern is a sequence of numbers that follow a specific rule or rules. These rules can involve addition, subtraction, multiplication, division, or a combination of these. The rule tells us how to get from one number in the sequence to the next. Describing a Number Pattern To describe a number pattern, you need to identify the rule. Is the pattern increasing (addition or multiplication) or decreasing (subtraction or division)? How much is being added, subtracted, multiplied, or divided each time?

Example 1: Increasing Pattern (Addition)

Consider the number pattern: 2, 5, 8, 11, ...

Step 1: Observe the pattern. What's happening to the numbers? They are getting bigger. This suggests addition or multiplication.

Step 2: Determine the difference between consecutive numbers. 5 - 2 = 3 8 - 5 = 3 11 - 8 = 3 Step 3: Identify the rule. The difference is constant (3).

Therefore, the rule is "add 3 to the previous number".

Step 4: Extend the pattern. To find the next three terms, keep adding 3: 11 + 3 = 14; 14 + 3 = 17; 17 + 3 =

2

0. The extended pattern is: 2, 5, 8, 11, 14, 17, 20 Example 2: Decreasing Pattern (Subtraction)

Consider the number pattern: 30, 25, 20, 15, ...

Step 1: Observe the pattern. The numbers are getting smaller, suggesting subtraction or division.

Step 2: Determine the difference between consecutive numbers. 25 - 30 = -5 20 - 25 = -5 15 - 20 = -5 Step 3: Identify the rule. The difference is constant (-5).

Therefore, the rule is "subtract 5 from the previous number".

Step 4: Extend the pattern. To find the next three terms, keep subtracting 5: 15 - 5 = 10; 10 - 5 = 5; 5 - 5 =

0. The extended pattern is: 30, 25, 20, 15, 10, 5, 0 Example 3: Combining Addition and Subtraction Sometimes, patterns can have a more complex rule that involves a combination of operations. This is less common at Grade 5 but good to be aware of. More Complex Patterns While the main focus is on addition and subtraction, introducing the concept of multiplication and division can be done gently through related patterns (e.g. repeated addition is multiplication). If you had a pattern such as 2,4,8,16,... you would be multiplying by 2 each time. Real-World Example (South African Context): A street vendor in Durban sells bunny chows. On Monday, she sells 10 bunny chows. On Tuesday, she sells

1

3. On Wednesday, she sells

1

6. If this pattern continues, how many bunny chows will she sell on Friday?

Step 1: Identify the pattern.

The numbers are increasing: 10, 13, 16,...

Step 2: Determine the difference. 13 - 10 = 3; 16 - 13 = 3 Step 3: Determine the rule. The rule is "add 3 to the previous number".

Step 4: Extend the pattern.

Thursday: 16 + 3 = 19 Friday: 19 + 3 = 22 The vendor will sell 22 bunny chows on Friday. Guided Practice (With Solutions)

Question 1: Identify the rule and extend the following number pattern to the next three terms: 7, 14, 21, 28, ...

Solution: Step 1: Observe the pattern. The numbers are increasing.

Step 2: Determine the difference. 14 - 7 = 7; 21 - 14 = 7; 28 - 21 = 7 Step 3: Identify the rule. The rule is "add 7 to the previous number". Alternatively, one could also recognize this as the multiples of

7. Step 4: Extend the pattern. 28 + 7 = 35; 35 + 7 = 42; 42 + 7 = 49 Answer: The extended pattern is 7, 14, 21, 28, 35, 42,

4

9. Question 2: Identify the rule and extend the following number pattern to the next three terms: 50, 45, 40, 35, ...

Solution: Step 1: Observe the pattern. The numbers are decreasing.

Step 2: Determine the difference. 45 - 50 = -5; 40 - 45 = -5; 35 - 40 = -5 Step 3: Identify the rule. The rule is "subtract 5 from the previous number".

Step 4: Extend the pattern. 35 - 5 = 30; 30 - 5 = 25; 25 - 5 = 20 Answer: The extended pattern is 50, 45, 40, 35, 30, 25,

2

0. Question 3: A farmer plants mielies in rows. The first row has 5 mielies, the second row has 8 mielies, and the third row has 11 mielies. If the pattern continues, how many mielies will be in the fifth row?

Solution: Step 1: Identify the pattern.

The numbers are increasing: 5, 8, 11,...

Step 2: Determine the difference. 8 - 5 = 3; 11 - 8 = 3 Step 3: Identify the rule. The rule is "add 3 to the previous number".

Step 4: Extend the pattern.

Fourth row: 11 + 3 = 14 Fifth row: 14 + 3 = 17 Answer: There will be 17 mielies in the fifth row.

Question 4: Identify the rule and extend the following number pattern to the next three terms: 1, 4, 7, 10, ...

Solution: Step 1: Observe the pattern. The numbers are increasing.

Step 2: Determine the difference. 4 - 1 = 3; 7 - 4 = 3; 10 - 7 = 3 Step 3: Identify the rule. The rule is "add 3 to the previous number".

Step 4: Extend the pattern. 10 + 3 = 13; 13 + 3 = 16; 16 + 3 = 19 Answer: The extended pattern is 1, 4, 7, 10, 13, 16,

1

9. Independent Practice (Questions Only) Identify the rule and extend the following number pattern to the next three terms: 12, 22, 32, 42, ... Identify the rule and extend the following number pattern to the next three terms: 95, 85, 75, 65, ..