Lesson Notes By Weeks and Term v5 - Grade 3

Lesson Video

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Performance objectives

• Find and describe number patterns.
• Continue number patterns.
• Create your own number patterns.
• Recognise and describe shape patterns.
• Guess the next shape in a pattern.

Lesson summary

Patterns are everywhere around us, from the colours in a traditional Ndebele house to the arrangement of desks in our classroom. Understanding patterns helps us predict what comes next, solve problems, and make sense of the world. This week, we'll be focusing on identifying, continuing, and creating our own number and geometric patterns. These skills are essential for building a strong foundation in mathematics and will help you in subjects like science and even art! Think of a pattern like a recipe – if you know the ingredients and how they're combined, you can predict the final dish. Similarly, understanding the rule in a pattern allows you to predict the next numbers or shapes.

Lesson notes

What is a Pattern? A pattern is a sequence that repeats or follows a specific rule. It could be a sequence of numbers, shapes, colours, or anything else that follows a predictable order. Identifying the rule is key to understanding and continuing the pattern. Number Patterns (Addition and Subtraction) These patterns involve adding or subtracting the same number each time to get the next number in the sequence. This number is called the 'constant difference'.

Example 1: Increasing Pattern (Addition)

Consider the pattern: 2, 4, 6, 8, __, __ Step 1: Find the difference between consecutive numbers. 4 - 2 = 2, 6 - 4 = 2, 8 - 6 =

2. The difference is always

2. Step 2: Identify the rule. The rule is to add 2 to the previous number to get the next number.

Step 3: Continue the pattern. To find the next number, add 2 to 8: 8 + 2 =

1

0. Then, add 2 to 10: 10 + 2 =

1

2. Therefore, the pattern is: 2, 4, 6, 8, 10, 12 Example 2: Decreasing Pattern (Subtraction)

Consider the pattern: 20, 17, 14, 11, __, __ Step 1: Find the difference between consecutive numbers. 17 - 20 = -3, 14 - 17 = -3, 11 - 14 = -

3. The difference is always -3 (or we are subtracting 3).

Step 2: Identify the rule. The rule is to subtract 3 from the previous number to get the next number.

Step 3: Continue the pattern. To find the next number, subtract 3 from 11: 11 - 3 =

8. Then, subtract 3 from 8: 8 - 3 =

5. Therefore, the pattern is: 20, 17, 14, 11, 8, 5 Example 3: Pattern with a starting point in South African context. Imagine Sipho saves R5 every week. If he starts with R10, how much money will he have after 5 weeks?

Let's write out the pattern: Week 1: R10 Week 2: R10 + R5 = R15 Week 3: R15 + R5 = R20 Week 4: R20 + R5 = R25 Week 5: R25 + R5 = R30 So, Sipho will have R30 after 5 weeks. The rule here is to add R5 each week. Geometric Patterns (Shapes and Colours) These patterns involve a sequence of shapes or colours that repeat or change according to a specific rule.

Example 1: Shape Pattern Imagine a pattern with the shapes: Square, Circle, Triangle, Square, Circle, Triangle, __, __ Step 1: Identify the repeating sequence. The sequence is Square, Circle, Triangle.

Step 2: Continue the pattern. The next shape would be a Square, followed by a Circle.

Therefore, the pattern is: Square, Circle, Triangle, Square, Circle, Triangle, Square, Circle Example 2: Colour Pattern Imagine a pattern with the colours: Red, Blue, Red, Blue, __, __ Step 1: Identify the repeating sequence. The sequence is Red, Blue.

Step 2: Continue the pattern. The next colour would be Red, followed by Blue.

Therefore, the pattern is: Red, Blue, Red, Blue, Red, Blue Example 3: Combining Shapes and Colour Imagine a pattern: Red Star, Blue Circle, Red Star, Blue Circle, __, __ Step 1: Identify the shapes and colours being used. We see stars and circles in red and blue.

Step 2: See the order in which shapes and colour appear. Red star comes first, followed by Blue Circle, then Red Star, then Blue Circle Step 3: Continue the pattern. Since the Blue Circle came last, the next object would be the Red Star, followed by Blue Circle. Creating Your Own Patterns You can create your own patterns by choosing a starting number or shape and applying a rule repeatedly. The rule must be consistent to create a pattern. For example, start with 3 and add 4 each time, or repeat a sequence of three colours. Guided Practice (With Solutions)

Question 1: What are the next two numbers in the pattern: 5, 10, 15, 20, __, __?

Solution: Step 1: Find the difference: 10 - 5 = 5, 15 - 10 = 5, 20 - 15 =

5. The difference is

5. Step 2: Identify the rule: The rule is to add 5 to the previous number.

Step 3: Continue the pattern: 20 + 5 = 25, 25 + 5 =

3

0. Answer: 25, 30 Question 2: What are the next two numbers in the pattern: 30, 27, 24, 21, __, __?

Solution: Step 1: Find the difference: 27 - 30 = -3, 24 - 27 = -3, 21 - 24 = -

3. The difference is -3 (or subtracting 3).

Step 2: Identify the rule: The rule is to subtract 3 from the previous number.

Step 3: Continue the pattern: 21 - 3 = 18, 18 - 3 =

1

5. Answer: 18, 15 Question 3: What are the next two shapes in the pattern: Triangle, Square, Triangle, Square, __, __?

Solution: Step 1: Identify the repeating sequence: The sequence is Triangle, Square.

Step 2: Continue the pattern: The next shape would be a Triangle, followed by a Square.

Answer: Triangle, Square Question 4: Complete the pattern: 12, 15, __, 21, __ Solution: Step 1: Find the difference: 15 - 12 =

3. So we are adding

3. Step 2: Continue the pattern by adding 3. 15 + 3 = 18. 21 + 3 = 24 Step 3: Check the pattern. 12, 15, 18, 21, 24 looks like the correct pattern.

Answer: 18, 24 Independent Practice (Questions Only) What are the next three numbers in the pattern: 7, 14, 21, 28, __, __, __? What are the next three numbers in the pattern: 50, 45, 40, 35, __, __, __? What are the next two shapes in the pattern: Circle, Circle, Square, Circle, Circle, Square, __, __?