Lesson Notes By Weeks and Term v5 - Grade 3

Lesson Video

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Performance objectives

• Find and continue number patterns.
• Describe the rule for a pattern.
• Create and continue shape patterns.
• Use function machines to find answers.

Lesson summary

Patterns are all around us! From the colourful designs on our traditional Ndebele houses to the way days and nights follow each other, patterns help us understand and predict the world. In mathematics, patterns are sequences that repeat or change according to a rule. Understanding patterns helps us to make predictions, solve problems, and think logically. Functions and relationships show how different numbers or quantities are connected. This week, we'll be exploring number patterns, geometric patterns, and how to find the rules that govern them. This is important because recognizing and understanding patterns builds a foundation for more advanced maths like algebra later on.

Lesson notes

What is a Pattern? A pattern is a sequence that repeats or changes in a predictable way. Patterns can be found with numbers, shapes, colours, or even sounds.

Number Patterns: These patterns use numbers and follow a specific rule, such as adding the same number each time (increasing pattern) or subtracting the same number each time (decreasing pattern).

Geometric Patterns: These patterns use shapes and can repeat or grow in a specific way.

Understanding the Rule: The rule is the instruction that tells us how to continue the pattern. The rule explains how to get from one number/shape to the next. We can use words like "add 2" or "subtract 5" to describe the rule. For geometric patterns, the rule might be "add one square to each row." Examples of Number Patterns: Increasing Pattern: 2, 4, 6, 8, ...

Rule: Add 2 to the previous number.

Next number: 10 (8 + 2 = 10)

Decreasing Pattern: 15, 12, 9, 6, ...

Rule: Subtract 3 from the previous number.

Next number: 3 (6 - 3 = 3)

Mixed Pattern: 1, 3, 2, 4, 3, 5, ...

Rule: Add 2, then subtract 1, repeat.

Next number: 4 (5 - 1 = 4)

Examples of Geometric Patterns: Triangle, Square, Triangle, Square, ...

Rule: Repeat Triangle, Square.

Next shape: Triangle One circle, two circles, three circles...

Rule: Add one circle.

Next shape: Four circles Function Machines: A function machine is like a mathematical vending machine. You put a number IN, the machine does something to it (according to the rule), and a new number comes OUT. We usually represent function machines with a box, an 'IN' arrow, an 'OUT' arrow and the rule written on the machine.

Example: Function Machine Rule: Add 3 IN: 5 OUT: 8 (5 + 3 = 8)

Example: Function Machine Rule: Subtract 2 IN: 10 OUT: 8 (10 - 2 = 8) More complex patterns using operations beyond adding and subtracting: Grade 3 CAPS primarily focuses on addition and subtraction for number patterns and function machines. We do NOT get into multiplying or dividing at this grade level.

However, recognizing that repeating sequences exist (e.g. ABABAB) forms a vital foundation. Guided Practice (With Solutions)

Question 1: What is the next number in the pattern: 5, 10, 15, 20, ...? What is the rule?

Solution: To find the rule, we need to see how the numbers are changing. 10 - 5 = 5, 15 - 10 = 5, 20 - 15 =

5. So, the numbers are increasing by 5 each time.

The rule is: Add 5 to the previous number. To find the next number, we add 5 to 20: 20 + 5 =

2

5. Answer: The next number is

2

5. Question 2: What is the next number in the pattern: 30, 27, 24, 21, ...? What is the rule?

Solution: Here, the numbers are getting smaller. 27 - 30 = -3, 24 - 27 = -3, 21 - 24 = -

3. The numbers are decreasing by 3 each time.

The rule is: Subtract 3 from the previous number. To find the next number, we subtract 3 from 21: 21 - 3 =

1

8. Answer: The next number is

1

8. Question 3: Draw the next shape in the pattern: Circle, Square, Circle, Square, ...

Solution: This is a repeating pattern. It goes Circle, Square, Circle, Square.

The rule is: Repeat Circle, Square. The next shape is a Circle.

Answer: Draw a Circle.

Question 4: A function machine's rule is: Add

4. If the IN number is 7, what is the OUT number?

Solution: The rule is Add

4. The IN number is

7. We need to add 4 to 7: 7 + 4 = 11 Answer: The OUT number is

1

1. Question 5: A function machine's rule is: Subtract

5. If the IN number is 12, what is the OUT number?

Solution: The rule is Subtract

5. The IN number is

1

2. We need to subtract 5 from 12: 12 - 5 = 7 Answer: The OUT number is

7. Independent Practice (Questions Only)

What is the next number in the pattern: 1, 4, 7, 10, ...? What is the rule?

What is the next number in the pattern: 25, 20, 15, 10, ...? What is the rule?

What is the next number in the pattern: 2, 5, 8, 11...? What is the rule?

Draw the next shape in the pattern: Triangle, Triangle, Square, Triangle, Triangle, Square, ...

Draw the next shape in the pattern: Star, Circle, Star, Circle, Square, Star, Circle, Star, Circle, Square, ...

A function machine's rule is: Add

6. If the IN number is 3, what is the OUT number?

A function machine's rule is: Subtract

4. If the IN number is 9, what is the OUT number? A function machine has an IN of 5 and an OUT of

9. What is the rule?

Complete the following pattern: ____, 10, 15, 20, ____ Create your own geometric pattern using three different shapes and draw the next three elements in the pattern. Describe the pattern rule.