Lesson Notes By Weeks and Term v5 - Grade 3

Lesson Video

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Performance objectives

• Identify and extend simple number patterns.
• Describe patterns using words like 'add' or 'subtract'.
• Complete simple flow diagrams, or function machines.
• Create your own simple number patterns.

Lesson summary

Patterns are all around us! From the colourful beadwork made by Ndebele artists to the way houses are arranged in a township street, patterns help us understand and predict things. In mathematics, patterns are sequences that repeat or change in a predictable way. Understanding patterns helps us to predict what comes next and solve problems more easily.

Functions are like simple machines: you put something in (an input), and you get something out (an output), based on a specific rule. This week, we will focus on recognizing, describing, and extending number patterns, as well as identifying simple functions and relationships between numbers.

Lesson notes

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

Number Patterns: Number patterns are sequences of numbers that follow a rule. This rule tells us how to get from one number to the next. The rule is often addition or subtraction, but it can also involve multiplication or division (we'll focus on addition and subtraction for Grade 3).

Increasing Patterns: The numbers get bigger. These patterns usually involve addition.

Example: 2, 4, 6, 8... (The rule is "add 2")

Decreasing Patterns: The numbers get smaller. These patterns usually involve subtraction.

Example: 10, 8, 6, 4... (The rule is "subtract 2")

Example 1: Increasing Pattern Consider the pattern: 3, 6, 9, 12, __, __ Identify the rule: To find the rule, look at the difference between consecutive numbers. 6 - 3 = 3, 9 - 6 = 3, 12 - 9 =

3. The rule is "add 3." Extend the pattern: To find the next numbers, we add 3 to the last number. 12 + 3 = 15, 15 + 3 =

1

8. The complete pattern: 3, 6, 9, 12, 15, 18 Example 2: Decreasing Pattern Consider the pattern: 20, 17, 14, 11, __, __ Identify the rule: To find the rule, look at the difference between consecutive numbers. 17 - 20 = -3, 14 - 17 = -3, 11 - 14 = -

3. The rule is "subtract 3." Extend the pattern: To find the next numbers, we subtract 3 from the last number. 11 - 3 = 8, 8 - 3 =

5. The complete pattern: 20, 17, 14, 11, 8, 5 Functions (Function Machines) A function is like a machine that takes an input, applies a rule, and gives you an output. We often represent functions using flow diagrams.

Input: The number that goes into the machine.

Rule: What the machine does to the input (e.g., add 5, subtract 2).

Output: The number that comes out of the machine.

Example 3: Function Machine | Input | Rule: Add 4 | Output | |---|---|---| | 2 | | | | 5 | | | | 8 | | | Apply the rule to each input: Input 2: 2 + 4 = 6 Input 5: 5 + 4 = 9 Input 8: 8 + 4 = 12 Complete the table: | Input | Rule: Add 4 | Output | |---|---|---| | 2 | | 6 | | 5 | | 9 | | 8 | | 12 | Example 4: Function Machine (Finding the Rule) | Input | Rule: ? | Output | |---|---|---| | 3 | | 7 | | 6 | | 10 | | 9 | | 13 | Find the relationship: Look at how the input changes to get the output. 7 - 3 = 4, 10 - 6 = 4, 13 - 9 =

4. Identify the rule: The rule is "add 4." Guided Practice (With Solutions)

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

Solution: Step 1: Find the rule. The difference between consecutive numbers is 5 (10 - 5 = 5, 15 - 10 = 5, 20 - 15 = 5). The rule is "add 5".

Step 2: Apply the rule. 20 + 5 = 25, 25 + 5 = 30 Answer: The next two numbers are 25 and

3

0. The complete pattern is: 5, 10, 15, 20, 25,

3

0. Question 2: What are the next two numbers in the pattern: 30, 25, 20, 15, __, __?

Solution: Step 1: Find the rule. The difference between consecutive numbers is -5 (25 - 30 = -5, 20 - 25 = -5, 15 - 20 = -5). The rule is "subtract 5".

Step 2: Apply the rule. 15 - 5 = 10, 10 - 5 =

5. Answer: The next two numbers are 10 and

5. The complete pattern is: 30, 25, 20, 15, 10,

5. Question 3: Complete the function machine: | Input | Rule: Subtract 2 | Output | |---|---|---| | 7 | | | | 12 | | | | 15 | | | Solution: Step 1: Apply the rule to each input. 7 - 2 = 5 12 - 2 = 10 15 - 2 = 13 Step 2: Complete the table. | Input | Rule: Subtract 2 | Output | |---|---|---| | 7 | | 5 | | 12 | | 10 | | 15 | | 13 | Independent Practice (Questions Only) What are the next two numbers in the pattern: 1, 3, 5, 7, __, __? What are the next two numbers in the pattern: 18, 15, 12, 9, __, __? What are the next two numbers in the pattern: 2, 6, 10, 14, __, __? What are the next two numbers in the pattern: 45, 40, 35, 30, __, __?

Complete the function machine: | Input | Rule: Add 7 | Output | |---|---|---| | 3 | | | | 8 | | | | 11 | | | Complete the function machine: | Input | Rule: Subtract 5 | Output | |---|---|---| | 10 | | | | 13 | | | | 18 | | | Find the rule for the following function machine: | Input | Rule: ? | Output | |---|---|---| | 2 | | 9 | | 5 | | 12 | | 8 | | 15 | Find the rule for the following function machine: | Input | Rule: ? | Output | |---|---|---| | 10 | | 6 | | 12 | | 8 | | 15 | | 11 | Create your own increasing number pattern, starting with the number 4 and using the rule "add 3." Write down the first 5 numbers. Create your own decreasing number pattern, starting with the number 20 and using the rule "subtract 2." Write down the first 5 numbers.