Lesson Notes By Weeks and Term v5 - Grade 5

Lesson Video

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Performance objectives

• Identify and extend number patterns.
• Find the rule for a number pattern.
• Use flow diagrams to show patterns.
• Use tables to show patterns.

Lesson summary

Patterns, functions, and relationships are the building blocks of understanding how things change and connect in the world around us. This week, we will be focusing on recognizing and extending number patterns, identifying rules governing these patterns, and representing these relationships in different ways, including using flow diagrams and tables. Understanding patterns helps us predict what comes next, solve problems logically, and even understand things like music, art, and coding!

Lesson notes

What is a Number Pattern? A number pattern is a sequence of numbers that follows a specific rule. This rule tells us how to get from one number to the next. These patterns can involve addition, subtraction, multiplication, or division, or even a combination of these operations. The rule helps us predict which numbers will come next in the sequence. Identifying the Rule The most important part of working with number patterns is identifying the rule. Look closely at the numbers and try to figure out what is being added, subtracted, multiplied, or divided to get from one number to the next. Sometimes, the rule might involve two operations, like multiplying by one number and then adding another.

Example 1: Simple Addition Pattern Consider the pattern: 2, 4, 6, 8, 10, ... What is happening from one number to the next? We are adding 2 each time.

Rule: Add 2 to the previous number. The next three numbers in the pattern would be: 12, 14,

1

6. Example 2: Simple Subtraction Pattern Consider the pattern: 20, 17, 14, 11, 8, ... What is happening from one number to the next? We are subtracting 3 each time.

Rule: Subtract 3 from the previous number. The next three numbers in the pattern would be: 5, 2, -

1. Example 3: Multiplication Pattern Consider the pattern: 3, 6, 12, 24, 48, ... What is happening from one number to the next? We are multiplying by 2 each time.

Rule: Multiply the previous number by

2. The next three numbers in the pattern would be: 96, 192,

3

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4. Example 4: Division Pattern Consider the pattern: 100, 50, 25, 12.5, ... What is happening from one number to the next? We are dividing by 2 each time.

Rule: Divide the previous number by

2. The next three numbers in the pattern would be: 6.25, 3.125, 1.

5

6

2

5. Example 5: A More Complex Pattern Consider the pattern: 1, 4, 9, 16, 25, ... This pattern might seem tricky at first. Let’s look at the numbers more closely. 1 = 1 x 1 = 1 squared (1 2 ) 4 = 2 x 2 = 2 squared (2 2 ) 9 = 3 x 3 = 3 squared (3 2 ) 16 = 4 x 4 = 4 squared (4 2 ) 25 = 5 x 5 = 5 squared (5 2 )

Rule: Square the natural numbers (1, 2, 3, 4, 5...). The next three numbers in the pattern would be: 36 (6 2 ), 49 (7 2 ), 64 (8 2 ). Flow Diagrams A flow diagram is a visual way to represent a number pattern. It shows how an "input" number is changed by a specific rule to produce an "output" number. The rule is often written inside a box or circle in the diagram.

Example: Input -> [Multiply by 3] -> Output If the input is 2, the output is 2 x 3 =

6. If the input is 5, the output is 5 x 3 =

1

5. If the input is 10, the output is 10 x 3 =

3

0. Tables A table is another way to organize input and output values in a number pattern. The input values are usually in one column (or row), and the corresponding output values are in another. The rule connects the input and output values.

Example: | Input | Output | |---|---| | 1 | 5 | | 2 | 10 | | 3 | 15 | | 4 | 20 | What is the rule? We are multiplying the input by 5 to get the output.

Rule: Output = Input x 5 Guided Practice (With Solutions)

Question 1: Identify the rule and find the next two numbers in the pattern: 5, 10, 15, 20, ____, ____.

Solution: What is happening from one number to the next? We are adding 5 each time.

Rule: Add 5 to the previous number.

Next two numbers: 25, 30 Question 2: Complete the flow diagram: Input -> [Subtract 7] -> Output If the Input is 15, what is the Output? If the Input is 22, what is the Output? If the Input is 30, what is the Output?

Solution: We need to apply the rule (Subtract 7) to each input. If Input is 15, Output = 15 - 7 = 8 If Input is 22, Output = 22 - 7 = 15 If Input is 30, Output = 30 - 7 = 23 Question 3: Complete the table and identify the rule: | Input | Output | |---|---| | 1 | 3 | | 2 | 6 | | 3 | 9 | | 4 | ? | | 5 | ? | Solution: Looking at the table, we can see that the output is always 3 times the input.

Rule: Output = Input x 3 If Input is 4, Output = 4 x 3 = 12 If Input is 5, Output = 5 x 3 = 15 Completed Table: | Input | Output | |---|---| | 1 | 3 | | 2 | 6 | | 3 | 9 | | 4 | 12 | | 5 | 15 | Question 4: Identify the rule and find the next number in the pattern: 1, 3, 6, 10, ___.

Solution: This is a trickier pattern. Let's look at the differences between consecutive numbers: 3 - 1 = 2 6 - 3 = 3 10 - 6 = 4 The differences are increasing by 1 each time. So the next difference should be

5. The next number in the pattern is 10 + 5 = 15 Rule: Add consecutive numbers to the previous term (add 2, then 3, then 4, then 5...) Independent Practice (Questions Only) Identify the rule and find the next three numbers in the pattern: 3, 7, 11, 15, ____, ____, ____. Identify the rule and find the next three numbers in the pattern: 48, 24, 12, 6, ____, ____, ____.

Complete the flow diagram: Input -> [Multiply by 4, then add 2] -> Output If the Input is 2, what is the Output? If the Input is 5, what is the Output? If the Input is 8, what is the Output?