Patterns and algebra (T2 W7)
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Patterns are sequences that follow a specific rule. They can be found in numbers, shapes, and even in everyday life. For example, the sequence 2, 4, 6, 8 is a number pattern where each number increases by 2. In this lesson, we will explore how to identify and create different types of patterns, including repeating patterns and growing patterns.
Let's look at the pattern: 5, 10, 15, 20. This is a growing pattern where each number increases by 5. To find the next number, we add 5 to the last number: 20 + 5 = 25. Now, let's create a similar pattern starting from 3 and increasing by 3. The pattern would be 3, 6, 9, 12, and the next number would be 15.
Now, let's work together to create a pattern. I will start with the number 1 and increase by 4. The pattern will be 1, 5, 9, 13. What do you think the next number will be? (Students will respond with 17). Great! Now, let's try a shape pattern. If we have a circle, triangle, circle, triangle, what comes next? (Students will respond with a circle).
Now it's your turn! Create your own number pattern starting from 7 and increasing by 3. Write down the first five numbers. Then, solve the following problems: 1) What is the 10th number in the pattern? 2) If you start a new pattern with 2 and double each time, what are the first five numbers? Show your working clearly.
Answer: 16
The pattern increases by 4 each time, so 12 + 4 = 16.
Answer: Circle, Square, Circle, Square
A repeating pattern is one that has a sequence that repeats itself.
Answer: 10, 15, 20, 25
The pattern increases by 5 each time, starting from 10.
Answer: 12
The pattern increases by 3 each time, so the 5th number is 9 + 3 = 12.
Answer: Triangle
The pattern alternates between Triangle and Circle.
Answer: 10
The pattern consists of odd numbers, and 10 is an even number.
Answer: 32
This is a doubling pattern, so 16 x 2 = 32.
Answer: Add 5
The pattern increases by 5 each time.