Mathematics - Term 2 - Week 7

Patterns are sequences that follow a specific rule or formula. In mathematics, we often encounter numerical patterns, such as arithmetic sequences where each term increases by a constant value. For example, in the sequence 2, 4, 6, 8, the pattern is that each number increases by 2. Recognizing these patterns helps us predict future numbers in the sequence and forms the basis for algebraic expressions.

Algebra involves using symbols and letters to represent numbers in equations and expressions. For instance, if we let 'n' represent the position in a sequence, we can express the nth term of the sequence 2, 4, 6, 8 as 2n. This allows us to generalize the pattern and solve problems more efficiently.

Consider the pattern 3, 6, 9, 12. To find the nth term, we observe that each term increases by 3. Thus, we can express the nth term as 3n. For example, when n=4, the term is 3*4 = 12. This method can be applied to any arithmetic sequence.

Let's solve the expression 2n + 5 for n = 3. Substituting 3 into the expression gives us 2(3) + 5 = 6 + 5 = 11. This shows how we can evaluate algebraic expressions by substituting values for the variables.

Now, let's work together on identifying the pattern in the sequence 5, 10, 15, 20. What is the rule? Students should recognize that each term increases by 5. Ask them to express the nth term using algebra. The correct expression is 5n. Encourage students to share their thoughts and reasoning.

Next, evaluate the expression 4n - 3 for n = 2. Guide students through the substitution process: 4(2) - 3 = 8 - 3 = 5. Discuss the steps taken and ensure students understand how to substitute and simplify.

1. Identify the pattern in the sequence 1, 4, 7, 10 and write the nth term. 2. Evaluate the expression 3n + 2 for n = 5. 3. Find the 6th term of the sequence defined by the expression 2n - 1. 4. If n = 4, what is the value of the expression n^2 + 3n? Encourage students to show their working clearly.

After completing the problems, review common mistakes as a class. Discuss why certain answers were incorrect and how to approach similar problems differently in the future. This reflection will help solidify their understanding of patterns and algebra.

• 10
• 12
• 14
• 16

Answer: 10

The pattern increases by 2, so the next number is 8 + 2 = 10.

• n + 5
• 5n
• n + 10
• 10n

Answer: 5n

Each term increases by 5, so the nth term can be expressed as 5n.

Answer: 11

Substituting n = 4 gives 2(4) + 3 = 8 + 3 = 11.

• 12
• 15
• 18
• 21

Answer: 15

Substituting n = 5 into 3n gives 3(5) = 15.

Answer: 5

Substituting n = 3 gives 3^2 - 4 = 9 - 4 = 5.

• 17
• 19
• 21
• 23

Answer: 19

The pattern increases by 2, so the 10th term is 1 + 2(9) = 19.

Answer: 10n

The pattern increases by 10, so the nth term is 10n.

• 8
• 10
• 12
• 14

Answer: 8

Substituting n = 2 gives 5(2) - 2 = 10 - 2 = 8.