2 Predict how many matchsticks will be needed for Pattern 10. Explain how you get your answer. 3.3 Write down the general rule for the pattern in the form T_n=

Let $T_n$ be the number of matchsticks for Figure $n$.

• Figure 1: $1 \times 1$ grid + 1 square on top. Matchsticks = $2(1)(1+1) + 3 = 4 + 3 = 7$.
• Figure 2: $2 \times 2$ grid + 1 square on top. Matchsticks = $2(2)(2+1) + 3 = 12 + 3 = 15$.
• Figure 3: $3 \times 3$ grid + 1 square on top. Matchsticks = $2(3)(3+1) + 3 = 24 + 3 = 27$.
• Figure 4: $4 \times 4$ grid + 1 square on top. Matchsticks = $2(4)(4+1) + 3 = 40 + 3 = 43$. The general rule for the number of matchsticks is $T_n = 2n(n+1) + 3$.

Substitute $n=10$ into the formula:

$$T_{10} = 2(10)(10+1) + 3$$ $$T_{10} = 2(10)(11) + 3$$ $$T_{10} = 220 + 3$$ $$T_{10} = 223$$

Number of matches in pattern 10 = $\boxed{\text{223}}$.
This is found by using the general rule $T_n = 2n(n+1) + 3$, where $n$ is the pattern number. For Pattern 10, we substitute $n=10$ into the rule.