You know place value and all your facts. Now use them for numbers like $4 \times 30$. The trick is to think in tens.
Why it works
$30$ is 3 tens. So $4 \times 30$ is 4 groups of 3 tens, which is $4 \times 3 = 12$ tens. Twelve tens is 120. The fact $4 \times 3$ does all the work; the tens tell you what kind of thing you have 12 of.
Key idea
To multiply by a multiple of 10, use the fact, then count tens: $6 \times 70 = 6 \times 7$ tens $= 42$ tens $= 420$.
Worked example: Count tens
Find $4 \times 30$.
- $30$ is 3 tens.
- $4 \times 3$ tens $= 12$ tens.
- 12 tens is 120.
Answer: $120$
Worked example: Bigger
Find $9 \times 80$.
- $9 \times 8 = 72$, so $9 \times 80$ is 72 tens.
- 72 tens is 720.
Answer: $720$
Worked example: A missing factor
$\square \times 50 = 300$
- $300$ is 30 tens, and $50$ is 5 tens.
- What times 5 makes 30? $6 \times 5 = 30$.
Answer: $6$
Common mistake
"Just add a zero" without knowing why. The zero is there because the answer is a number of tens: 12 tens is written 120. Thinking in tens keeps working later, when "add a zero" stops working (with decimals, for example).