Getting through multiplication by 4 actually isn't the nightmare it sounds like
I keep seeing people overcomplicate this. You double twice. That's literally all it is. Four times something equals two times two times that thing. If a kid already knows their doubles, you're basically done. The real work is getting them to see the connection instead of memorizing a separate list of facts. The ones I've actually used are usually free downloads from sites like K5 Learning, Math Drills, or Super Teacher Worksheets. The K5 sheets are decent because they're scaffolded. They start with repeated addition and arrays before moving into straight recall. Most generic worksheets skip straight to "4 x 1 through 4 x 12" and expect fluency out of nowhere, which doesn't work for most kids. Here are a couple that have worked for me: K5 Learning multiplication section and Super Teacher Worksheets. Both let you generate printable sheets without signing up for anything.
The actual method I use when someone is stuck
Start with the doubling strategy. Pick a number, say 7. Ask what 7 plus 7 is (14), then ask what 14 plus 14 is (28). Write it out: 4 x 7 = 7 + 7 + 7 + 7 = 14 + 14 = 28. Do this maybe six or eight times until the kid notices the pattern on their own. Once they do, you can shortcut to "double it, then double it again" and cut the practice time significantly. Arrays help too. Draw a 4 by 6 grid of dots. Have them count by rows. Then cover half and show that 4 x 6 equals 2 x 6 doubled. It's visual reinforcement without being flashy about it. The standard drill sheets are fine for maintenance, but if someone is still struggling after a week of doubling practice, the worksheet alone isn't going to fix it. You need to go back to concrete materials. Counters, blocks, anything they can physically split into two groups of two.
One specific problem I ran into that nobody warns you about
A few years ago I was working with a student who could double any number cold but completely froze on anything past 4 x 8. The doubling strategy was solid up to 16, but once the intermediate sum hit three digits mentally, she'd just blank out. Her working memory was the bottleneck, not her understanding of multiplication. The workaround was writing down the intermediate step. Instead of holding "4 x 6 = 12, then double 12 = 24" in her head, she wrote "12 + 12 = 24" on paper. Once she had the scaffolding externalized, she breezed through. After a couple weeks, she gradually stopped needing the paper. Most people don't consider that working memory could be the actual issue here. They assume the kid just doesn't "get it."
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Things that are harder than they should be
The 4 x 9 fact is annoying. 36 comes out of nowhere if you're relying on doubles. The workaround is the finger trick or the "times 10 minus itself" move: 4 x 9 = 36 because 40 - 4 = 36. Teach that separately. Also, zero and one feel trivial but kids mix them up here just like everywhere else. 4 x 0 = 0 and 4 x 1 = 4. One worksheet question at the start of every set as a checkpoint prevents a lot of careless errors later.
When this whole approach breaks down
If a student hasn't internalized addition facts through 20, doubling is going to feel like a trick instead of a strategy. They'll get the right answer sometimes but won't trust it. In that case, go back to basic addition fluency first. The multiplication by 4 work doesn't fix gaps in something earlier. Similarly, this approach assumes the kid has basic number sense. If they're counting on their fingers for anything above 5, drilling 4 times tables isn't going to help much. Build the foundation, then come back to the worksheet. Practice schedule that works: five minutes a day, five days a week, using a worksheet that mixes new facts with review. Thirty minutes a week max. Anything more is just busywork at this point. The retention comes from spaced repetition, not volume.