Multiplication facts for 2, 3, 4, and 5 build on equal groups and repeated addition. Fluency with these facts (within ~2 seconds) is essential for third grade. Arrays and skip-counting are the primary models.
Start with manipulatives or drawings of equal groups (e.g., 3 groups of 4 circles). Practice skip-counting aloud first (2, 4, 6, 8...). Use arrays to show products visually. Daily practice with flashcards or games for automaticity.
You already know that multiplication means equal groups and that skip-counting generates the sequence of products. Now the goal is fluency — answering facts within a couple of seconds without having to count out groups. Fluency matters because when you later solve word problems or do multi-digit multiplication, you need to recall 3 × 7 instantly the same way you recall your own name; rebuilding it from scratch every time is too slow.
Each table from 2 through 5 has a strategy that connects to something you already know. The 2s are just doubling: 2 × 6 is the same as 6 + 6. The 5s match the clock face: 5, 10, 15, 20 — you have been reading clock minutes in multiples of 5 for years. The 4s are double-the-2s: 4 × 7 = 2 × 7 doubled = 14 doubled = 28. The 3s can be built as "one more group than the 2s": 3 × 6 = 2 × 6 plus one more 6 = 12 + 6 = 18. Using these strategies first builds understanding; daily practice with flashcards or games then converts understanding into instant recall.
The commutative property cuts your memorization work in half: 3 × 4 and 4 × 3 are the same fact. So rather than 20 separate 2s-through-5s facts, you actually need to learn only about 10 new ones (the other 10 are repeats you have already seen from the other direction). Once you have solid fluency with the 2s through 5s, the 6s through 9s are within reach — and many of them are just commutative versions of facts you already know (6 × 3 = 3 × 6, which you learned with the 3s table).