Multiplication describes repeated equal groups. If you have 3 groups of 4 objects each, multiplication (3 × 4) tells you there are 12 objects total. The first number is the number of groups; the second is the size of each group.
Use counters, drawings, or objects to create visible groups. Have students count the total and record it as a multiplication sentence. Progress from concrete to pictorial to abstract.
You already understand equal groups: collections where every group holds the same number of objects. Multiplication is simply a compact notation for that idea. Instead of writing 4 + 4 + 4, mathematicians write 3 × 4, which is read "3 groups of 4." The multiplication symbol (×) is shorthand for "groups of," and the two numbers on either side answer the two questions you have been practicing: how many groups, and how many in each group.
The first number in a multiplication expression is the number of groups and the second is the group size. So 3 × 4 means 3 groups with 4 in each, giving a total of 12. You can verify this with the repeated addition you already know: 4 + 4 + 4 = 12. Both expressions describe the same situation — multiplication is just a faster way to write it. As the numbers get bigger, this shortcut becomes more and more valuable.
One of the most surprising and useful facts about multiplication is that 3 × 4 = 4 × 3, even though "3 groups of 4" and "4 groups of 3" describe different physical arrangements. If you draw 3 rows of 4 dots and then turn the paper sideways, you see 4 rows of 3 dots — same dots, same total, different grouping. This is called the commutative property, and it means the order of the two numbers doesn't change the product. This will save you enormous effort when you memorize multiplication facts: if you know 3 × 7, you automatically know 7 × 3.
The key skill right now is translating freely between the picture, the repeated addition, and the multiplication sentence. Given a picture of 5 groups of 2, you should be able to write 2 + 2 + 2 + 2 + 2 = 10 and also 5 × 2 = 10. Given the multiplication sentence 6 × 3, you should be able to draw 6 groups of 3 objects and count to confirm the total is 18. This back-and-forth between representations — concrete objects, pictures, and symbols — builds the deep understanding that makes later multiplication fluency feel effortless rather than mechanical.