Multiplication tables of 3, 4

1Summary 重點摘要

×3, ×4 tables. 3×4=12.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Part 1: Multiplication is repeated additionMultiplication is repeated addition, and this is the base for understanding every times table. 3×4 means adding 3 four times: 3+3+3+3 = 12. You can also see it as adding 4 three times: 4+4+4 = 12. Swap the order and the answer stays the same: 3×4 = 4×3 = 12. Why is it the same swapped? The total collection is the same size, only grouped differently. Take care that the number of addends must match the multiplier; 3×4 is four 3s added, not three.
2. Part 2: The 3 times tableBuild the 3 times table by starting at 3 and adding 3 each time: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30; this skipping way of counting is called skip counting. To work out 3×7, count to the 7th number in the list, which is 21. Practise until you can answer at once. The usual error is forgetting the first number 3 and starting from 6, which turns the 7th number into 24; remember the table starts with 3 itself, and 3 holds the first place.
3. Part 3: The 4 times tableBuild the 4 times table by starting at 4 and adding 4 each time: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40. To work out 4×8, count to the 8th number: 32. Say it out loud with claps a few times and it is easy to remember; rhythm is a fine helper for learning tables. Take care that the table of 4 overlaps the table of 2: 4, 8 and 12 appear in both, because they are multiples of 2 as well as of 4; this is normal and no reason to doubt yourself.
4. Part 4: See it with an arrayMultiplication can be seen with an array, where beads form a tidy rectangle and the rows and the beads per row are plain to see. Example: arrange beads into 3 rows with 4 beads in each row, making a rectangle; one row has 4 beads, and 3 rows give 3×4 = 12 beads. Rows times beads per row equals the total, and the picture supports the idea. Take care that turning rows into columns changes the sentence: 3 rows of 4 is written 3×4, 4 rows of 3 is 4×3, though the totals agree and both are correct.
5. Part 5: Build new facts from known onesIf you forget 4×6, do not worry; reach it from a product you already know, which is the clever way through the tables. You know 4×5 = 20, so add one more 4: 20+4 = 24, and that is 4×6. Why does it work? A times table is just skip counting, each step adding the same number, so the next product always equals the previous product plus one more. Take care of the direction: from 4×5 to 4×6 you add 4 and nothing else; after building, check once more.
6. Part 6: Everyday useMultiplication is useful in daily life, and any situation with equal groups should bring it to mind. Example: a box holds 4 chocolates, so 3 boxes give 3×4 = 12 chocolates, and 7 boxes give 7×4 = 28. One multiplication finds the total, far faster than counting box by box. Take care to check before writing the sentence that every box holds the same number; if one box has 5, work that box separately and add it to the rest.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Multiplication is a quick way to add equal groups
• The 3 times table adds 3 each time: 3, 6, 9, 12…
• The 4 times table adds 4 each time: 4, 8, 12, 16…
• Order does not change the product: 3×4 = 4×3
• Build from facts you know: 4×5=20, add 4 to get 24