Multiplication: learn and practice

Who this lesson is for

This multiplication lesson is for grades 3–4. Grade 3 builds facts from equal groups, including 2, 5, and 10. Grade 4 keeps the same facts and adds the harder one-digit products. The practice link opens the core facts. The page has one address, and both grade hubs link here.

Equal groups make a fact

Multiplication counts equal groups. 6 × 4 means 6 groups of 4, or 4 groups of 6. Either picture gives 24. The first number and the second number can trade places, and the product stays the same. That trade is useful when one order is easier to see. Six groups of 4 can be counted as 4, 8, 12, 16, 20, 24.

A fact you can check

A multiplication fact is finished only when you can undo it. If 7 × 8 = 56, then 56 ÷ 7 = 8 and 56 ÷ 8 = 7. The division does not replace the fact. It checks it. Skip-counting also checks a product: eight jumps of 7 land on 56. If the jumps land somewhere else, the fact was remembered wrong.

Worked example 1: groups of four

Find 6 × 4. Draw 6 groups with 4 in each group. Count by fours: 4, 8, 12, 16, 20, 24. The product is 24. You can also draw 4 groups of 6 and count 6, 12, 18, 24. Both pictures end at 24, so the order of the factors did not change the answer. 6 + 4 = 10 is a different question. Adding the factors is not the product.

Worked example 2: seven times eight

Find 7 × 8. One way is to start from a fact you know. 5 × 8 = 40, and two more eights are 16, so 40 + 16 = 56. Another way is 7 × 10 = 70, then take away 7 × 2 = 14, because 8 is 2 less than 10. 70 − 14 = 56. The two paths agree. Check with division: 56 ÷ 8 = 7.

Worked example 3: nine times five

Find 9 × 5. Count by fives nine times, or count by nines five times. Fives are quicker: 5, 10, 15, 20, 25, 30, 35, 40, 45. The product is 45. A nine fact also sits one less than the matching ten fact: 10 × 5 = 50, and 50 − 5 = 45. Use that only as a check. The board practice asks for the product itself.

Checks before you leave the problem

Say the product, then undo it with division or with one more equal group. If 6 × 4 is 24, one more group of 4 makes 28, not 25. Adding 1 to the product is the usual slip. Then practice the core facts on the board.

Common questions about multiplication

Do I have to memorize every fact?

Knowing the facts makes later division and multi-digit work faster. Equal groups and a nearby fact are how you rebuild one you forget. The practice on this page is the one-digit facts themselves.

Is 6 × 4 the same as 4 × 6?

Yes. Both are 24. The pictures look different, six rows of four against four rows of six, and the total number of objects matches.

What if I add instead of multiply?

6 + 4 is 10, and 6 × 4 is 24. The multiplication sign means equal groups, not a single join. If the story says groups of, use the product.