How to teach multiplication: tricks that work

Multiplication is a big step in elementary math, usually introduced in second grade and practised heavily in third grade (Years 3 and 4 in the UK). Children understand multiplication best when they start with real objects and pictures, then move to numbers, facts and tricks. This guide explains how to teach multiplication step by step, the best order to learn times tables, helpful tricks, how to teach division and how to make practice fun.

What is multiplication?

Multiplication is a quick way of adding equal groups. Three groups of four is 4 + 4 + 4, which is 12, or 3 × 4 = 12. When children understand this idea, multiplication makes sense rather than being a list of facts to memorize.

Step 1: Equal groups

Start with real objects. Make 3 plates with 4 grapes each. How many grapes are there? Let children build their own groups with toys, blocks or buttons. Use the words "groups of": "3 groups of 4 is 12."

Step 2: Repeated addition

Show that multiplication is the same as adding the same number again and again. 3 × 4 = 4 + 4 + 4 = 12. This helps children see the link between addition and multiplication.

Step 3: Arrays

Arrange counters or draw dots in rows and columns. An array of 3 rows of 4 shows 3 × 4. Turn the array sideways and it shows 4 × 3. Both make 12. This shows that multiplication works in any order (the commutative property), which halves the facts children need to learn.

Step 4: Skip counting

Counting by 2s, 5s and 10s is the same as those times tables: 5, 10, 15, 20 is the 5 times table. Sing skip counting songs and practise with skip counting worksheets.

Step 5: Learn the times tables in order

Learning the tables in a sensible order makes it easier:

1. 2, 5 and 10. These are the easiest and build confidence.
2. 3 and 4. The 4 times table is double the 2s.
3. 8. Double the 4s.
4. 6. Double the 3s, or 5s plus one more group.
5. 9. There is a great finger trick.
6. 7. The trickiest, but by now children already know most of the facts.
7. 11 and 12. If your curriculum includes them.

Our times tables worksheets have one sheet for every table from 1 to 12, and the multiplication worksheets mix facts for review.

How to teach multiplication to grade 3

Third graders usually learn all the facts to 10 × 10 and start solving word problems. A good weekly routine:

• Monday: introduce or review one table with arrays and skip counting.
• Tuesday: practise with a worksheet or game.
• Wednesday: word problems with that table. Try word problem worksheets.
• Thursday: mixed review with earlier tables.
• Friday: a fun timed challenge with mad minute drills.

In the UK, children in Year 4 take the multiplication tables check, so regular practice of all facts to 12 × 12 is especially useful. See our Year 4 worksheets and Grade 3 worksheets.

Multiplication tricks that help

• Zeros: any number times 0 is 0.
• Ones: any number times 1 is itself.
• Tens: add a zero (6 × 10 = 60).
• Fives: the answers end in 0 or 5, and are half of the tens (6 × 5 is half of 60, which is 30).
• Twos: double the number.
• Fours: double, then double again.
• Eights: double three times.
• Nines finger trick: hold up ten fingers. For 9 × 3, fold down the third finger. There are 2 fingers to the left (tens) and 7 to the right (ones): 27.
• Nines pattern: the digits of the answer add up to 9 (9 × 6 = 54, and 5 + 4 = 9).
• Elevens to 9: repeat the digit (11 × 4 = 44).
• Turn it around: if you know 3 × 8, you know 8 × 3.

How to teach division

Division is sharing into equal groups or finding how many groups fit. It is the opposite of multiplication.

1. Sharing. Share 12 sweets between 3 friends. How many each? That is 12 ÷ 3 = 4.
2. Grouping. How many groups of 4 can you make from 12? Three groups.
3. Fact families. Show how 3 × 4 = 12, 4 × 3 = 12, 12 ÷ 3 = 4 and 12 ÷ 4 = 3 are all connected. Our fact families worksheets help.
4. Use times tables. "What times 4 makes 12?" Knowing tables makes division much easier.

Practise with division worksheets, then move on to long division in fourth grade.

Making multiplication fun

• Times table songs and chants.
• Card games. Flip two cards and multiply; the biggest answer wins.
• Dice games. Roll two dice and multiply.
• Multiplication bingo.
• Color by number. Solve facts to reveal a picture with color by number math sheets.
• Real life. How many wheels on 4 cars? How many legs on 6 spiders?
• Beat your score. Time a mad minute and try to beat yesterday's record.
• Make your own sheet. Create fresh practice with the math worksheet maker.

Common difficulties

• Forgetting facts. Little and often works better than long sessions. Review old tables while learning new ones.
• Mixing up addition and multiplication. Go back to equal groups with objects.
• Anxiety about timed tests. Focus on beating their own score, not on speed alone.

Most importantly, keep a positive attitude. Children who believe they can get better at math usually do. Celebrate progress, not just perfect scores, and remind them that every expert once had to learn their times tables too.

Frequently asked questions

What is the best way to teach multiplication?

Start with equal groups of real objects, move to arrays and skip counting, then learn the tables in order (2, 5, 10 first) with tricks and plenty of short, fun practice.

In what order should times tables be learned?

Start with 2, 5 and 10, then 3 and 4, then 8, 6, 9 and 7, and finally 11 and 12.

How do I teach division to my child?

Use sharing and grouping with real objects, then show how division is the reverse of multiplication using fact families.