How to teach multiplication to kids, step by step

Quick answer

Start with equal groups (3 groups of 4), then link multiplication to repeated addition, skip counting and arrays. Learn facts in a smart order: 0, 1, 2, 5, 10, then 3 and 4, then 6 and 9, then 7 and 8, using strategies like doubling. Practice 5–10 minutes a day. Common Core expects all one-digit products from memory by the end of 3rd grade.

Multiplication is the big math milestone of 3rd grade, and it builds on things your child already knows: counting, adding and spotting patterns. Children learn it best in stages, from real groups of objects, to pictures like arrays, to facts they recall in a second. Here is each stage, with examples you can try tonight.

What to expect by grade

Here is what the Common Core State Standards, used by most U.S. states, expect. Your state or school may differ a little.

Many schools also teach ×11 and ×12. That's common and useful, but not a Common Core requirement. For the full picture of each year, see our 2nd grade, 3rd grade and 4th grade skills guides.

Step 1: Start with equal groups

Multiplication answers one question: how many in all, when every group has the same amount? Set out 3 plates and put 4 grapes on each. Ask: “How many plates? How many on each plate? How many grapes altogether?”

Teach the words before the symbol: “3 groups of 4.” Then show that × is a short way to write “groups of.” The Common Core reads 5 × 7 as 5 groups of 7 (3.OA.A.1), so the first number is the number of groups.

Step 2: Connect to repeated addition and skip counting

Once groups make sense, show two quicker ways to find the total. Repeated addition: 3 groups of 4 is 4 + 4 + 4 = 12. Skip counting: “4, 8, 12.”

A number line makes skip counting visible: each jump is one group. Count by 2s, 5s and 10s first, because those patterns are the easiest to hear, then add 3s and 4s. Our skip counting guide has hundred-chart patterns and movement games.

Repeated addition is a bridge, not the destination: adding six 7s is slow and easy to get wrong, which is why kids eventually learn the facts.

Step 3: Build arrays and use the turn-around rule

An array is objects arranged in equal rows: a muffin tin, an egg carton, a chocolate bar. Arrays are one of the most useful multiplication pictures, because you can see every group and count it two ways.

Turn the array sideways and the total doesn't change: 3 × 5 = 5 × 3. This turn-around rule (the commutative property) nearly halves the facts to learn. Build arrays with LEGO bricks or cereal, then turn the plate and say the turn-around fact.

Step 4: Learn the facts in a smart order

Don't start at the 1s and march to the 12s. Start with the tables that follow simple rules, then use them to unlock the harder ones.

Our guide to the fastest way to learn times tables counts how few facts are left at each stage and has a sample weekly plan.

Step 5: Teach strategies for the harder facts

A strategy turns a fact your child doesn't know into one they do. These are the classics:

• ×4 = double, then double again. 4 × 7: double 7 is 14, double 14 is 28.
• ×8 = double the ×4 fact. 8 × 6: 4 × 6 = 24, and double 24 is 48.
• ×6 = ×5 plus one more group. 6 × 7: 5 × 7 = 35, plus one more 7 is 42.
• ×9 = ×10 minus one group. 9 × 6: 10 × 6 = 60, minus 6 is 54. Your child may also enjoy the 9 times table finger trick.

The break-apart strategy

The most powerful strategy works for any fact: split a number into friendlier parts, multiply each part, then add. For 7 × 8, split the 8 into 5 and 3: 7 × 8 = 7 × 5 + 7 × 3 = 35 + 21 = 56.

Schools call this the distributive property (3.OA.B.5). For more ways into the trickiest facts, see our tricks for the 6, 7 and 8 times tables.

Step 6: Build fluency with short, spaced practice

Fluency means answering accurately and efficiently, with a strategy to fall back on, not racing a clock. The U.S. Institute of Education Sciences recommends spacing practice over time and using quick quizzes to bring material back. For times tables:

• 5–10 minutes a day beats an hour on Sunday.
• Work on one small set at a time (say, the ×3 facts), mixed with facts your child already knows.
• Have your child answer from memory before checking: flash cards, or quick questions in the car.
• Bring missed facts back tomorrow, then in a few days, then next week.
• Play: flip two playing cards and multiply them, or roll two dice.

A printed multiplication chart is a fine support at first; cover facts as they become automatic.

What comes after the facts

Place value carries the facts further. In 3rd grade, 3 × 40 is 3 groups of 4 tens: 12 tens, or 120 (3.NBT.A.3). In 4th grade, the break-apart idea handles bigger numbers: 23 × 4 = 20 × 4 + 3 × 4 = 80 + 12 = 92.

123×492

Multiplication also unlocks division: if 4 × 6 = 24, then 24 ÷ 6 = 4. Our division guide picks up from there.

Common mistakes (and how to help)

• Adding instead of multiplying. A child writes 4 × 3 = 7. Go back to groups: draw 4 circles with 3 dots in each and count.
• Thinking × 0 keeps the number. 5 × 0 = 5 is an easy slip. Ask: “5 plates with nothing on them. How many cookies?”
• Mixing up neighbors like 6 × 8 = 48 and 7 × 8 = 56. Connect them: 7 × 8 is one more 8 than 6 × 8, and 48 + 8 = 56.
• Freezing under time pressure. Drop the timer for a while and focus on accuracy. Speed follows.

Practice problems

Try these together and ask which strategy your child used.

Multiplication practice (with answers)

1. 3 × 4 = ?
2. 5 × 6 = ?
3. 2 × 9 = ?
4. 10 × 7 = ?
5. 4 × 6 = ?
6. 3 × 8 = ?
7. 6 × 7 = ?
8. 9 × 4 = ?
9. 8 × 8 = ?
10. 7 × 8 = ?
11. 3 × 40 = ?
12. 23 × 4 = ?

Show answers

Want more? Print our free multiplication worksheets and a multiplication chart for the fridge.

Frequently asked questions

What age do kids learn multiplication?

The groundwork starts in 2nd grade (ages 7–8) with skip counting and repeated addition in arrays. Multiplication is the big topic of 3rd grade (ages 8–9): under the Common Core, children should know all products of two one-digit numbers from memory by the end of that year. In 4th grade they multiply bigger numbers.

How do I teach my child multiplication for the first time?

Start with real objects in equal groups. Put 4 crackers on each of 3 plates and ask how many there are altogether. Say “3 groups of 4 is 12” before you write 3 × 4 = 12, then show the same idea as repeated addition, skip counting and an array.

What is the best order to learn times tables?

Start with the tables that follow simple rules: 0, 1, 2, 5 and 10. Then learn 3 and 4, which build on doubles. Next come 6 and 9, which build on the 5s and 10s. Leave 7 and 8 for last, because by then the turn-around rule means only a few of those facts are new.

Should kids memorize their times tables?

Yes, eventually. The Common Core expects all one-digit products from memory by the end of 3rd grade, and instant recall frees up attention for bigger problems. But memorizing works best after understanding: teach what multiplication means and a strategy for each fact first, then practice until recall is automatic.

Do kids need to learn the 11 and 12 times tables?

Many schools teach them, and they are handy for dozens and inches in a foot, but the Common Core only requires products of one-digit numbers. If your child learns them, use strategies: 11 times a single digit repeats the digit (11 × 6 = 66), and ×12 is ×10 plus ×2.

How can I help my child who is struggling with multiplication facts?

Shrink the job. Show how few facts are really left once the easy tables and the turn-around rule are known, then work on two or three at a time, each with a picture and a strategy. Keep practice short and daily, and drop timed drills if they cause stress.

Sources

• Common Core State Standards for Mathematics — CCSSI
• Common Core State Standards: Grade 2, Operations & Algebraic Thinking — CCSSI
• Common Core State Standards: Grade 2, Number & Operations in Base Ten — CCSSI
• Common Core State Standards: Grade 3, Operations & Algebraic Thinking — CCSSI
• Common Core State Standards: Grade 3, Number & Operations in Base Ten — CCSSI
• Common Core State Standards: Grade 4, Number & Operations in Base Ten — CCSSI
• Organizing Instruction and Study to Improve Student Learning (practice guide) — Institute of Education Sciences, What Works Clearinghouse

Written by The Mathing Team for parents and teachers. Grade expectations follow the Common Core State Standards for Mathematics; your state or school may sequence skills a little differently.