Multiplication for kids

What kids learn about multiplication, grade by grade

• Grade 2 (2.OA.C.3, 2.OA.C.4): equal groups, odd and even, and arrays up to 5 × 5 written as repeated addition.
• Grade 3 (3.OA.A.1 to 3.OA.C.7): what multiplication means, its properties, and all times tables to 10 × 10 from memory. Also multiplying by multiples of 10.
• Grade 4 (4.NBT.B.5): up to 4 digits by 1 digit and 2 digits by 2 digits, using place value and the area model.
• Grade 5 (5.NBT.B.5): multi-digit multiplication with the standard method, plus decimals and fractions.

Where to start with multiplication

With equal groups of real things: 3 plates of 4 cookies, egg cartons, pairs of socks. Count them by adding, then show the shortcut: 3 × 4. Only start memorizing facts once the meaning is clear.

The big idea behind multiplication

4 × 6 means 4 equal groups of 6. Arranged in rows, that is an array: 4 rows of 6 dots. Arrays show three things at once: why 4 × 6 = 6 × 4 (turn the picture), how multiplication and division are linked, and later why area is length × width.

Learning the times tables

There are 100 facts up to 10 × 10, but far fewer to learn than it seems:

• × 1, × 2, × 5 and × 10 follow easy patterns: same number, doubles, ends in 0 or 5, add a zero.
• Turn-arounds: 3 × 8 = 8 × 3, so every fact you learn gives you another one.
• × 4 is double-double; × 8 is double-double-double.
• × 9: the digits add to 9 (9 × 7 = 63), and one less than the multiplier is the tens digit.
• That leaves only a handful of hard facts: 6 × 7, 6 × 8, 7 × 8 and their turn-arounds.

Five minutes a day beats an hour on Sunday. The times tables lesson has the full plan.

Multiplying bigger numbers

Bigger numbers are split into tens and ones, multiplied in parts and added. The area model shows every part, and the written method is a shorthand for the same steps.

Where kids get stuck with multiplication

Counting instead of knowing

Skip-counting up to 7 × 8 every time is slow and error-prone. Fix: learn the hard facts with a strategy (7 × 8: 5, 6, 7, 8 → 56), then practice them daily.

Losing the zero in bigger numbers

34 × 26 worked as 34 × 2 instead of 34 × 20. Fix: say the place value: “34 times 2 tens is 68 tens, which is 680.”

Mixing up multiplication and addition

3 × 4 answered as 7. Fix: go back to groups. Three plates of four is not seven cookies.

Forgetting carried digits

In 47 × 6, 7 × 6 = 42: write 2, carry 4. Fix: write the carried digit small above the next column and add it after multiplying.

Multiplication worksheets

• Multiplication factsGrade 3
• Mixed times tablesGrades 3–4
• 2 times tableGrade 3
• 3 times tableGrade 3
• 4 times tableGrade 3
• 5 times tableGrade 3
• 6 times tableGrade 3
• 7 times tableGrade 3
• 8 times tableGrade 3
• 9 times tableGrade 3
• 10 times tableGrade 3
• 11 times tableGrades 3–4
• 12 times tableGrades 3–4
• 2-digit by 1-digit multiplicationGrade 4
• 2-digit by 2-digit multiplicationGrade 4
• Multi-digit multiplicationGrade 5
• Multiply and divide by 10, 100 and 1000Grades 3–5

Make a fresh times tables test · Make a multi-digit multiplication test · Multiplication chart · Math Galaxy practice

How to teach multiplication at home

Find arrays everywhere

Egg cartons (2 × 6), muffin tins (3 × 4), window panes and chocolate bars are all arrays. Ask “how many, without counting one by one?”

Five minutes a day

One table per week, said forwards, backwards and mixed up, in the car or over breakfast.

Play multiplication war

Each player flips two cards and multiplies them. The bigger product wins all four cards.

Shop in multiples

“Four packs of 6 yogurts: how many yogurts?” Real groups make the facts stick.

Related: division (the reverse of multiplication) · factors and multiples · 3rd grade math