"3 × 4 = ?" A 7-year-old who doesn't know multiplication counts: 4, 8, 12. Or: 3+3+3+3 = 12. Both work. Both are the foundation of multiplication. This article shows how to introduce multiplication as repeated addition in groups — then build to memorised tables.
At Kluriko multiplication is trained in the Learning Games with visual aids and patterns — but at home with blocks, beads and the 100-grid the first understanding happens.
What is multiplication?
Definition 1: Repeated addition. 3 × 4 = 4 + 4 + 4. (Three fours.)
Definition 2: Groups. 3 × 4 = three groups of four.
Definition 3: Rectangle area. 3 × 4 = a rectangle with sides 3 and 4 (= 12 squares).
All three are right. They should see all three — then multiplication becomes powerful.
When to start?
Age 7: introduce as repeated addition.
Age 8: start memorising 2s and 5s tables.
Age 9: full tables to 10×10.
Age 10: they should know all tables automatically.
Step 1: Concrete — groups
Lay 3 piles of 4 beads each. "How many total?" They count: 4+4+4=12.
Say: "This is called multiplication. Three times four is twelve."
Write: 3 × 4 = 12.
Do the same with 2 groups of 5. 4 groups of 3. Etc.
Step 2: Concrete — rectangles
Lay beads in a rectangle. 3 rows, 4 columns. They see the area is 12.
Important for later geometry.
Step 3: Pictorial
Draw a rectangle with cells: 3×4. They count 12 cells.
Or draw 3 groups of 4 dots. They count.
Step 4: The tables
They learn systematically.
1s table: 1×1=1, 1×2=2, 1×3=3, 1×4=4... 1×10=10. (Trivial — they learn it in 5 minutes.)
2s table: 2×1=2, 2×2=4, 2×3=6, 2×4=8, 2×5=10, 2×6=12, 2×7=14, 2×8=16, 2×9=18, 2×10=20.
The even-number pattern. (See the 2s table article.)
5s table: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. (Clock minute marks! Concrete connection.)
10s table: 10, 20, 30... 100. (The easiest — just add a 0.)
Then 3s, 4s, 6s, 7s, 8s, 9s tables — in that order, easiest to hardest.
Tables to master
By 10: all tables 1×1 to 10×10 = 100 facts. Plus 11×11 and 12×12 if they're strong.
Strategies for memorising
Patterns in the tables
2s: always even. End in 0, 2, 4, 6, 8.
5s: always end in 0 or 5.
10s: always end in 0.
9s: digit sum = 9. 9×3 = 27 (2+7=9). 9×7 = 63 (6+3=9). Magic pattern!
Finger trick for 9s: They hold both hands in front. For 9×3, bend the third finger. Fingers to the left of bent = 2. Fingers to the right = 7. Answer: 27.
Double and halve
4×6 = 8×3 = 24. (Double one, halve the other.) Helpful between tables.
Squares
The diagonal of the table: 1×1, 2×2, 3×3, 4×4... Squares. They learn these by heart.
Commutative law
3×4 = 4×3. They only need to learn half the table! Huge relief.
Volume
Practice 5 minutes a day. No more. Daily beats lots at the weekend.
Use:
- Flashcards
- Songs (there are many multiplication songs)
- Games (Kluriko)
- Quizzes at dinner
Common problems
They can chant but not use. They say "2×3=6" quickly but can't work it out themselves. Back to concrete: beads in groups.
They mix the tables. Common. Solve: learn one table fully, then the next. Not several at once.
They tire. Multiplication can become a chore. Vary games, songs, play.
Multiplication in daily life
- "We're 5 people. Each gets 3 biscuits. How many biscuits?" 5×3=15.
- "A car has 4 wheels. 6 cars. How many wheels?" 6×4=24.
- "12 in a carton. 5 cartons. How many total?" 12×5=60.
Everyday problems make multiplication meaningful.
Multiplication and division
Division is multiplication in reverse. "20 ÷ 4 = ?" is "what number × 4 = 20?". Answer: 5.
At 9-10 they learn both at the same time.
How Kluriko helps
Kluriko Learning Games have multiplication games progressing from concrete-visual representation to table memorisation. Systematic training across all multiplication levels.