Young Fermats · Multiplication Facts · Grades 3–5 · NYC Math Class
Multiplication Facts ×3, ×4, and ×6 — 25 Practice Questions with Theory & Hidden Answers (Young Fermats)
A complete class-ready lesson on multiplication by 3, 4, and 6: theory, patterns, skip counting, doubling shortcuts, and 25 practice questions with click-to-reveal step-by-step answers. Built for the SOMATH Young Fermats program (grades 3–5) on the Upper West Side of Manhattan.
This is a full lesson plan and practice set on the multiplication tables for 3, 4, and 6 — the three tables that unlock most of the multi-digit multiplication work in grades 3, 4, and 5. Every question below has a hidden button that reveals the answer and the reasoning, so a student can practice honestly and then check their thinking.
Written by the same team that teaches Young Fermats at SOMATH, a math-focused school on the Upper West Side of NYC run by cofounder Marcelo Ambrozio (Northwestern) and cofounder Vivianne Wright (Harvard).
- Warm-up: read the theory boxes aloud (10 min).
- Skip-counting chant for 3, 4, and 6 (5 min).
- Students attempt the 25 questions with the answers hidden (20 min).
- Reveal answers as a group and re-teach any that missed 3+ students (10 min).
Video walkthrough
Watch cofounder Marcelo Ambrozio walk through the multiplication facts for 3, 4, and 6 in one class-length lesson. This pairs with the theory boxes and the 25 practice questions below.
What’s in this lesson
- Video walkthrough
- What multiplication actually is
- The commutative property (order doesn’t matter)
- Skip counting — the shortcut to the times tables
- Theory: multiplying by 3
- Theory: multiplying by 4 (double, then double)
- Theory: multiplying by 6 (times 3, then double)
- The distributive property (break it up)
- 25 practice questions
- Answer key summary
- About SOMATH & Young Fermats
1. What multiplication actually is
Multiplication = repeated addition
Multiplication is a fast way to add the same number over and over. When we write 4 × 3, we mean “4 groups of 3”:
4 × 3 = 3 + 3 + 3 + 3 = 12
Every multiplication fact tells a story:
- Groups — how many groups you have
- Size of each group — how many are in each group
- Total (product) — how many altogether
Example: 6 baskets of 4 apples each = 6 × 4 = 24 apples.
2. The commutative property — order doesn’t matter
a × b = b × a
Multiplication is commutative: you can swap the two numbers and the answer stays the same.
3 × 8 = 8 × 3 = 24
This is a huge shortcut. If you know 3 × 8, you already know 8 × 3. That means learning the times table for 3 automatically teaches you a piece of every other times table.
3. Skip counting — the shortcut to the times tables
Counting by 3s, 4s, and 6s
Skip counting means jumping forward by the same number each time. Every jump is one group; every number you land on is a multiple.
Counting by 3:
Counting by 4:
Counting by 6:
Notice that 12 and 24 show up in all three lists — they are common multiples of 3, 4, and 6. This is not an accident: it’s the same reason a clock has 12 hours and a foot has 12 inches. 12 is friendly with 3, 4, and 6.
4. Theory: multiplying by 3
Times 3 = triple it
Multiplying by 3 is called “tripling.” It’s the same as adding a number to itself three times.
Two ways to think about n × 3:
- As repeated addition: 7 × 3 = 7 + 7 + 7 = 21
- As double + one more: 7 × 3 = (7 × 2) + 7 = 14 + 7 = 21
The full ×3 table:
| Fact | Product | Fact | Product |
|---|---|---|---|
| 3 × 1 | 3 | 3 × 6 | 18 |
| 3 × 2 | 6 | 3 × 7 | 21 |
| 3 × 3 | 9 | 3 × 8 | 24 |
| 3 × 4 | 12 | 3 × 9 | 27 |
| 3 × 5 | 15 | 3 × 10 | 30 |
Pattern to notice: If you add the digits of any multiple of 3, the sum is also a multiple of 3.
Example: 27 → 2 + 7 = 9 ✓ 18 → 1 + 8 = 9 ✓ 24 → 2 + 4 = 6 ✓
5. Theory: multiplying by 4 (double, then double)
Times 4 = double twice
Multiplying by 4 is the same as multiplying by 2, then doubling the answer. That’s because 4 = 2 × 2.
Example: 7 × 4 = (7 × 2) × 2 = 14 × 2 = 28
This is the easiest trick in the whole lesson — if a student knows their doubles, they know the ×4 table.
The full ×4 table:
| Fact | Product | Fact | Product |
|---|---|---|---|
| 4 × 1 | 4 | 4 × 6 | 24 |
| 4 × 2 | 8 | 4 × 7 | 28 |
| 4 × 3 | 12 | 4 × 8 | 32 |
| 4 × 4 | 16 | 4 × 9 | 36 |
| 4 × 5 | 20 | 4 × 10 | 40 |
Pattern to notice: Every multiple of 4 is an even number. In fact, the ones digit follows a repeating pattern: 4, 8, 2, 6, 0, 4, 8, 2, 6, 0…
6. Theory: multiplying by 6 (times 3, then double)
Times 6 = triple, then double
Multiplying by 6 is the same as multiplying by 3, then doubling the answer. That’s because 6 = 2 × 3.
Example: 8 × 6 = (8 × 3) × 2 = 24 × 2 = 48
Because the ×3 table is easier to learn first, the ×6 table becomes almost free once ×3 is memorized.
The full ×6 table:
| Fact | Product | Fact | Product |
|---|---|---|---|
| 6 × 1 | 6 | 6 × 6 | 36 |
| 6 × 2 | 12 | 6 × 7 | 42 |
| 6 × 3 | 18 | 6 × 8 | 48 |
| 6 × 4 | 24 | 6 × 9 | 54 |
| 6 × 5 | 30 | 6 × 10 | 60 |
Pattern to notice: Every multiple of 6 is both even and a multiple of 3. That’s why the digit-sum trick from the ×3 table also works for ×6.
7. The distributive property — break it up
a × (b + c) = (a × b) + (a × c)
If a fact is hard, break the big number into friendly pieces you already know. This is called the distributive property.
Example 1: 7 × 6 feels tricky. Break 7 into 5 + 2:
7 × 6 = (5 × 6) + (2 × 6) = 30 + 12 = 42Example 2: 9 × 4. Break 9 into 10 − 1:
9 × 4 = (10 × 4) − (1 × 4) = 40 − 4 = 36This is the single most important idea in the whole lesson. Every multiplication trick a student will ever meet is built from this one property.
25 Practice Questions
All 25 questions cover ×3, ×4, and ×6. Each one has a hidden button that reveals the answer and step-by-step reasoning.
Question 1
What is 3 × 7?
Answer: 21
Skip count by 3 seven times: 3, 6, 9, 12, 15, 18, 21. Or double 7 (14) and add one more 7: 14 + 7 = 21.
Question 2
What is 4 × 8?
Answer: 32
Double twice: 8 × 2 = 16, then 16 × 2 = 32.
Question 3
What is 6 × 9?
Answer: 54
Triple, then double: 9 × 3 = 27, then 27 × 2 = 54. Or use distributive: (10 × 6) − (1 × 6) = 60 − 6 = 54.
Question 4
Fill in the missing number: 3 × ___ = 24.
Answer: 8
Ask: 3 times what equals 24? Skip count by 3s and count the jumps: 3, 6, 9, 12, 15, 18, 21, 24 — that’s 8 jumps.
Question 5
Fill in the missing number: 4 × ___ = 28.
Answer: 7
Ask: 4 times what equals 28? From the ×4 table: 4 × 7 = 28.
Question 6
Fill in the missing number: 6 × ___ = 42.
Answer: 7
Ask: 6 times what equals 42? From the ×6 table: 6 × 7 = 42. Check: 7 × 3 = 21, then 21 × 2 = 42. ✓
Question 7
A pack of markers has 4 markers. Mia buys 6 packs. How many markers does she have?
Answer: 24 markers
6 groups of 4 = 6 × 4 = 24. (Or use commutativity: 4 × 6 = 24.)
Question 8
A triangle has 3 sides. If you draw 9 triangles, how many sides did you draw in total?
Answer: 27 sides
9 triangles × 3 sides each = 9 × 3 = 27. Or use double + one: 9 × 2 = 18, then 18 + 9 = 27.
Question 9
A carton holds 6 eggs. How many eggs are in 8 cartons?
Answer: 48 eggs
8 × 6 = 48. Trick: 8 × 3 = 24, then double: 24 × 2 = 48.
Question 10
Which is greater: 4 × 6 or 3 × 9?
Answer: 3 × 9 is greater
4 × 6 = 24 and 3 × 9 = 27. Since 27 > 24, 3 × 9 is greater.
Question 11
What is the next number in this skip-counting sequence?
6, 12, 18, 24, 30, ___
Answer: 36
The sequence counts by 6. After 30, the next multiple of 6 is 30 + 6 = 36. Check: 6 × 6 = 36.
Question 12
Ben is arranging chairs into rows. He makes 4 rows with 7 chairs in each row. How many chairs did Ben use?
Answer: 28 chairs
4 rows of 7 = 4 × 7 = 28. Or: 7 × 2 = 14, then double: 14 × 2 = 28.
Question 13
Use the distributive property to solve: 7 × 6. Break 7 into 5 + 2.
Answer: 42
Break 7 into 5 + 2:
7 × 6 = (5 × 6) + (2 × 6) = 30 + 12 = 42Question 14
Use “10 minus 1” to solve: 9 × 3.
Answer: 27
Break 9 into 10 − 1:
9 × 3 = (10 × 3) − (1 × 3) = 30 − 3 = 27Question 15
Ana skip counts by 4s. What is the 6th number she says?
Answer: 24
Counting by 4s: 4 (1st), 8 (2nd), 12 (3rd), 16 (4th), 20 (5th), 24 (6th). This is the same as 6 × 4 = 24.
Question 16
True or false: 3 × 8 = 8 × 3. Explain why.
Answer: True
This is the commutative property: the order of the two numbers in a multiplication doesn’t change the product. Both sides equal 24.
Question 17
A soccer team has 6 players on the field. If 4 teams are playing today (2 games at the same time), how many players are on the field in total?
Answer: 24 players
4 teams × 6 players each = 4 × 6 = 24. Trick: 6 × 2 = 12, then double: 12 × 2 = 24.
Question 18
Which of these is NOT a multiple of 3?
(a) 15 (b) 21 (c) 26 (d) 27
Answer: (c) 26
Use the digit-sum trick. 15 → 1+5 = 6 ✓. 21 → 2+1 = 3 ✓. 26 → 2+6 = 8 ✗ (8 is not a multiple of 3). 27 → 2+7 = 9 ✓. Only 26 is not a multiple of 3.
Question 19
A movie theater row has 6 seats. If 7 rows are full, how many people are seated?
Answer: 42 people
7 rows × 6 seats each = 7 × 6 = 42. Trick: 7 × 3 = 21, then double: 21 × 2 = 42.
Question 20
Fill in the missing number: ___ × 3 = 30.
Answer: 10
What times 3 equals 30? 10 × 3 = 30. Any number times 10 just adds a zero: 3 → 30.
Question 21
A pizza is cut into 6 slices. If SOMATH orders 5 pizzas for a class party, how many slices are there in total?
Answer: 30 slices
5 pizzas × 6 slices each = 5 × 6 = 30. This is the same as counting by 6s five times: 6, 12, 18, 24, 30.
Question 22
Compare: which is greater, 6 × 6 or 4 × 9?
Answer: They are equal
6 × 6 = 36 and 4 × 9 = 36. Both equal 36 — different factors, same product. This is a classic example of how different times-table facts can point to the same number.
Question 23
A book has 4 chapters and each chapter is 8 pages long. How many pages is the book?
Answer: 32 pages
4 chapters × 8 pages each = 4 × 8 = 32. Trick: 8 × 2 = 16, then double: 16 × 2 = 32.
Question 24
A bakery makes 3 trays of muffins every morning. Each tray holds 12 muffins. How many muffins does the bakery make in one morning?
Answer: 36 muffins
3 trays × 12 muffins each = 3 × 12 = 36. Use distributive: 3 × 12 = (3 × 10) + (3 × 2) = 30 + 6 = 36.
Question 25
Challenge: A month has 4 weeks, and each week has 6 school days (Monday through Saturday at SOMATH). How many school days are in 3 months?
Answer: 72 school days
First find school days in one month: 4 × 6 = 24 days.
Then multiply by 3 months: 3 × 24 = 72.
You can also stack the multiplications: 3 × 4 × 6 = 12 × 6 = 72. This problem uses all three tables at once — the ×3, ×4, and ×6 tables together.
Answer key summary
| Q# | Answer | Q# | Answer | Q# | Answer |
|---|---|---|---|---|---|
| 1 | 21 | 10 | 3 × 9 | 19 | 42 |
| 2 | 32 | 11 | 36 | 20 | 10 |
| 3 | 54 | 12 | 28 | 21 | 30 |
| 4 | 8 | 13 | 42 | 22 | equal (36) |
| 5 | 7 | 14 | 27 | 23 | 32 |
| 6 | 7 | 15 | 24 | 24 | 36 |
| 7 | 24 | 16 | True | 25 | 72 |
| 8 | 27 | 17 | 24 | ||
| 9 | 48 | 18 | (c) 26 |
About SOMATH & Young Fermats
SOMATH — School of Math is a math-focused school on the Upper West Side of Manhattan for students in grades 1–12. The Young Fermats program (grades 3–5) drills multiplication fluency, division, fractions, area, and pre-algebra in small groups of 6–8 students.
Classes are taught by cofounder Marcelo Ambrozio (Northwestern-trained, 15+ years teaching math in NYC) and the SOMATH team.
Location: 226 W 79th St, 1st Floor, New York, NY 10024 (Upper West Side)
Phone: (646) 668-6151
Email: hello@schoolofmath.us
Book a free evaluation for your child — we’ll assess where they are and place them in the right small group.
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