Basic Multiplication

Let’s Start with a Question! 🤔

Imagine you’re setting up tables for a party, and each table needs 4 chairs. If you have 6 tables, how many chairs do you need in total? You could count them one by one, but that would take forever! The answer is multiplication - one of the most powerful shortcuts in mathematics that makes calculations lightning-fast!

What is Multiplication?

Multiplication is a smart way of doing repeated addition - adding the same number multiple times. It’s like having a superpower that lets you skip count and find totals in seconds!

Think of it like this:

• If you have 5 bags with 3 sweets in each bag, multiplication tells you that you have 15 sweets total (5 × 3 = 15)
• The symbol we use for multiplication is × (called “times” or “multiplied by”)
• The answer we get is called the product
• Another symbol you might see is · (a dot) or sometimes just brackets like 3(5)

Why is Multiplication Important?

Multiplication is one of the most useful skills you’ll ever learn! You use it when you:

• Calculate how much items cost when buying multiple of the same thing
• Work out areas and perimeters in geometry
• Understand fractions (3/4 is really 3 × 1/4!)
• Double or triple a recipe when cooking
• Calculate scores in games where points multiply

Multiplication makes you faster at maths and opens doors to algebra, division, and advanced problem-solving. Once you master it, you’ll wonder how you ever managed without it!

Understanding Multiplication Through Pictures

Imagine you have 3 groups of apples, with 4 apples in each group:

Group 1: 🍎🍎🍎🍎 Group 2: 🍎🍎🍎🍎 Group 3: 🍎🍎🍎🍎

Instead of counting “1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12” you can multiply!

3 groups × 4 apples = 12 apples

So 3 × 4 = 12

The Rectangle Way

You can also think of multiplication as making rectangles! 3 × 4 means a rectangle with 3 rows and 4 columns:

⚫ ⚫ ⚫ ⚫
⚫ ⚫ ⚫ ⚫
⚫ ⚫ ⚫ ⚫

Count them: 12 dots! That’s 3 × 4 = 12

Teacher’s Insight 👨‍🏫

Here’s what I’ve learned from teaching thousands of students: Multiplication isn’t about memorising times tables by rote - that’s boring and ineffective! The real secret is understanding the patterns and relationships between numbers. When students see that 6 × 4 is just double 3 × 4, or that 7 × 8 is the same as (7 × 7) + 7, suddenly multiplication becomes a fascinating puzzle rather than tedious memorisation.

My top tip: Learn the “easy” facts first (×1, ×2, ×5, ×10) and use them as stepping stones to figure out the “harder” ones. For example, if you know 5 × 6 = 30, then 6 × 6 is just one more 6, making it 36. Building on what you know is how mathematicians think!

The Connection Between Addition and Multiplication

Here’s the beautiful truth: Multiplication is just fast addition!

Think about it:

• 4 + 4 + 4 = 12 is the same as 3 × 4 = 12
• 7 + 7 + 7 + 7 + 7 = 35 is the same as 5 × 7 = 35

When you write 5 × 7, you’re saying “I have 5 groups of 7” or “add 7 to itself 5 times.”

The Commutative Property: Here’s brilliant news - order doesn’t matter in multiplication!

• 3 × 5 = 15 and 5 × 3 = 15
• You can flip the numbers around and get the same answer!
• This means you only need to learn HALF the times tables! If you know 3 × 7, you automatically know 7 × 3!

Strategies for Multiplication

Strategy 1: Skip Counting

This is perfect for the “easy” times tables!

Example: For 4 × 5, count by 5s four times: “5, 10, 15, 20” - the answer is 20!

This works brilliantly for ×2, ×5, and ×10 tables.

Strategy 2: Doubling and Halving

Use what you already know to figure out new facts!

Example: To find 6 × 4

• If you know 3 × 4 = 12
• Then 6 × 4 is just double that!
• 12 + 12 = 24

Another example: For 8 × 5

• You might know 4 × 5 = 20
• 8 is double 4, so double the answer!
• 20 + 20 = 40

Strategy 3: The Distributive Property (Breaking Apart Numbers)

Break bigger numbers into smaller, easier chunks!

Example: For 7 × 6

• Break 7 into 5 + 2
• So 7 × 6 = (5 × 6) + (2 × 6)
• = 30 + 12
• = 42

This strategy is incredibly powerful for mental maths!

Strategy 4: Using Arrays and Rectangles

Visualise the multiplication as a rectangle!

Example: For 3 × 5, picture a rectangle:

⚫ ⚫ ⚫ ⚫ ⚫
⚫ ⚫ ⚫ ⚫ ⚫
⚫ ⚫ ⚫ ⚫ ⚫

Count: 15 dots total! This helps you “see” the maths.

Strategy 5: The “Tricks” for Special Numbers

Multiplying by 1: Any number × 1 stays the same (7 × 1 = 7)

Multiplying by 0: Any number × 0 = 0 (because you have zero groups!)

Multiplying by 2: Just double the number (2 × 8 = 16 is the same as 8 + 8)

Multiplying by 5: Half the number, then multiply by 10!

• 5 × 8 = ? Think: half of 8 is 4, then 4 × 10 = 40

Multiplying by 10: Add a zero! (6 × 10 = 60)

Multiplying by 9: Use your fingers! (See Memory Aids section below)

Key Vocabulary

• Times (×): The symbol that tells us to multiply
• Product: The answer in multiplication (in 3 × 4 = 12, the product is 12)
• Factors: The numbers being multiplied (in 3 × 4, both 3 and 4 are factors)
• Multiple: The result of multiplying a number by an integer (10 is a multiple of 5)
• Array: A rectangular arrangement of objects in rows and columns
• Commutative Property: The rule that says you can swap the order (3 × 5 = 5 × 3)
• Repeated Addition: Adding the same number multiple times (what multiplication really is!)

Worked Examples

Example 1: Starting Simple

Problem: 3 × 2

Solution: 6

Detailed Explanation:

• This means “3 groups of 2” or “2 + 2 + 2”
• Think: ⚫⚫ | ⚫⚫ | ⚫⚫
• Count all: 6
• Or skip count by 2s: “2, 4, 6”

Think about it: If you have 3 pairs of socks, you have 6 individual socks! Multiplication helps you count groups quickly.

Example 2: Using Doubles

Problem: 4 × 6

Solution: 24

Detailed Explanation:

• If you know 2 × 6 = 12
• Then 4 × 6 is just double that!
• 12 + 12 = 24
• Or think: 6 + 6 + 6 + 6 = 24

Think about it: Doubling is a powerful strategy. If you know your 2× table, you can use it to figure out the 4× table!

Example 3: The Commutative Property

Problem: 5 × 3 and 3 × 5

Solution: Both equal 15!

Detailed Explanation:

• 5 × 3 means 5 groups of 3: ⚫⚫⚫ | ⚫⚫⚫ | ⚫⚫⚫ | ⚫⚫⚫ | ⚫⚫⚫ = 15
• 3 × 5 means 3 groups of 5: ⚫⚫⚫⚫⚫ | ⚫⚫⚫⚫⚫ | ⚫⚫⚫⚫⚫ = 15
• Different arrangements, same total!

Think about it: This is amazing news! It means if you know one fact, you get another one free! Learn half the work, get all the answers!

Example 4: Breaking Numbers Apart

Problem: 8 × 7

Solution: 56

Detailed Explanation:

• This one seems tricky, but let’s break it apart!
• Think: 8 × 7 = (8 × 5) + (8 × 2)
• 8 × 5 = 40 (easy!)
• 8 × 2 = 16 (easy!)
• 40 + 16 = 56

Think about it: Breaking big problems into smaller pieces is a strategy mathematicians use all the time. You can always make maths easier!

Example 5: Multiplying by 10

Problem: 7 × 10

Solution: 70

Detailed Explanation:

• Multiplying by 10 is super easy!
• Just add a zero to the number
• 7 becomes 70
• Or think: 10 + 10 + 10 + 10 + 10 + 10 + 10 = 70

Think about it: The 10× table is one of the easiest - and it’s incredibly useful for mental maths and estimating!

Example 6: Real-Life Multiplication

Problem: You buy 4 packs of trading cards. Each pack contains 6 cards. How many cards do you have altogether?

Solution: 24 cards

Detailed Explanation:

• 4 packs × 6 cards per pack
• 4 × 6 = 24
• You could count: 6, 12, 18, 24
• Or use the array method: imagine 4 rows of 6 cards

Think about it: Multiplication saves you from counting individual items when you have equal groups!

Example 7: Zero and One Rules

Problem A: 9 × 0 and Problem B: 9 × 1

Solution A: 0 Solution B: 9

Detailed Explanation:

• 9 × 0 = 0 because you have ZERO groups of 9 (nothing!)
• 9 × 1 = 9 because you have ONE group of 9 (just 9)
• These are special rules that work for ANY number

Think about it: These rules might seem simple, but they’re super important! Anything times zero is zero. Anything times one stays the same. Remember these!

Common Misconceptions & How to Avoid Them

Misconception 1: “Multiplication always makes numbers bigger”

The Truth: When you multiply by numbers greater than 1, yes! But multiplying by 1 keeps the number the same (5 × 1 = 5), and multiplying by 0 makes it zero (5 × 0 = 0). Later you’ll learn about multiplying decimals and fractions where this gets even more interesting!

How to think about it correctly: Multiplication by whole numbers greater than 1 creates bigger numbers because you’re making multiple groups.

Misconception 2: “You must memorise all the times tables separately”

The Truth: Learn the patterns and relationships! If you know 5 × 6 = 30, you can figure out 6 × 6 by adding one more 6 (= 36). Use what you know to build new knowledge!

How to think about it correctly: Times tables are connected. Learn the easy ones (×1, ×2, ×5, ×10) and use strategies to figure out the rest.

Misconception 3: “There’s only one way to solve a multiplication problem”

The Truth: There are LOADS of ways! You can skip count, use repeated addition, draw arrays, break numbers apart, or use memorised facts. Choose the method that makes sense to YOU.

How to think about it correctly: Maths is creative! Different people solve problems differently, and that’s brilliant!

Misconception 4: “Multiplication and addition are the same thing”

The Truth: They’re related but different! Addition combines any numbers. Multiplication is specifically for equal groups - it’s a special, faster type of addition.

How to think about it correctly: Multiplication = repeated addition of the SAME number. 3 + 3 + 3 can be written as 3 × 3, but 3 + 4 + 5 cannot be written as multiplication.

Common Errors to Watch Out For

Memory Aids & Tricks

The Nines Finger Trick

This is AMAZING for the 9× table!

1. Hold both hands in front of you, fingers spread
2. To solve 9 × 4, put down your 4th finger (from the left)
3. Count fingers BEFORE the down finger (3) - that’s the tens!
4. Count fingers AFTER the down finger (6) - that’s the ones!
5. Answer: 36!

Works for 9 × 1 through 9 × 10!

The Rhymes

“6 × 6 fell from heaven, landed in the mud = 36!” “5, 6, 7, 8… 56 is 7 times 8!” “Twos are easy, just add and add. Fives end in 5 or 0 - isn’t that rad?”

Patterns to Notice

The 5× table: Always ends in 0 or 5 (5, 10, 15, 20, 25…) The 10× table: Always ends in 0 (10, 20, 30, 40…) The 2× table: Always even numbers (2, 4, 6, 8, 10…) The 9× table: Digits always add up to 9! (18: 1+8=9, 27: 2+7=9, 36: 3+6=9)

The Square Facts Song

“1 × 1 is 1, that’s easy peasy fun! 2 × 2 is 4, knock knock on the door! 3 × 3 is 9, that one works out fine! 4 × 4 is 16, nicest you’ve ever seen! 5 × 5 is 25, keeps the math alive!”

Practice Problems

Easy Level (×1, ×2, ×5, ×10)

1. 5 × 2 Answer: 10 (Count by 2s five times: 2, 4, 6, 8, 10)

2. 3 × 5 Answer: 15 (Count by 5s: 5, 10, 15)

3. 7 × 1 Answer: 7 (Remember: anything times 1 stays the same!)

4. 4 × 10 Answer: 40 (Add a zero to 4!)

Medium Level (×3, ×4, ×6)

5. 6 × 3 Answer: 18 (Think: 3+3+3+3+3+3 or count by 3s)

6. 4 × 7 Answer: 28 (Double 2×7: 14+14 = 28)

7. 6 × 6 Answer: 36 (Remember the rhyme: “6×6 fell from heaven = 36!”)

8. 5 × 8 Answer: 40 (Half of 8 is 4, then 4×10 = 40)

Challenge Level (×7, ×8, ×9)

9. 9 × 7 Answer: 63 (Use the finger trick, or (9×5)+(9×2) = 45+18 = 63)

10. 8 × 8 Answer: 64 (An important square number to memorise!)

Real-World Applications

At the Shop 🏪

Scenario: Chocolate bars are £3 each. If you buy 4 chocolate bars for your friends, how much do you spend?

Solution: 4 × £3 = £12

Why this matters: Multiplication helps you calculate total costs quickly when buying multiple items of the same price!

Planning for Parties 🎉

Scenario: You’re having a party with 6 friends. Each person needs 4 slices of pizza. How many slices do you need?

Solution: 6 × 4 = 24 slices

Why this matters: Event planning requires multiplication to make sure you have enough for everyone!

In Games 🎮

Scenario: In a game, you earn 50 points for each level you complete. If you complete 7 levels, what’s your score?

Solution: 7 × 50 = 350 points

Why this matters: Games use multiplication constantly for scoring, resources, and game mechanics!

Gardening and Nature 🌱

Scenario: A gardener plants flowers in 5 rows, with 8 flowers in each row. How many flowers are planted?

Solution: 5 × 8 = 40 flowers

Why this matters: Arrays appear in nature, gardens, and farming - understanding multiplication helps with planning and organisation!

Sports Statistics ⚽

Scenario: A footballer scores 3 goals per match. After 9 matches, how many goals have they scored?

Solution: 9 × 3 = 27 goals

Why this matters: Sports statistics rely heavily on multiplication to track performance over time!

Study Tips for Mastering Multiplication

1. Master One Table at a Time

Start with the easiest (×1, ×2, ×10) and gradually work up. Don’t try to learn them all at once!

2. Practice with Physical Objects

Use blocks, coins, or toys to create groups. Actually making 3 groups of 4 helps your brain understand what 3 × 4 means.

3. Learn the Patterns

Notice that the 5× table always ends in 0 or 5, the 10× table adds zeros, and the 9× table has that cool finger trick!

4. Make It a Game

Quiz yourself, race against a timer, challenge family members, or use apps and online games.

5. Use What You Know to Figure Out What You Don’t

If you know 5 × 6, you can figure out 6 × 6 by adding one more 6!

6. Practice a Little Every Day

Just 5 minutes of daily practice beats one hour of cramming once a week. Consistency is key!

7. Don’t Just Memorise - Understand

Know WHY 3 × 4 = 12, not just that it does. Understanding beats memorisation every time!

8. Celebrate Progress

Learned your 2× table? Celebrate! Mastered the 9× finger trick? That’s brilliant! Acknowledge your wins!

How to Check Your Answers

1. Reverse it: Use division to check. If 6 × 4 = 24, then 24 ÷ 4 should equal 6!
2. Use the commutative property: Does 3 × 7 equal 7 × 3? It should!
3. Draw it out: Create an array or groups to visualise and count
4. Repeated addition: Add the number to itself and see if you get the same answer
5. Use a calculator: For checking (but try to solve without it first!)
6. Estimate first: 6 × 8 should be close to 50 (because 5 × 10 = 50). Does your answer make sense?

Extension Ideas for Fast Learners

• Explore larger multiplication (up to 12 × 12 or even 20 × 20)
• Learn about square numbers (1², 2², 3², 4²…)
• Investigate the relationship between multiplication and area
• Try mental maths challenges: can you multiply 2-digit numbers in your head?
• Explore what happens when you multiply three numbers together
• Learn about prime numbers and factor pairs
• Discover how multiplication relates to fractions and division
• Create your own multiplication word problems for others to solve

Parent & Teacher Notes

Building Fluency vs. Understanding: The goal is both! Students need to understand what multiplication means (repeated addition, equal groups) AND develop fluency with basic facts. One without the other is incomplete learning.

Common Struggles: If a student struggles with multiplication, check if they:

• Can skip count confidently (2s, 5s, 10s)
• Understand what “groups of” means
• Have mastered addition facts (which form the foundation)
• Are trying to memorise without understanding patterns

Differentiation Tips:

• Struggling learners: Use lots of concrete materials (counters, blocks, drawings). Start with ×1, ×2, ×5, ×10 only. Celebrate small wins!
• On-track learners: Encourage mental strategies and pattern recognition. Practice daily with mixed tables.
• Advanced learners: Challenge with larger numbers, multi-step problems, and exploring the relationship between multiplication, division, area, and arrays.

Multi-Sensory Approaches:

• Visual: Arrays, number lines, multiplication charts
• Auditory: Songs, rhymes, skip counting aloud
• Kinaesthetic: Jumping, clapping, using manipulatives
• Try all approaches to find what works best for each child!

The Power of Games: Multiplication war (with cards), online games, board games with multiplication, and app-based practice can make learning feel like play.

Assessment Tip: True mastery isn’t just speed - it’s flexibility. Can the student solve 6 × 4 in multiple ways? Can they explain their thinking? That’s real understanding!

Remember: Multiplication is a life skill that builds confidence and opens doors in maths. Every child can master it with the right support, strategies, and encouragement! 🌟