Solved Exercises on Multiplication Facts 6–10 in Grade 3

Master multiplication facts 6–10: fact families, patterns, and multiplication strategies through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Multiplication Facts 6–10
Exercise 1
Calculate the following multiplication facts: 6×7, 8×4, 9×3, 7×5, 10×6
Definition:

Multiplication: A mathematical operation representing repeated addition

Factors: The numbers being multiplied together

Product: The result of multiplication

Multiplication Facts: Basic multiplication combinations

Multiplication Strategies:
  1. Memorization: Know basic facts by heart
  2. Patterns: Recognize patterns in multiples
  3. Breaking Down: Use known facts to find unknown ones
  4. Visual Models: Use arrays or equal groups
6×7
42
8×4
32
9×3
27
Step 1: Calculate 6×7

6×7 = 42 (think: 6 groups of 7, or 7 groups of 6)

Step 2: Calculate 8×4

8×4 = 32 (think: 8 groups of 4, or 4 groups of 8)

Step 3: Calculate 9×3

9×3 = 27 (think: 9 groups of 3, or 3 groups of 9)

Step 4: Calculate 7×5

7×5 = 35 (think: 7 groups of 5, or 5 groups of 7)

Step 5: Calculate 10×6

10×6 = 60 (think: 10 groups of 6, or 6 groups of 10)

6×7=42, 8×4=32, 9×3=27, 7×5=35, 10×6=60
Final answer:

6×7=42, 8×4=32, 9×3=27, 7×5=35, 10×6=60

Applied rules:

• Commutative Property: 6×7 = 7×6

• Multiplication Facts: These are basic facts to memorize

• Pattern Recognition: Notice how multiples increase

2 Fact Families
Exercise 2
Write the fact family for 6, 8, and 48. Show all related multiplication and division facts.
Definition:

Fact Family: A group of related multiplication and division facts using the same numbers

Related Facts: Facts that use the same three numbers

Numbers
6, 8, 48
Multiplication
6×8=48
Division
48÷6=8
Step 1: Identify the three numbers

The fact family uses 6, 8, and 48

Step 2: Write multiplication facts

6×8 = 48 and 8×6 = 48

Step 3: Write division facts

48÷6 = 8 and 48÷8 = 6

Step 4: Verify all facts

Check that each fact is correct and uses the same three numbers

6×8=48, 8×6=48, 48÷6=8, 48÷8=6
Final answer:

Fact family for 6, 8, 48: 6×8=48, 8×6=48, 48÷6=8, 48÷8=6

Applied rules:

• Multiplication-division relationship: These operations are inverses

• Fact Family Structure: Uses same three numbers in 4 different ways

• Commutative Property: 6×8 = 8×6

3 Multiplication Patterns
Exercise 3
Find the pattern in the multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90. What do you notice about the digits?
Definition:

Pattern: A repeated or regular sequence

Multiple: The product of a number and any integer

Multiples
9, 18, 27, 36, 45
Continued
54, 63, 72, 81, 90
Pattern
Digit sum = 9
Step 1: List the multiples of 9

9, 18, 27, 36, 45, 54, 63, 72, 81, 90

Step 2: Analyze the digits

Notice: 1+8=9, 2+7=9, 3+6=9, 4+5=9, 5+4=9, 6+3=9, 7+2=9, 8+1=9

Step 3: Identify the pattern

For multiples of 9, the sum of digits equals 9

Step 4: Verify the pattern

Check: 9→9, 18→1+8=9, 27→2+7=9, etc.

Sum of digits in multiples of 9 equals 9
Final answer:

For multiples of 9, the sum of the digits always equals 9. For example: 18 (1+8=9), 27 (2+7=9), 36 (3+6=9), etc.

Applied rules:

• Pattern Recognition: Look for repeated sequences

• Digit Sum Property: Sum of digits in multiples of 9 equals 9

• Number Patterns: Understanding mathematical relationships

Multiplication Facts 6–10 Rules & Strategies
\( a \times b = b \times a \)
Commutative Property
Commutative Property
\(a \times b = b \times a\)
Order doesn't matter in multiplication
Multiplication Facts
Basic Combinations
Memorize for quick recall
Fact Families
Related Facts
Uses same numbers in different ways
Key Definitions:

Multiplication: Repeated addition of the same number

Factors: Numbers that are multiplied together

Product: Result of multiplication

Multiplication Facts: Basic multiplication combinations to memorize

Multiplication Strategies:
  1. Memorization: Know basic facts by heart
  2. Patterns: Recognize patterns in multiples
  3. Breaking Down: Use known facts to find unknown ones
  4. Visual Models: Use arrays or equal groups
  5. Fact Families: Use related facts
Tip 1: Practice skip counting to build multiplication fluency.
Tip 2: Use the commutative property to reduce memorization (6×7 = 7×6).
Tip 3: Look for patterns in multiples (like digits adding to 9 for 9s).
Tip 4: Practice with flashcards or games to make memorization fun.

Common Mistakes: Forgetting facts, confusing multiplication with addition, not recognizing patterns.
Success Strategies: Regular practice, using patterns, checking work with addition.
Important Rules to Remember:

• Commutative Property: a × b = b × a

• Multiplication Facts: Memorize for quick recall

• Fact Families: Related multiplication and division facts

• Patterns: Look for number relationships

Solution: Exercises 4 to 5
4 Multiplication Word Problems
Exercise 4
Sarah has 7 boxes of crayons. Each box contains 8 crayons. How many crayons does Sarah have in total? Use a multiplication fact to solve.
Definition:

Word Problems: Real-life situations requiring mathematical operations

Equal Groups: Sets containing the same number of items

Groups
7 boxes
Items per Group
8 crayons
Total
56 crayons
Step 1: Identify the groups and items

Sarah has 7 boxes (groups) with 8 crayons in each box (items per group)

Step 2: Set up the multiplication

Number of groups × Items per group = Total items

7 × 8 = ?

Step 3: Use multiplication fact

7 × 8 = 56 (this is a basic multiplication fact)

Step 4: State the final answer

Therefore, Sarah has 56 crayons in total.

7 × 8 = 56 crayons
Final answer:

Sarah has 56 crayons in total.

Applied rules:

• Equal Groups Rule: Total = Number of groups × Items per group

• Multiplication Connection: Equal groups relate to multiplication

• Problem-Solving Strategy: Systematic approach to word problems

5 Advanced Multiplication Patterns
Exercise 5
Complete the pattern: 6, 12, 18, ___, 30, 36, ___. Then write the multiplication facts that correspond to each number.
Definition:

Numerical Patterns: Sequences following a specific rule

Pattern Recognition: Identifying the rule governing a sequence

Sequence
6, 12, 18, ?, 30, 36, ?
Rule
Skip count by 6
Answers
24, 42
Step 1: Observe the pattern

Looking at the sequence: 6, 12, 18, ___, 30, 36, ___

We notice: 6, 12, 18 are multiples of 6

Step 2: Identify the rule

This is skip counting by 6s: 6×1, 6×2, 6×3, 6×4, 6×5, 6×6, 6×7

Step 3: Complete the missing numbers

The 4th number: 6×4 = 24

The 7th number: 6×7 = 42

Step 4: Write all multiplication facts

6×1=6, 6×2=12, 6×3=18, 6×4=24, 6×5=30, 6×6=36, 6×7=42

Pattern: 6, 12, 18, 24, 30, 36, 42
Facts: 6×1=6, 6×2=12, 6×3=18, 6×4=24, 6×5=30, 6×6=36, 6×7=42
Final answer:

The missing numbers are 24 and 42. The pattern is skip counting by 6s: 6×1=6, 6×2=12, 6×3=18, 6×4=24, 6×5=30, 6×6=36, 6×7=42.

Applied rules:

• Pattern Recognition: Look for consistent changes between numbers

• Multiplication Connection: Skip counting relates to multiplication

• Sequencing: Understanding positions in ordered lists

Multiplication Facts 6–10 Mastery Guide
\( a \times b = b \times a \)
Commutative Property
Key definitions:

Multiplication Table: A grid showing products of small numbers

Factors: Numbers multiplied together

Products: Results of multiplication

Multiplication Strategies:
  1. Memorization: Know basic facts by heart
  2. Patterns: Recognize patterns in multiples
  3. Breaking Down: Use known facts to find unknown ones
  4. Visual Models: Use arrays or equal groups
  5. Fact Families: Use related facts
Tip 1: Start with doubles (6×6, 7×7, 8×8, etc.) as they're easier to remember.
Tip 2: Use the commutative property to reduce memorization (knowing 6×7 helps with 7×6).
Tip 3: Practice with concrete objects like blocks or counters to visualize multiplication.
Tip 4: Connect multiplication to addition to build understanding gradually.

Common Errors: Mixing up multiplication and addition, forgetting the commutative property, misremembering facts.
Success Strategies: Regular practice, using multiple representations, connecting to real-world applications.
Essential Facts to Remember:

• Any number × 0 = 0

• Any number × 1 = itself

• Order doesn't matter (commutative property)

• Multiplication is repeated addition

• Arrays help visualize multiplication

Multiplication Facts 6–10

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What are Multiplication Facts?

Multiplication facts are basic products that should be memorized:

• 6×6=36, 6×7=42, 6×8=48, 6×9=54, 6×10=60

• 7×7=49, 7×8=56, 7×9=63, 7×10=70

• 8×8=64, 8×9=72, 8×10=80

• 9×9=81, 9×10=90

• 10×10=100

Memorize for quick recall
Key Properties

Commutative: a × b = b × a

Identity: a × 1 = a

Zero: a × 0 = 0

Multiplication Process
1
Identify Factors
2
Recall Fact
3
State Product
4
Verify
Multiplication Patterns

• Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

• Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70

• Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80

• Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90

• Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100

Practice multiplication facts daily for mastery!

Questions & Answers

Question: My third-grade students are struggling with multiplication facts 6–10. How can I help them memorize these more effectively?

Answer: Use multiple strategies to build multiplication fact fluency:

  • Start with easier facts like doubles (6×6, 7×7, 8×8) and build from there
  • Use the commutative property to reduce memorization (if they know 6×7, they know 7×6)
  • Incorporate games, songs, and rhymes to make memorization fun
  • Practice with visual models like arrays or equal groups
  • Focus on patterns in multiples (like the digit sum pattern in 9s)

Provide regular practice sessions with immediate feedback. Use timed drills sparingly and only after students have developed conceptual understanding.

Connect multiplication to real-world situations to help students see its relevance.

Question: My child knows the multiplication facts but struggles with word problems. How can I help them connect multiplication to real-world situations?

Answer: Help your child recognize multiplication in everyday contexts:

  • Shopping: If apples cost $3 each and you buy 5, you calculate 5 × $3 = $15
  • Cooking: Doubling a recipe that calls for 4 cups of flour means 2 × 4 = 8 cups
  • Arranging things: Setting up chairs in 6 rows of 7 each means 6 × 7 = 42 chairs total
  • Time calculations: 3 weeks have 3 × 7 = 21 days
  • Money: 8 quarters equal 8 × 25 cents = 200 cents = $2

Practice identifying keywords like "each," "per," "times," "groups of," and "sets of" that signal multiplication.

Use manipulatives or drawings to model word problems before solving them.

Question: Why do I need to learn multiplication facts? When will I use them in real life?

Answer: Multiplication facts are incredibly useful in daily life:

  • Shopping: Calculating total costs quickly (5 items at $6 each)
  • Cooking: Adjusting recipes for more people
  • Planning: Figuring out how many supplies are needed
  • Sports: Calculating scores or statistics
  • Travel: Converting units (miles per hour, hours to minutes)

Knowing multiplication facts makes math faster and easier, saving time on calculations.

These facts are building blocks for more advanced math topics you'll study later.

Practice makes them automatic, so you can focus on solving more complex problems!