Solved Exercises on Single Digit Multiplication Problems in Grade 3

Master single digit multiplication: basic facts, word problems, missing factors, and problem solving strategies through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic Multiplication Facts
Exercise 1
Calculate: 7 × 8 = ?
Definition:

Single Digit Multiplication: Multiplying two single-digit numbers (0-9) to find their product

Basic Multiplication Methods:
  1. Memory: Recall multiplication facts
  2. Repeated Addition: 7 × 8 = 8 + 8 + 8 + 8 + 8 + 8 + 8
  3. Skip Counting: Count by 8s seven times
  4. Array Model: 7 rows of 8 items
Factor 1
7
Factor 2
8
Product
7 × 8 = 56
Step 1: Recognize the factors

First factor: 7, Second factor: 8

Step 2: Apply multiplication

7 groups of 8 items each

Step 3: Calculate using repeated addition

7 × 8 = 8 + 8 + 8 + 8 + 8 + 8 + 8 = 56

Step 4: Verify using skip counting

Count by 8s: 8, 16, 24, 32, 40, 48, 56

7 × 8 = 56
Final answer:

7 × 8 = 56

Applied rules:

• Commutative Property: 7 × 8 = 8 × 7 = 56

• Basic Fact: 7 × 8 is a fundamental multiplication fact

• Verification: Multiple methods confirm the same result

2 Missing Factor Problems
Exercise 2
Find the missing number: 9 × ? = 54
Definition:

Missing Factor: Finding an unknown number in a multiplication equation using division or fact families

Known Factor
9
Product
54
Missing Factor
54 ÷ 9 = 6
Check
9 × 6 = 54
Step 1: Identify known values

One factor is 9, the product is 54

Step 2: Set up the equation

9 × ? = 54

Step 3: Solve using division

To find the missing factor: 54 ÷ 9 = 6

Step 4: Verify the answer

Check: 9 × 6 = 54 ✓

Step 5: Alternative method - fact families

If 9 × ? = 54, then ? × 9 = 54, and 54 ÷ 9 = ?, 54 ÷ ? = 9

9 × 6 = 54
Final answer:

The missing number is 6.

Applied rules:

• Division Relationship: To find a missing factor, divide the product by the known factor

• Fact Families: Multiplication and division are inverse operations

• Verification: Always check by substituting back into the original equation

3 Word Problem Application
Exercise 3
Maya buys 4 packs of stickers. Each pack costs $3. How much money does Maya spend in total?
Definition:

Word Problems: Real-life scenarios requiring mathematical operations to solve

Number of packs
4
Cost per pack
$3
Total cost
4 × $3 = $12
Step 1: Read the problem carefully

Maya buys 4 packs of stickers, each pack costs $3

Step 2: Identify what to find

Total money spent = ?

Step 3: Identify equal groups

4 equal groups (packs) of $3 each

Step 4: Set up the multiplication

Number of groups × Amount per group = Total amount

4 × $3 = $12

Step 5: Verify with repeated addition

$3 + $3 + $3 + $3 = $12

4 × $3 = $12
Final answer:

Maya spends $12 in total.

Applied rules:

• Equal Groups: Word problems often involve equal groups

• Keywords: "each", "per", "times" suggest multiplication

• Units: Include units in the final answer

Single Digit Multiplication Summary
\(a \times b = c\)
Multiplication Formula
Commutative Property
a × b = b × a
Order doesn't affect the product
Identity Property
a × 1 = a
Multiplying by 1 keeps the number
Zero Property
a × 0 = 0
Multiplying by 0 always gives 0
Key definitions:

Multiplication: Adding equal groups together

Factors: Numbers being multiplied together

Product: The result of multiplication

Single Digit: Numbers from 0 to 9

Problem Solving Steps:
  1. Read: Understand what the problem asks
  2. Identify: Find the numbers and operation needed
  3. Solve: Perform the multiplication
  4. Check: Verify your answer makes sense
Commutative Property: 3 × 4 = 4 × 3 = 12
Zero Property: Any number × 0 = 0
Identity Property: Any number × 1 = itself
Tip 1: Practice multiplication tables regularly.
Tip 2: Use arrays or drawings to visualize problems.
Tip 3: Look for keywords like "each", "times", "product".
Tip 4: Always check your answer by reversing the operation.
Solution: Exercises 4 to 5
4 Multiplication Equations
Exercise 4
Solve for the missing number: 6 × 7 = ? × 3
Definition:

Equation Solving: Finding the unknown value that makes both sides of the equation equal

Left side
6 × 7 = 42
Right side
? × 3
Solve
42 ÷ 3 = 14
Check
14 × 3 = 42
Step 1: Calculate the known side

Left side: 6 × 7 = 42

Step 2: Set up the equation

42 = ? × 3

Step 3: Solve for the unknown

To find ?: 42 ÷ 3 = 14

Step 4: Verify the solution

Check: 14 × 3 = 42 ✓

Step 5: Complete the original equation

6 × 7 = 14 × 3 = 42

6 × 7 = 14 × 3 = 42
Final answer:

The missing number is 14.

Applied rules:

• Equation Balance: Both sides must be equal

• Inverse Operations: Division undoes multiplication

• Verification: Always substitute back to check

5 Advanced Word Problem
Exercise 5
A classroom has 5 rows of desks. Each row has 6 desks. If each desk holds 2 books, how many books are there in total?
Definition:

Multistep Problems: Problems requiring multiple operations to solve

Rows
5
Desks per row
6
Books per desk
2
Total
5×6×2=60
Step 1: Identify all given information

5 rows, 6 desks per row, 2 books per desk

Step 2: Find total number of desks

Rows × Desks per row = 5 × 6 = 30 desks

Step 3: Find total number of books

Total desks × Books per desk = 30 × 2 = 60 books

Step 4: Alternative method - multiply all together

5 × 6 × 2 = 30 × 2 = 60 books

Step 5: Verify using associative property

(5 × 6) × 2 = 5 × (6 × 2) = 30 × 2 = 5 × 12 = 60

5 × 6 × 2 = 60 books
Final answer:

There are 60 books in total.

Applied rules:

• Associative Property: (a × b) × c = a × (b × c)

• Multistep Problems: Solve one step at a time

• Organization: Keep track of units (desks, books)

Single Digit Multiplication Mastery Guide
\(a \times b = c\)
Multiplication Fundamentals
Key definitions:

Multiplication: A mathematical operation that represents repeated addition of equal groups

Factors: The numbers being multiplied together

Product: The result obtained when multiplying factors

Single Digit: Whole numbers from 0 to 9

Fact Family: Related multiplication and division facts using the same numbers

Multiplication Strategies:
  1. Memorization: Learn multiplication tables through practice
  2. Repeated Addition: Add the same number multiple times
  3. Skip Counting: Count by equal intervals
  4. Array Model: Arrange objects in rows and columns
  5. Number Line: Make equal jumps forward
Tip 1: Start with easier facts (0s, 1s, 2s, 5s, 10s) before moving to harder ones.
Tip 2: Use the commutative property to reduce the number of facts to memorize (3×4 = 4×3).
Tip 3: Practice daily with flashcards or games to build fluency.
Tip 4: Use visual aids like multiplication charts or grids.
Commutative Property: a × b = b × a (order doesn't matter)
Associative Property: (a × b) × c = a × (b × c) (grouping doesn't matter)
Identity Property: a × 1 = a (multiplying by 1 doesn't change the number)
Zero Property: a × 0 = 0 (multiplying by 0 always equals 0)
Important Patterns:

• Multiples of 2: Always even numbers

• Multiples of 5: End in 0 or 5

• Multiples of 10: End in 0

• Multiples of 9: Sum of digits equals 9 (up to 9×10)

• Squares: Numbers multiplied by themselves (3×3, 4×4, etc.)

Multiplication Facts Visualization
Single Digit Multiplication Table Analysis
Explore patterns in single digit multiplication facts:
1. Commutative pairs (3×4 and 4×3)
2. Squares (numbers multiplied by themselves)
3. Multiples of 5
4. Multiples of 9

Analysis: The chart reveals important patterns in multiplication facts.

  • Commutative pairs: 3×4 = 4×3 = 12
  • Squares: 3×3 = 9, 4×4 = 16, 5×5 = 25
  • Multiples of 5: End in 0 or 5
  • Multiples of 9: Sum of digits equals 9

Questions & Answers

Question: I have trouble remembering the multiplication facts. How can I get better at them?

Answer: Here are effective strategies to master multiplication facts:

  • Start with patterns: Learn multiples of 2, 5, and 10 first since they have clear patterns
  • Use the commutative property: If you know 3×4=12, you also know 4×3=12
  • Practice daily: Even 10 minutes a day makes a big difference
  • Use multiple methods: Flashcards, games, songs, or apps
  • Focus on one family at a time: Master 2s, then move to 3s, etc.

Remember, it's okay to use strategies like skip counting or repeated addition while you're still learning. With practice, the facts will become automatic!

Example: For 6×7, you might think "6 groups of 7" or "7+7+7+7+7+7" until 42 becomes automatic.

Question: How do I know if my answer to a multiplication problem is reasonable?

Answer: Here are ways to check if your multiplication answer is reasonable:

  • Estimate first: Round numbers and do mental math (6×7 ≈ 6×7, but 6×8 is close to 5×8=40)
  • Check the last digit: The last digit of the product follows patterns (7×8 ends in 6)
  • Use the opposite operation: Divide the product by one factor to see if you get the other
  • Think about size: The product should be larger than both factors (except when multiplying by 0 or 1)

For example, if you calculate 7×8=54, you know it's wrong because 7×8 should be larger than 54. The correct answer is 56.

Always ask yourself: "Does this answer make sense in the context of the problem?"

Question: My child struggles with word problems involving multiplication. How can I help them identify when to multiply?

Answer: Here are strategies to help identify multiplication in word problems:

  • Look for keywords: "each", "per", "times", "groups of", "rows of", "sets of", "total"
  • Identify equal groups: Multiplication involves equal-sized groups
  • Draw pictures: Visualize the situation described
  • Ask: "How many in total?": If you're combining equal groups, multiply
  • Practice with real examples: Use objects like blocks or coins

For example: "There are 4 boxes with 6 pencils in each box" → 4 equal groups of 6 → 4 × 6 = 24 pencils

Encourage your child to read the problem multiple times and identify what is being asked before solving.