Solved Exercises on Word Problems with Times Tables in Grade 3

Master multiplication in real-world contexts: arrays, groups, repeated addition, and practical applications through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Array multiplication
Exercise 1
A bakery arranges cupcakes in 4 rows with 6 cupcakes in each row. How many cupcakes are there in total?
Definition:

Array multiplication: Arranging items in rows and columns, where total = rows × columns

Multiplication method:
  1. Identify the number of rows
  2. Identify the number of items per row
  3. Multiply rows by items per row
  4. Verify with repeated addition if needed
Rows
Cols
Total
4
6
24
Step 1: Identify the given information

Number of rows: 4

Number of cupcakes per row: 6

Step 2: Set up the multiplication equation

Total cupcakes = Number of rows × Cupcakes per row

Total cupcakes = 4 × 6

Step 3: Calculate the multiplication

4 × 6 = 24

Step 4: Verify with repeated addition

6 + 6 + 6 + 6 = 24 ✓

There are 24 cupcakes in total
Final answer:

There are 24 cupcakes in total

Applied rules:

• Array formula: Total = Rows × Columns

• Multiplication principle: Repeated addition shortcut

• Verification: Check with repeated addition

2 Equal groups problem
Exercise 2
There are 5 boxes of crayons. Each box contains 8 crayons. How many crayons are there altogether?
Definition:

Equal groups multiplication: Finding total when you have equal groups of items

5 boxes
× 8 crayons each
40 total
crayons
Step 1: Identify the given information

Number of boxes: 5

Number of crayons per box: 8

Step 2: Set up the multiplication equation

Total crayons = Number of boxes × Crayons per box

Total crayons = 5 × 8

Step 3: Calculate the multiplication

5 × 8 = 40

Step 4: Verify with repeated addition

8 + 8 + 8 + 8 + 8 = 40 ✓

There are 40 crayons altogether
Final answer:

There are 40 crayons altogether

Applied rules:

• Equal groups: Total = Groups × Items per group

• Multiplication principle: Faster way to add equal amounts

• Verification: Check with repeated addition

3 Repeated addition pattern
Exercise 3
Sarah saves $3 every day for 7 days. How much money does she save in total?
Definition:

Repeated addition: Adding the same number multiple times, equivalent to multiplication

Days
$/day
Total $
7
3
21
Step 1: Identify the given information

Number of days: 7

Amount saved per day: $3

Step 2: Set up the multiplication equation

Total savings = Days × Amount per day

Total savings = 7 × $3

Step 3: Calculate the multiplication

7 × 3 = 21

Step 4: Express the final answer

Sarah saves $21 in total

Step 5: Verify with repeated addition

$3 + $3 + $3 + $3 + $3 + $3 + $3 = $21 ✓

Sarah saves $21 in total
Final answer:

Sarah saves $21 in total

Applied rules:

• Repeated addition: 7 groups of 3 = 7 × 3

• Multiplication principle: Faster than adding repeatedly

• Real-world context: Money, time, quantities

Multiplication Fundamentals
a \times b = c
Basic Multiplication
Array Model
Rows × Columns
Items arranged in rows and columns
Equal Groups
Groups × Items per group
Same number in each group
Repeated Addition
a + a + a ... (b times)
Multiplication as addition shortcut
Key definitions:

Multiplication: Repeated addition of the same number

Factors: Numbers being multiplied together

Product: Result of multiplication

Times table: Multiplication facts for numbers 1-12

Array: Objects arranged in rows and columns

Multiplication methods:
  1. Arrays: Organize in rows and columns
  2. Equal groups: Same amount in each group
  3. Repeated addition: Add same number multiple times
  4. Number lines: Skip counting
Tip 1: Any number multiplied by 0 equals 0.
Tip 2: Any number multiplied by 1 equals itself.
Tip 3: Draw pictures or use objects to visualize problems.
Common errors: Mixing up factors and products, forgetting multiplication facts, miscounting groups.
Key relationships: Multiplication is repeated addition, division is the inverse of multiplication.
Important multiplication facts to remember:

• Commutative property: a × b = b × a

• Identity property: a × 1 = a

• Zero property: a × 0 = 0

• Multiplication as grouping: 3 groups of 4 = 3 × 4 = 12

Solution: Exercises 4 to 5
4 Grouping problem
Exercise 4
A farmer has 6 baskets. Each basket holds 9 apples. How many apples does the farmer have?
Definition:

Grouping multiplication: Finding total when items are organized in equal groups

6 baskets
× 9 apples each
54 total
apples
Step 1: Identify the given information

Number of baskets: 6

Apples per basket: 9

Step 2: Set up the multiplication equation

Total apples = Number of baskets × Apples per basket

Total apples = 6 × 9

Step 3: Calculate the multiplication

6 × 9 = 54

Step 4: Verify with repeated addition

9 + 9 + 9 + 9 + 9 + 9 = 54 ✓

The farmer has 54 apples
Final answer:

The farmer has 54 apples

Applied rules:

• Grouping principle: Total = Groups × Items per group

• Multiplication fact: 6 × 9 = 54

• Verification: Check with repeated addition

5 Real-world application
Exercise 5
A parking lot has 4 rows of cars. Each row has 7 cars. During lunch, 3 more rows with 7 cars each were added. How many cars are in the parking lot now?
Definition:

Multi-step multiplication: Solving problems that require multiple multiplication operations

Initial
Added
Total
4×7=28
3×7=21
49
Step 1: Calculate initial cars

Initial rows: 4, Cars per row: 7

Initial cars = 4 × 7 = 28 cars

Step 2: Calculate added cars

Added rows: 3, Cars per row: 7

Added cars = 3 × 7 = 21 cars

Step 3: Calculate total cars

Total cars = Initial cars + Added cars

Total cars = 28 + 21 = 49 cars

Step 4: Alternative calculation

Total rows = 4 + 3 = 7 rows

Total cars = 7 × 7 = 49 cars ✓

There are 49 cars in the parking lot now
Final answer:

There are 49 cars in the parking lot now

Applied rules:

• Multi-step problem: Solve in parts then combine

• Array multiplication: Rows × Columns

• Addition principle: Combine separate totals

Detailed Summary: Multiplication Concepts and Problem-Solving Strategies

Complete Summary of Multiplication Concepts

Definitions

Multiplication: Repeated addition of the same number

Factors: Numbers being multiplied together

Product: Result of multiplication

Array: Objects arranged in rows and columns

Equal Groups: Same number of items in each group

Core Properties

Commutative: a × b = b × a (order doesn't matter)

Identity: a × 1 = a (multiplying by 1 gives same number)

Zero: a × 0 = 0 (multiplying by 0 gives zero)

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

Problem-Solving Steps

Step 1: Read the problem carefully and identify what's being asked

Step 2: Identify the groups and items per group

Step 3: Set up the multiplication equation

Step 4: Calculate the multiplication

Step 5: Check if answer makes sense in context

Examples

Simple: 3 × 4 = 12 (3 groups of 4)

Intermediate: 5 × 6 = 30 (5 rows of 6)

Advanced: 7 × 8 = 56 (7 groups of 8)

Multi-step: (4 × 5) + (3 × 5) = 20 + 15 = 35

Tips & Tricks

Tips: Draw arrays for visualization, use skip counting, check with repeated addition

Common Mistakes: Mixing up factors and products, forgetting multiplication facts

Pitfalls: Not identifying equal groups correctly, calculation errors

Memorization Aids

Patterns: Even numbers in 2s table, ending in 5 or 0 in 5s table

Tricks: 9s finger trick, doubles for 2s table

Practice: Daily drills, flashcards, games

Additional Practice Problems
Problem A
A classroom has 5 rows of desks with 6 desks in each row. How many desks are there?
Problem B
A store has 8 packages of markers. Each package has 4 markers. How many markers in total?
Problem C
A baker makes 3 batches of cookies. Each batch has 9 cookies. How many cookies altogether?
Problem D
A garden has 6 rows of flowers with 7 flowers in each row. How many flowers total?

Questions & Answers

Question: I don't understand when to use multiplication in word problems. How do I know?

Answer: Look for these clues in word problems that indicate multiplication:

  • "Each" - "5 boxes, each with 8 items"
  • "Per" - "3 dollars per day"
  • "Every" - "every week for 4 weeks"
  • "Groups of" - "3 groups of 4"
  • Rectangular arrangements - "rows and columns"

Ask yourself: "Am I dealing with equal groups?" If yes, use multiplication. Example: "3 bags with 5 apples each" → 3 × 5 = 15 apples.

Think of multiplication as a fast way to add equal amounts!

Question: What's the difference between multiplication and addition in word problems?

Answer: Use multiplication when you have EQUAL groups:

  • Addition: Different amounts ("I have 3 apples and 5 oranges" → 3 + 5 = 8)
  • Multiplication: Same amount in each group ("3 bags with 5 apples each" → 3 × 5 = 15)

Multiplication is really just a shortcut for repeated addition:

3 × 5 = 5 + 5 + 5 = 15

So if you see the same number being added multiple times, think multiplication!

Question: How can I help my child practice multiplication word problems at home?

Answer: Here are effective ways to practice multiplication word problems at home:

  • Use real objects: arrange toys in arrays, count items in packages
  • Create story problems: "We have 4 plates with 3 cookies each..."
  • Play multiplication games: dice games, card games, online apps
  • Practice daily: even 10-15 minutes of focused practice helps
  • Connect to real life: shopping, cooking, organizing items

Focus on helping them identify equal groups and the relationship between multiplication and repeated addition. Make it fun and relevant to their world!