Solved Exercises on Word Problems with 1-Digit Multiplication in Grade 3

Master word problems with 1-digit multiplication: equal groups, arrays, and real-world applications through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Equal Groups Problem
Exercise 1
Sarah has 4 bags of apples. Each bag has 6 apples. How many apples does Sarah have in total?
Definition:

Equal Groups Problem: A word problem where you have multiple groups with the same number of items in each group. You multiply the number of groups by the number of items in each group.

Problem Solving Method:
  1. Read the problem carefully and identify what is being asked
  2. Find the number of groups (how many bags, boxes, etc.)
  3. Find the number of items in each group (apples per bag, books per shelf, etc.)
  4. Multiply the number of groups by the number of items in each group
  5. Write the answer with the correct units
Sarah has 4 bags of apples. Each bag has 6 apples. How many apples does Sarah have in total?
Number of groups: 4 bags
Items per group: 6 apples per bag
Groups
4
Per Group
6
Total
24
1
Identify the number of groups: 4 bags
2
Identify items per group: 6 apples per bag
3
Multiply: 4 × 6 = 24
4
Answer: Sarah has 24 apples in total
Bag 1
Bag 2
Bag 3
Bag 4
4 × 6 = 24 apples
Final answer:

Sarah has 24 apples in total because 4 bags × 6 apples per bag = 24 apples

Applied rules:

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

• Multiplication Strategy: Connect to repeated addition (6 + 6 + 6 + 6 = 24)

• Unit Consistency: Answer includes correct units (apples)

2 Array Problem
Exercise 2
A parking lot has 5 rows of cars. Each row has 7 cars. How many cars are in the parking lot?
Definition:

Array Problem: A word problem that describes objects arranged in rows and columns. You multiply the number of rows by the number of columns.

A parking lot has 5 rows of cars. Each row has 7 cars. How many cars are in the parking lot?
Number of rows: 5
Number of columns: 7 cars per row
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Rows
5
Columns
7
Total
35
1
Identify the number of rows: 5
2
Identify the number of columns: 7 cars per row
3
Multiply: 5 × 7 = 35
4
Answer: There are 35 cars in the parking lot
5 × 7 = 35 cars
Final answer:

There are 35 cars in the parking lot because 5 rows × 7 cars per row = 35 cars

Applied rules:

• Array Property: Total = Number of rows × Number of columns

• Rectangular Model: Shows the spatial arrangement of objects

• Visualization: Drawing arrays helps understand multiplication

3 Time Problem
Exercise 3
Emma practices piano for 3 hours each day. How many hours does she practice in 6 days?
Definition:

Time Problem: A word problem involving equal amounts of time over multiple periods. You multiply the amount per period by the number of periods.

Emma practices piano for 3 hours each day. How many hours does she practice in 6 days?
Amount per day: 3 hours
Number of days: 6
Hours per day
3
Days
6
Total hours
18
1
Identify the amount per day: 3 hours
2
Identify the number of days: 6
3
Multiply: 3 × 6 = 18
4
Answer: Emma practices 18 hours in 6 days
Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
3 × 6 = 18 hours
Final answer:

Emma practices 18 hours in 6 days because 3 hours per day × 6 days = 18 hours

Applied rules:

• Rate × Time = Total: Amount per unit × Number of units = Total amount

• Consistent Units: Hours per day × Days = Total hours

• Repetition Pattern: Same amount every day for multiple days

Word Problem Solving Strategies
Total = Groups × Items per Group
Word Problem Formula
Type 1
Equal Groups
3 bags × 4 apples = 12 apples
Type 2
Arrays
4 rows × 5 seats = 20 seats
Type 3
Time/Rates
2 hours × 5 days = 10 hours
Key definitions:

Word Problem: A mathematical problem presented in everyday language that requires multiplication to solve.

Keywords: Words that indicate multiplication (each, per, times, total, altogether, in all).

Clue Words: "Each," "every," "per," "a," "an" often signal multiplication.

5-Step Problem Solving Method:
  1. READ: Carefully read the entire problem
  2. FIND: Identify what you need to find (the question)
  3. IDENTIFY: Find the important numbers and what they represent
  4. SOLVE: Set up the multiplication equation and solve
  5. CHECK: Make sure your answer makes sense in the context
Common Keywords: Each, every, per, times, total, altogether, in all, product, groups of, sets of
Common Errors: Adding instead of multiplying, misidentifying groups vs. items per group
Tip 1: Draw pictures or diagrams to visualize the problem.
Tip 2: Circle clue words that suggest multiplication.
Tip 3: Ask yourself: "How many groups are there?" and "How many in each group?"
Solution: Exercises 4 to 5
4 Books and Shelves Problem
Exercise 4
A bookshelf has 8 shelves. Each shelf holds 5 books. How many books can the bookshelf hold in total?
Definition:

Capacity Problem: A word problem that asks for the maximum number of items that can be held, stored, or contained using equal groups.

A bookshelf has 8 shelves. Each shelf holds 5 books. How many books can the bookshelf hold in total?
Number of shelves: 8
Books per shelf: 5
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Shelves
8
Books per shelf
5
Total books
40
1
Identify the number of shelves: 8
2
Identify books per shelf: 5
3
Multiply: 8 × 5 = 40
4
Answer: The bookshelf can hold 40 books
8 × 5 = 40 books
Final answer:

The bookshelf can hold 40 books in total because 8 shelves × 5 books per shelf = 40 books

Applied rules:

• Capacity Calculation: Total capacity = Number of containers × Capacity per container

• Unit Consistency: Shelves × Books per shelf = Total books

• Array Model: 8 rows of 5 books each

5 Garden Planting Problem
Exercise 5
A gardener plants 7 rows of flowers. Each row has 4 flowers. How many flowers did the gardener plant?
Definition:

Garden/Agriculture Problem: A word problem involving planting, arranging, or organizing items in rows and columns.

A gardener plants 7 rows of flowers. Each row has 4 flowers. How many flowers did the gardener plant?
Number of rows: 7
Flowers per row: 4
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Rows
7
Flowers per row
4
Total flowers
28
1
Identify the number of rows: 7
2
Identify flowers per row: 4
3
Multiply: 7 × 4 = 28
4
Answer: The gardener planted 28 flowers
7 × 4 = 28 flowers
Final answer:

The gardener planted 28 flowers because 7 rows × 4 flowers per row = 28 flowers

Applied rules:

• Array Property: Total = Number of rows × Number of items per row

• Real-world Application: Connects math to practical scenarios

• Visualization: Drawing arrays helps solve garden problems

Advanced Word Problem Concepts
a × b = Total
Multiplication Relationship
Key definitions:

Factor: A number that is multiplied by another number (a and b in a × b)

Product: The result of multiplication (Total in a × b = Total)

Rate: A measure of how much of something happens in a given time or quantity

Problem Recognition Techniques:
  1. Look for clue words: Each, every, per, times, total, altogether
  2. Identify the structure: Equal groups, arrays, or rates
  3. Find the quantities: What numbers are given and what they represent
  4. Determine the operation: Multiplication vs. addition vs. subtraction
  5. Set up the equation: Create the multiplication sentence
Tip 1: Practice identifying multiplication problems by looking for equal groups.
Tip 2: Draw pictures to represent the problem situation.
Tip 3: Always check if your answer makes sense in the real-world context.
Tip 4: Use the commutative property to verify your answer (a×b = b×a).
Common Mistakes: Confusing groups with items per group, adding instead of multiplying, misreading the question.
Success Strategies: Underline key information, draw models, check reasonableness of answers.
Properties to remember:

• 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 0)

• Distributive: a × (b + c) = (a × b) + (a × c)

Problem Type
Example
Multiplication
Equal Groups
3 boxes × 4 toys
= 12 toys total
Arrays
5 rows × 6 chairs
= 30 chairs total
Rates
2 miles × 4 hours
= 8 miles total

Questions & Answers

Question: How do I know when a word problem needs multiplication instead of addition?

Answer: Look for these key differences:

  • Multiplication: When you have equal groups ("3 bags with 4 apples each", "5 rows with 6 chairs each")
  • Addition: When you combine different amounts ("3 apples and 5 oranges", "4 red cars and 2 blue cars")

Look for clue words that suggest equal groups:

  • Multiplication clues: "each", "per", "times", "product of", "groups of"
  • Addition clues: "and", "together", "combined", "in all", "total"

Example: "3 boxes with 4 toys each" → 3 × 4 = 12 toys (multiplication)

Example: "3 red toys and 4 blue toys" → 3 + 4 = 7 toys (addition)

Question: My child sometimes confuses which number is the number of groups and which is the number in each group. How can I help?

Answer: This is a common challenge! Try these strategies:

  • Circle key information: Have your child circle the number of groups and underline the number in each group
  • Ask specific questions: "How many groups are there?" and "How many in each group?"
  • Draw pictures: Visual representations help clarify the relationship
  • Use physical objects: Manipulatives like blocks or counters make the concept concrete

For example, in "4 bags with 3 apples each":

  • "4 bags" = number of groups
  • "3 apples each" = number in each group
  • So: 4 × 3 = 12 apples total

Question: What if the word problem has extra information that I don't need? How do I know what to use?

Answer: Many word problems include extra details to test your understanding! Here's how to handle them:

  • Read the question first: Know what you're solving for before reading the details
  • Identify the question: Usually at the end: "How many...?", "What is the total...?"
  • Find necessary information: Only look for numbers that help answer the question
  • Ignore extra details: Information that doesn't affect the answer

Example: "Sarah has 4 bags of red apples and 3 bags of green apples. Each bag has 5 apples. How many apples does Sarah have?"

The colors are extra information! You only need: 7 bags × 5 apples per bag = 35 apples