Multi Step Problem Solving Examples in 3rd Grade Math

Master multi-step problem solving: multiplication and division problems with step-by-step solutions, rules, and practice exercises.

Multi-Step Problems: Exercises 1 to 3
1 Apple Picking Problem
Exercise 1
Sarah picked 4 baskets of apples. Each basket has 6 apples. She gave 8 apples to her friend. How many apples does she have left?
Definition:

Multi-step problem: A problem requiring more than one mathematical operation to solve

Problem-solving method:
  1. Read the problem carefully
  2. Identify what you need to find
  3. Determine the operations needed
  4. Solve step by step
  5. Check your answer
Step 1
Find total apples
Step 2
Subtract given apples
Step 3
Calculate remaining
Step 1: Find total apples picked

Sarah picked 4 baskets with 6 apples each

4 × 6 = 24 apples

Step 2: Subtract apples given to friend

Total apples: 24

Apples given away: 8

24 - 8 = 16 apples

Step 3: Final calculation

Sarah has 16 apples left

Sarah has 16 apples left
Final answer:

Sarah has 16 apples left

Applied rules:

• Multiplication: Finding total when you know groups and items per group

• Subtraction: Finding what remains after taking away

• Order of operations: Multiply before subtracting in this context

2 Party Planning Problem
Exercise 2
There are 3 tables at a party. Each table seats 4 children. If 2 children leave early, how many children remain at the party?
Definition:

Grouping concept: Using multiplication to find total number in equal groups

Step 1
Total children
Step 2
Children leaving
Step 3
Remaining children
Step 1: Find total children initially

3 tables with 4 children each

3 × 4 = 12 children

Step 2: Children who leave

Number of children leaving: 2

Step 3: Calculate remaining children

12 - 2 = 10 children

10 children remain at the party
Final answer:

10 children remain at the party

Applied rules:

• Equal grouping: When items are arranged equally, multiply groups by items per group

• Subtraction: Removing part from whole

• Multi-step logic: First find total, then subtract part

3 Pizza Sharing Problem
Exercise 3
Mom bought 2 pizzas. Each pizza has 8 slices. If 5 people each eat 2 slices, how many slices are left?
Definition:

Distribution concept: Dividing total amount among equal shares

Step 1
Total slices
Step 2
Slices eaten
Step 3
Slices remaining
Step 1: Find total pizza slices

2 pizzas with 8 slices each

2 × 8 = 16 slices

Step 2: Calculate slices eaten

5 people eating 2 slices each

5 × 2 = 10 slices eaten

Step 3: Calculate remaining slices

Total slices: 16

Eaten slices: 10

16 - 10 = 6 slices remaining

6 slices are left
Final answer:

6 slices are left

Applied rules:

• Multiplication: Finding total in multiple groups

• Subtraction: Finding remainder after some is taken

• Multi-step problem: Requires multiple operations

Multi-Step Problem Solving Rules and Methods
Total = Groups × Items per Group
Multiplication Rule
Rule 1
Groups × Items = Total
Finding totals
Rule 2
Total ÷ Groups = Items per Group
Sharing equally
Rule 3
Total - Used = Remaining
Finding remainders
Key definitions:

Multi-step problem: A problem requiring more than one mathematical operation to solve

Equal groups: Sets containing the same number of items

Remainder: What's left after some is taken away

Complete methodology:
  1. Read carefully: Understand what the problem asks
  2. Identify operations: Look for keywords indicating addition, subtraction, multiplication, or division
  3. Plan steps: Decide the order of operations needed
  4. Solve step-by-step: Perform calculations in sequence
  5. Check answer: Verify if the answer makes sense
Tip 1: Look for words like "each", "per", "groups of" for multiplication.
Tip 2: Words like "left", "remaining", "more than" often indicate subtraction.
Tip 3: Always read the question twice to understand what you need to find.
Tip 4: Draw pictures or make lists to visualize the problem.
Common errors: Forgetting to perform all steps, misreading the question, calculating in wrong order.
Success strategies: Circle important numbers, underline the question, work step by step.
Multi-Step Problems: Exercises 4 to 5
4 Book Reading Problem
Exercise 4
Emma reads 3 books each week for 4 weeks. Then she gives 2 books to her sister. How many books does she have now?
Definition:

Time-based multiplication: Finding totals over repeated periods

Step 1
Books read
Step 2
Books given away
Step 3
Books remaining
Step 1: Calculate total books read

Emma reads 3 books per week for 4 weeks

3 × 4 = 12 books

Step 2: Books given to sister

Emma gives 2 books to her sister

Step 3: Calculate remaining books

Total books: 12

Books given away: 2

12 - 2 = 10 books

Emma has 10 books now
Final answer:

Emma has 10 books now

Applied rules:

• Repeated addition: 3 books each week for 4 weeks means 3 × 4

• Subtraction: Taking away part of the total

• Multi-step logic: First multiply, then subtract

5 Cookie Baking Problem
Exercise 5
Mom baked 3 batches of cookies. Each batch had 12 cookies. She put 5 cookies in each of 4 jars. How many cookies are left?
Definition:

Distribution and remainder: Sharing total amount into equal containers

Step 1
Total cookies
Step 2
Cookies in jars
Step 3
Cookies left
Step 1: Calculate total cookies baked

3 batches with 12 cookies each

3 × 12 = 36 cookies

Step 2: Calculate cookies placed in jars

4 jars with 5 cookies each

4 × 5 = 20 cookies in jars

Step 3: Calculate remaining cookies

Total cookies: 36

Cookies in jars: 20

36 - 20 = 16 cookies left

16 cookies are left
Final answer:

16 cookies are left

Applied rules:

• Multiplication: Finding total in multiple groups (batches)

• Distribution: Placing equal amounts in containers (jars)

• Subtraction: Finding what remains after distribution

Multi-Step Problem Solving: Laws, Methods, and Definitions
(Groups × Items) - Taken = Remaining
Multi-Step Formula
Key definitions:

Multi-step problem: A problem requiring more than one mathematical operation to solve

Equal groups: Sets containing the same number of items

Remainder: What's left after some is taken away

Distribution: Sharing items equally among containers or people

Keywords: Words that indicate specific operations (each, per, total, left, remaining)

Complete methodology:
  1. Read and understand: Read the problem carefully to understand what's being asked
  2. Identify key information: Circle numbers and underline important words
  3. Determine operations: Decide which operations (+, -, ×, ÷) are needed
  4. Plan the steps: Write down the order of operations needed
  5. Solve step by step: Perform each operation in sequence
  6. Check your answer: Verify if the answer makes sense in context
Tip 1: Keywords for multiplication: "each", "per", "groups of", "times", "product".
Tip 2: Keywords for subtraction: "left", "remaining", "less", "take away", "difference".
Tip 3: Always ask yourself: "What am I trying to find?" before solving.
Tip 4: Draw diagrams to visualize the problem situation.
Tip 5: Check if your answer is reasonable by estimating first.
Common errors: Forgetting steps, misreading numbers, calculating in wrong order, not checking the final answer.
Success strategies: Work systematically, write out each step, use visual aids, double-check calculations.
Key formulas: Total = Groups × Items per group; Remainder = Total - Amount used.
Essential rules for multi-step problems:

• Order matters: Solve operations in the logical sequence described in the problem

• Read twice: First for understanding, second to identify numbers and operations

• Visualize: Draw pictures or make lists to represent the problem

• Check reasonableness: Ask if your answer makes sense in the real-world context

• Label answers: Always include units (apples, cookies, books, etc.)

Questions & Answers

Question: I get confused about which operation to do first in multi-step problems. How do I know whether to multiply or subtract first?

Answer: Great question! In multi-step problems, you should follow the logical sequence described in the story:

  • First, identify what happens in the problem. Does something happen before another thing?
  • Look for the natural order of events in the story
  • Often you need to find a total first (using multiplication or addition), then do something with that total (subtracting, dividing, etc.)

For example, in "Sarah picked 4 baskets with 6 apples each, then gave 8 away":

  • First: Find total apples (multiply: 4 × 6 = 24)
  • Then: Subtract the ones given away (subtract: 24 - 8 = 16)

The order follows the story sequence. Practice reading problems slowly and identifying what happens first, second, and so on.

Question: My child struggles to identify whether a word problem requires multiplication or addition. Any tips to help distinguish?

Answer: The key is to look for specific clue words and the structure of the problem:

  • Multiplication clues: "each", "per", "groups of", "times", "sets of", "rows of", "every"
  • Addition clues: "altogether", "total", "sum", "combined", "in all", "plus"
  • Context matters: Multiplication is used when you have equal groups; addition is used when combining different amounts

Examples:

  • "3 boxes with 5 pencils each" → Multiplication (equal groups)
  • "5 red pencils and 3 blue pencils" → Addition (different amounts combined)

Encourage your child to visualize or draw the situation. Equal groups suggest multiplication; combining different parts suggests addition.

Question: Sometimes I solve the problem but my answer doesn't seem right. How do I check if I got it correct?

Answer: Checking your answer is a crucial skill! Here are several ways to verify:

  • Estimation: Round numbers and estimate to see if your answer is close
  • Reverse operation: If you subtracted, try adding back to see if you get the original number
  • Reasonableness: Ask if the answer makes sense in the real world
  • Re-read: Go back and check if you answered the exact question asked

For example, if you found that Sarah has 16 apples left after giving away 8 from 24 total, check: 16 + 8 = 24 ✓

Always ask yourself: "Does this answer make sense for the situation described in the problem?"