Sarah bought 48 stickers and gave 12 to her friend. She wants to put the remaining stickers in albums with 6 stickers on each page. How many pages will she fill?
Multi-Step Problems: Division problems requiring multiple operations before the final division.
Advanced Components: Subtraction first, then division; identifying relevant information; sequential operations.
Learning Objectives: Solve problems with multiple operations, identify relevant information, apply division after other operations.
- Read carefully: Identify all information and operations needed
- Plan the steps: Determine order of operations
- Solve sequentially: Complete each operation in order
- Apply division: Use final result for division calculation
- Verify answer: Check if solution makes sense
Sarah has 48 stickers, gives away 12, then divides remaining into groups of 6
48 - 12 = 36 stickers left
36 ÷ 6 = ? (how many groups of 6 can be made)
36 ÷ 6 = 6 pages
6 pages × 6 stickers per page = 36 stickers ✓
Sarah will fill 6 pages.
• Sequence Matters: Complete operations in logical order
• Identify Steps: Plan which operations come first
• Verify Sequentially: Check each step before proceeding
There are 50 students going on a field trip. Each bus can hold 12 students. How many buses are needed, and how many seats will be empty on the last bus?
Remainder Problems: Division problems where items don't divide evenly.
Real-World Context: Situations requiring whole numbers (you can't have partial buses).
Interpretation Skills: Understanding what remainder means in context.
50 students ÷ 12 students per bus = ?
50 ÷ 12 = 4 remainder 2
4 buses can hold 48 students, 2 students remain
Since 2 students remain, we need 1 more bus
Total buses needed: 4 + 1 = 5
Last bus has 2 students, so 12 - 2 = 10 empty seats
4 buses × 12 + 1 bus × 2 = 48 + 2 = 50 students ✓
They need 5 buses, and there will be 10 empty seats on the last bus.
• Context Interpretation: Remainder has meaning in real-world problems
• Whole Number Requirement: Sometimes need to round up for practical purposes
• Verification: Check that (quotient × divisor) + remainder = dividend
During a 5-day school week, a teacher uses 120 pencils. On Monday she used 25 pencils, Tuesday she used 30 pencils, and Wednesday she used 20 pencils. If she used the same number of pencils on Thursday and Friday, how many pencils did she use each day?
Multi-Day Problems: Division problems involving distribution over time periods.
Missing Information: Problems requiring calculation of remaining quantities.
Equal Distribution: Problems where remaining amount is divided equally.
25 + 30 + 20 = 75 pencils used
120 - 75 = 45 pencils for Thu & Fri
45 ÷ 2 = ? (dividing between Thursday and Friday)
45 ÷ 2 = 22.5 pencils each day
25 + 30 + 20 + 22.5 + 22.5 = 120 ✓
The teacher used 22.5 pencils each on Thursday and Friday.
• Sequential Operations: Subtraction first, then division
• Equal Distribution: Remaining amount divided equally
• Verification: Sum of all parts equals total
Multi-Step Problem Strategy:
- Read thoroughly: Understand the entire problem context
- Identify operations: List all operations needed in order
- Plan sequence: Determine which operation comes first
- Solve step-by-step: Complete each operation in sequence
- Verify each step: Check that each part makes sense
- Check final answer: Ensure the complete solution fits
Multi-Step Division Problems: Problems requiring multiple operations before division.
Division with Remainders: Problems where division doesn't result in whole numbers.
Rate and Average Problems: Problems involving distribution over time or equal sharing.
Contextual Interpretation: Understanding what mathematical results mean in real-world situations.
- Analyze structure: Identify all components and operations needed
- Plan approach: Determine the order of operations
- Execute sequentially: Complete operations in planned order
- Handle remainders: Interpret remainder in context
- Verify completeness: Ensure answer addresses all parts of question
• Order of Operations: Complete operations in logical sequence
• Remainder Interpretation: Understand what remainder means in context
• Reasonableness Check: Verify answers make sense in real-world scenarios
• Complete Solutions: Address all parts of multi-part questions
| Criteria | Excellent (4) | Good (3) | Fair (2) | Needs Work (1) |
|---|---|---|---|---|
| Multi-Step Planning | Clear plan with correct sequence | Mostly correct sequence | Partial planning evident | Little to no planning |
| Operations Accuracy | All operations correct | Most operations correct | Some operations correct | Few operations correct |
| Remainder Interpretation | Correct interpretation in context | Mostly correct interpretation | Sometimes correct interpretation | Rarely correct interpretation |
| Reasonableness Check | Thorough verification of answer | Some verification attempted | Limited verification | No verification |
- Level 1: Two-operation problems (add/subtract then divide)
- Level 2: Three-operation problems with context
- Level 3: Multi-step problems with remainders
- Level 4: Complex rate and average problems
- Level 5: Critical thinking and pattern recognition
- Level 6: Open-ended and extension problems
Questions & Answers
Question: What do I do when I get a decimal answer in a division word problem?
Answer: Look at the context of the problem:
- Measurable items: Things like time, distance, or liquid can be fractional (2.5 hours, 3.75 liters)
- Countable items: People, buses, or discrete objects usually need to be rounded up if there's a remainder
- Money: Usually rounded to nearest cent (0.50 dollars)
In the pencil example, 22.5 pencils means she uses 22.5 pencils each day, which could mean alternating between 22 and 23 pencils.
Question: How can I help my child with multi-step division problems?
Answer: Use these strategies:
- Break it down: Have them write out each step separately
- Visual organization: Use boxes or tables to separate each operation
- Practice sequencing: Start with simple two-step problems
- Check each step: Verify each calculation before moving to the next
- Relate to real life: Use familiar scenarios to make problems meaningful
Encourage them to ask "What do I need to find first?" before starting.
Question: When do I need to round up when there's a remainder?
Answer: Round up when dealing with countable things that can't be divided:
- Transportation: If you need 4.2 buses, you need 5 buses (can't have partial buses)
- Containers: If you need 3.7 boxes, you need 4 boxes
- People: If you have 25 people and each table seats 6, you need 5 tables (not 4.17)
- Items: If you need 8.3 bags to carry items, you need 9 bags
Round up when having "part of" something isn't practical in the real world.