Comparison problem: A word problem that asks for the difference between two quantities. Keyword phrases include "how many more", "how much more", "more than", "fewer than", "less than".
- Identify the two quantities being compared (Sarah: 15, Tom: 9)
- Determine which is larger (Sarah has more)
- Subtract the smaller quantity from the larger quantity
- State the answer with proper units
Sarah has 15 stickers
Tom has 9 stickers
15 > 9, so Sarah has more stickers than Tom
Difference = Larger number - Smaller number
Difference = 15 - 9 = 6
Sarah has 6 more stickers than Tom
Sarah has 6 more stickers than Tom.
• Comparison Formula: Difference = Larger Quantity - Smaller Quantity
• Subtraction: Calculate the numerical difference
• Units: Include appropriate units in the final answer
Multi-step comparison: A comparison problem that may involve addition or subtraction before making the comparison. In this case, we compare two individual amounts.
Monday: 24 seashells
Tuesday: 17 seashells
24 > 17, so Monday had more seashells than Tuesday
Difference = 24 - 17 = 7
Emma collected 7 more seashells on Monday than on Tuesday
Emma collected 7 more seashells on Monday than on Tuesday.
• Comparison Formula: Difference = Larger Quantity - Smaller Quantity
• Subtraction: Calculate the numerical difference
• Context: Relate the answer back to the original problem
Time comparison: A comparison problem involving time units. The same subtraction principle applies, but units must be consistent.
Jake: 35 minutes
Maya: 28 minutes
35 > 28, so Jake ran longer than Maya
Difference = 35 - 28 = 7 minutes
Jake ran 7 more minutes than Maya
Jake ran 7 more minutes than Maya.
• Comparison Formula: Difference = Larger Quantity - Smaller Quantity
• Unit Consistency: Both quantities must have the same units
• Subtraction: Calculate the numerical difference
Comparison problem: A mathematical problem that asks for the difference between two quantities.
Difference: The result of subtracting one number from another.
More than: Indicates which quantity is larger.
Less than: Indicates which quantity is smaller.
Keywords: Phrases like "how many more", "how many less", "more than", "fewer than", "greater than", "less than".
- Read the problem carefully: Identify what quantities are being compared
- Find key words: Look for phrases like "how many more", "how many less"
- Identify the larger and smaller quantities: Determine which number is greater
- Set up the subtraction: Larger number - Smaller number
- Calculate the difference: Perform the subtraction
- State the answer: Include units and relate back to the problem
• Always subtract the smaller number from the larger number
• The result is always positive
• Include units in your final answer
• Check that your answer is reasonable
Money comparison: A comparison problem involving monetary amounts. The same subtraction principle applies, but with dollar units.
Anna: $42
Ben: $35
$42 > $35, so Anna has more money than Ben
Difference = $42 - $35 = $7
Anna has $7 more than Ben
Anna has $7 more than Ben.
• Comparison Formula: Difference = Larger Quantity - Smaller Quantity
• Unit Consistency: Both quantities must have the same units ($)
• Subtraction: Calculate the numerical difference
Measurement comparison: A comparison problem involving measurements like length, weight, or capacity. Same subtraction principle with measurement units.
Red rope: 48 inches
Blue rope: 39 inches
48 > 39, so the red rope is longer than the blue rope
Difference = 48 - 39 = 9 inches
The red rope is 9 inches longer than the blue rope
The red rope is 9 inches longer than the blue rope.
• Comparison Formula: Difference = Larger Quantity - Smaller Quantity
• Unit Consistency: Both quantities must have the same units (inches)
• Subtraction: Calculate the numerical difference
Comparison problem: A mathematical problem that asks for the difference between two quantities.
Difference: The result of subtracting one number from another.
"How many more": A phrase that indicates subtraction is needed to find the difference between two quantities.
Quantity: A measurable amount or number of items.
Keywords: Words that indicate the type of operation needed (more, less, than, difference).
- Read the problem carefully: Understand what is being asked
- Identify the quantities: Find the two numbers being compared
- Find key words: Look for phrases like "how many more", "how many less"
- Determine which is larger: Compare the two quantities
- Set up subtraction: Larger number - Smaller number
- Calculate: Perform the subtraction
- Check and answer: Verify the answer makes sense and state it clearly
• Always subtract the smaller number from the larger number
• The difference is always positive
• Include units in your final answer
• Verify your answer makes sense in the context of the problem
• Look for key words that indicate comparison
Subtraction indicators: "how many more", "how many less", "more than", "less than", "fewer than", "difference", "exceeds", "greater than", "shorter than", "longer than", "heavier than", "lighter than"
Bar models: Draw bars to represent quantities and their differences.
Number lines: Use number lines to visualize the distance between quantities.
Part-whole thinking: Consider how the difference fits between the two quantities.
Verification: Always check by adding the difference to the smaller quantity.
• Subtraction Rhyme: "Find the difference, subtract with precision!"
• More/Less Rule: "More or less, always subtract the lesser!"
• Check Your Work: "Add the answer back to verify it works!"
Questions & Answers
Question: I sometimes get confused about which number to subtract from which. How do I know which one is bigger?
Answer: Here are some strategies to identify the larger number:
- Look at the place value: Compare digits from left to right (highest place value first)
- Use benchmarks: Think about familiar numbers (like 10, 50, 100) to estimate
- Visualize: Imagine the numbers on a number line
- Remember: In "how many more" problems, you always subtract the smaller from the larger
Example: Between 24 and 17, since 2 > 1 in the tens place, 24 is larger.
Always subtract the smaller number from the larger number!
Question: What if I see "how many less" instead of "how many more"? Is it still subtraction?
Answer: Yes, "how many less" also requires subtraction!
Both "how many more" and "how many less" are asking for the difference between two numbers.
Example: If Tom has 12 apples and Jane has 8 apples:
- "How many more apples does Tom have than Jane?" → 12 - 8 = 4 more
- "How many fewer apples does Jane have than Tom?" → 12 - 8 = 4 fewer
Both questions use the same subtraction: 12 - 8 = 4!
Question: How can I check if my answer is correct?
Answer: Here are effective verification methods:
- Add the difference back: Add your answer to the smaller number to see if you get the larger number
- Reasonableness check: Does your answer make sense in the context of the problem?
- Estimation: Round numbers to check if your answer is close to your estimate
- Visual verification: Draw or model the problem to confirm your answer
Example: If you found that 15 - 9 = 6, check: 9 + 6 = 15 ✓
This confirms your answer is correct!