Problems About Comparing
Problems about comparing use subtraction to find how much greater or lesser one quantity is relative to another. In Grade 6 Saxon Math Course 1, the pattern is Greater − Lesser = Difference. The same structure applies to elapsed-time problems: Later Time − Earlier Time = Elapsed Time. For example, a city with 10,000 people compared to one with 7,500 has a difference of 2,500. Recognizing the comparing pattern — asking 'how much more?' — is a key problem-solving strategy.
Key Concepts
New Concept Comparison and elapsed time problems use a subtraction pattern to find the difference between two values, whether they are quantities or points in time.
Problems About Comparing Comparison problems have a subtraction pattern. We write the numbers in the equation in this order: $$ \text{Greater} \text{lesser} = \text{difference} $$ Or, using letters: $$ g l = d $$.
Elapsed Time Problems Elapsed time is the length of time between two events. Elapsed time problems also have a subtraction pattern: $$ \text{Later} \text{earlier} = \text{difference} $$ Or, using letters: $$ l e = d $$ What’s next This card introduces the core subtraction pattern. Next, you'll apply this pattern by solving worked examples involving populations, historical dates, and personal ages.
Common Questions
What is the pattern for problems about comparing?
Greater − Lesser = Difference. Use subtraction to find how much more one quantity is than another.
City A has 10,000 people; City B has 7,500. How many more people does City A have?
10,000 − 7,500 = 2,500 more people.
How do you solve elapsed-time problems?
Later time − earlier time = elapsed time. Example: from 1:30 PM to 4:15 PM is 2 hours 45 minutes.
What key words signal a comparing problem?
Phrases like 'how much more,' 'how much greater,' 'how much taller/faster/longer,' and 'difference between' signal a comparing subtraction problem.
Can comparing problems involve decimal or fraction values?
Yes. Apply the same Greater − Lesser pattern: 4.75 − 2.3 = 2.45 more, or 5/6 − 1/3 = 1/2 more.