Equations are sentences
An equation says how quantities are related.
A cyclist and a flag
A flag stands 60 m from the start. A cyclist wants to reach it.
If she doubles her speed, what happens to the time she needs?
What this lesson covers
The idea
Mathematics is a language of science: an equation is a compact statement of how quantities are related, used by first understanding the situation, then identifying the relevant quantities, then reasoning with the relationships.
A cyclist and a flag
A flag stands 60 m from the start. A cyclist wants to reach it.
If she doubles her speed, what happens to the time she needs?
- It doubles too
- It becomes half
- It stays the same
Reach the flag
Set the speed and the time. Watch how distance, speed and time are linked.
The equation says it all
Mathematics is a language of science. An equation is a compact statement of how quantities are related.
s = v × t says: distance grows when speed grows, and grows when time grows. Double the speed and you need half the time for the same distance.
How to use an equation: 1. Understand the situation. 2. Find the quantities that matter. 3. Use the relationship to reason.
- Speed v | Time t | Distance s = v × t
- 5 m/s | 12 s | 60 m
- 6 m/s | 10 s | 60 m
- 10 m/s | 6 s | 60 m
Notes
An equation is a compact statement of how quantities are related. First understand the situation, then find the quantities, then reason with the relationship.
Check yourself
A cyclist rides at 5 m/s for 12 s. How far does she go?
Answer: 60 m
s = 5 m/s × 12 s = 60 m.
She must cover 40 m at 8 m/s. For how many seconds must she ride?
Answer: 5 s
t = 40 m ÷ 8 m/s = 5 s.
What does the equation s = v × t tell us?
What is the best order for solving a problem with an equation?
- How distance, speed and time are related. Double the time and the distance doubles — correct. Yes. An equation is a statement about relationships.
- A number to memorise before the exam. An equation is a statement about how quantities are related, not just a number to memorise.
- It works only for cyclists. It works for anything moving at a steady speed.
- Pick a formula, put in numbers, hope. That treats the equation as a calculation tool only.
- Understand the situation, find the quantities, then reason with the relationship — correct. Yes. Understanding comes first.
- Guess an answer, then check. Reasoning with the relationship is better.