Mississippi Math C.S.28
The Standard
Utilize integrals to model and find solutions to real-world problems such as calculating displacement and total distance traveled.
2025 Mississippi College- and Career-Readiness Standards for Mathematics · Employ Various Integration Properties and Techniques to Elevate Integrals
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use a velocity function or graph to find where an object ends up. They split the time interval when direction changes, then use signed area for net change and absolute area for how far it traveled.
What Mastery Looks Like
- For v(t) = t - 2 meters per second from 0 to 4 seconds, a student marks the turnaround at 2 seconds. They find 0 meters of net change and 4 meters traveled.
Common Misconceptions
- Students may add signed areas to find total travel, getting zero when an object returns to its start. Others take the absolute value only after integrating or treat negative velocity as negative distance.
How to Assess It
- Exit ticket: A cart has velocity v(t) = 2t - 6 meters per second from 0 to 5 seconds. Find its net change in position and total path length, showing where you split the integral.
Lesson moves
Ways to Teach It
Cut out positive and negative regions from a printed velocity-time graph; flip the negative pieces up to compare net change with total travel.
Ask: A runner returns to the start after 10 seconds. Can the runner's total travel be zero? Explain with a velocity-time graph.
Give pairs four velocity-time graph cards; have them mark each zero and calculate net change and total travel before checking answers.
From a cyclist's log, 4 m/s east for 30 seconds, then 2 m/s west for 20 seconds, calculate final position and odometer change.
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