Question
scenario: swim training
instructions:
view the video found on page 1 of this journal activity.
using the information provided in the video, answer the questions below.
show your work for all calculations.
the students' conjectures: two students, ernest and denise, are training for a swim half-marathon in 10 weeks, and they disagree about their training schedule. if they follow ernest's suggested training schedule, will they be ready to swim 5 km in time for the half-marathon?
complete the table to summarize each student’s suggested training schedule. (2 points: 1 point for each row of the chart)
classmate conjecture
ernest
denise
do the distances they swim every week make an arithmetic sequence? why? (1 point)
analyzing the data:
fill out the schedules for the first four weeks of training. (2 points: 1 point for each person)
ernest's schedule
denise's schedule
week kilometers to swim daily week kilometers to swim daily
1 1
2 2
3 3
4 4
write the recursive formula for each sequence: an = an – 1 + d.
(4 points: 2 point for each formula)
student
d
recursive formula
ernest
denise
find the explicit formula for each arithmetic sequence: an = a1 + (n – 1) • d.
(4 points: 2 points for each formula)
student
explicit formula
ernest
denise
using the explicit formula, calculate how far the students will be swimming on week 10 using ernest’s schedule. (3 points)
using the explicit formula, calculate how far the students will be swimming on week 10 using denise’s schedule. (3 points)
making a decision
which training schedule will get them ready to swim 5 km in time for the half-marathon? (1 point)
prompt
i'm ernest. my friend denise and i have decided to enter an open-water swimming race. it's a half-marathon, and we'll be swimming 5 kilometers. the race is in 10 weeks. ["half-marathon in 10 weeks! " appears on screen.]
but we can't decide on a training schedule. i think we should start by swimming 1 km a day the first week, then add 0.25 km each week. so we'd swim 1 km the first week, 1.25 km the second week, 1.5 km the third week, and so on. it's a perfect schedule! [the following text appears on screen: ]
ernest's schedule:
1 km a day the first week
add 0.25 km each week
1, 1.25, 1.5,
but denise is worried that if we follow my schedule, we won't be ready to swim 5 km in 10 weeks. she thought of a different schedule.
she agrees we should swim 1 km a day the first week. but denise says we should swim an additional 0.5 km each week. so we'd be swimming 1 km the first week, 1.5 km the second week, 2 km the third week, and so on. [the following text appears on screen: ]
denise's schedule:
1 km a day the first week
add 0.5 km each week
1, 1.5, 2.0,
[the man disappears and the following text appears on screen:
ernest's schedule:
1, 1.25, 1.5, 1.75, (week 10)
denise's schedule:
1, 1.5, 2, 2.5, (week 10)
the man reappears.]
so who has the better plan? we need to calculate the distance we'll be swimming in the 10th week for each schedule. these numbers have a repeating pattern and look like an arithmetic sequence. what do you think?
by using arithmetic sequences, decide which training schedule will get us ready to swim 5 km in 10 weeks: my schedule or denise's schedule?
[the following text appears on screen:
ernest's schedule:
1 km the first week
add 0.25 km each week
denise's schedule:
1 km the first week
add 0.50 km each week.]