Kahoot is amazing for compare/contrast and for taking the temperature of the class. The anonymity helps students express their thoughts without judgment.
Those who voted “negative” explained that it would be beneficial to lower money owed or cholesterol levels. The “positive” folks shared their examples of money saved or growth chart of a child.
But without knowing the application, one cannot tell if a positive or negative slope would be better. In hindsight, this would have been good to revisit right before the midterm exam! Kahoot link (this is the first of 7 questions).
Q: If 6 people take 3 days to dig 8 ditches, working at the same rate how long will it take 4 people to dig 10 ditches?
A: 5.625 days
18 people days to dig 8 ditches = 2.25 people days per ditch
10 ditches = 22.50 people days
22.50 / 4 = 5.625 days.
Q: On an analog clock, how many times do a clock’s hands overlap in a one week period?
At 12:00, the hands exactly overlap but not at other times — for example, at 1:05, the hour hand has moved slightly… and at 6:30, the hour hand is halfway between the 6 and the 7.
Making the times that they will overlap only 11 times in 12 hours (60 minutes /11).
12:00, 1:05ish, 2:10ish, 3:15ish, 4:20ish, 5:25ish, 6:30ish, 7:35ish, 8:40ish, 9:45ish, 10:50ish.
In one day they will overlap 22 times so in one week, 154 times.
A wooden cube that is 20 cm on each side is composed of 1 cm x 1 cm x 1 cm cubes.
Q1: If you paint all 6 sides of the outside of the cube blue, how many cubes will have no blue paint?
With a 3 by 3 by 3 cube, there is just one cube in the middle that would have no paint.
With a 4 by 4 by 4 cube, there are 8 cubes in the center of the cube (2 x 2 x 2) with no paint.
With a 5 by 5 by 5 cube, there are 27 cubes in the center of the cube (3 x 3 x 3) with no paint.
Answer: The pattern continues so a 20 by 20 by 20 cube, there would be 18 x 18 x 18 (5832) cubes in the center of the cube with no paint.
Q2: What if the 20 x 20 x 20 cm cube is composed of 2 cm x 2 cm x 2 cm cubes?
Answer: There would now be 1000 cubes (10 x 10 x 10), there would be 8 x 8 x 8 (512) cubes in the center of the cue with no paint.
The pressure’s on!
Thanks to @jaz_math for the Day 1 Silent Conversation idea. The PreFreshman Seminar students had amazing ideas on how to be a great Math teacher including content knowledge, attitude and leadership.
Students appreciate teachers who care, who know the material and can impart that knowledge. Hope I can live up to some if not most of these suggestions.