Today’s Question (Jan 3): A student started writing a test at 3:15 and finished at 4:52. How long did it take the student to finish the test?
Some students figured out the distance between the two times by adding chunks of time (from 3:15) until they arrived at the answer (end time of 4:52):
Other groups used a timeline to leapfrog from the start time to the end time:
Consolidation – The students discussed how using easy or friendly chunks made it easier to figure out the answer. Often the focus was moving the time up to the top of an hour (i.e.: it takes 45 minutes to mover 3:15 to 4:00).
The students also brought up the importance of remembering that there are 60 minutes in an hour. This was an interesting thought to students who tried using an algorithm to answer the question, because it can work (as seen by the attempt below), but not always… perhaps we will look at this more closely tomorrow.
Today’s Question (Jan 4):
The students had a variety of brilliant answers, most of which involved jumping back and forth (leap frogging) on a timeline using various chunks of time:
This answer managed to always leap forward, moving up to ‘friendly’ times to make it easy to make the next leap (i.e.: adding 42 seconds to 18 seconds to get up to the next minute):
Most of the answers moved back and forth on the time line:
Some students tried using a kind of algorithm to answer the question:
Consolidation: We discussed the trick to using an algorithm when calculating time. We are used to adding and subtracting using base 10 numbers, but when you use time, it’s slightly different. In this case, in order to subtract 7:30:18 from 9:11:05:
9:11:05 – 7:30:18
First the student tried to subtract the seconds (05 – 18), It did not work, so they borrowed from the minutes. They took 1 minute from the minutes column (making the 11 a 10, and carried it (as 60 seconds) into the seconds column, making the 05 a 65. They then subtracted the seconds (65 – 18 = 47).
Then the student tried subtracting the minutes (10 – 30). It did not work so they borrowed an hour (60 minutes) from the hours column, making it 70 – 30 = 40.
Lastly they subtracted the hours (8 – 7 = 1).
Therefore the answer is 1 hour, 40 minutes and 47 seconds.
Today’s Question (Jan 5):
Some students used a timeline to answer the question:
Some students added time in chunks:
Many students were able to use the algorithm, putting yesterdays consolidation to practice (very efficient):
Consolidation: We noticed that some students had an answer of 12:44:63. This opened up a discussion (again) about the importance of remembering that with time, answers over 60 seconds need to be converted to minutes, and answers over 60 minutes need to be converted to hours. Well done!
Today’s problem (Jan 6):
An interesting question (in blue). To make sure everyone was doing the same problem we decided on some clarifications (in red).
Most students took a random group of activities and added them up together to get as close to 15 minutes as they could:
Some students, however, noticed a pattern, based on two of the chores. If you added up the time it took to do both chores (writing thank-you cards; 1 min 33 sec, and washing paint brushes; 1 min 27 sec) it equalled 3 minutes exactly, and 15 minutes divides into 3 minutes 5 times:
Consolidation: Today we talked about a few of the problems that occurred. Some of the work had a great deal of information and ideas, but was poorly organized and labelled making it very difficult to follow.
So we discussed the importance of organization.
Secondly we re-visited the ideas of making sure, when using an algorithm, to carry minutes whenever you reach 60 seconds. It was easy to make this mistake:
And lastly we talked about the importance of patterns in math, reflecting upon our last unit in math. Well done!