Problem # 5
Name___________________
Due Date________________
Homework Checklist
Check all boxes that apply
Peer Teacher
Criteria
Investigation
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The student does not meet any of the descriptions below.
The student attempts to investigate the problem.
The student minimally investigates the problem using one approach.
The student investigates the problem, using more than one approach as needed.
The student thoroughly investigates a problem, trying a variety of approaches as needed.
Communication
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The student does not meet any of the descriptions below.
The student attempts to explain their thinking process.
The student explains some of their thinking process.
The student explains their thinking process.
The student clearly explains their thinking process.
Reflection
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The student does not meet any of the descriptions below.
The student attempts to reflect on their process.
The student reflects on their process.
The student reflects on their process and attempts to extend the problem.
The student reflects on their process and extends the problem into unfamiliar contexts.
Peer Comments: (one strength, one area to improve on)
Peer Name:_________________
Teacher Comments:
Question:
How many times in a 12 hour period does the sum of the digits on a digital clock equal 6? Try to think of a way
to solve this without going through every single time. Describe what you did.
Working Side
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Write in pen
Show all work
Use a ruler to cross out errors with a single
line (like this)
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,
1:50, 1:05, 1:41, 1:14, 1: 23, 1:32 – 6 sets
2:40, 2:04, 2:13, 2:31, 2:22 – 5 sets
3:03, 3:30, 3:12, 3:21 – 4 sets
4:02, 4:20, 4:11 – 3 sets
Thinking/Communicating Side
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What am I trying to do?
What am I thinking?
What do I notice?
I read the question then realize that in a 12 hour time
period only hours 1-6 will give you totals of 6.
Because anything higher won’t work.
I then am trying to find out with 1:00 how many times
does it add up to 6 – I notice to do that have to have
combinations for the minutes that add up to five ex.
3+2 = 5 = 1:32
I then try to find the how many times it adds up to 6 in
2:00 so I use the same method. I notice that the
numbers in the minutes place have to add up to 4 as 2
– 6 = 4. As so the minutes have to add up to 4
5:01, 5:10 – sets
6:00 – 1 set
I notice that the amount of sets in each hour decrease
by 1 from the previous one this is because the number
the minutes have to add up to gets smaller because the
hour gets larger so to add up to 6 each time the
minutes get smaller and have less possibilities to add
up to smaller numbers.
The way to solve it is that you have 6 hours and in
each hour the number of sets decrease by one starting
with 6 so 6+5+4+3+2+1 = 21 so 21 sets
Reflection:
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Reflect on the problem. Was it challenging and/or interesting? Why or why not?
The problem was pretty easy but it was interesting at the same time because it involved more of problem
solving skills to eliminate numbers. And then to come up with the rule you had to observe what you already had
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Does my answer make sense? Why or why not?
My answer i think does make sense because i came up with the method that will allow you to find the answer
without going through it every single time
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Is there another way to solve this?
There can be another way to solve this by finding possibilities that add up to 5, 4, 3, 2, 1, 0 and then sort it with
the appropriate hour.
Extension:
Can I find a general solution to this question?
Can I explore further with a different example?
Can I change the question to look at a different problem?
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The general solution is that list all the hours 1-12 eliminate 7-12. Do the calculations for 1:00 you get 6
sets then the rest minus one from the amount of sets.
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Rather than in a 12 hour period you can make it a 24 hour period adding to 12. In this case the same
strategies are used with the 12 hour period. However you have to remember that 1:00pm is 13:00and so
on.
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Another problem would be if in a 12 hour clock for 24 hours how many times does 12 come?