# Using number lines for Time problems

The newest addition to our family finally slept through the night.  So besides the panic wake up at 3:30, rushing to his bedside to ensure he was in fact still alive, it was a great night of sleep.  When he woke up at 5 am, I was feeding him and of course figuring out a math problem. :) Here is how it would be written in a typical math textbook:

Riggins went to bed at 8:00 PM.  He woke up at 5:00 AM.  How many hours did he sleep?

These elapsed time problems are difficult for children who are used to just pulling out numbers and either adding or subtracting, because neither of those works.  So what we typically teach children is to picture the clock hands going around the clock from 8 all the way to 5.  Then the kids actually draw that happening.  Two things are wrong with this model for solving time problems.  1) Kids spend too much time drawing the clock.  They want to add in all the numbers on the clock face and draw the hands.  2) When they model the hands moving around the clock, it gets really hard to keep track of all the circles they are making round and round the clock.

So, instead, a more efficient model is a number line, or in this case a time line. Starting in 2nd grade, children start using number lines to help them solve math problems. Before 2nd grade children should be using a number path instead of a number line, but that I will save for another post. The more children solve problems on number lines, the more they look for "friendly" numbers.  Those are numbers that are nice numbers to jump or nice to jump to.  Here are two examples for a brief demonstration on using number lines for addition:

As children transition from using a number line to using a time line, the emphasis should be on knowing what those friendly numbers are when it comes to time.  With whole numbers children like getting to the multiples of ten and/or the hundreds.  But with time problems, the friendly numbers are getting to 12 pm/am and getting to 60 minutes in order to get to the next hour. So this morning as I was contemplating how long Riggins slept last night, I was visualizing the problem on a number/time line that looked like this:
The distance from 8 pm to 5 am is 9 hours because it is 4 hours to that friendly time of 12 am and then another 5 hours to get to 5 am.  Those were nice, easy jumps for me but what does this look like when the times are not so nice.

Jaeger starts school at 7:50 am.  School gets out at 3:15.  How long is he in school?

As you can see, they jumped to the next hour (8am), then to noon, again to the closest hour (3pm) and then to the ending time of 3:15.  The answer is the amount of time from 7:50 to 3:15, so when you add the hours and minutes together you get 7 hours 25 minutes.  The number/time line is useful for all types of time problems.  Here are a few more examples.

Sierra's softball game started at 11:30 am.  It lasted for 1 hour and 40 minutes.  What time did her game end?

Camden woke up at 6:15 am.  He slept for 9 hours and 45 minutes.  What time did he go to bed?

Next time you are working on time problems, encourage your kids to make use of a time line.

Labels: ,

K-5 Math is Fun: Using number lines for Time problems

## Saturday, October 19, 2013

### Using number lines for Time problems

The newest addition to our family finally slept through the night.  So besides the panic wake up at 3:30, rushing to his bedside to ensure he was in fact still alive, it was a great night of sleep.  When he woke up at 5 am, I was feeding him and of course figuring out a math problem. :) Here is how it would be written in a typical math textbook:

Riggins went to bed at 8:00 PM.  He woke up at 5:00 AM.  How many hours did he sleep?

These elapsed time problems are difficult for children who are used to just pulling out numbers and either adding or subtracting, because neither of those works.  So what we typically teach children is to picture the clock hands going around the clock from 8 all the way to 5.  Then the kids actually draw that happening.  Two things are wrong with this model for solving time problems.  1) Kids spend too much time drawing the clock.  They want to add in all the numbers on the clock face and draw the hands.  2) When they model the hands moving around the clock, it gets really hard to keep track of all the circles they are making round and round the clock.

So, instead, a more efficient model is a number line, or in this case a time line. Starting in 2nd grade, children start using number lines to help them solve math problems. Before 2nd grade children should be using a number path instead of a number line, but that I will save for another post. The more children solve problems on number lines, the more they look for "friendly" numbers.  Those are numbers that are nice numbers to jump or nice to jump to.  Here are two examples for a brief demonstration on using number lines for addition:

As children transition from using a number line to using a time line, the emphasis should be on knowing what those friendly numbers are when it comes to time.  With whole numbers children like getting to the multiples of ten and/or the hundreds.  But with time problems, the friendly numbers are getting to 12 pm/am and getting to 60 minutes in order to get to the next hour. So this morning as I was contemplating how long Riggins slept last night, I was visualizing the problem on a number/time line that looked like this:
The distance from 8 pm to 5 am is 9 hours because it is 4 hours to that friendly time of 12 am and then another 5 hours to get to 5 am.  Those were nice, easy jumps for me but what does this look like when the times are not so nice.

Jaeger starts school at 7:50 am.  School gets out at 3:15.  How long is he in school?

As you can see, they jumped to the next hour (8am), then to noon, again to the closest hour (3pm) and then to the ending time of 3:15.  The answer is the amount of time from 7:50 to 3:15, so when you add the hours and minutes together you get 7 hours 25 minutes.  The number/time line is useful for all types of time problems.  Here are a few more examples.

Sierra's softball game started at 11:30 am.  It lasted for 1 hour and 40 minutes.  What time did her game end?

Camden woke up at 6:15 am.  He slept for 9 hours and 45 minutes.  What time did he go to bed?

Next time you are working on time problems, encourage your kids to make use of a time line.

Labels: ,