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.

Teachers Pay Teachers Freebies

I don't know if all of you know about Teachers Pay Teachers (TpT), but I learned of the site about a year ago.  Teachers share documents they have created for use in their classroom, some are for free but some are for sale.  I contribute files to the site (some free, some for sale) as well.  But as I think all teachers would agree, free is always nice...but free doesn't always mean the product is good.  So each month I will be posting files that I find on TpT that are FREE and GREAT.  This month I am going to start off with some of the free files that I have on TpT, since I made them they must be GREAT!!! :)

Subitizing Activity
I got this idea from another blog (Learning 4 Kids) but had to create the game boards myself.  So, once I had drawn them I thought other teachers might like to use them and not have to draw their own.  The basic idea is that children roll a die, take that many pom poms, and cover the circles on their board.  The first person to fill all their circles wins.

Place Value Cards
The origin of these cards can be credited to Montessori, I believe.  I first saw an adaptation of them in an NCTM publication, which I then adapted.  My version has the numerals in the corners of each card so that you can see the expanded form even when you place the cards on top of each other to create the standard form, but I also put a Rekenrek visual of each number on the back of each card because kids need to have visuals to correspond to numerals.

What the Heck is a Rekenrek???
If you asked yourself that question after reading about the activity above, then you need this file.  This file explains what they are, how you can make a homemade version, and a few activities you can do with rekenreks.

Pinterest Pins I Love!

I really tried avoiding Pinterest because I heard how addicting it is.  I finally gave in and yes it is addicting but it is because of how much wonderful stuff there is out there!  I just can't stop learning.  Here are a few of my favorite pins that I thought you might enjoy:

Use paint color sample strips to create Missing Number Sequencing Strips.

 From A Kentucky Kindergarten

Place Value Cups are a wonderful visual to help children see the value of each digit within a number.

From My 2nd Grade Journal

A great way to make Attendance be a math activity.

From Joyful Learning in KC

A fun apple themed array model for multiplication.

From Math Coach's Corner

 

If you like these, follow me on Pinterest to see more.

October Math Read-A-Loud

I have always loved children's literature and compiled quite a collection of books during my pre-service years.  But then when I got my first teaching job as a middle school math teacher I didn't use them much.  As I've become a more well-rounded math teacher I have come to see all the great ways mathematics can be brought into a classroom through books.  So every month I will share a favorite children's book and talk about ways to use it in your classroom.

This month I choose a pumpkin themed book.  How Many Seeds in a Pumpkin? by Margaret McNamara and G. Brian Karas, leads you through an activity done in little Charlie's classroom.  The kids make guesses about how many seeds are in a pumpkin.  Most kids think the bigger pumpkin will have the most seeds but, as the kids in Charlie's class discover, the small pumpkins actually have the most.

Ways to use this book:

• Use it as a lead into doing the seed counting activity in your own classroom - but watch out it is messy!!!  Young kids can count the seeds one-by-one while older kids can organize their seeds into piles of 10.
• Label each pumpkin with a number and have groups of 2-3 kids pick up each pumpkin.  Have them list the pumpkins from Heaviest to Lightest.  Then after each group has made their list, weigh each pumpkin and line them up from Heaviest to Lightest.
• Different types of pumpkins have different numbers of "lines" on the outside.  Have children count the lines on the outside and then compare to other pumpkins in the room.  Or add up all the lines from all the pumpkins in the classroom.
• Pumpkins take 4 months to grow, what fraction of a year is that?
• One-half cup of cooked pumpkin seeds provides you with a day's supply of Vitamin A.  If I have 4 cups of cooked pumpkin seeds, how many days worth of Vitamin A can I get?
• When planting pumpkins you should plan to give each vine at least a 3-foot diameter mound.  If my garden has a 4ft x 5ft area that I want to plant pumpkins in, how many vines could I fit in my garden?
• Pumpkin vines typically grow 3 or 4 pumpkins each.  If I have 5 vines what are all the possible amounts of pumpkins those vines can produce? 

Check out this other wonderful post, Quick and Easy Pumpkin Math Activities, by Playdough to Plato.

What are some of your favorite books to use in October?  Any of them have an underlying math theme?