Elapsed Time Using an Open Number Line

Elapsed Time Using an Open Number Line

Determining elapsed time can be a huge issue for many students for several reasons:

It often involves the conversion of units.  For example, hours to minutes, minutes to seconds, etc.

Students are often confused as to whether they should more forward (from the earlier time to the later time) or backwards as they start to determine elapsed time.

When given the elapsed time and either a starting OR ending time, and asked to determine the missing piece of information (starting or ending time), students often want to simply add (or subtract) the given elapsed time as a total.  For example, if a question involved an activity that started at 9:50 and lasted 1 hour and 15 minutes, students often simply add 950 + 115= 1065, and record that the final time was 10:65.

Open Number Line to the Rescue!

Once I feel that my Grade 5/6 students have a good understanding of the unit conversions (ie. 60 seconds= 1 minute, 60 minutes = 1 hour, etc.) and are ready to work with elapsed time situations, we use an open number line.  Because my students do "number talks" every day to strengthen their mental math skills, they are already familiar with closed and open number lines.  

Sample question:  It is now 9:45 and our recess bill rings at 11:10.  Determine how much time will pass before the bell rings.

Students begin by drawing a straight line across their desks. (Yes, I have them write directly on their desks with whiteboard markers.  It saves a TON of paper, and it's a snap to clean up with a dampened old sock, piece of felt, or other material.)

They then record the beginning time (9:45) at the start of their line, and the finishing time (11:10) at the end of their line.  

Then students work in "chunks" of time, usually working from the left to right, to determine the elapsed time.  There are an infinite number of ways to chunk, depending upon the particular comfort level of your students. 

Grade 5 Elapsed Time Using an Open Number Line

This Grade 5 student is most comfortable starting with smaller units and working up to the nearest hour.  She jumps by 5 minutes to 9:50, and then by 10 minutes to 10:00.  From there she was able to continue on to add an hour from 10:00 to 11:00, and then add 10 minutes on to reach the ending time of 11:10.  She then added the minutes together (5+10+10=25) and attached them to the hour, reaching the correct time of 1 hour and 25 minutes.

Grade 6 Elapsed Time Using an Open Number Line

Meanwhile, this Grade 6 student approached the situation a bit differently, first adding a full hour from 9:45 to 10:45, and then chunking by 15 minutes to reach 11:00 and then another 10 minutes to reach the ending time.  This method makes it very easy for this student to determine the elapsed time (1 hour plus 15 minutes plus 10 minutes = 1 hour & 25 minutes.

The joy of this open number line strategy is that students can use it working either forwards OR backwards, depending on each student's comfort level.  This was particularly important in my split-grade classroom last year, which contained a very wide range of ability levels.  Everyone met with success, with each student deciding on how best to "chunk" measurement units and whether to work forwards or backwards.  

While this is not the only strategy for determining elapsed time, it is the one that has met with the greatest success in my classes.  What have YOU found to be helpful in approaching this challenging concept?

Check out my "Coach's Corner" TPT store for some great products inspired by my students!

  

Halloween Data Management - Grade 5/6

Hi Everyone,

Sorry I haven't been on here in a while. I've been hard at work on another big project, and now that that is done I'll try to post more often.

As you may know, I'm a "numeracy facilitator" for my school board this year, working between 2 schools at the moment in Grades 1 to 6.  Right now everyone is transitioning to our data management strand, and I thought I would share a couple of great ideas that happened last week in our Grade 5 classes.   

DAY 1/Hallowe'en:

On October 31st, students were asked to sort their Halloween treats at home that evening, and record their findings in some way, as they would be using the results the next day at school. Students had been given pre-determined categories: Candy, Pop, Chips, Chocolate Bars, and Other.  They also then had to sort the chocolate bars into brand names.  The teachers did not tell the students how to record their results.

DAY 2:  November 1st

The next morning students brought in tally charts, bar graphs, lists, etc.  Students then worked in groups of 4 to add their numbers together to find out how many chips the group got altogether, how much pop, etc.  The last step was to show this information in a graph.  Here's one group's bar graph:

The great thing about this was....it was the first day of data management, and the kids weren't given any instruction at all!  They did such a great job showing us how much they already knew about graphing, that the teachers and I realized that most of the "review" we had originally planned on doing to refresh their minds was completely unnecessary.  

We did discover that while most students knew they needed titles and subtitles, they really didn't know how to create these important features in a meaningful manner.  Tomorrow I'll share how we addressed this quickly, in a manner in which the kids told us what was needed; we didn't need to tell them!

Day 3:  November 2nd

Students took their graphing skills one step further and created pop-up graphs to show their data.  Take a peek at this graph showing the different brands of chocolate bars one group collected!  (Note:  the idea for this activity came from the Interactive Math Journal from Runde's Room on TPT!!)

While I know Halloween is passed, you could do the same activity by having students gather loose change at home and bring their results (not the coins themselves) to school.  You will likely be amazed at how much your kids already know about how to show information in graph form!

Roll & Risk Place Value Game Grades 2-4

Our school board has a "numeracy framework" from Grades 1 to 8, which sets out the order in which the various math units and strands are taught, and also indicates which lessons from our core resource (Nelson Math) can be used, as well as additional resources such as the Ontario Guides to Instruction in Mathematics, Super Source lessons, etc.  At the moment all grades are working on the first Number Sense strand, which focuses on counting, the "how muchness" of a number, and representing numbers in a variety of ways.

Grade 3/4

Today I worked in a Grade 3/4 classroom, introducing the game Roll & Risk.  This game reviews regrouping 2 digit numbers using dice and Base 10 blocks in an engaging manner.  After creating a two-digit target number by rolling a die twice (first roll for the tens digit; second roll for the ones), pairs of students work towards rolling the die and adding the appropriate number of Base 10 blocks, getting as close to their target number as possible without going over.  Each roll can be taken as either a tens or ones.  For example, with a target number of 43, and a first roll of 5, students will have to decide if they should take 5 tens or 5 ones.  They soon realize that taking 5 tens will immediately push them over their target number of 43, so take it as 5 ones, and continue rolling, regrouping ones as tens when necessary.  As they get closer and closer to their target number, they must decide when they should stop rolling.  After a couple of rounds of the game students realize that once their within 6 numbers of their target number, it is getting risky to roll again.                                                                                                                                                
                                                                                                                                                                                                   

The classroom was humming as the students discussed game strategies with their partners, and when I walked around with guiding questions, I could see that they were understanding not only the regrouping that was being reviewed from a previous year, but also the probability concepts necessary to success for this game.  When students got off track (one pair had a target number of 99 which I naturally questioned), it took only a quiet question or two to get them back on track (ie. "What is the largest possible number you can roll on one die?").

I can't take credit for the creation of the game; it was developed as part of the Ontario Ministry of Education's "Edugains" site, and full lesson plans can be found at this link:  Roll and Risk  On the right you will see "Counting & Representation; if you scroll down under that title you will find "Base Ten - Game 1" and Base Ten - Game 2".  Game 1 is for 2 digit numbers and Game 2 is for 3 digit numbers.  The full game summary as well as the recording sheet can be found by clicking on "Printable Documents" over Counting & Representation.

I've also created a Smart Notebook resource to introduce both versions of the game.  Students love coming up and rolling the interactive dice, and the cloned Base 10 blocks make it easy for students to understand the regrouping that is part of the game.  Check it out here:  Roll & Risk Smart Notebook Place Value Game

 Tomorrow I'll be doing a similar game, only with subtraction, with a Grade 6 class.  Have a great day!
Margie