# Telling Time Part 4: Elapsed time (continued)

by C. Elkins, OK Math and Reading Lady

In my last post, I shared my favorite model for elapsed time (Mountains, Hills, and Rocks) using an open number line. In this post I will share another version of the # line some of you might like — I’ll list the pros and cons of it as well as show the std. algorithm / convert version.

I hope all of you are doing well. I realize many of you are involved in distance learning with your students – and this may be in addition to taking care of your own children’s needs at home. So I understand my blog might not be on your top list of priorities, but I do hope you will bookmark it and keep it for future reference.  But again, if you are home with kid, then dealing with elapsed time is a perfect real-life math situation they can apply on a daily basis.

The Z Model:

The Z model is a straight number line “bent” into 3 parts of the Z:

• 1st “leg”:  From start time to next full hour – determine how many minutes
• 2nd “leg”: From hour to hour – determine how many whole hours
• 3rd “leg”: From last hour to end time – determine how many minutes

Here is an example to see the steps involved:

Here’s another in one single view to determine elapsed time between 7:50 and 1:10:

Pros:

1. It helps break time down into smaller chunks.
2. It’s a visual model which can help a child mentally process the elapsed time in these chunks.

Cons:

1. Students would more likely have to know automatically how much time has elapsed on the first “leg” of the Z. In other words, can they mentally figure that the time from 8:25 to 9:00 (the nearest hour) is 35 minutes?  Or the elapsed time from 3:47 to 4:00 is 13 minutes?
2. In my opinion, this model is mostly just helpful when start and end times are given and the task is to compute the total elapsed time. It would not be very helpful if the task was to determine the start or end time.
3. If a child can figure the minutes of elapsed time of the first “leg” of the Z, they might not need the visual model to solve.

The Std. Algorithm / Converting Model

This model resembles a std. algorithm problem because time is aligned vertically and added or subtracted.

• When adding, any minutes which total 60 or over would be converted to hours.
• When subtracting, exchange 1 hour for 60 minutes.

Here is an example to see the progression from start to finish when start time and elapsed time are the known parts:

Here’s another example in one view:

Contextual scenario: At 2:45 I went to the zoo. We stayed there 3 hours and 25 minutes. What time did I leave the zoo?

Here’s an example that involves a known end time and elapsed time. The problem is to determine the start time which involves subtracting time:

And another problem in one view:

Before I got ready for bed at 9:20 p.m., I spent 2 hours and 35 minutes doing homework. What time did I start my homework?

Pros:

1. Students who are ready for more abstract strategies might enjoy this model.
2. This model is more useful when solving problems in which the task is to find the end time or start time.
3. This can be utilized with hours, minutes, and seconds problems.

Cons:

1. Having strong knowledge of number combinations that equal 60 is needed.
2. There may be two or three steps involved to arrive the final answer.
3. The regrouping in the subtraction version may involve two types which could be confusing: minutes vs. base 10 (as shown in picture directly above)
4. Understanding what converting time means and why we subtract and add within the same problem (subtract 60 minutes, but add 1 hour).

I miss seeing my friends in person!  Let me know how you are coping during these crazy times!

# Telling Time Part 3: Elapsed Time – Start and end time known

by C. Elkins, OK Math and Reading Lady

Wow! What a difference a couple of weeks makes.  My last post (Time Part 2) was 2 weeks ago, and life was pretty normal here then. Maybe you are using your extended time off to just try to calm down, maybe you are catching up on home chores or your favorite Netflix series, or maybe you are digging out some favorite recipes. Just in case you are using this time to help your own children with learning objectives or catching up on some PD for yourself, I am here to help any way I can. Remember in the black bar above you can access my learning aids without reading all of the articles to find them. Or type what you are looking for in the search box. Or look at the categories list to pull up by topic.

Today’s post will focus on concepts related to elapsed time.

As I mentioned in Telling Time Parts 1 and 2, it is important for students to have a concept of time. How long is a second, a minute, an hour? What tasks can be accomplished in those amounts of time. These are foundational concepts students need to better understand elapsed time. Are you making notes of time during the school day (or at home now) to make it relevant?  Questions or statements such as these are helpful:

• “We have 10 minutes to finish attendance and lunch count. Look at the clock so you can keep track.”
• “Lunch will be ready at 12:00 noon.  Look at the clock. It’s 11:30 now, so lunch will be ready in 30 minutes.”
• “It’s time to get ready to go home. Look at the clock. What time is it?  You should be ready in 5 minutes. What time will be it then? What will the clock look like?”
• To help speed up time for transitions and work on a class management goal at the same time, try this for a procedure such as lining up: “Boys and girls, it’s time to line up to go to PE.” As students line up, you as the teacher will silently keep track of how much time it takes students to get ready. When they are ready, say someting like:  “It took you 3 minutes 20 seconds to get ready. We miss learning time when it takes this long.  Let’s see if we can beat that next time.”   Most kids respond well to this mini challenge.  If it’s a real contentious issue in your class, this can be followed with an easy reward such as: “It took 3 min. 20 seconds to line up and get ready. That is too long. Next time we line up if you can get ready in less than that time, I will keep track by building the word G-A-M-E.  You earn a letter each time you beat the previous time to line up.  The time starts when I say line up and the time stops when everyone is facing the front, quiet, and hands to themselves. You must walk to do this.”  Building a short word helps students earn a reward in a short amount of time so they are more likely to strive to meet the goal. It is easy to implement and can easily be incorporated into a reading or math game.  The word to build could also be F-U-N.  Then it’s wide open to what that could be:  A video, talk time, drawing time, a few minutes extra recess.  Yes, this takes time also – but it helps students work together toward a common goal, and may save your sanity.  This “time” technique can also be applied to other procedures such as getting out materials, staying quiet, etc.  One hint:  Don’t do a countdown or let students know how much time they are taking as you are keeping track.  If you announce, “We are at 2 minutes . . . you might make it.” this gives students knowledge they have time to waste.” We are trying to build an awareness of time along with a sense of urgency and teamwork. So wait until they are all ready to announce the time it took.

Okay, a little off topic – but showing how there are many ways to help students become more aware of time in their daily lives.

As in most story problems related to time, there are 3 components.  The story gives 2 of them, and the problem is to find the missing one:

1. Start time
2. Elapsed time – the time it takes for something to be finished
3. End time

There are several common strategies, some which are more pictorial and some which are more abstract.  Of course, I am in favor of those which provide some visual representation at first such as an open number line or a Z-chart. I will feature the number line model today.  More abstract models are the T-chart and lining up times vertically like you would doing a standard algorithm and adding / converting times. I’ll focus on those in future posts.

Number line:  There are a few versions of time number lines out there which help students move from start time to end time. Some already have time increments noted on the line, some use jumps that all look the same.  I happen to love the “Mountains, Hills, and Rocks” look because it helps immediately to differentiate between the hours and minutes and doesn’t require any advance preparation as with pre-marked number lines. The mountains represent hours, the hills increments of minutes, and rocks are individual minutes.  I will share 3 types of elapsed time problems, but just elapsed time unknown in this post:

• elapsed time unknown
• end time unknown, and
• start time unknown

Elapsed time unknown: This features stories in which the start and end time are given.  So students must find the elapsed time. Bobbi went to the movie theater at 7:15 p.m.  It ended at 9:45 p.m.  How long did the movie last?

• Put the known parts on the number line and label  (start at 7:00 / end at 9:45).
• Underline the hour part of the number.  Can we add an hour to the 7? Yes.  What time would it be then? 8:15.  Now here is how we show an hour (with a mountain). Can we add another hour? Yes. What time would it be then? 9:15. Add another mountain and keep track of the time under the line.  Can we add another hour? No. Why not? It would be 10:15 which is past the end time.
• Now we will switch to minutes (called the hills).  The hills are used to show increments of 5, 10, 15, 20, 30, etc. Since we all write different sizes, etc., I continuously tell students this:  “It’s the number we write inside of the hill that matters more than the size or length of the hill.”  This is because sometimes due to space limitations, my 5 min. hill looks the same length as my 10 minute hill.
• Underline the minutes part of the number 9:15.  Now let’s add minutes until we get to 9:45.  This can be done several ways depending on students’ understanding.  I might make hills of 5 minutes each.  In this problem, I might make hills of 15 minutes each.  I might want to add 5 minutes in one jump to get my minutes to a number ending in 0. Some students would realize that 30 minutes would connect us from 9:15 to 9:45.  When teaching and modeling, we all do the same way. Then when they seem comfortable, we look at different ways to show the same problem.  This provides a safety net for some, while a challenge for those who enjoy it. For this example, I would say: “Let’s get our 9:15 to an easier time to work with . I’m going to just add 5 minutes. Looking just at the minutes part of the number, what is 15 + 5??” Yes, 20. So what time would it be now? Yes, 9:20. Our number now ends in a zero, which we can add to mentally. Let’s add 10 min. to that. What is 20 + 10? Yes, 30. So what time is it now? Yes, 9:30. Let’s add another 10 minutes. Can we do that? Yes, because 30 + 10 is 40 and 9:40 is before 9:45. Now how much time is there between 9:40 and our end time of 9:45? Yes, just 5 minutes. So that will connect us to the end time of the movie at 9:45, and we are almost done!
• The last step is to look at the numbers we wrote inside our mountains and hills and combine them. You will see Bobbi was at the movie theater for 2 hours (2 mountains) and 30 minutes (5 + 10 + 10 + 5) = 2 hours, 30 minutes.

Stay tuned for more examples of elapsed time problems through the next few posts. Future posts will provide some freebie story problem practice and good resources you might like.              And stay safe and well!!!

# Telling Time Part 1: Basic concepts

by C. Elkins, OK Math and Reading Lady

Concepts of time are one of the subjects we teach at school, but often has more application at home:  Time for bed, time to eat, time to clean up your room, time to play, and so on. I have found when working with students in 3rd and 4th grades about elapsed time, that they often don’t have a very good concept of time. It’s no wonder. We (as teachers or parents) say, “You have 1 minute to . . .” or “I’ll be there in a minute!”  But in reality that minute has stretched to much more like 5 or 10.

So what can we do to help with concepts of time at school (or home)?

• Post a copy of the daily schedule. Refer to it often.
• Use a timer for certain tasks.
• If you announce a time, stick to it.

Try these activities with students. The ones you use will depend on the grade level. Click here for a FREE copy of the brainstorming recording sheets (pictured below): What can you do in 1 sec., min., hour

1. “Tick-tock” — It takes about 1 second to say this word.  Brainstorm what things can be done in this amount of time. Try some of them out (clap, blink, snap, swallow, etc.). It’s effective and engaging to have students brainstorm first with a partner before sharing with the whole class.
2. Watch an analog clock for 1 minute:  Observe the second hand going around 1 complete time. It feels like a long time has passed when actually watching it. Brainstorm things that can typically be completed in one minute (brush teeth, put on socks and shoes, drink some water, etc.)
3. You may want to discuss other chunks of time (especially 5 minutes or 15 minutes since we eventually want students to be able to read a clock in these increments). 5 minutes — eat a snack, get dressed, walk across the school.  15 minutes — walk to school, finish a worksheet, eat a sandwich.
4. Brainstorm events that take about 30 minutes (eat lunch, watch a sit-com, take a bath) and an hour (basketball practice, chores, shopping, math period).
5. Incorporate writing and drawing to name a start time and an end time with a label or a couple of sentences about the activity (see attached). Even 1st and 2nd graders can begin to think about this amount of elapsed time.

Once students have a better understanding of how long something takes to finish, then students will have a better grasp of telling time and determining reasonableness of elapsed time problems. Plus it may enable them to become better judges of their own time with regards to home chores and school assignments and events.

Enjoy your week! Time Part 2 coming next.