Grade 5 FREE PEP CLASS

追加: 2026-05-24

[00:00:11]Good afternoon.

[00:00:15]Yes, miss.

[00:00:22]So Good afternoon again everyone.

[00:00:29]We are joining in the Zoom class or on YouTube.

[00:00:35]Thank you for joining. Today we're going to be looking at mathematics.

[00:00:40]We're going to be looking specifically at a problem-solving strategy which is to draw a diagram to solve a problem. So in general, we're going to be looking at the problem-solving steps, the four steps involved in solving any math worded problem.

[00:01:02]And simultaneously or at the same time, we're going to be looking at the strategy of drawing a diagram to solve our problem. So I'm going to be sharing the notes that we're going to be looking at to the screen now and we're going to begin.

[00:01:23]Does everyone see what is on the screen?

[00:01:26]Yes, miss.

[00:01:28]Okay. Yes.

[00:01:33]So we're going to look at some smaller problems and then we're going to look at our main problem.

[00:01:41]So we're going to do an introduction to the main problem that we're going to look at later on, but we're going to solve some smaller problem leading up to this main problem.

[00:01:50]So let's look at the introduction, the tiled floor.

[00:01:55]On the last day with Uncle Larry, Travis worked with Mr. Wilson on laying tile on the kitchen floor. Travis worked hard all morning, and he was a bit discouraged when he reached his first break and realized that he had only finished about 1/3 of the floor.

[00:02:21]It had taken Travis 2 hours to tile 1/3 of the floor. He thought about this as he drank from his water bottle and ate an apple. "If it took me this long to tile 1/3, how long will it take me to finish?"

[00:02:39]Travis wondered. The floor is divided into 12 sections. If he has finished 1/3 of them, how many sections has he completed? This is the number that he completed in the 2 hours.

[00:02:55]How many sections does he have left to complete? And about how long will it take him to finish the rest?

[00:03:03]So, there are many strategies that you could use to help Travis to solve this problem, but drawing a diagram is probably the most useful.

[00:03:13]In this lesson, we will show how to effectively use a diagram to solve a problem.

[00:03:20]What will you learn?

[00:03:22]By the end of this lesson, you will be able to demonstrate the following skills.

[00:03:27]You're going to be able to read and understand given problem situations, develop and use the strategy draw a diagram, plan and complete alternative approaches to solve problems, and to solve real-world problems using selected strategies as a part of a plan.

[00:03:51]So, let's look at the first thing that going to be looking at, which is the read and understand given problem situation.

[00:03:59]So, we're going to be learning about fractions and mixed numbers and about how to add and subtract them.

[00:04:06]Many of the examples we're going to be looking at today will use pictures to help us to solve the problems.

[00:04:16]So, drawing a diagram or picture is a strategy to help you solve many different problems.

[00:04:27]The first thing that you have to do when approaching a problem is to read and understand the problem and solve it.

[00:04:38]So, let's look at one of the simpler problems that we spoke about.

[00:04:42]So, for this simple problem, it says, "John, I'm going to copy the link and share it in the chat."

[00:04:48]I'm also going to be sharing the link to the YouTube channel so that we can follow from the web page.

[00:05:01]Is everyone seeing the link in the chat?

[00:05:05]Yes, miss.

[00:05:07]Yes, miss.

[00:05:08]Great.

[00:05:15]I'm going to be sharing the link to the YouTube students shortly.

[00:05:21]All right. So, we're going to be looking at the first problem and we're going to be drawing a diagram to solve the problem. Get your notebooks, get your pencil, and your ruler, as this is an interactive session where you're going to be completing questions as well.

[00:05:39]All right?

[00:05:43]If you have crayons, you can also get those as well, so you can shade the portion of the fraction bar or diagram that you're drawing. So, let's look at the first example.

[00:05:59]John ate 1/5 of the cake. What fraction is left? So, we're going to be doing two things here. We're going to be first understanding what this problem is asking us to do. So, we're going to read it on our own and try to figure out what this problem is asking us to do. This might be a simpler problem and it doesn't require as much to understand, but for more challenging questions, you may have to read more than once for you to understand what it is asking you to do.

[00:06:27]All right?

[00:06:37]So, first we need we First, you can see what we that we have the amount of cake that John ate and we need to know how much is left, right? So, that's what the problem is asking us to do.

[00:06:58]So, now we're going to identify the keyword. What is the keyword in this problem? So, keywords are words that tells us what operation we should perform. What is the keyword in this problem that tells us what operation we're going to be perform performing?

[00:07:14]Does anyone want to answer?

[00:07:18]Yes, miss.

[00:07:20]Go ahead.

[00:07:22]The keyword is left. Left, very good.

[00:07:25]>> Left tells us that we're supposed to subtract. Very good.

[00:07:30]So, based on the keyword left, it tells us we're going to be subtracting.

[00:07:35]So, let's draw a diagram to show what we know about John's and his about John and his cake. So, we could draw a whole cake, but you can also draw a shape that resembles a cake, right?

[00:07:50]Which is a circle.

[00:07:54]Right? So, I want everyone to draw a circle. If not, you can just draw a fraction bar. Draw a circle and I want you to shade the portion that John has eaten and then we're going to look for what is left based on the diagram. So, we're using the diagram solely to solve the problem, okay? And that's what it means by drawing a diagram as a part of a plan to solve the problem, right? So, there are four steps in the problem-solving process. The first step is to understand what the problem is asking us to do, which we just did.

[00:08:30]The second step is to make a plan to solve the problem, and the plan that we're using or just simplifying a strategy, that's what a plan is.

[00:08:40]The plan or strategy that we're using today is to draw a diagram. We've also identified keywords, that's also another strategy.

[00:08:50]The second So, that's the second step in the problem-solving process. Now, the third step in the problem-solving process is to carry out the plan to solve the problem. So, when you're drawing your diagram now, that's carrying out the plan to solve the problem.

[00:09:09]So, draw your cake and shade the portion that John has eaten.

[00:09:18]Or draw a circle, and how many parts will the circle be cut into? Five.

[00:09:24]Five parts.

[00:09:28]Five.

[00:09:32]All right, great, because we see that the denominator is five, right? Is everyone seeing that?

[00:09:39]Yes, miss.

[00:09:48]So, now that we have a look at what we know and what we need to know, we can draw the diagram, right?

[00:10:00]So, we can draw a diagram of fraction bars to represent John's cake or we can draw a circle to represent John's cake, right? And shade the section that shows how much of the cake John has eaten.

[00:10:15]And the unshaded parts will represent the amount of the cake that is left, right? Does everyone follow?

[00:10:22]Yes, miss.

[00:10:57]All right then. Are we finished with the diagram?

[00:11:01]Yes, miss.

[00:11:04]Okay.

[00:11:08]Does it look something like what I have here?

[00:11:16]All right then. Are we finished with the diagram?

[00:11:32]So, even though this is our fraction bar, essentially, this is what your diagram should look like, right? So, you should have five parts, and one part is shaded because he ate 1/5 of the cake, right?

[00:11:47]Yes, miss. Five parts are shaded part should represent the amount of cake that is left, right?

[00:11:56]So, here we can see that John ate 1/5 of the cake. How many How much of the cake is left?

[00:12:07]4/5.

[00:12:09]4/5. So, we can see that there are 4/5 left. All right? So, the answer to the problem is 4/5. Are we seeing that?

[00:12:18]Yes, miss.

[00:12:19]Cuz I'm trying to share the link to the YouTube students.

[00:15:24]>> Mhm.

[00:17:19]>> Mhm.

[00:18:15]>> My electricity went, students.

[00:18:24]I was trying to connect back on YouTube.

[00:18:30]I think I have to connect connect.

[00:18:33]Okay, great.

[00:18:34]What is that?

[00:18:36]My electricity went, students.

[00:20:04]>> Okay, so I'm just getting everything set up. Okay.

[00:20:09]Are you seeing what is on the screen now?

[00:20:14]Is everyone seeing what is on the screen?

[00:20:18]Yes, miss. Yes, miss.

[00:20:21]Okay, great.

[00:20:26]All right, so everyone understood how we got to our answer there just now?

[00:20:31]Yes, miss.

[00:20:34]Okay, let's look at our next problem.

[00:20:38]So, sometimes we can set up a problem as an addition, and sometimes we can set it up as a subtraction. Often time, both work ways will work, but one will make more sense than the other. So, let's look at the example.

[00:20:53]Again, we're going to draw a diagram to solve this problem because that's the strategy that we're using today.

[00:21:00]So, let's read the example. Shannon jogged 1 and 3/20 miles yesterday.

[00:21:07]Today, she jogged 1/2 mile.

[00:21:10]How many total miles did Shannon jog?

[00:21:14]So, we're going to use two methods to solve the problem. We're going to draw the diagram, and we're going to also use the method that you probably are accustomed to, which just work which is just working out the fraction as is.

[00:21:27]And we're going to see which one is easier for us to solve the problem.

[00:21:34]So, the first way we're going to look at is to draw the diagram to solve the problem. So, let's look at the first distance that Shannon jogged.

[00:21:42]So, we can draw two same-size rectangles and divide one rectangle into 20 equal sections, and then shade 1 and 3 out of 20 of the diagram. So, the solid bar here would represent one whole. Are we seeing that?

[00:22:01]Copy it down.

[00:22:03]Yes, miss.

[00:22:04]And this little bar here with three out of the 20 parts would represent 3 over 20. Do we understand?

[00:22:16]Yes, miss.

[00:22:18]Okay, copy down the diagram.

[00:22:21]So, this rep diagram would represent the 1 and 3 over 20 miles Shannon jogged yesterday. All right?

[00:22:45]Let me know when you're finished copying down so I can continue.

[00:22:57]All the students that are joining on YouTube, I've shared the link for this webpage that we're using so you can follow from the web page.

[00:23:21]You can also copy down the problem as well. It is highlighted in yellow.

[00:23:37]Are we finished with the diagram?

[00:23:48]Miss, I'm not finished.

[00:23:51]Miss, I'm finished.

[00:23:53]You're finished, okay.

[00:23:54]All right, I'm going to leave it here still but we're going to start looking at for the persons who are finished, let's start thinking about the half mile action and jog today. How would we represent half mile? Can anyone say?

[00:24:09]I don't know how to say.

[00:24:14]How could we represent half mile?

[00:24:19]Miss.

[00:24:21]Go ahead.

[00:24:23]You could put two boxes and shade one.

[00:24:29]Okay.

[00:24:31]If you shade one, that's a whole, right?

[00:24:34]Think about half. So, if this is the whole mile, think about it or if the top diagram here, if all the parts were shaded because this is cut into 20 pieces, but because all of it is shaded, we don't have to necessarily cut it into 20 pieces. We can just draw a solid bar and just shade it, right?

[00:24:58]But think of it as being 20 pieces, but all of the parts are shaded, right?

[00:25:03]So, what fraction would represent half?

[00:25:08]That's what I'm asking.

[00:25:10]So, to be clearer, what fraction would represent half? What is an equivalent fraction to half?

[00:25:21]4/8 It can't be 4/8.

[00:25:24]>> 10/20 10/20, very good. What Can you explain why you said 10/20?

[00:25:36]Can you say why you said said 10/20?

[00:25:43]Because you would shade um 10 of um 10 on one side and 10 on the other side.

[00:25:53]Well, 10 out of the 20 pieces that we have here, right? Yes, miss.

[00:25:57]denominator is 20 then if we are to find a fraction which is equivalent to half, we have to find a fraction which is equivalent to half with 20 as the denominator, right?

[00:26:11]So, a half of 20 is 10. So, if we shade 10 of these parts, that would be a half.

[00:26:17]Do we follow?

[00:26:18]Yes, miss. Yes, miss.

[00:26:21]You could to represent the next half of a mile that Shannon jogged, you could draw a separate bar.

[00:26:30]You could draw a separate bar and shade 10 parts out of the 20 parts, or you could use this original diagram here.

[00:26:43]And because three parts are already shaded, you could just shade an additional 10 parts, and that would still give you the whole. Do we follow?

[00:26:51]Yes, miss.

[00:26:54]All right. So, with that being said, you can go ahead and share share that part now and tell me now how many total miles did Shannon jog?

[00:27:05]So, the keyword in this problem is what?

[00:27:14]What's the keyword in this problem?

[00:27:18]How many?

[00:27:20]And total.

[00:27:22]Total. What does total tell us we should do? Total tells us to add.

[00:27:28]Yes. So, what we're doing is adding on whatever miles that Shannon jogged yesterday, which is the 1 and 3/20, which we've already represented. Now, with the new diagram, which is what she jogged today, which is the 10/20, and I showed you two ways of how that could be done, right?

[00:28:08]All right.

[00:28:10]Anyone finished with that?

[00:28:13]Yes, miss.

[00:28:15]Okay. What's the total miles that Shannon jogged now?

[00:28:19]Shannon The total miles that Shannon jogged jogged jogged was is 1 and 13 over 12.

[00:28:32]13 over 20.

[00:28:38]All right?

[00:28:41]So, make the correction. So, we'll shade the half of the partially filled rectangle to represent the distance that Shannon jogged today. Are we seeing that?

[00:28:53]Yes. So here's the diagram now with the 10 shaded. So the diagram is 1 and 13 over 20 shaded. So Shannon jogged a total of 1 and 13 out of 12 20, sorry, miles on those two days. Are we seeing that?

[00:29:14]Yes, miss.

[00:29:20]Finish copying on the table.

[00:29:37]Let me know when you're finished with this part. Does everyone understand?

[00:29:42]Yes, miss.

[00:29:44]Great.

[00:29:53]So we're going to look at how we can set up an addition problem. So that's method two. And this is one the one that you're most accustomed to.

[00:30:02]But here's the thing. Let's talk a little bit more about drawing diagrams to solve the problem. So when you draw a diagram to solve the problem, this gives you a graphical representation of what is being done.

[00:30:15]It is very unlikely for you to make a mistake because you can see clearly where you're making the mistake and then you can make that correction to get the correct answer.

[00:30:27]All right?

[00:30:28]Whereas with working out like what we're going to do, especially if you're working out multiple things, it can get cumbersome and you may get lost in the working out.

[00:30:38]So we are learning different strategies that we can employ in order for us to solve our math worded problem than solely relying on working out.

[00:30:50]So, we're comparing these two things now, whether you're working it out as a addition problem or drawing the diagrams, and we can see which one would be better suited to utilize to help us to solve our problem.

[00:31:04]Are we finished with the diagrams now?

[00:31:07]Yes, miss. Yes, miss.

[00:31:10]All right, let's move on to method two.

[00:31:15]So, look at how this is even daunting. Some children do not know how to work with online frac- um unlike fraction. So, that alone will pose a challenge to them, right?

[00:31:29]So, to find out how many miles Ann and John altogether, we need to add 1 and 3/20 and 1/2.

[00:31:36]But, the fractional part is of mixed numbers, and it has a different denominator than a half. So, the first thing we have to do before we can do anything with the these unlike fraction is to find the least common multiple of both denominators.

[00:31:55]Now, the least common multiple of 20 and two is 20.

[00:32:06]So, next we can rename the problems. So, just like what we did before and found out that a half would be 10/20, we still have to do it for the working out problem.

[00:32:17]So, now we have a half to be 10/20, and now we can work to add them together because they're now like fractions. Is everyone following?

[00:32:27]Yes, miss.

[00:32:29]So, now we can add the two together.

[00:32:32]We'll just leave the whole number as is cuz there's no other whole number to add it to, so we just leave it as is and carry it over with the one here and then we'll add 3 + 10 gives us 13 and the 20 is the same, so we'll just put back the 20 as the denominator and we got the same 1 and 13 over 20.

[00:32:52]So, notice that our answer is the same for both methods.

[00:32:58]So, you can choose the method that you find easiest when working on problems like these in your examination, right?

[00:33:05]It's just to have an alternative to work with rather than just working it out, you can also draw diagrams, all right?

[00:33:15]Is everyone following?

[00:33:17]Yes, miss.

[00:33:19]All right, so let's look back at the original problem that we looked at the first place with Travis and the tiled floor.

[00:33:26]So, let's use a diagram to help Travis with tiling the floor. So, here's the problem once again.

[00:33:35]Can I have a reader?

[00:33:39]Me, miss.

[00:33:41]Yes, you may. Go ahead and read.

[00:33:47]On his last day with Uncle Larry, Travis worked with Mr. Wilson on laying tile on the kitchen floor.

[00:33:58]Travis worked hard all morning and he was a bit discouraged when he reached his first break and realized that he had only finished about 1/3 of the floor.

[00:34:13]It had taken Travis 2 hours to tile 1/3 of the floor.

[00:34:18]He thought about this as he drank from his water bottle and ate an apple.

[00:34:26]If it took me this long to tile 1/3, how How will it take me to finish? Oh boy, I I have a touch screen laptop and I just touched the screen to scroll down and it just went all the way down. I can see you.

[00:34:42]"How long will it take me to finish?"

[00:34:44]Travis wondered.

[00:34:46]The floor is divided into 12 sections.

[00:34:50]If he was finished on third of them, how many sections has he completed? This is the number that he completed in the 2 hours.

[00:35:01]How many section sections does he have left to complete?

[00:35:07]About how long will it take him to finish the rest?

[00:35:12]All right. So, first let's highlight all of the important information to help us read and understand the problem. Are we seeing the highlighted portion?

[00:35:24]Yes, miss.

[00:35:26]Okay.

[00:35:28]So, this will help us to understand the problem. So, we know from the highlighted section that Travis took 2 hours to tile 1/3 of the floor, right?

[00:35:40]Yes, miss. The problem also told us that the floor is divided into 12 sections.

[00:35:46]And we're asked if he had has finished 1/3 of them, how many sections does he have left to complete, right?

[00:35:55]How many sections has he completed? This is the number that he has completed in the 2 hours. But, also how many sections does he have left to complete and how how long it will take him to finish the rest. So, we asked three questions there. Those three questions we have to solve in order to solve the problem in its entirety.

[00:36:14]So, one, we need to find out if he has finished 1/3 of the sections, how many sections has he completed?

[00:36:23]How many sections does he have left to complete and how long it will take. Are we following?

[00:36:29]So, we've successfully understood what the problem is asking us.

[00:36:34]So, now let's figure out how much of the floor Travis has finished.

[00:36:38]First, let's find the equivalent fraction of 1/3 with the denominator 12.

[00:36:43]What would be the equivalent fraction of 1/3 with the denominator 12?

[00:36:49]4/12 4/12, very good.

[00:36:55]So, next we can draw a diagram for the finished part of the floor. Remember, there are 12 sections, so now we can draw four sections out of the 12 that are shaded. Are we seeing that?

[00:37:12]Yes, miss. Yes, miss.

[00:37:14]Quickly copy down.

[00:37:42]All right.

[00:37:44]My son is also in the class with me, so I'm giving him some instructions as well.

[00:37:50]All right.

[00:37:54]Are we finished with the diagram?

[00:37:58]Yes.

[00:37:59]>> Yes, miss.

[00:38:01]So, we can see the picture of what Travis has finished. Now, looking at the diagram, I'm telling you students, these diagrams are lovely, especially when we talk about fractional diagrams. You can just look at the problem. You don't need to work out anything. Just look at the problem and you can see how much he has left. Can we see that?

[00:38:21]Yes, miss. Yes. How much does he have left?

[00:38:27]8/12 8/12, very good cuz we can just count 1 2 3 4 5 6 7 8 and we know that there were 12 parts in total, very good.

[00:38:40]So, we can count the units and see that he has eight out of 12 of the floor left to tile.

[00:38:46]This is double what he did in 2 hours.

[00:38:49]Are we seeing that?

[00:38:51]Yes, miss. Yes, miss.

[00:38:54]So, let's look at the next part next question now. So, we found out one the 1/3 of the floor that he tiled, which is 4/12.

[00:39:06]We also know what he has left with his eight eight out of 12.

[00:39:14]So, now the final question is about how long will it take for him to complete the remainder of the floor.

[00:39:26]And I just gave a hint.

[00:39:33]Does anyone have the answer?

[00:39:39]Or you're still trying to figure it out?

[00:39:52]Miss, I think he he took 24 hours to complete to complete the floor.

[00:40:00]>> look at it. Look back at it. If I'm going to remind you of the key detail, he took 2 hours to do 4/12, right? And this is So, 8/12 would be double what he did in the 2 hours.

[00:40:15]Liam, you were saying something?

[00:40:20]Yes, miss. I was just going to say answer shoot him for he would take 4 hours to finish tiling the floor.

[00:40:29]Very good. So, Travis has about 4 hours of work left, right?

[00:40:36]So, Travis finish his his break and get back to work. If he continues working at the same pace, he will finish working around 2:00 p.m. just in time for some pizza for lunch.

[00:40:50]All right, I'm going to extend this problem. We finish with this problem and we've solved our problem successfully.

[00:40:55]We've not looked at the final step in the problem-solving process, which is to check our answer.

[00:41:02]So, the final step would be to check our answer. So, if we know add the 4 over 12 that Travis completed and then add the 8 out of 12 to the 4 over 12, we'll see that the 12 sections of the floor is finished, right? So, that's something we can do to check our answer.

[00:41:21]Simultaneously, when we did the alternative to work out the problem with Shannon, that could be a way of our checking the answer. So, if you draw the diagram and the answer you got Yeah. matches the answer if you worked it out, then that means your answer checked out because you used two separate ways and you got the same answer. Do we follow?

[00:41:46]Yes, miss.

[00:41:48]Great.

[00:41:52]I'm going to extend this problem. Let's see if our thinking skills are our thinking muscles are working, right?

[00:42:00]If it took Travis 2 hours to tile 4 over 12 of the floor and 4 hours to tile 8 out of 12 of the floor, how long did it take Travis to complete the entire floor?

[00:42:17]Less than a minute.

[00:42:28]How long did it take Travis to tile the entire floor?

[00:42:32]Miss, it took 8 hours for him to tile the floor.

[00:42:36]Not correct. Let's think again.

[00:42:41]6 hours?

[00:42:43]6 hours, very good. So, it took 2 hours to tile 4 over 12 and 4 hours to tile 8 over 12, so that's 6 hours in total.

[00:42:54]Now, this website has some practice questions where it says time to practice, so you can now go ahead and practice some of these questions and solve each of the following problems by drawing a diagram and show your answer and show your diagrams. All right?

[00:43:15]I'm going to leave my email address in the chat that when you're finished, you can take pictures of your diagrams and email them to me and I'll look at them and I can give you some feedback.

[00:43:28]So, my email address is shared in the chat.

[00:43:32]Are there any questions?

[00:43:37]No, miss.

[00:43:39]Okay. Have we understood all of what was taught today?

[00:43:44]Yes, miss. Yes.

[00:43:46]>> we will also be >> Yes, miss.

[00:43:50]using this problem-solving strategy that we've just learned in our classes at school to solve our math worded problems.

[00:44:01]So, I'll see you all next week for our next class.

[00:44:07]Until then, just continue to practice, continue to watch the videos on the website so that you can learn more, and I wish you all the best on your examinations come June 10. Just continue to practice. Practice, practice, practice until you're able to do amazingly well on your examinations. All right? So, until next time. Bye, everyone.

[00:44:32]Bye, miss. Bye, miss.

[00:44:44]Bye.

[00:44:46]Bye, miss.

[00:44:48]Bye. Bye.