Year 4 - Mathematics - Q2 2025

追加: 2026-05-15

[00:00:01]Okay, year fours, can you believe it?

[00:00:05]Term two, here we are. You guys have only about one term left of your final year of school. Well done. I'm so proud of you. You guys have really come a long way. So, let's see. This is your demarcation for the um exam of Friday 9th June.

[00:00:29]Um remember you are writing about term one as well as term two's work. It is quite a lot. You have to have to have to practice this. Don't just read through your book. Um you have to practice this.

[00:00:43]Okay. Then let's see if I start with activity one. The most important part on activity one is just to know um like I said here the classification of numbers.

[00:00:56]um you get the three counting numbers, natural numbers and integers and you have to know which symbols are which where do they start, where do they end.

[00:01:04]So it's basically this piece here is very important. You um so natural numbers start at one, counting numbers start at zero, integers start basically in the middle and they go to infinity on the sides. Um and know that what their symbols are. If you go to activity two in your book where you had to um match column A and column B, you don't have to worry about that. We're not going to do not going to ask you anything about that. If you go to the next activity, activity number two, so we've done one and two is place value.

[00:01:44]You have to be able to order the numbers um from big to small before we go on there. Uh you have to know uh what the value of each one is and what the the place value of each one is also. So for this one um the the value of the underlined one is 3,000. So I'm I'm not going to ask you it like this exactly.

[00:02:14]uh it might pop up in a tool files or um just giving you the multiple choice options of which one to choose. Then if we go to the second one here, you need to be able to order the numbers from big to small and small to big um which is here activity 2.6. So this is very important. Um remember when I do the number line, uh let me show you a number line here. Remember when I do the number line? If I go to this side of the number line, the numbers go bigger. If I go to this side, the numbers go smaller. Even though they look like they are big numbers with a minus in front, the numbers become smaller. So what I suggest you do when I give you something like this uh let's say for instance number C and I ask you to write them in ascending order or descending order in this case it's from small to big ascending order if you keep on forgetting which ones are the biggest write down a number line for yourself 0 1 2 3 4 5 and 0 -1 -2 -3 and then you will remember the numbers to this side go bigger. So if I look at -7 um I'm sorry they go smaller. So if I look at this one -7 in this case here is much smaller than 17 which is on this far side. So draw a number line on your paper quickly um just to make sure that you don't mix the two up.

[00:04:05]Then we go to addition and subtraction of um addition and subtraction of uh what is it there six-digit numbers with the user calculator. So this is basically to um make sure that you can do it accurately. Um do have a look at the word sums. Um go through them, practice them.

[00:04:36]And remember when you do a word sum, word sums have words. So you need to uh have words in your answer. This is this one. Then activity three, doubling and halfing and word sums with double and half. Okay, remember when I double it means I times by two. You don't have to do it the way we did it. So you can just take your calculator in the test and say okay 18 * 2 and that gives me 36. If you get that in a um word sum like we did in activity 3.3 remember you need to go um look for the keywords to tell you whether it's half or whether it's double. So go back through that um practice them again.

[00:05:30]Check out, watch out for the uh keywords. Um half obviously tells you that you have to divide by two. Um and means they plus it together. 50% off and buy one get one free. Those are both half sums. Um and then remember what we did with the cupcakes. On the one side we doubled and the one side we halfed.

[00:05:56]Remember that please. Then the next one is bodmas activity four on your demarcation order of operations. Bodmas remember um the order that you have to use them. You're not going to get this. You need to know what order um you have which one you have to do first and what order you have to use them. I'm not going to give you this. You have to know by heart but that you know by now. Um and then if you have a look at activity four the calculations that we did. Then activity five on your demarcation is LCM and HCF.

[00:06:43]You need to know what the abbreviations mean.

[00:06:47]Um so LCM means lowest common multiple.

[00:06:53]HCF is the highest common factor. You need to know this. And if you write the um the wrong words in the exam, I'm going to um penalize you because by this time now you need to know that it's multiple um and common multiple there.

[00:07:10]So multiples here mean you count in two fours or threes or whatever the case may be. So if I do the sum, I would ask you to get the LCM of four, five and 10 for instance.

[00:07:26]So you get the multiples of four, multiples of five, multiples of 10.

[00:07:31]Remember how we do that on our calculator again. If I do the multiples of four, I say 4 + 4 equals and then plus will change to answer and I go + 4 equal equal equal equal and it will give me the next one and the next one and the next one so that you don't waste time. Um, so practice this. If you don't practice this, you're not going to remember how to do it with a calculator. And this is a way to help you save time in a test.

[00:08:08]Okay. Um, so that is LCM. Remember, you get a you get a mark for each row of multiples if you have the multiples correct. And then you have to remember to write there the LCM is you cannot just highlight them and let me decide if that is because sometimes you get multiple LCMs. It's the lowest one, the first one that you get. So you do get a mark for that last part where you actually say the LCM is 20. If you go to the next part which is HCF highest common factor if you are going to write fractions there for me in the test and the exam I'm going to mark it wrong. You have to have the words right. Spelling doesn't count but there's a huge difference between a factor and a fraction. So make sure that you know it's the highest common factor not fraction. So here if I give you just go through the examples with you. So this is not the one where I can count in twos and count in. So 24 remember what I said to you where do I start? I always start with one. Okay. So starting with one remember 1 * 24. Then the next one I do is I say what about 2? So 24 / 2. If it gives me a complete answer without a comma, I know yes, I can do two. So 2 * 12 is the one that I'm using. Then the next one, 24 / 3. Yes, 3 can work. So 3 * 8 is what I'm going to write. Then I'm going to test four. So 24 / 4 that gives me 6. Yes. So that will work. 4 * 6. The next one that I'm trying is 5. So 24 / 5 is 4.8. So I know uh-uh this one is not going to work. So the next one is six. But I already have six. So the minute I repeat a number, I know I can stop. And then I do my little baky and I know 1 2 3 4 6 8 12 24. These are my all my factors of 24. If I do the next number again one I always start with one then try two three four five go through the whole row like I showed you now. And if I write them I highlight all the ones that are the same. But in this case I get the highest one. So the biggest one here is 12 and I have to because you get a mark for that. The highest common factor is 12. Okay. So that is on your learning paper or your demarcation that is LCM and highest common factor done.

[00:11:17]Then if we go to activity six, integers.

[00:11:20]Remember integers also called whole numbers. Those are where you get all the negative numbers. So this is sort of almost a repeat of what we did earlier. Um you can do that with your calculator.

[00:11:36]remember um if I so the first you can now uh um arrange them in order because you know that these one numbers on this side go smaller and the numbers on that side go to that side go bigger and if you look at the temperature it works exactly the same so these ones the temperature just go colder and colder and colder you have to uh I'm not going to ask you um bigger than smaller than but if you understand what Which one is bigger than the other one? Then there shouldn't be a problem. So this 6.6 6.6 is really important. You have to be able to do this. You can do it with a calculator. Let me quickly remind you.

[00:12:21]This one is straightforward because it's 4 + 9. So 4 + 9 straight forward. It gives you an answer of 13. Same. See here 15 - 9 8 - 9. If I get to where I have to change the number to a negative like -4 minus 5. So I must say 14 but can you see the number is not negative.

[00:12:45]I must tell the calculator to make that number negative. And that is where I go to this button here at the bottom. This one here. If I press that it will put a minus in front of it. So there now it reads -4 - 5 oh excuse - 5 equals and it gives you -9. So remember how to do that. So pause the video, rewind to have a look if you get stuck and you don't know how to do it.

[00:13:24]Then remember we practiced this one. Uh it's actually just a practice to get it done quickly. So this is a good exercise for you um to make sure that you can do it quickly and you do it accurately. So um you know hide the answers um and then you try them again with a calculator to see challenge yourself to see whether you can get them um correct or not. And don't be in too much of a hurry especially when you're writing exam.

[00:13:53]Make sure that you are typing in the correct things.

[00:13:57]Um, then if you turn around, if you turn over the page, activity seven, we go to square numbers and cube numbers. Okay, so square numbers start here. You have to be able to recognize a square number. Remember, how did I get the square number? I said 2 * 2 is the same as 2²ar 2 ^ of 2 and that is 4. So 4 9 16 these are the square numbers. Two is not a square number. Three is not a square number. Four is not a square number. The answer there is a square number because I can pack that in a square. Nine I can pack in a square.

[00:14:45]Three 1 2 3 and 1 2 3. Remember that's why they are called square numbers because they make a square. You have to be able to recognize them. Um I'm not going to ask it to you like this um like I did in the class test in the exam. I can ask it in a multiplechoice question to say the which of the following numbers is a square number and I can list any of these numbers A B C D and let's say number D is 144. And then you need to know that 144 is a square number. The what goes hand in hand with that is cube numbers. Remember cube numbers is when I say 2 * 2 * 2 2 to the^ of 3 is 8. Um 4 to the^ of 3 means 4 * 4 * 4 and that's 64. Remember these are the cube numbers.

[00:15:48]Again, you have to be able to recognize them. If I give it to you in a multiplechoice question, then at the end of each of these activities, you will notice um activity 8.4 and also activity 7.5 is where you have calculations. So you have to be able to do it on a calculator. Show me your calculations.

[00:16:19]So 7 to the power of two. How do I do that on my calculator? Again, I say 7 to the^ of 2. You will see it shows on your screen and then equals 45. So I need to write 45 + 3 to the^ of 2 = 9 and 45 + 9 is 54. Please make sure how I ask the question. If I ask you to show the calculations which I do, you have to show me that and that and the answer. If you show only the answer, you will lose marks. So remember, I know that you can do it on your calculator easily and say um what is 49?

[00:17:17]49 + 9.

[00:17:20]Oops. Uh, 49 + 9 is 58.

[00:17:26]Apologies. 58. So, remember if if I do it in one step. Yes, I can. A lot of you do.

[00:17:37]7² + 3² is = 58. I would have then realized that I made a mistake there. So yes, do it in one step, but when you do it on the paper, you have to show me um all your steps for the extra marks. The same goes for cube numbers. If I do this one here, how do I do a cube number again on my calculator?

[00:18:05]So 7 square I just showed you 7 squared and it gives me 49. Okay. Uh plus 3² is 3 to the^ of 3.

[00:18:20]3 cub. So 3 remember there is my cube number the orange part. So for me to go to the orange part I need to tell my calculator I want to go to the orange part. So the second function and to the power oh no that's it there's a no I'm completely wrong oh my goodness guys but if I stop the video now I have to start again so let's let's start again if I do the to the power of three I just use that number there so 3 to the^ of 3 = 27 okay and then you write plus the 27 7 and 49 plus the 27 will give you then your answer.

[00:19:07]So if I go to the next step which is square roots and cube roots it is just the opposite. Remember if I reverse I said 5 * 5 5 * 5 is 5 to the^ of 2 is 25. Now I go backwards and I say okay so that square root is eating up that two so my answer will be five. How do I do that? Listen to what you are saying to know what you have to type in first. If I for instance do this activity 9.3 the square root of 49. So listen to what I'm saying first.

[00:19:54]square<unk> of 49 = 7 square root of uh what is the next one 64 = 8 so what the words that I'm saying first these are the things that I put in first the square root of 25 = 5 the same goes for cube root. If I go to cube root, this is what I wanted to show you earlier. So cube root is that orange part there. So in order for me to get to that orange part, I need to show the calculator. I want to go to the orange part, the cube root, and read what is written on your screen, face. So there I put in 64. If I want to do number G for instance equals 4. If I have a multiple one like I do with number K where I have them mixed, I say the square root of 81.

[00:21:10]Square root of 81 of 81 is 9. Then the uh cube root second function cube root of 125 is 5.

[00:21:27]So 9 + 5 9 + 5 9 + 5 it will give me 14.

[00:21:36]So please remember how to use that because this is very easy and if you don't practice it at home you will not remember how to do it and then you are throwing away easy marks. Okay then we get to fractions. So fractions remember we get the three. I'm not going to ask you which is a proper fraction which is a mixed number and whatever the case may be. Um, you know by now that an improper fraction is the top one is bigger than the smaller one. The bottom one and the mixed numbers have a whole number as well as a um proper fraction. I'm not going to ask you any of the wording or definitions on this. So what do you have to do? Remember we did the summary.

[00:22:31]Okay, the summary of the fractions. I can plus and minus two ways when it comes to fractions. The first one is when the denominators denominators are the same.

[00:22:48]So if I have three at the bottom, three at the bottom as a denominator, then I know yes, I can add them together. Then if the denominators are different, I plus or a minus is where I do butterfly.

[00:23:03]4 * 1 is 4. 3 * 3 is 9. What do I have to do? I have to plus them. So 4 + 9 is 13. 3 + 4 is 12. And that's my fraction.

[00:23:20]If I want to, I can change that into a mixed number but you don't have to. If it if it makes you ti macar then you can just leave it like that. That's enough marks.

[00:23:35]Then the other way of doing plus and minus is when I have mixed numbers. So in the same way I have two types. I have one where the denominators are the same. Oh yeah denominators are the same. That means I can just add everything. So if I add the whole numbers in front, 2 + 3 is 5. I keep my fraction. 1 + 2 is 3. So these are the easiest ones. When the denominators are the same, when the denominators are different, I first work with this. 5 - 2 is 3. And then I take the fractions and I butterfly. 4 * 1 is 4. 2 * 1 is 2. In this case, I'm minus 4 - 2 is 2. So there's my 3 already. 4 - 2 is 2. And then 2 * 4 is 8. So I have 2 over 8. You can stop there. Or if you know how to simplify this to say that it's 3 and 1/4ide by two top, divide by two at the bottom. But if you understand how to get there, that's more than enough. So that's plus and minus. Then I get times and division. Times and division go hand in hand. But you need to know when I times I cannot work with a mixed number.

[00:25:08]I have to change them to improper fractions. So how do I do that? Okay, let's first look at if I have normal in uh proper fractions 2 over 3 * 4 over 5. This is not the butterfly. This is straightforward. 2 * 4 is 8. 3 * 5 is 15. And that's my answer. If they are, because most of you did this wrong in the in the class test, I cannot times 2 * 1. I need to change them to improper fractions first. 2 * 2 is 4 plus that 1 is 5 and my fraction is two. 4 * 1 is 4 plus that 3 is 7 and that's my fraction. Then I go back to that step. Times at the top times at the bottom. 5 * 7 is 35. 2 * 4 is 8. I can turn that into a mixed number if I want to to simplify it. But if you get to that, that's where you will get your marks. Then when I go to division, remember I cannot do division in mathematics. So there's a trick. I need to switch and flip. So the first thing I need to switch out that division for the times and then I need to flip only that number. Some of you flip this number in the test also. you you leave this number the same. Can you see 2 over three? The division changes into a times and this number is flipped. So instead of the four being at the bottom, the four goes to the top and the one goes to the bottom. Now I have a straightforward time sum like I had in the beginning. 2 * 4 is 8. 3 * 1 is 3. Again, you can write it as a mixed number, but you can stop there. That's perfectly fine. So please guys make sure this is very easy.

[00:27:11]If you do not practice it then you will not remember that I only have to switch and flip. It's actually very easy. Okay.

[00:27:20]So that is fraction. So work through all the activities we did in fractions. Um you can also work through the assessment 2.1. Um I wrote it here at number 11 on your work through that assessment 2.1 that we did. Um practice that please. Then the next part is when we go now to activity two financial mathematics. So, we've covered um square roots, cube roots, uh we've covered uh let me see here. We've got covered fractions. And now we get to uh oh, the last bit of fractions here is how to change mixed numbers into improper fractions and improper fractions to mixed numbers. So, let me quickly just remind you this is where we are.

[00:28:19]It was activity 1.3. So activity 1.3 + 1.4 change the mixed numbers into improper fractions. So remember 2 and 1/5. If I change that I say 2 * 5 * 2 is 10 plus that 1 is 11 and my fraction is 5. Okay. Then when I go to the other part which was how do I turn them back if I have um activity 1.5 activity 1.5 if I have an improper fraction I need to see that line there means divided by So if I have to do it, I say 16 / 5. It will give me a comma something.

[00:29:27]But I'm interested in that whole number in front. So then I say 5 * 3 is 15 and I have to minus 16 - 5 is 1 and my fraction is five. So please go back to that also. You're going to have to be able to do that as well.

[00:29:48]Then we can go to activity two from term two which is financial mathematics. If I go to financial mathematics this part where you have to do the terminology that is really really important. This um you have to know income expenses what's the difference. Um, I'm not going to ask you to write down a whole meaning of everything, but I will give it to you in a true, false, or a multiplechoice or whatever. Understand what these terms mean. Um, because if you don't understand what the terms mean, you're also not going to understand what I'm asking you. For instance, I'm definitely going to ask you if you look at the So, there's the terminology. First of all, you have to be able to set up a budget. So again I'm going to give it to you like this.

[00:30:45]Remember you need to find the keywords in here to see which of these ones are um seen as income and which of these are seen as expenses expenses. So these ones I give you all the expenses but in here you need to know that your income is what your bank balance is in the beginning of the month and that investment where you get interest is that's also seen as an income. So when you draw up your budget, you need to know which ones are green and which ones are red. So you are welcome to use green and red in your test as well because it will help you um to remember. So opening balance is the one and I'm not going to give that word to you in the test. You need to be able to write yourself.

[00:31:31]Opening balance is 55. The interest that I've earned is 2,000.

[00:31:37]there there aren't any other amounts for income. So then I add this um and I get 57500 and then if I go to these are all my expenses and these are all the ones that I have to. So as you can see I was lazy here and I didn't write all of them. You must write all of them.

[00:32:00]Remember when you add these up go to your original numbers here so that you don't add them up incorrectly because you copied them incorrectly for instance I cannot give you a mark on this side if it is wrong if you copied the the the amount incorrectly but if you add them up here you will not make mistakes so if you get that total here of 67600 for instance you will know that I've I I've calculated the correct total. So even if you have some of these wrong here, you will have the correct total. So add them up from here. These are all your expenses. So part of my budget is also to determine whether um this company of mine or this business of mine, am I running at a loss or am I making a profit or a surplus? That's why you need to know what surplus means. So sur income minus expenses is how you calculate whether you have it's always income minus expenses. If your answer is a plus that means you made a profit because your income is less than your is more than your expenses. If it's the other way around like in this case my income was a smaller am smaller amount.

[00:33:25]So then my answer will be a minus which means I'm going to put in a loss. I don't have enough money in my bank and I need to relook my expenses otherwise I'm going to end up with a loss. Okay. So question number three was just again you need to know uh a surplus. What is a surplus? What is a deficit? Then question number four um I might ask you this also. I gave you five five examples here of how to use the surplus in your business. You can choose any two of them. Um so go through this as well please. Then remember you need to know the difference between fixed expenses and variable expenses.

[00:34:10]Fixed expenses are expenses that stay the same every month. So, your rent, your vehicle payment, insurance, if you have a telephone contract, salaries, they are the same every single month and the same amount is going to be deducted.

[00:34:24]Um, if I look at variable expenses, those are things that can change.

[00:34:29]They're not the same every month because I'm not using the same amount of water and electricity every month. I'm not buying the same stationery every month.

[00:34:38]I don't need a stapler every month. I'm not going to buy one every month. and like 12 months later you ending up with 12 staplers to do what? So you're saving money and these are the ones that you can change should you um see that you're running into a loss like we are doing currently. So things like water, electricity, products for manufacturing, marketing, advertising, stationary, fuel, these are variable expenses that can change and then I just ask you here to get the totals of each two. So how do I calculate? You don't have to do number eight for the test. How do I calculate um again with whe where whether I've made a profit or a loss? I say income minus my expenses. If it's a minus, it is a loss. If it's a positive number, I know that I've made a profit. Then I go to question number nine, which is more to goods. So that Mr. And of course he in his business I he's making shopping bags and he's selling them. So I have to determine calculate if he's making a profit or a loss. So this one counts two marks. You have to first calculate the number and then you have to say to me whether it's a profit or a loss. So how do I calculate this? And by the way I'm giving you these um these formula. I'm giving you this in the test so you don't have to know this by heart. I'm giving it to you at the end in one page and then you can just rip off the page and decide which one is which. So how do I do this selling price minus the cost price? So the selling price is $8.90 minus the cost price is 400. So that gives me an amount of 490 because it is a positive amount. I know that I'm I'm making a profit of 490. If I have to calculate the percentage of profit, just follow the formula. Profit divided by the selling price. So, what was my profit? 490 divided by the selling price. The selling price is $8.90* 100 and I get 55.05 something something something. Let me just do that sum for you so that you can see. So it's 490 divided by 890 * 100 = 55.05617978. I cannot write all of these numbers. I have to round them off. And in the beginning of the paper I tell you that you need to write round them off um up to two decimal places. Okay. So that means my answer I only want last the last two digits. So if I look at this five next to it is a six that six is more than five. It's going to make that one a six. And then that's why my answer is there 55.06 and not 55.05%.

[00:37:52]55.06%. So remember that you have to be able to do that. Then the next one um in your uh book is value added tax. Um we are not doing value added tax in this um coming exam because we need to practice some of these sums more. It was very hectic the it's been very hectic the last couple of weeks. So I'm not going to ask you this in the exam now but this is definitely you are going to get this in the GC paper. The next one is the pay slip. You have to be able to read a pay slip and get certain information from that. So if I look at number A, the total earnings, remember earnings here, these are the ones that you the extra money. This is your salary and this is the extra money that you get paid. This these are your deductions.

[00:38:48]All the things that get deducted or minused from your account.

[00:38:55]So, my gross pay is all of these added together. I get that amount there.

[00:39:05]Uh, I don't know why I didn't write it in here. We will do I will give you a memo of this as well. So, if you add them up, you get the total amount there.

[00:39:18]If you add these up, you get the total amount here. How do I calculate my net pay? My net salary, it is the earnings minus the deductions. And that amount is the amount that's going to get paid into your account. So, let's do this quickly just so that you know what's going on.

[00:39:37]So, 18850 + 900 + 1,500 = 2150. So that is 2150 is my total earnings.

[00:39:55]21250. If I look at my deductions, 1835 + 1850 plus 2125 + 50.

[00:40:14]That gives me 5860 5860. That's my total deductions. So to calculate my net pay, I say 21250 - 5860 and I get 15 390. That's my net salary. 15 390. So this amount is what is being paid into my bank account. So even though it looks fantastic that I'm earning 18,000 rand, in fact when I minus all the deductions, I'm only getting paid 15,390 into my bank account. So then when does she get paid? You can read the date. And then who's receiving income tax?

[00:41:10]um SARS or you can also say there the government is getting that money and then what is the abbreviation UIF stand for? What is it? Why are we paying that?

[00:41:23]Go to your um definitions. You need to know um what to do or you need to understand that what um is UIF is.

[00:41:39]So here's UIF is unemployment insurance fund and it's a deduction from your salary that helps workers if they lose their job.

[00:41:47]Remember I said you it's also when you um are on maternity leave and things like that. So have a look at that one.

[00:41:55]You have to know what UI is. And that is that. So I hope you study hard for the for the exam. Please don't just read through it the night before. You have to practice it. And please don't go jawing over the weekend because you know that you're writing on a Monday. So you have to at least um practice that over the weekend. You will not be able to do it just in one night. Please guys um time is running out. The year is almost over and all of these marks count um towards the end of the year report. So enjoy. I will see you when you get your report card.