Volume in unit cubes by decomposing shape Measurement and data 5th grade Khan Academy
Voiceover So these are two pictures of the same figure. This is a front view of the object, and this is the back view of the object. And if a unit cube looks like this, what I want to do is I want to figure out the volume of this figure in terms of unit cubes, or in terms of cubic units. I encourage you to pause the tutorial and think of it on your own before we try it together. All right, well, there's a bunch of ways that.
We could tackle this, all of them kind of breaking this figure up in different ways. One way we could do it, we could break it up into this. I guess we could call it a rectangular prism. So, if you could see through there, it would be like this, so this piece right over here, this piece right over here. And I'll redraw it here, so you can visualize it. So, if I were to redraw it, it looks like this. It looks like this. And what are its dimensions.
Well, its four units wide. It's two units high. And then it's four units, we could say long, or four units deep. So just like that. So what's the volume of this yellow part Well, the volume is just you multiply these three dimensions, the length times the width, times the height. So the volume is going to be our length times our width times our height. Four times four is 16 times two is 32. But we're not done. That's just the volume of this yellow part. We still have to take into consideration the volume.
Of this piece right over here that we haven't figured out yet, this piece right over there. Now, this one might just jump out at you. You could just count the unit cubes, but I'll redraw it here, just to show you what's going on. All right. So it looks like this. It looks like this. And what are its dimensions Well, it's two wide, two high, and we could say one deep or one long. So its volume is going to be equal to your length times your width times your height,.
Which is equal to four. And you just see that. There's one, two, three, four unit cubes in this object. So the total volume is going to be 32 plus 32 plus four is equal to 36. Now, of course, there's other ways to tackle it. You could just say, hey, let's figure out the volume of the blue layer and then just double it because that red layer has the same volume as the blue layer. And the blue layer, you could, say, well, look, it's only one deep. So we just have to count the cubes up here,.
And then we'll know how many unit cubes fit into it. So you literally could just count one, two. Let me do it a color you can actually see. You just have to go one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18. So you see there are 18 cubes in the blue layer, and there are going to be another 18 in the red layer, plus 18, that also gets you to 36 unit cubes, or a volume of 36 cubic units.
Volume through decomposition Measurement and data 5th grade Khan Academy
Voiceover Let's see if we can figure out the volume of this figure over here. They've given us some of the dimensions. We see this side over here is two centimeters, this is seven centimeters, this is 12 centimeters, this is five centimeters, this is three centimeters. And so like always, pause this tutorial and see if you can figure it out. Well there's a bunch of ways to do this, but the way I'd like to do it is just to break it up into two rectangular prisms. So what I'm gonna do is, in fact most.
Of the reasonable ways to do this would be to break it up into two rectangular prisms, and the ones that jump out at me is one prism like this that is three centimeters wide, five centimeters high, and then it is seven centimeters long, or seven centimeters deep. So this one right over here. And if this part right over here was transparent you would see it look just like this. You would see it look just like this. And so this one once again, it is three centimeters wide,.
Seven centimeters long. So this distance right over here is going to be the same as this distance right over here. So seven centimeters long. So the width times the length times the height is five centimeters. Gets us to, let's see. Three times seven is 21, times five is equal to, 20 times five is 100, one times five is five. So it's going to be 105. We can say 105 cubic centimeters, cause you have centimeters times centimeters times centimeters. So this blue part right over here, this blue rectangular prism,.
Has a volume of 105 cubic centimeters. So now we can separately figure out the volume of what I'm now highlighting in this magenta color. What I'm highlighting in this magenta color. If this was transparent, you would see this part back over here and right over here. So what are its dimensions Well, we know its height is two centimeters, we know that this dimension right over here, I guess you could say its depth, we could call it that, is seven centimeters. But what is this right over here.
If we want to consider this, maybe it's length, or maybe it's width, depending on what we want to call it. Well, let's see, this whole thing is 12 centimeters, from here to here is 12 centimeters, and we know that from here to here is three centimeters, so this piece right over here must be nine centimeters. So that must be nine centimeters, is this distance right over here. So the volume of this magenta part is going to be nine centimeters times seven centimers times the height, times two centimeters.
Which is going to get us, let's see, nine times seven is 63, 63 times two is equal to, 60 times two is 120, three times two is six, so it's 126 cubic centimeters. So the total volume of the entire thing is going to be the volume of the magenta stuff, which is 126 cubic centimeters, plus the volume of the blue stuff, plus 105 cubic centimeters. And that's going to give us, for the entire figure, six plus five is 11, so one plus two is three, that's really.
Multiplying fractions and whole numbers two approaches Fractions 5th grade Khan Academy
Let's think a little bit about what it means to multiply 23 times 6. One way to think about it is to literally take six 23 and add them together. This is six 23 right over here. And if we wanted to actually compute this, this would be equal to well, we're going to take these six 2's and add them together. So we could view it as 2 times 6 over 3. 2 times 6 over 3, which is the same thing, of course, as 2, 4, 6, 8, 10, 12, 123.
And what is 123 equal to Well, we could rewrite 12 as so this is equal to we could rewrite 12 as 3 plus 3 plus 3 plus 3 over the yellow 3. Let me do it like this so I don't have to keep switching colors. This is going to be the same thing as 33 plus 33 plus 33 plus 33. And each of these are obviously a whole. Each of these equal 1. That's 1 and that's 1, so this is going to be equal to 4. So that's one way to conceptualize 23 times 6.
Another way to think of it is as 23 of 6. So let's think about that. Let me draw a number line here. And I'm going to draw the number line up to 6. So what I care about is the section of the number line that goes to 6. So that looks pretty good. So this is 1, 2, 3, 4, 5, and 6. So if we want to take 23 of 6, we can think of this whole section of the number line between 0 and 6 as the whole.
And then we want to take 23 of that. So how do we do that Well, we divide it into thirds, to three equals sections. So that's one equal section, two equal sections, and three equal sections. And we want two of those thirds. So we want 13 and 23. Now where does that get us That gets us to 4. So we get, obviously, to the same answer. We would be in a tough situation if somehow we got two different answers. Either way, 23 times 6 or 6 times.
Unit conversion centimeters to meters Measurement and data 5th grade Khan Academy
Convert 37 centimeters to meters. Let me write this over. 37, and I'll write centi in a different color to emphasize the prefix. 37 centimeters, and we want to convert it to meters. So we really just have to remind ourselves what the prefix centi means. Centi literally means 1100th, or one hundredth of a meter. So this is really saying 37 hundredth meters, so let's write it that way. This is literally 37100 of a meter. So 1100 meters. These are equivalent statements. So what are 37100 of a meter.
Well, that's going to be 37100 of a meter, which can be rewritten as, if you wanted to write it as a decimal, that's 0. you could view it as 310 and 7100, or 37100. So 0.37, 0.37 meters. Another way that you could have thought about this is look, I'm going to go from centimeters to meters. I have 100. I need 100 centimeters to get to one meter, so I'm going to have to divide by 100 in order to figure out how many meters I have. And you should always do a reality check.
If I convert centimeters to meters, should I get a larger number or a smaller number Well, however many centimeters I have, I'm going to have a fewer number of meters. Meters is a larger unit. So you should have a smaller value here, and it should be a smaller value by a factor of 100. So you literally could have started off with 37 centimeters. Let me write it this way, 37 centimeters. And actually, let's go through a couple of the units right over here. Now, if you wanted to turn it to decimeters, so this is 1100.
Decimeters, one over 110. So you would divide. This would be 3.7 decimeters. Let me write this as 3.7 decimeters. And a decimeter is 110 of a meter, so you would divide by 10 again. So this is 0.37 meters. So one way to think about it is to go from centimeters to meters, you're going to divide by 100. Dividing by 100, you would move the decimal space over to the left two times. Doing it once divides by 10. Doing it twice divides by 100. So you get to 0.37 meters.
Coordinate plane graphing points word problem Geometry 5th grade Khan Academy
We're told that Naomi lives at 2nd Avenue and 3rd Street representing 2, 3 on the graph below. Her school is it 4th Avenue and 10th street, representing 4, 10 on the graph. She walks over to 4th Avenue and up to 10th Street. Plot her home and school on the map. How many blocks does Naomi walk to school So let's plot her home first, 2nd Avenue and 3rd Street, which they are giving us the coordinates 2, 3. So the xaxis right over here, this is representing the avenues.
And then the yaxis, or the vertical axis, this represents the street. So 2, 3. So this right over here is 2nd Avenue and 3rd Street. So you see here, we went to 2nd Avenue and then we went up to 3rd Street. This is where she lives at home. We could have also said 3rd Street and 2nd Avenue. Now her school is a 4th Avenue and 10th street. And now we're going to go, so if we start at the origin, we go to 4th Avenue and then go up 10 to 10th Street.
So this is the coordinate 4, 10. So this is where our home is. This is where a school is. They say she walks over to 4th Avenue and up to 10th Street. So she walks from 2nd Avenue to 4th Avenue and then up to 10th Street. How many blocks does Naomi walk to school Well as she walks from 2nd Avenue to 4th Avenue, she's going to walk 2 blocks. 1 block and 2 blocks. You shouldn't get confused by they're actually marking off with these lines every half a block.
Quadrilaterals classifying shapes Geometry 5th grade Khan Academy
A parallelogram is a blank with two sets of parallel lines. So let's see what the options are. So one option is a quadrilateral. And a parallelogram is definitely a quadrilateral. A quadrilateral is a foursided figure, and it is definitely a foursided figure. A parallelogram is not always a rhombus. A rhombus is a special case of a parallelogram where not only do you have to sets of parallel lines as your sides, two sets of parallel sides, but all of the sides are the same length in a rhombus.
And a square is a special case of a rhombus where all of the angles are 90 degrees. So here, all we can say is that a parallelogram is a quadrilateral. And so let's check our answer. And it's always a good idea to look at hints. And so it'll kind of say the same thing that we just said, but it would say it for the particular problem that you're actually looking at. Let's do a few more of these. Suzanne is on an expedition to save the universe. Sounds like a reasonable expedition to go on.
For her final challenge, she has to play a game called Find the Rhombuses. A wizard tells her that she has a square, a quadrilateral, and a parallelogram, and she must identify which of the shapes are also rhombuses. Which of these shapes should she pick to save the universe So a square is a special case of a rhombus. Just to remind ourselves, a rhombus, the opposite sides are parallel to each other. You have two sets of parallel sides. A square has two sets of parallel sides, and it has the extra condition that all of the angles.
Are right angles. So a square is definitely going to be a rhombus. Now, all rhombuses have four sides. So all rhombuses are quadrilaterals. But not all quadrilaterals are rhombuses. You could have a quadrilateral where none of the sides are parallel to each other. So we won't click this one. Once again, a parallelogram. So all rhombuses are parallelograms. They have two sets of parallel sides, two sets of parallel line segments representing their sides. But all parallelograms are not rhombuses. So I would say that if someone gives you square,.
Number patterns visualizing sequence relationships Algebric thinking 5th grade Khan Academy
Voiceover You are given the following starting numbers and rules for two sequences of numbers. The first sequence, Sequence x, starting number should be one, and then the rule is add one. Sequence y, starting number should be five, and then the rule should be add five. Fill in the table with the first three terms of x and y. Then plot the ordered pairs x,y on the graph below. So let's see, Sequence x. They say, the starting number, the starting number should be one. So the starting number is one,.
And then the rule, to get to the next number, you just add one. So, one plus one is two. Two plus one is three. Fairly straight forward. Now, let's look at Sequence y. They're saying the starting number should be five. Starting number five, and then the rule is, to get the next term, we just add five. So, five plus five is ten, ten plus five is fifteen. Now they want us to plot these things. Let's see, we plot them as ordered pairs, so we're going to have the point 1,5.
When x is one, y is five. We see that there, x is one, y is five. When x is two, y is ten. When x is two, y is ten, and then when x is three, y is fifteen. When x is three, y is fifteen, and wee see that. For every one we move to the right, for every one we increase in the horizontal direction, every one we increase in x, we increase five for y. We increase one for x, we increase five for y. So now we just have one last thing to answer.
The terms in Sequence y are blank, times the terms in Sequence x. So you immediately see, this term, five, is five times one. Ten is five times two. Fifteen is five times three, and it makes sense. You started five times higher, and here you added one each time, and we see that visually right over here, we add one each time, while here we add five times as much each time. We add five each time. The terms in Sequence y are five times the terms in Sequence x.
Subtracting decimals example 2 Arithmetic operations 5th grade Khan Academy
Let's try to calculate 10.1 minus 3.93. And I encourage you to pause this tutorial and try it on your own first, and then we can think about whether we did it the same way. So let's just rewrite it, aligning the decimal and the different place values. So 10.1 minus the 3 is in the ones place, so I'll put it right under the 0 3.93. Now, let's just try to calculate this. Now, before we subtract, we want all the numbers on top to be larger than the numbers on the bottom.
And we don't even have a number here. We could stick a 0 here. Let me do that in a different color here. We could stick a 0 here. 10.1 is the same thing as 10.10, but we still face an issue here. 0 is less than 3. 1 is less than 9. 0 is less than 3. So we're going to do a little bit of regrouping. So let's do that regrouping. So we could take a 10 away, one 10 away, and then one 10 is the same thing as 10 ones.
So I could write a 10 in the ones place. And I could take one of those ones away so I'm going to have nine ones, and give that one to the tenths place. Well, one is 10 tenths. 10 tenths plus 1 tenth is going to be 11 tenths. Now, I could take one of those tenths away and give it to the hundredths place. 1 tenth is 10 hundredths. And now I have a higher digit in the numerator, or at least as equal in the numerator as I have in the denominator.
A Pep Talk from Kid President to You
KID PRESIDENT I think we all need a pep talk. slow electric guitar riff music KID PRESIDENT The world needs to stop being boring. Yeah, you! Boring is easy, everybody can be boring. But you're gooder than that. Life is not a game people. Life isn't a cereal either. Well, it is a cereal. And if life is a game, aren't we all on the same team I mean really right I'm on your team, be on my team. This is life people, you've got air coming through your nose! You've got a heart beat! That means it's time to do somethin'!.
A poem. Two roads diverged in the woods. and I took the road less traveled. AND IT HURT MAN! Really bad. Rocks! Thorns! Glass! My pants broke! NOT COOL ROBERT FROST! But what if there really were two paths I want to be on the one that leads to awesome. It's like that dude Journey said, don't stop believing, unless your dream is stupid. Then you should get a better dream. I think that's how it goes. Get a better dream, then keep goin', and goin', and keep goin'. What if Michael Jordan had quit Well, he did quit. But he retired, yeah that's it,.
He retired. But before that In highschool What if he quit when he didn't make the team He would have never made Space Jam. And I love Space Jam. What will be your Space Jam What will you create when you make the world awesome Nothing if you keep sittin' there! This is why I'm talking to you today! This is your time. This is my time. This is our time. We can make everyday better for each other. If we're all on the same team, let's start acting like it. We've got work to do.
We can cry about it, or we can dance about it. You were made to be awesome. Let's get out there! I don't know everything, I'm just a kid, but I do know this It's everybodies duty to do good, and give the world a reason to dance. So get to it. You've just been pep talked. Create something that will make the world awesome. electric guitar riff Play ball! movie reel sound crashing noise Oh hi everybody! We're all workin' hard to make this an awesome year for other people, and you guys are doin' it!.
You've been super encouraging to me, so I want to return the favor. Who do you know that needs some encouragement Pass this pep talk along, and get the whole world to dance. I dedicate this tutorial today to my friend Gabbi. She's a cool kid, she likes pancakes, and she's fighting cancer. Like a BOSS. And to all you watching, who encourages you Send them this tutorial, and let them know. So get to it! music burst Bye! continue soulful music Harmonized Voice SoulPancake! Subscribe! Kid President Not cool Robert Frost!.
Coordinate plane graphing points Geometry 5th grade Khan Academy
We are asked to plot 8 comma 10. So the first number in this ordered pair, this is our xcoordinate. This tells us how far do we move in the x direction. It's a positive 8, so we move 8 in the x direction. And then the second number in our ordered pair is 10. That is our ycoordinate. That tells us how far we move in the y direction. Since it's positive, we move up 10. So we move up 10, all the way over here. And you could have thought about it either way.
You could have said, hey, look this is our ycoordinate. This is 10. So I could move up 10. And then my xcoordinate is positive 8. So I'll move 8 along the positive xaxis, or I'll move 8 to the right. You see right over here I have moved 8 to the right 1, 2, 3, 4, 5, 6, 7, 8. And I have moved 10 up 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. You might be tempted to move 8 up and then 10 to the right, which would put you there.
But then you would have had the two numbers mixed up. You would have had the x and the ycoordinates mixed up. The 8 tells you how far to move in the horizontal direction. The 10 tells you how far to move in the vertical direction. Let's do a couple more of these. Plot 6 comma 10. Well once again, the first number in the ordered pair is the xcoordinate, how far we move in the x direction. So we move 6 to the right. And then the second number, the 10,.
Tells us our vertical coordinate, our ycoordinate. So it's positive 10. So we move 10 up. Let's do one more 5 comma 7. So my horizontal coordinate is 5, so I move 5 to the right. And then my vertical one is 7, or my ycoordinate is 7. So I move 7 up 1, 2, 3, 4, 5, 6, 7. And as long as you remember which one is horizontal and which one is vertical or which one is the xcoordinate and which one is the y, you should be fine.
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