Lesson video

Hello and welcome to this lesson on upper and lower bound with me Miss Bramley.

You'll be needing your paper and a pen, or something to write on.

And with, as usual for this lesson, I also ask that you minimise distractions and put away anything that could distract you.

And let's get ready to start the lesson.

So pause this video should you need to do need to go and get your equipment and press play when you are ready.

In this lesson, you'll be able to find the upper bound and lower bound for a value that has been rounded.

And you are going to be learning two key words before we proceed with the lesson.

The first one is upper bound.

If you have to guess what you think upper bound might mean, what you, what might you say? Yeah, it has to do with something greater than, because something that's upper is greater than.

It's a value that is greater than or equal to every number in a set of data.

And I will explain what that means later on.

But upper bound just means a value that is greater.

If upper bound means a value that is greater, what do you think lower bound would mean? If you said a value that is less than or equal to, then yes, you're correct.

So lower bound will be a number that is less than or equal to every other number in that data set.

Okay, you will try this task.

It is to complete the fill in the blank.

So you've got some options on the bottom here, that you're meant to use to fill in this empty box, this empty box and this empty box.

So pause the video now and try this task.

And once you're done, press play to proceed with the lesson.

Okay, let's answer the question.

A number when rounded to a certain significant figure would give us 6000.

We have some options on the bottom here.

So what do you think that number would be, that when is rounded to a certain significant figure would give us 6000? It's one.

Now, if we member, let's do a bit of recap.

If the circle is filled in, this is a number line.

If a circle is filled in a number line, what does that tell us? It tells us that whatever value we write here, it is included in our range.

Whatever value we put here, it is included in our range.

And an open circle tells us that yes, the value is not included in our range.

So we want a range of values, that when we round to one significant figure, would give us 6000.

Out of the options here, what is the minimum value, that when it's rounded, when that number itself is rounded to one significant figure, it would give us 6000? Yes, the number is 5500.

Okay, let's go to the maximum value then.

What is the maximum value, and that number itself is not included, that when I round to one significant figure, it would give me 6000? Yes, it is 6500.

So how do we write this using an equality? So we can say x is greater than or equal to 5500.

But x must be less than 6000 digit.

So, I hope you got that in your book.

If you didn't, please correct your That should be a zero.

Please correct your work as it is going to be very useful for what we're doing next.

A number has been rounded to 150 to the nearest 10.

We want to figure out the range of values that when rounded to the nearest 10, would give us 150.

So what would be the minimum value that we can round to the nearest 10 that will give us 150? And that is 145.

What is the greatest value that when rounded to the nearest 10 would give us 150? And that is 154.

9999 and so on.

Okay, let's say the number we started with.

The number we rounded up to is x.

We know that x is within the range of 145 and 155.

But we know that x will be greater than or equal to 145, but it would be less than 155 Okay.

This 145 is known as the lower bound.

And this 155 is known as the upper bound.

Do you see how 145 and 155 links to the range? The range of values that x could possibly be.

The minimum range is the lower bound and the maximum range is the upper bound.

So the lower boundary tells us the lowest number, the lowest boundary it could possibly be.

And the upper boundary tells us the upper, the largest number it could possibly be to the nearest 10, that would give us 155.

Okay, let's think about this question.

A race takes 140 seconds, rounded the nearest 10 seconds.

Work out the lower and upper bound for the time of the race.

Now, the lowest number that when rounded to the nearest 10 would give us 140, we know that that's 130.

What is going to be the highest value that when we round to the nearest 10 would give us 140? And that value would be 145.

So we're going to write S for the potential value.

The initial value that was rounded up or down, and that was getting the S is going to be greater than or equal to 135.

But less than 145.

So then S here would be our lower bound, and 145 would be the upper bound.

Now we know that it can't be 145.

But that is the boundary, our value can't be 145 and above, but it can be anything below.

Let's think about this.

A piece of string measures six centimetre to the nearest centimetre.

Find the upper and lower bounds for the length of the string.

When it says nearest centimetre, it's the same as saying to the nearest integer.

So what would be the lowest value that when rounded to the nearest integer would round to six? That is going to be 5.

95.

Okay? What is the largest value, the maximum value that when rounded to the nearest integer, would round to six? Yeah, it's 6.

05.

Okay, write that as an inequality.

So I'm going to say s again for a string.

So the initial value could be greater than or equal to 5.

95 centimetre, but it would be less than 6.

05 centimetre.

And 5.

95 would be my lower bound, and 6.

05 would be my upper bound.

What of this one? The mass of a piece of metal is 7.

4 kilogrammes, accurate to one decimal place.

Find the upper and lower bounds for the mass of the metal.

Okay.

What would be the lower bound? What would be the minimum value that would round to 7.

4 kilogramme when rounded to one decimal place? Yeah, it's 7.

35 kilogrammes.

And what would be the maximum value that when rounded to one decimal place would round to 7.

4 kilogramme? It will be 7.

45.

So again, writing that as an inequality, I'm going to write m for mass is greater than or equal to 7.

35 kilogrammes, and less than 7.

45 kilogrammes.

The lower bound then, LP stands for lower bound, would be 7.

35.

And the upper bound would be 7.

45.

Okay.

The speed of an object is 300 miles per hour, to one significant figure.

Find the upper and lower bounds for the speed of the object.

Let's pause the video, have about five to 10 seconds to think about it, and then come back and see how we go on.

Okay, so this speed has been rounded to one significant figure.

So, what's the minimum value, that if I round to one significant figure would give me 300? It would be 250.

You should looked here.

One significant figure I'll be looking at the second digit, which is the five.

Because it's five I round it up, so it's going to be 300 to one significant figure.

What's the greatest, therefore, value that when I round to one significant figure would give me 300? It'd be any number less than 250.

Okay, so again, if I write it as an inequality, s for speed, it would be greater than or equal to 250 miles per hour, but less than 350 miles per hour.

My lower bound is 250 miles per hour, and my upper bound would be 350 miles per hour.

It is now time for you to attempt your independent tasks.

So I want you to pause the screen now.

Attempt all the questions on your screen, and then come back when you're finished to go through the answers.

Okay, your answers are given here.

I'll just go free, see very quickly.

We want numbers, the lower and upper bound that when we round to two decimal place would give us 3.

06 seconds.

So, if we look at this one, if I around that to two decimal place, I would get 3.

88.

And any value less than 0.

065, if I round down, I should get 0.

06.

Your explore task ask you for the upper and lower bound for the perimeter of this shape.

So the measurements have been measured to the nearest 10 centimetre.

So we have 20 centimetre here, and 70 centimetre here.

But the question ask you to find the upper and lower bound of the perimeter.

So pause the video now and attempt this task.

Once you finish, press play to resume.

If you're struggling with this task and you don't really know where to go or how to start it, you keep watching the video, will help provide you with further help.

Xavier giving you advice, and he's saying, he would work out the lower bound for 70 centimetre, and then for 20 centimetre, and then work out the perimeter for that because that would be the lower bound values.

But if I want to work out the lower bound for 70 centimetre, what's that going to be? It's going to be 65, isn't it? And the lower bound 20 centimetre is going to be 15 because if I around 65 to the nearest 10, I would get 70.

And if I around 15 to the nearest 10, I would get 20.

So to find the perimeter, I would do 65 plus 65 plus 15 plus 15.

Because the perimeter is measuring the area, the distance around the shape.

So I'm going to be adding all my values together.

The parameter is measuring the distance around the shape.

So I'm adding all the values together for the lower bounds.

So the lower bound parameter is this.

Now pause the video again and see if you can find the answer, and also calculate the upper bound perimeter of that shape.

Okay, we have now reached the end of today's lesson.

Good job for staying right to the end and working hard.

Share your work with your teacher, share work with your parents.

Show off how excellent you've been for all this lesson.

And I will see you at the next lesson.