A classroom is measured 5.4 x 3.4 metres, measured to 1 d.p. Calculate the lower bound of the area of the room.

James ran a distance of 400m in a time of 25.2 seconds. The distance of 400m was measured to the nearest 10 metres. The time of 25.2 was measured to the nearest tenth of a second. Work out the upper bound James' average speed.

James ran a distance of 400m in a time of 25.2 seconds. The distance of 400m was measured to the nearest 10 metres. The time of 25.2 was measured to the nearest tenth of a second. Work out the lower bound James' average speed.

Carl measured the length and width of a rectangle. He measured the length to be 19cm correct to the nearest centimetre. He measured the width to be 20cm correct to the nearest 10cm. Calculate the lower bound for the area of this rectangle.

6 heights are listed, given to one decimal place: 4.6cm, 6.3cm, 9.8cm, 3.2cm, 5.7cm, 3.6cm. Work out the greatest possible mean.

A circle has an area of 130cm^2 to the nearest 10cm^2. Work out the upper bound of the radius. Give your answer to 3 d.p.

Solving Problems with rounding

﻿Hello, and welcome to today's lesson on estimation with me, Miss Oreyomi, you will be needing a paper and a pen for today's lesson. So please pause the video now, if you need to get that, and once you're ready, press play to resume. In this lesson, you'll be able to use estimation to work out answers to your calculations before we proceed, if I tell you the word overestimate, what do you think that word might mean? It does mean to make an estimate that is greater than the exact answer. So something is over the exact answer. What of underestimate? Well, it's going to be the opposite, isn't it? It's going to be making an estimate that is lower than the exact answer, okay. Let's start with this try this activity. For each question, using an approximation. Can you choose what the correct answer would be? So pause the screen now and attempt these six questions and when you're ready, come back and let's go over it together. Okay, let's go for it together very quickly. If I'm using approximation to work out this, what do I think the value might be? Well, I might go five times 20 rounded to the nearest integer, rounded the nearest integer. So I know that my value would be somewhere on here. For this one, I will be thinking, well, this might be 21 times three, So around 23 times three or 20 times three. So it'll be somewhere around 60 and seven to nine is the closest one to 60 that I have here. So I'll be choosing that. Eight times six is 48. So I know my answer would be somewhere around here. For this one, 7.18 times 200. When I know that seven times two approximately will be 14. So I would go in here. This one, I would have rounded this to 800 and this down to 400. I know that it will be somewhere between the 200 range. This value would be an overestimate. So I would rather choose an underestimate or rather underestimate for this. So I would go for one 193.25. Here, I would go four times five is 20. These values are more than four and five. So I would go for 21.41208. When we talk about estimating, people, some people use estimating and an approximating intellect. So they use us the same word. Estimating is when we guess we make a rough guess as to what our value should be as we did, when I tried this task. And usually we estimate to one significant figure and our estimated value are usually an overestimation or underestimation. It's really really rare that when we estimate we get the exact value, because the point of estimation is to make a rough guess. So let's look at this question here. Grace buys 64 packets of crisps at 23p each estimate the total cost. So as I said in the previous slide, when we estimate, we usually round the values to one significant figure. So if I want to round 64 to one significant figure, this is less than five. So my value rounds down to 60. So remember our squiggly line for approximate. So it's going to be 60, to one significant figure. And 23 to one significant figure would be well, 20. So, If I want to estimate the total cost, I am going to multiply 60 and 20 together. To do that once I finished writing this on the board to find the total of cost, I'm going to do 20, rather 20p times 64, rather time 60. And that is going to give me 12 pounds. So an approximate value use an estimation is 12 pounds. Okay, let's look at this example here. Kouthar is given to job offers. Job A, she would get 985 pounds a week and Job B, she would get 4215 pounds a month. Which job should she take? So if we're doing A, and she's getting 985 pounds a week, I want to round this to one significant figure. What would that be? Have gone 985 and I want to round to one significant figure, I'm looking at this number here and eight is greater than five. So I am going to round it up to 1000. And Job B, well, she gets 4,215 pounds a month, okay. Let's see, which one is better value or which job offer she should take? Well, if she's got an 1000 pounds a week and I multiply that by four, how much would she approximately get in a month? Well, she's going to approximately get 4,000 pounds. So which job offers should she take if she is based on the money? Yes, she should take job B because it is a better offer. Let's work out an estimation for 302 multiplied by 9.68 divided by 0.562, okay. So, rounded to one significant figure, 302 becomes 300 9.68 becomes 10 and 0.562 to one significant figure becomes well that rounds up. So it becomes 0.6. So I've got 3000 divided by 0.6. And that would give me 5,000. So using estimation to work up that calculation made it easier for me to workout and got a nice round number. I want you to pause your video now and complete your independent task. Once you're done with the independent task, you can then resume the video and continue with the lesson. For your explore task. You are to give an estimate for each of the following problems. And you also comment on whether the estimate is an overestimate or underestimate, or it is not clear. So pause the video now and attempt this task. And then once you're done, press play to carry on with the lesson. Well done, you have not reached the end of today's lesson, a very big well done for completing your work and sticking all the way through to the end. That is all for me. Bye bye.

Estimate the total cost of 32 books at £178 each and 57 markers at £22.30 each.

Student A estimated that 23.5 x 91 = 1800. Student B estimated that 23.5 x 91.4= 2160. What did student B do?

Work out an estimate for 9.97% of 3967

Estimate the value of: 6.2 + 7.9 x 3.2 - 9.8

I estimated that 7.85 x 29 = 240. Why is my estimated answer more than my exact answer?

Find an estimate for √78

Estimation

In this lesson, we will learn how to estimate and solve problems using estimation.

Maths

Y8 Maths

Key Stage 3

Year 8

Miss

Accuracy and estimation

Number

THEME

UNIT

Rounding numbers using a number line

Rounding from a calculator: Approximating

Rounding to significant figures (Part 1)

Rounding to significant figures (Part 2)

Rounding and Range

Upper and Lower Bound

Solving Problems with Rounding

A teacher asked two students to round the number 5,469,704. Their answers are below. Which student(s) rounded the number correctly? Explain your answer.

Lesson overview:Estimation

Core Content

Accuracy and estimation: