Problem solving with estimation and rounding | Maths | Quizalize & Oak National Academy

Starter quiz

A degree of accuracy shows how precise a ______ or measurement is. For example, to the nearest cm, nearest 10, 1 s.f. and so on.

'number' ✓
Alex buys paper £4.95, USB £ $\square$ , stamps £5.20, crisps £0.95, staples £1.10 and plug £1.99. He pays with a £20 note and receives about £2 back in change. Estimate the cost of the USB.

£1

£2

£4 ✓

£6

£12
An error interval for a number $y$ shows the range of possible values of $y$ . It is written as:

$a< y < b$

$a> y < b$

$a \geq y$

$a\leq y < b$ ✓
When a number, $x$ , is rounded to the nearest integer the result is 88. Identify the error interval.

$87.5< x < 88.4 \dot 9$

$87.5> x < 88.4 \dot 9$

$87.5\leq x < 88.4 \dot 9$

$87.5\leq x< 88.5$ ✓

$87.5 \geq x <88.4 \dot 9$
A triangle has lengths 3.5 cm (2 s.f), 4.1 cm (2 s.f) and 4.8 cm (2 s.f). Write the error interval for the perimeter $p$ of the triangle.

$12.25 \leq p < 12.55$ ✓

$12.2 \leq p < 12.5$

$12.25 \leq p < 12.5599$

$12.45 \leq p < 12.65$
A square has lengths in centimetres to 1 decimal place. The error interval of the area of the square is $17.2225 \leq x <18.0625$ . Work out the length of the square to 1 d.p.

3.8 cm

4.0 cm

4.2 cm ✓

4.4 cm

4.6 cm

Exit quiz

Work out an estimate for the area of the shape.

5 m²

10 m²

12 m²

19 m² ✓

25 m²
Here is a grassed garden with a summer house in the centre. Using estimation and rounding, estimate the area of the grass.

50 m²

90 m²

100 m²

164 m² ✓

800 m²
A piece of string was 32 cm measured to the nearest cm. A length of 5.6 cm (to 1 d.p) was cut off. What is the error interval for the remaining length $x$ cm?

$25.85 ✓$

$25.85\leq x<26.95$

$25.95$

$25.95\leq x<26.85$
Complete the statement. Fermi problems encourage:

critical thinking and well calculated estimates using data or information ✓

openness of answers and flexibility so answers can be achieved in different ways ✓

an appreciation there are a range of answers, the focus is on the working out ✓

random guesses but use estimation and or rounding
Fermi problem : How long will it take to count to 1 million (without breaks, sleep, etc)?

50 days

40 days

16 days ✓

5 days

3 days
Fermi problem : If you put 1 million pound coins in a box, what is the volume of the box in m³ ?

0.5 m³

1.2 m³ ✓

5 m³

8 m³

12 m³

Worksheet

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Lesson Details

Key learning points

It may be helpful to estimate an answer to check the magnitude is correct.
It can be useful to use rounding to significant figures when dealing with very big or very small numbers in context.
Estimates can help when making decisions about maximum or minimum possible answers in real life contexts.
You can use Fermi estimation to find approximate solutions to problems.

Common misconception

Using the wrong limits when dividing or subtracting in order to find the upper limit of a calculation or lower limit of a calculation.

Drawing a number line to show with subtraction will help students see how to achieve an upper or lower limits of an error interval calculation. When using division, reiterating the division of number is the same as multiplying by its reciprocal.

Keywords

Estimate - A quick estimate for a calculation is obtained from using approximate values, often rounded to 1 significant figure.