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Year 8

Using inequality notation for errors in calculations

I can use inequality notation $$a ≤ x < b$$ to express errors in calculations.

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New
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Year 8

Using inequality notation for errors in calculations

I can use inequality notation $$a ≤ x < b$$ to express errors in calculations.

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Share activities with pupils
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Lesson details

Key learning points

  1. You can use the values of a and b to see what the biggest and smallest answers to a calculation could have been.
  2. The range of possible answers is the error interval.

Keywords

  • Error interval - An error interval for a number $$x$$ shows the range of possible values of $$x$$. It is written as an inequality $$a ≤ x < b$$

Common misconception

When subtracting or dividing, the largest value is found by subtracting or dividing the upper limit of a number by the upper limit of the divisor or additive inverse.

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.

Discuss - When 5 m^2 is rounded to 1 s.f, is 4.5 m^2 as the lower limit a big deal? Show the class what 0.5m^2 looks like. Civil engineers claim that bridge collapse is due to miscalculations. How do they minimise error intervals? By using instruments that give answers to a high degree of accuracy.
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Equipment

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
An error interval for a number $$x$$ shows the range of possible values of $$x$$. It is written as $$ a\leq x < b$$. Explain what this means.
The range of values include $$a$$ and $$b$$
Correct answer: The range of values include $$a$$ and not $$b$$
The range of values includes all the numbers strictly in between $$a$$ and $$b$$
The range of values do not include $$a$$ but include $$b$$
Q2.
When a number, $$x$$, is rounded to the nearest integer the result is 63. Select the numbers which complete the error interval for $$x$$: $$\square \leq x <\square$$
62.5 and 65.5
63.5 and 64.5
62.5 and 64.5
Correct answer: 62.5 and 63.5
Q3.
When a number, $$x$$, is rounded to the nearest integer the result is 5. Select the numbers which complete the error interval for $$x$$: $$\square \leq x <\square$$
4.5 and 5.6
Correct answer: 4.5 and 5.5
3.5 and 6.5
4.5 and 5.49
Q4.
When a number, $$x$$, is rounded to the nearest integer the result is 10. Select the numbers which complete the error interval for $$x$$: $$\square \leq x <\square$$
9.5 and 10.4999
5 and 14.5
5 and 14.49999
Correct answer: 9.5 and 10.5
Q5.
Jun rounds a number to the nearest integer and the result is 5. Izzy rounds a number to 1 d.p. and the result is 5.0. Jun says, "We must both have rounded the same number." Is Jun correct?
Jun is correct as both are the same when rounded to 1 d.p
Jun is correct as both values will be the same when inputting into a calculator.
Correct answer: Jun is incorrect as they have different error intervals.
Q6.
$$x$$ and $$y$$ are both integers. $$x$$ = 650 (rounded to the nearest 10) and $$y$$ = 800 (rounded to the nearest 100). The greatest possible integer value of $$x+y$$ is .
Correct Answer: 1503, 1 503

Exit quiz

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6 Questions

Q1.
__________ are the digits in a number that contribute to the accuracy of the number. The first significant figure is the first non-zero digit.
Estimated numbers
Important numbers
Real numbers
Correct answer: Significant figures
Q2.
When a number, $$x$$, is rounded to the nearest integer the result is 35. Select the numbers which complete the error interval for $$x$$: $$\square \leq x <\square$$
$$35$$ and $$45$$
Correct answer: $$34.5$$ and $$35.5$$
$$34.999$$ and $$35.999$$
$$34.4 \dot 9$$ and $$35.4 \dot 9$$
Q3.
A long road is made up of 3 sub roads. The 1st road measures 35 m (2 s.f), the 2nd road is 41 m (2 s.f) and the 3rd road is 48 m (2 s.f). Find the error interval for the length $$x$$ of the long road.
Correct answer: $$ 122.5 \leq x < 125.5 $$
$$ 122 \leq x < 125 $$
$$ 122.5 \leq x < 125.59 $$
$$ 124.5 \leq x < 126.5 $$
Q4.
A wall is in an L-shape. All the lengths are given to 1 d.p or the nearest integer. Work out the error interval for the area of the wall.
An image in a quiz
$$19.6375 \leq x < 22.7875$$
$$18 \leq x <23 $$
$$18.96 \leq x <20.96 $$
Correct answer: $$18.7875 \leq x <23.6375 $$
Q5.
A square has lengths in cm given to 1 decimal place. The error interval of the perimeter of the square is $$31 \leq x <31.4 $$. Work out the length of the square correct to 1 d.p.
7.2
7.4
7.6
Correct answer: 7.8
8.0
Q6.
A square has lengths in cm to 1 decimal place. The error interval of the area of the square is $$30.8025 \leq x <31.9225 $$. Work out the length of the square to 1 d.p.
5.5 cm
5.4 cm
Correct answer: 5.6 cm
5.8 cm
5.3 cm