The upper bound for a rounded number is the smallest value that would round up to the next rounded value.

The lower bound for a rounded number is the smallest value that the number could have taken prior to being rounded.

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

Problem solving with rounding, estimation and bounds

Maths

Checking and securing understanding of rounding and truncating

Checking and securing understanding of estimating through rounding

In the prior unit, pupils learnt how to round to a given number of decimal places or significant figures and explored the effect of using rounded numbers for calculations. In this unit, pupils will investigate the bounds and perform calculations to determine a best/worst case scenario.

This unit explores the impact of upper and lower bounds on additive and multiplicative calculations.

Rounding, estimation and bounds

A quick estimate for a calculation is obtained from using {{ }} values, often rounded to 1 significant figure. 

The distance between London and Manchester $$\approx$$ 300 km

Area of a football pitch $$\approx$$ 7000 $$m^2$$

The length of a cats tail $$\approx$$ 0.03 m

Which of the following are reasonable approximations?

Using estimation only which of the following is the correct answer to $${{106^2\times1.587}\over35.06}$$

Estimate the value of $${23.87\times105.7}\over38.942$$

Andeep's dog is fed twice a day.  Each meal weighs 175 g.  A bag of food contains 7.5 kg.  Estimate how many days the bag of food will last.

An {{ }} interval for a number x shows the range of possible values of x. 

Considering the maximum number of boxes to safely fit onto a lorry.  Which of the following should be used? (Where $$l$$ represents the capacity of the lorry and $$b$$ represents the mass of a box?

A sack contains 50 kg of rice correct to the nearest kg.  What are the lower and upper boundaries of the rice?

A sack contains 50 kg of rice correct to the nearest kg.  This is put into smaller bags containing 1 kg correct to 0.01 kg.  What are the lower and upper boundaries of the bags?

A sack contains 50 kg of rice correct to the nearest kg.  This is put into smaller bags containing 1 kg correct to 0.01 kg.  Which calculation is correct to find the minimum number of bags produced?

A sack contains 50 kg of rice correct to the nearest kilogram.  This is put into smaller bags containing 1 kg correct to 0.01 kg.  What is the minimum number of bags produced?

Starter Quiz

An interval for a number x shows the range of possible values of x.