In this unit of work we are going to look at how to identify the upper and lower bounds for data given to a specified accuracy.
We will look at identifying the bounds for data given to the nearest 10, 100 and 1000, or to a specified number of decimal places or significant figures, through contextual examples and the use of a variety of card based activities. Learners following an extended curriculum, can investigate finding appropriate upper and lower bounds to solutions of simple problems.
Bounds is often a difficult topic to teach, because learners find considering the least and greatest values that would round to a particular number a challenge.
This is particularly the case when we are considering numbers which have been rounded to a given number of decimal places or significant figures. Learners find questions where the number appears to have been rounded to a different accuracy to that stated to be especially difficult, for example giving the upper and lower bounds for 200 which has been rounded to the nearest 10.
At extended, learners are expected to obtain the appropriate upper and lower bounds to solutions of simple problems. A common error here is for learners to work with the rounded values in the calculation, and then work with the answer to give bounds.
Giving the bounds for problems involving subtraction or division calculations can also cause learners issues. For example, learners often work solely with lower bounds in an attempt to find the lower bound of a subtraction not realising that lower bound subtract upper bound will give a smaller answer.
This unit of work is just one of several approaches that you could take when teaching this topic, and you should aim to adapt the resources to match the ability level of your learners, as well as your school context.