Topic outline
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Video transcriptThis unit of work is on Accuracy and Bounds.
Accuracy and Bounds are often difficult ideas to teach because students find it challenging to consider the least and greatest values which would round to a particular number.
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, 1000 or to a specified number of decimal places or significant figures and use these results to find the solutions to simple problems.
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 ability level of your learners as well as your school context.
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Lesson 4 video
Video transcript
We encounter rounded numbers every day, whether it’s telling us that 10% of people own 90% of global wealth, or that there are 85 million pet owners in the US.
The accuracy with which the number has been rounded tells us how large or small the real value could have been.
Let us consider an example. A newspaper reports that a local cheese factory has produced 24000 kg this year.
The newspaper is likely to have rounded the actual figure
If the newspaper had rounded to the nearest 1000 kg what is the smallest amount of cheese that could have been produced?
What is the largest amount of cheese?
This leads us to 2 questions
If the newspaper had rounded to the nearest 1000 what is the smallest amount of cheese that could have been produced?
What is the largest amount of cheese?
Let’s look at this on a number line.
If we are rounding to the nearest 1000, the smallest amount of cheese that could have been produced is 23500 kilograms.
If we are rounding to the nearest 1000, the largest amount of cheese that could have been produced is 24500 kilograms 23500 is the lower bound, the smallest value 24500 is the upper bound, the largest value.
But what if the newspaper had instead rounded to the nearest 100?
What would the smallest and largest possible values of the cheese be?
If we are rounding to the nearest 100, the smallest amount of cheese that could have been produced is 23950 kilograms
If we are rounding to the nearest 100, the largest amount of cheese that could have been produced is 24050 kilograms
In this case 23950 is the lower bound, the smallest value 24050 is the upper bound, the largest value
So what does this tell us?
When a number is rounded the accuracy of the rounding is important to tell us what the smallest and largest possible values of the number are.
These values are called the lower and upper bounds of the number.
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