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    IGCSE Mathematics Resource Plus overview
    • Number
      Accuracy and bounds
      • Further materials

      show/hide  Video transcript
      This 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.

    • Accuracy and bounds



    • 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.


    • Lesson resources




    • Lesson 4 video


      show/hide  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.


    • Interactive tools

    • show/hide  How can these tools be used?
      These resources are for use with any digital display in your classroom - including a projector, interactive whiteboard or any form of screen sharing technology. When selected, they fill the current available display. The resource is then ready for presentation and annotation.

      As part of your ongoing Resource Plus subscription, we plan to include additional tools. We'd love to know your thoughts and ideas for further development.

      • Graph A4 4mm axes

      • Graph A4 4mm axes

      • Graph A4 4mm


    • Test Maker - Accuracy and bounds past paper questions

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    • Test Maker is an online service that makes it easy for you to create high-quality, customised test papers for your learners using Cambridge questions.

      Test Maker is currently available for Cambridge IGCSE Mathematics 0580 and Cambridge IGCSE Additional Mathematics 0606 syllabuses, but although the grading differs for Cambridge IGCSE (9-1) syllabuses, the questions are valid for equivalent Cambridge IGCSE (9-1) and O Level syllabuses.

      Test Maker is available to all Cambridge schools through the Extra Services section of the School Support Hub.