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The objectives in the revised Framework make specific reference to calculators in the 'Using and applying mathematics' and 'Calculating' strands for Years 4, 5 and 6, and Year 6 progression to Year 7. These objectives are appended at the end of this paper for reference.
Below is an expanded set of learning objectives that cover Year 4 and upwards, which your school might use to review its policy and planned provision in the use of calculators in the teaching and learning of mathematics. These are divided into the technical knowledge and skills children need to use a calculator effectively, and the interpretive skills and understanding they need to apply these skills to support their learning. There is accompanying commentary on aspects of teaching and learning.
Recognise the operations that the keys on the calculator represent
Calculators can operate in different ways and the detail in the displays can vary. For example, some calculators display the full number sentence during a calculation, while others only display the number entered or the answer. Spend time becoming familiar with the calculator the children are to use. Be ready to show children how the different keys work (e.g. how the decimal point key is used). The decimal point may already appear on the display at the end of the number. After the key is pressed it appears to move with the number, which can confuse children. The [+/-] key changes the sign of the number displayed. It toggles between + and -. This can be used to highlight the difference between using + and - to represent the operations addition and subtraction, and to indicate whether the number is positive or negative. Children may miss the sign that indicates a number is negative when this appears on the extreme left of the display or after the number. Many calculators have a percentage key with the symbol %. Its use is likely to cause confusion and it is better not to use it with most primary children. Children need to be taught the essential features of the calculators available to them in the classroom.
Clear the display and memory before starting a calculation
It is good practice to remove any displayed numbers and to clear the calculator's memory if this is to be used to store new values. The clear key may be a combined clear and clear entry key with [C/CE] or [CE/C] on it. Clearing the memory can involve a [CM] (clear memory) or [MC] (memory clear) key. Children are less likely to make errors if they get into the habit of clearing the display, and where appropriate the memory, before starting a new calculation. Always ask children to check if there are any 'left-over' numbers on their calculator before they start using it.
Correct a wrong entry by using the clear entry key
Most children will clear the display and repeat the calculation if they think that they have made an error. This is fine, but in a more complex calculation it is quicker to clear the most recent entry. Children should be taught how and when to use the clear entry or [CE] key and when it is more appropriate to clear everything and just start again. Get children into to the habit of using the [CE] key correctly rather than starting again every time they make an incorrect entry.
Store a value in the calculator's memory and retrieve it during a multi-step calculation
As children become more confident users of the calculator they can be taught how to use the calculator's memory. The objective that relates to the use of the memory is in Year 6 progression to Year 7, so many Year 6 children could acquire these skills. Storing and retrieving numbers can assist them with multi-step calculations. The calculator may have four keys associated with the memory: [CM] or [MC] to clear the memory, [RM] or [MR] to retrieve the number stored in the memory, [M+] to add the number entered to the number in the memory and [M-] to subtract the entered number from the number in the memory. Make sure children understand the function of each key and ensure that they do not inadvertently change the number in the memory by using the wrong key. Remind children that if they are in doubt they should clear the memory before they start a calculation.
Keep track of a calculation and record the method used
When using a calculator, children should be taught to record their calculations, together with the answers they obtain, at each stage in a multi-step calculation. They should be encouraged to check whether each answer makes sense as they work through a problem. Children who are confident in using the memory should still be asked to record the calculations involved. Children need to understand the difference between recording their method and recording the steps they go through on the calculator. Emphasise that recording the method is about recording the number sentences or the calculations involved.
Use of other function keys
Children may have access to more sophisticated calculators that have additional function keys, such as square root, square or power keys, and fraction notation. Knowledge of how to use these keys can provide children with the opportunity to apply and extend their mathematics. The Year 6 progression to Year 7 includes the use of the square root key. For example, multiplying a number by itself or using the square or power key to generate the square numbers can involve identifying square numbers well beyond 100. Finding squares and then square roots demonstrates the inverse operation to children. Finding the positive square root of a non-square number such as 7, then re-entering the number displayed and squaring it, shows children the way calculators round their displays.
Recognise the likely size of the answer and check answers
Children recognise that calculation is a precise skill - there is only one correct answer. To be good at it requires a good understanding and knowledge of number. While children may believe the calculator is a precise tool, remind them that the calculator only responds to numbers entered and the keys pressed. Accuracy is required when it comes to entering values into the calculator. Errors occur when the wrong digit is entered or a key is not used correctly. When using a calculator, children must be reminded that they should always cast a questioning eye over their results. Children should be encouraged to use the checking strategies identified in the Framework's objectives, such as approximating, looking at the most and least significant digits, checking the number of digits in the answer, monitoring the position of the decimal point or carrying out the inverse operation.
Recognise negative numbers in the display
Children are introduced to negative numbers in Year 4 and use them in context. Errors in a subtraction calculation may lead to a negative number being displayed on the calculator. Children need to recognise when a number displayed is negative and not to simply ignore the sign. They should go back and check if a negative value was expected and makes sense. The calculator provides a useful tool for work around negative numbers. Year 6 children learn to find the difference between a positive and a negative integer and between two negative integers, again in a context that gives meaning to the numbers involved. Using a calculator for these calculations should be treated with caution as the manipulation of positive and negative integers can easily be misinterpreted. Using an image, such as a number line, is more reliable. For example, finding the difference between -3 °C and +4 °C could be misrepresented as 1 degree rather than 7 degrees if the - and + signs are used as operations. The context, too, can change the sign in the answer. The answer to the question: 'What is the change in temperature from -3 °C to 4 °C?' is: 'An increase of 7 degrees (or +7 degrees).' The answer to: 'What is the change in temperature from 4 °C to -3 °C?' is: 'A fall of 7 degrees or (-7 degrees).'
Enter and interpret money and measurement calculations
Children need to understand when and why the decimal point can disappear and can move about in the display. When £0.50 is entered, the number displayed is likely to be 0.5 as trailing zeros are not shown in decimal numbers. Multiplying 0.5 by 2 results in the number 1 being displayed and the decimal point has gone. Interpreting the results of a calculation often causes difficulties, for example 5.6 could mean £5.60, or 5 metres and 60 centimetres, or 5 kilograms and 600 grams, and so on. Children should be taught why and when it is important to convert all measurements into the same units before they carry out a calculation.
Calculations that involve time
Calculations that involve time are best not carried out with a calculator. Children will find it easier to use a clock face or a time line to do such work. This is less prone to error than using a calculator. Finding the interval of time on a journey that starts at 08:38 and ends at 14:19 does not involve the subtraction of decimal numbers and children too often fall into this trap. Using a calculator for time calculations should be avoided.
Carry out calculations with more than one step
Over time, children will use the calculator to carry out increasingly complex calculations, such as finding three eighths of a quantity or sharing equally the sum of four quantities between three. Using a calculator effectively, children need to know which operations to carry out first. Some calculators have brackets that children can use to help sequence the order of the operations. Entering a calculation for which the order of calculation is not left to right, such as £138.45 - (£8.24 × 6), can easily lead to errors. Most children should be encouraged to carry out the calculation in stages. Children should be taught how to select the correct sequence of operations in calculations that involve more than one step and record these for reference and checking.
Recognise and interpret rounding errors
Calculators generally work with more digits than those displayed. The numbers are often rounded before being displayed, rather than simply truncated at the point of display. This can sometimes lead to a build-up and magnification of errors, though this is unlikely to affect most of the calculations the children undertake. For example, if you divide 1 by 11, the answer displayed is 0.090909. Now multiply by 2, then by 4 and finally by 11. The answer should be 8 as we multiplied one eleventh by 2, 4 and 11. If there has been rounding at stages the number displayed will not be 8. There are situations in which the children need to interpret the number displayed. For example, sharing a sum of money may result in a number with three or more decimal places being displayed. In some situations the context will determine if the number is to be rounded up or down. Children should always ask if the number displayed makes sense in the context of the calculation or the problem.
Use the division operation to enter a fraction
Children should be taught how to enter fractions using the division operation and to recognise the decimal equivalent displayed. For example, when 
is entered as 3 [÷] 4, the number displayed is 0.75, its decimal equivalent. The calculator is a useful tool for children to establish that all tenths have equivalent decimal representations as numbers with one decimal place, while all hundredths have equivalent decimal numbers with one or two decimal places. Children should be taught to recognise decimal representations of familiar fractions and be able to convert one representation into the other.
Recognise recurring decimals
Using the calculator children will discover that some fractions entered on it will fill the display and often exhibit repeating patterns in the decimal digits displayed. They should recognise the decimal representation of some of the fractions they are familiar with. Many of these fractions, for example one third, have recurring decimal representations. The calculator offers children the opportunity to explore the decimal number patterns displayed.
Decide when a calculator is an appropriate tool to use
Children are usually given access to the calculators for a particular task. They recognise that on that occasion they are allowed to use them. Children need to recognise that any tool is designed for a purpose and the calculator is no exception. They should be given the opportunity to decide for themselves when a calculator might be helpful and to discuss when mental or written methods are more effective and efficient. Showing children that they have the knowledge and skills that enable them to calculate in less time than it takes them to enter the calculation into a calculator is a useful ploy. Spend time with the children discussing how the calculator supported the activity and what the children learned as a result of the activity.
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