Calculation Booklet 2023 - 2024
This booklet is aimed to help parents who would like to support their daughters with their maths. It is a guide to demonstrate the methods taught and how you can help if your daughter asks for guidance with her maths homework. The understanding of mathematics, and the ability to use and apply it appropriately and confidently, are key skills fundamental not just to school work but throughout life. It is therefore our aim to give pupils a full range of mathematical skills and experiences, and to foster their confidence in order to make their own decisions about how to use and apply their knowledge in different situations.
Mathematics is important because: • • • • •
It is the foundation for other areas of the curriculum, such as Science and Technology It is essential in the outside world, both in domestic and professional environments It develops important skills such as logical reasoning, systematic working and problem solving It is fun, challenging and motivating It provides the opportunity for children who may have difficulties with language based subjects to succeed academically
Aims for all our pupils: • • • • • • • • • •
To enjoy maths and to study it with confidence and a sense of achievement To achieve high standards in numeracy and a range of other mathematical skills To be able to apply their skills with confidence and understanding when solving problems or moving on to new methods and concepts To be prepared to experiment and to take risks without fearing mistakes To be able to make their own decisions about how to tackle their work To be given the opportunity to grapple To develop thinking skills through open questioning, independent work and investigations. To develop maths curiosity and creativity To become confident in reasoning and using maths to analyse and solve problems To explore and explain ideas using correct mathematical language, symbols and diagrams.
Pupils should take pride and care in their presentation of their work. It is important that all work is set out neatly in both classwork books and homework books as when methods and workings are clearly set out, simple mistakes are less common. • • • • • • • •
Each page should be divided into half vertically with a left hand and central margin (of 2 squares width) The numerical date should be written on the top left-hand side of the page and underlined. Titles should include the book and page number and should ne underlined. Only one digit should be written in a square to help with setting out sums clearly 2 squares should be left after the margin before writing—this ensures answers for calculations don’t end up in the margin! Question numbers should be written in the margin Pencils should be sharpened and lines drawn with a ruler Show all working out unless specifically asked not to!
As a school, we encourage pupils to take risks. The ‘having a go’ is as important as getting an answer correct. Making mistakes can be useful to help identify areas for development and are an important part of the learning process. When an error has been made, it will be marked with a cross or a dot. Mistakes should never be rubbed out after the work has been marked. Teachers may ask pupils to redo a question if a mistake has been made or write out additional questions after marking. When a pupil has been asked to make a correction, they should never rub out the sum. When a correction is marked, it will have a ‘c’ written next to it to show that it was a correction. In all year groups, pupils will receive maths homework up to twice a week. Homework is only set where necessary to reinforce skills or prepare for the next lesson. As well as set homework, pupils are encouraged to practise their mental arithmetic skills.
Homework gives pupils the chance to review, practise and further develop the skills they have learnt in class. The work given should encourage them to develop good homework habits and promote independent learning. Homework provides parents with the opportunity to engage in their child’s maths and while we encourage parents to give a little help or guidance, we ask that homework is completed by your daughter rather than by you! If any homework is causing stress, is a bit too tricky or it is taking a long time, please inform your daughters’ maths teacher via the homework diary or junior-office@lehs.org.uk
How to help at home ✓
Make maths fun – too much pressure will turn her off Maths
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Stay positive – even if you have negative feelings about Maths
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Encourage your daughter to ‘have a go’ - even if they make mistakes they can learn from them
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Praise achievements, however small
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Encourage discussion about how to work things out and estimating – use the school methods outlined in the appendix as alternative ones may cause confusion.
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Remember that asking questions is a vital part of learning – let her figure it out without giving her the answer.
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Make maths real—bring everyday maths into conversations e.g. restaurant bills, receipts and discounts, cooking, timetables, sporting events.
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Practise telling the time and durations on an analogue clock.
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Let her teacher know if an activity was too hard – they can go through it together in school.
In maths, oral and mental work is essential. They lay the foundations by providing a sound understanding of how the four operations build on counting strategies and a secure knowledge of place value and number facts. Your daughter will learn how the operations are related and how rules are used and applied. Mental and oral work gives your daughter the opportunity to apply what she has learned and to make decisions and choices for herself. Mental calculations are the basis of all methods of calculations and need to be maintained and refined. Fluency and a proficient knowledge of numbers is the result of repetition and practice. In school, pupils are taught a range of mental calculation strategies. They are encouraged to try many methods so they can choose and use appropriate ones depending on the type of calculation. You can help with mental mathematic skills at home by: •
Practising times tables, division facts and number bonds so they can be recalled instantly
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Practising counting forwards and backwards in different sized steps
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Multiplying and dividing numbers and decimals by 10, 100, 1000. Reinforce that the decimal point does not move!
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Multiplying and dividing by multiples of 10, 100, 1000
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Multiplying and dividing by single digit numbers
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Multiplying by 2-digit numbers
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Doubling and halving
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Using known facts to find new facts
The maths your daughter is doing at school may look very different to the sums you remember. Children are now encouraged to work mentally, where appropriate, using jottings to support their thinking. Your daughter should use formal written methods, as shown in the appendix, when the sum cannot be solved mentally and must always show her workings. By the end of her time in the Junior School, your daughter will be able to use her knowledge of all four operations to carry out calculations both mentally and written. Determining the appropriate operation and method to use and to know why. She should know how and when to use inverse operations to check answers and solve problems, including missing numbers, number facts, place value and more complex calculations. When faced with a calculation, your daughter should ask herself…
What strategy should I use?
Can I do this in my head with jottings or drawings?
Do I need to use a written method?
Pupils in the Junior School are taught written calculations in a clear progression of stages. This starts off by learning how written methods can support mental calculations and move on to using standard written methods. It is important that pupils have a secure knowledge of the methods for all four operations. The standard methods taught in the Junior School are outlined on the following pages. They can be used for any calculation involving numbers and/or decimals. These methods help girls keep track of their working out and provide them with an efficient method to use for written work. The methods may look a little different to the ones you were taught, however we ask that you support your daughter in using the methods taught at school as these are recognised as standard written methods pupils are expected to know and use. In Form 1, pupils will start with addition and subtraction of 2 and 3-digit numbers. This progresses on to pupils working with much larger numbers and decimals. By the end of Lower 2, pupils should be able to use an efficient written method for each operation with confidence and understanding, with the majority of pupils extending their use of methods to include decimals. They will have been introduced to the method for long division.
Addition method 1. Estimate the answer 2. Starting with the lowest value column, add all the digits in that column. 3. Write the answer below the sum with any ‘carried’ digits below the line in the column to the left. 4. Repeat with each consecutive column to the left. 5. It should be reinforced that when adding tens, for example, girls are not adding 5 + 6, but 50 + 60. 6. When adding decimals, the decimal points must line up. 0 can be written as a place holder to make the calculation easier.
Subtraction method
1. Ensure the larger number is written on top 2. Estimate the answer 3. Starting with the lowest value column, subtract the bottom number from the top number. Write the answer below the sum. 4. When the top number is smaller than the bottom number you should ‘exchange’ from the column to the left. For example, exchange 1 ten for 10 units, 1 hundred for 10 tens. 5. Exchanged numbers are written at the top left of the column they are going in to. 6. If you cannot exchange from the column to the left, you need to take from the next column first and then you can exchange again. 7. When subtracting decimals, ensure the decimal points line up. 0 can be written as a place holder to make the calculation easier.
Throughout their time in the Junior School, pupils will build up from multiplying 2 by 1-digit numbers to long multiplication of 3 or 4 digit numbers by a 2-digit number. They will predominantly use the following standard methods for multiplication. However, they may also be shown alternative methods in the lower school to ensure understanding of the processes used.
Short multiplication method 1. Estimate the answer 2. Starting with the lowest value column, multiply the top number by the bottom number. 3. Repeat with each column to the left. 4. In this method, ‘carried’ digits are written below the line. 5. Numbers below the line should be added on in the next part of the calculation. 6. When multiplying decimals, the decimal points do not line up. Solve the multiplication sum as above and then position the decimal point after.
Long multiplication method When pupils are secure with multiplication of a 2-digit number by a 2-digit number, they will not have difficulty using the same method for harder long multiplication sums.
1. Estimate the answer first. 2. Multiply each digit of the top number (starting from the units) by the units digit of the bottom number. 3. Multiply the top number by the digit in the tens column of the bottom number, again starting with the units. 4. Girls should be reminded to write a 0 in the units column of the second set of calculations before beginning multiplication by the tens column. This is because they are multiplying by tens, not units.
When multiplying decimals, ignore the decimal point, calculate the sum as normal and then put the decimal point in at the very end. To do this, they need to count how many decimal places (numbers after the decimal point) there are in total in the question. This will be the same as the number of decimal places in the answer.
Short division method As with multiplication, pupils will build up to dividing with decimals, a 4-digit number by a single digit and a 3 digit number by a 2 digit number using long division.
1. Pupils ask themselves if the divisor, 3 in the first example, can divide into the first digit. 2. Write the number of times the divisor goes into the dividend on the top line. 3. The remainder or ‘carried’ digit is written as superscript to the left of the next digit.
Long division method
Some pupils are apprehensive about learning long division at first. They need to remember that division is simply repeated subtraction and should use their knowledge of both division and subtraction to solve sums.
1. Set out the sum and write the first few table facts for the divisor at the side. 2. Ask if the divisor (17) goes in to the first 2 digits (52). 3. Record the number of times it goes in at the top of the sum on the line 4. Subtract the product of the multiplication from the first two digits. 5. ‘Carry down’ the next digit and repeat the process using an arrow. 6. Continue until the answer from the subtraction is 0 or a number less than the divisor. 7. Pupils will learn to give answers with remainders, fractions and decimals.
There are many fantastic digital resources available. The following are a few we recommend to support your daughters’ mathematical learning.
www.mymaths.co.uk www.Drfrostmaths.com www.timestables.co.uk www.bbc.co.uk/schools www.bbc.co.uk/bitesize/ks2/maths www.mathszone.co.uk www.mathsisfun.com www.topmarks.co.uk