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Cakes and Calculations

Cakes and Calculations. Addition. Mental Strategies for Addition. Secure mental addition requires the ability to: recall number facts instantly (number pairs to 10, 20 & 100, doubles etc)

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Cakes and Calculations

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  1. Cakes and Calculations Addition

  2. Mental Strategies for Addition Secure mental addition requires the ability to: • recall number facts instantly (number pairs to 10, 20 & 100, doubles etc) • recognise that addition can be done in any order and use this to mentally add different combinations of one and two digit numbers • partition two-digit numbers in different ways, including adding the tens and units separately before recombining • understand the language of addition including more than, sum, plus, greater than, total, altogether etc

  3. Written methods for Addition Expanded method in columns Children can now move on to a layout showing the addition of the tens to the tens and the ones to the ones separately. NB The addition of the tens in the calculation 47 + 76 is described as 40 + 70 = 110 as opposed to 4 + 7 = 11.

  4. In action Use the expanded column method to find answer to this question. 315 + 72

  5. Written methods for Addition Column method In this method, recording is reduced further. Carry digits are recorded below the line, using the words 'carry 10' or 'carry 100', not 'carry 1'. Later, extend to adding three two-digit numbers, two three-digit numbers, numbers with different numbers of digits and decimals.

  6. In action Use the compact column method to find answer to this question. 167 + 47

  7. Cakes and Calculations Subtraction

  8. Mental Strategies for Subtraction Secure mental subtraction requires the ability to: • recall subtraction facts (inverse of number pairs to 10, 20 & 100, halves etc) • mentally subtract combinations of one and two digit numbers • understand that subtraction is the inverse of addition and it ‘finds the difference’ between 2 numbers • understand the language of subtraction (less, minus, take away, difference between etc)

  9. Written methods for Subtraction The empty number line The empty number line helps to record the steps in mental subtraction. There are several ways to do this: • Counting Back - a calculation like 74 - 27 can be recorded by counting back 27 from 74 to reach 47. • Counting On - the steps can also be recorded by counting up from the smaller number to find the difference

  10. Written methods for Subtraction The empty number line With practice, children will need to record less information and decide whether to count back or forward. With three-digit numbers the number of steps can again be reduced, provided that children are able to work out answers to calculations such as: 178 + ? = 200 and 200 + ? = 326 mentally. or

  11. In action Use a number line to find answers to this question. 142 - 35

  12. Written methods for Subtraction Column method A classic method we all remember from our school days! It is very important that the higher number goes on top and you start subtracting from the ones column first.

  13. In action Use the compact column method to find answer to this question. 166 - 47

  14. Cakes and Calculations Multiplication

  15. Mental Strategies for Multiplication To multiply successfully, children need to be able to: • recall all multiplication facts to 12 × 12 • apply times tables facts to similar calculations such as 7 x 5 70 × 5 • partition numbers into multiples of Hundreds, Tens and Units • understand the language of multiplication including lots of, groups of, times, multiply, product

  16. Written methods for Multiplication Mental multiplication using partitioning This allows the tens and ones to be multiplied separately. These are then added to find the total product.

  17. Written methods for Multiplication The Grid Method This links directly to the mental method. It is an alternative way of recording the same steps. • Draw the Grid • Partition • Multiply • Add • 35x7=

  18. Written methods for Multiplication

  19. In action We will have a go at solving this question using the grid method. 67 x 6 =

  20. Written methods for Multiplication Expanded short multiplication The next step is to represent the method in a column format, but showing the working. The first step in 38 × 7 is ‘thirty multiplied by seven’, not ‘three times seven’, although the relationship is highlighted. Most children should be able to use this expanded method for TU × U by the end of Year 4.

  21. In Action Now we will use the expanded column method to solve this question. 32 x 8

  22. Cakes and Calculations Division

  23. Mental Strategies for Division To divide successfully, children need to be able to: • partition two-digit and three-digit numbers • recall multiplication and division facts to 12 × 12 • know how to find a remainder working example, find the remainder when 48 is divided by 5; • understand and use multiplication and division as inverse operations. • understand and use the vocabulary of division

  24. Written methods for Division Mental division using partitioning 84 ÷ 7 might be:

  25. Written methods for Division 'Expanded' method for TU ÷ U and HTU ÷ U This method, often referred to as 'chunking', is based on subtracting multiples of the divisor, or 'chunks

  26. Written methods for Division Refining the 'Expanded' method for HTU ÷ U Initially children subtract several chunks, but with practice they should look for the biggest multiples that they can find to subtract, to reduce the number of steps.

  27. In Action Now we will use the ‘chunking’ method to solve this question. 86 ÷ 7

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