Summary of the Steps for Written Calculation Multiplication 1

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1 Summary of the Steps for Written Calculation Multiplication Steps - lead children through the necessary stages for mastering the traditional column method of short multiplication and begin to prepare them for long multiplication. This method involves setting out digits vertically and in columns, multiplying the digit in each column by the multiplier, from right to left and, where a total of more than 9 is made, carrying a digit to the column to its left and adding it to the next product. As with column addition, the carried digit is placed below the answer line (carried digits are in red in this document). Children should always be encouraged to estimate the answer first to give them an idea of how correct their final answer is likely to be. If children are not fully secure with their multiplication tables, they should be provided with multiplication squares when completing column multiplication as this will enable them to master the method without their fluency being hampered by lack of rapid recall. (However, it is obviously vitally important to continue to work on teaching and practising rapid recall of multiplication facts). Step : Two-digit x one-digit no carrying; eg: 3 x = Step : Two-digit x one-digit carrying units to tens; eg: 6 = Carrying is introduced in Step. Begin with easier multipliers (eg:, 3, 4) then progress to more difficult multipliers (eg: 6, 7, 8, 9). For pupils who struggle to understand why we carry, show the expanded form of the multiplication (digit in bold is the carried digit). This form may be used at any stage to aid understanding but it is the concise column method in which the children must be proficient. 6 8 (3 x 6) +60 (3 x 0) 78 Step 3: Three-digit x one-digit carrying units to tens; eg: 38 = Step 4: Three-digit x one-digit carrying tens to hundreds; eg: 6 =

2 In Steps 3 and 4, carrying takes place in the same way but with three-digit numbers. The expanded form can be demonstrated again to explain why/where we carry (digit in bold is the carried digit): 6 3 (3 x ) 80 (3 x 60) (3 x 00) 783 Step 5: Two-digit x one-digit carrying tens to hundreds; eg: 8 = In Step 5 children are reminded that, if there are no hundreds to be multiplied but there is a carried digit, this carried digit ( in the example above)must be written into the hundreds column of the answer. Children will gradually learn that the carried digit can be written straight into the answer. Step 6: Two-digit x one-digit carrying twice; eg: 94 x 7 = x Step 7: Three-digit x one-digit carrying twice with answers greater than 000; eg: 97 x 5 = 4, x By this stage, children are becoming more familiar with the process of carrying but mistakes may now involve inaccurate recall of tables facts. This is where multiplication squares can help. In Step 7 there are no thousands to be multiplied but there is a carried digit (4 in the example). This digit must be written into the thousands column of the answer. Step 8: Four-digit x one-digit carrying up to four times; eg: 5,847 = 7, Step 9: Four- and five-digit x one-digit; eg: 9,786 x 6 = 8, x

3 By now, children should be proficient in the carrying technique with column multiplication and will realise that the process of multiplication is the same for very large numbers. They can then be provided with opportunities to name and use large numbers and to multiply them to make larger totals. Practise reading the larger numbers with the children and discuss the place value of each of the digits. Explain how digits in larger numbers are grouped into sets of 3 from the right, ie:,653,40. (Do not use commas in column multiplication to avoid confusion with decimal points in later calculations). Step 0: Three-digit x 0 or x 0; eg: 37 x 0 = 4, x A zero is placed in the units column as we are multiplying by a multiple of 0. Then multiply 37 x but writing the digits one place to the left. Step : Three-digit x any two-digit multiple of 0; eg: 638 x 40 = 5, x A zero is placed in the units column as we are multiplying by a multiple of 0. 3 Then multiply 638 x 4, writing the digits one place to the left. Step : Four- and five-digit x any two-digit multiple of 0; eg: 0,64 x 70 = 744, x A zero is placed in the units column as we are multiplying by a multiple of 0. 4 Then multiply 064 x 7, writing the digits one place to the left.

4 Summary of the Steps for Written Calculation Multiplication Steps 3-9 lead children on from mastering the traditional column method of short multiplication to mastering long multiplication. There is also practice in multiplying decimals. Long multiplication involves setting out digits vertically in columns, multiplying each digit of the first number by each digit of the multiplier in turn (giving a line for each) and then adding to find the total. Carried digits are shown directly under each answer, then crossed out when no longer required to avoid confusion when adding to reach the final answer. Children should continue to estimate the answer first to give them an idea of how correct their final answer is likely to be. Step 3: Two- and three-digit x a teens number no carrying in the addition; eg: 04 x 3 =,65 04 x (Write the top number x unit of the multiplier here) x 0 (Write the top number x multiple of 0 of the multiplier here) 65 NB: The small red is the carried ten from 3 x 4. The children should be encouraged to write these carried digits as small as possible then cross them off as they are added, so as not to cause confusion when calculating the final addition. Children should be taught to firstly multiply the top number by the unit of the multiplier, as with short multiplication. In the next row they multiply the top number by 0. A zero is placed in the units column (place holder) to indicate x by 0, then the top number is multiplied by, writing the digits one place to the left. This process will then be used in more difficult calculations when multiplying by any multiple of 0. Finally, the two answers are added together. It is good practice for children to write which numbers are being multiplied together, next to each row; 04 and 04 x 0 in the example above, as this helps their understanding of the construction of the calculation. As they become more proficient, this is not always necessary. Step 4: Two- and three-digit x a teens number carrying in the addition; eg: 364 x 8 = 6, x x x Step 5: Two- and three-digit x two-digit no carrying in the addition; eg: 8 5 = 9, x NB: Children should be reminded here to be careful not to add the carried digits used when multiplying, but only to add the digits of the two answers, ie:, ,430. The carried digits can be crossed out as they are used.

5 Step 6: Two- and three-digit x two-digit with carrying in the addition; eg: 73 6 = 9, x Step 7: Three-digit x two-digit with five-digit answers; eg: 984 x 73 = 7, x x By now, children should be proficient in the long multiplication technique and will realise that the process of long multiplication is the same for very large numbers. They can then be provided with opportunities to name and use larger numbers and to multiply them by any two-digit number using long multiplication. Continue to practise reading the larger numbers with the children and discuss the place value of each of the digits. Recap how digits in larger numbers are grouped into sets of 3 from the right, ie:,653,40. (Do not use commas in long multiplication to avoid confusion with decimal points in later calculations). Step 8: Simple decimals x one- and two-digit numbers; eg: = x 4 (Write the top number x unit of the multiplier here) (Write the top number x multiple of 0 of the multiplier here) 56 Once the answer has been calculated the decimal point is put back in, ie: 56 becomes 5.6 When multiplying decimals, the multiplication should be written without the decimal point. Once the answer has been calculated, the decimal point must be put back in; eg: in the example above there is one decimal place in the question, therefore the answer should have one decimal place ie 5.6 Step 9: Multiplying two decimals with one or two decimal places; eg: 9.84 x x (Write the top number x unit of the multiplier here) x 70 (Write the top number x multiple of 0 of the multiplier here) Once the answer has been calculated the decimal point is put back in, ie: 783 becomes 7.83 As in Step 8, the multiplication is written without the decimal point. In the question there is a total of three decimal places, therefore the answer must have three decimal places, so 783 becomes 7.83

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