 Extend written methods to column addition and subtraction of numbers involving decimals

Examples of what pupils should know and be able to do
Working with numbers to two decimal places, including:
 sums and differences with different numbers of digits
 totals of more than two numbers.
 Primary mathematics exemplification: Pencil and paper procedures (addition)
 Primary mathematics exemplification: Pencil and paper procedures (subtraction)
 Assessment example: Money problems: Azadur and Samantha (PDF927 KB) Attachments
 Assessment example: Money problems: Sam (PDF401 KB) Attachments
Probing questions
Make up an example of an addition/subtraction involving decimals that you would do in your head and one you would do on paper. Explain why.
Give pupils some completed questions to mark. All questions need to be written horizontally as well as in column form. Include incorrect answers such as $12.3+9.8=21.11$; $4.071.5=3.92$; $3.21.18=2.18$. Which are correct/incorrect? How do you know? Explain what has been done wrong and correct the answers.
What if pupils find this a barrier?
Ask pupils to bring in some old receipts, tear off the total part and pass the receipt to the pupil beside them to find the total. Can they do it on the receipt or do they need to lay it out differently?
For information on addition and subtraction with decimal notation refer to Mental and written calculation (PDF233 KB) Attachments .
 Targeting level 4 lesson: Decimals and money
 Targeting level 4 lesson: Adding and subtracting decimals
 Extend written methods to long multiplication of a threedigit by a twodigit integer

Examples of what pupils should know and be able to do
 Primary mathematics exemplification: Pencil and paper procedures (multiplication)
Calculate $324\times 56$ using the grid method.
Probing questions
Give pupils a multiplication question (for example, $147\times 32$) calculated by both the grid method and long multiplication. Ask questions such as: What two numbers multiplied together give 4410? Or 294?
Give pupils three or four long multiplications with mistakes in them. Ask them to identify the mistakes and talk through what is wrong and how they should be corrected.
What if pupils find this a barrier?
Download Mathematics ITP: Multiplication grid (SWF19 KB) Attachments . Hide some of the numbers around the outside but show some of the answers in the grid: discuss what the question could have been.
Mental and written calculation (PDF233 KB) Attachments
 Extend written methods to short division of TU by U (mixednumber answer)

Examples of what pupils should know and be able to do
 Primary mathematics exemplification: Pencil and paper procedures (division)
$21\xf75=4\frac{1}{5}$
Probing questions
Can you give me an example of a division question that will have a mixednumber answer? How would you need to change it so that it did not have a mixednumber answer?
If $21\xf75=4\frac{1}{5}$, what question would have the answer $4\frac{2}{5}$? Why?
What if pupils find this a barrier?
 Targeting level 4 lesson: Remainders
For information on written division refer to Mental and written calculation (PDF233 KB) Attachments .
 Extend written methods to division of HTU by TU (long division, whole number answer)

Examples of what pupils should know and be able to do
As with short division, use efficient methods of repeated subtraction, by subtracting multiples of the divisor, before moving to long division.
 Primary mathematics exemplification: Pencil and paper procedures (division)
Probing questions
How do you go about estimating the answer to a division?
Explain how you got the answer to this division.
Give pupils some long divisions (extended methods using multiples of the divisor and possibly a standard method) with typical mistakes in them. Ask them to find the mistakes and talk through what the person has done wrong. Ask them to correct the mistakes.
What if pupils find this a barrier?
Pupils may need to use repeated subtraction and then move to efficient repeated subtraction before they use a standard formal written method.
For information on written division refer to Mental and written calculation (PDF233 KB) Attachments .
 Extend written methods to short division of numbers involving decimals

Examples of what pupils should know and be able to do
 Primary mathematics exemplification: Pencil and paper procedures (division)
 Assessment example: Long multiplication and division: Jennie (PDF694 KB) Attachments
Probing questions
How can I use the answer to $56\xf77$ to work out $5.6\xf77$?
What advice would you give a friend about how best to do the calculation $0.49\xf77$? How do you think your friend could check their answer?
What if pupils find this a barrier?
 Targeting level 4 lesson: Dividing a decimal by a singledigit number
 Lesson idea: Written methods for division
 Identify and use the appropriate operations (including combinations of operations) to solve word problems involving numbers and quantities, and explain methods and reasoning

Examples of what pupils should know and be able to do
 Primary mathematics exemplification: Making decisions
 Assessment example: Gingerbread men: Chloe and Indi (PDF489 KB) Attachments
Probing questions
What clues do you look for in the wording of the problem to decide which operation(s) you need to use?
Could you solve the problem another way? Which is the most efficient?
What if pupils find this a barrier?
Model the process of solving word problems. Focus on vocabulary and how words relate to operations.
Encourage pupils to look at the numbers to decide on an appropriate way of calculating – mentally or using written methods.
 Targeting level 4 lesson: Word problems involving decimals
 Targeting level 4 lesson: Reasoning about numbers (✕ and ÷ problems)
Attachments
Related downloads
 Money problems: Azadur and Samantha [ pdf : 927 KB ]
 Money problems: Sam [ pdf : 401 KB ]
 Long multiplication and division: Jennie [ pdf : 694 KB ]
 Gingerbread men: Chloe and Indi [ pdf : 489 KB ]
 Mathematics ITP: Multiplication grid
 [Windows executable]  [ exe : 4.1 MB ]
 [Flash]  [ swf : 19 KB ]
 Mental and written calculation [ pdf : 233 KB ]
 Download all [ 2.6 MB ]