Sums and Things for Parents

1
Sums and Things for Parents
I think of a number and add 6. My answer is
negative 7, what number did I start with?
2
Sums and Things for Parents
Negative 13
Well done Lucie. How did you think that through?
3
The story so far .

• childrens recall of number facts has
  become more accurate and faster
• children are more aware of the strategies
  they use to calculate
• they use vocabulary correctly
• they are more confident about maths
• maths is more fun!

4
What can a numerate child do?

• By the age of 11 they should
  
• have a sense of the size of number and
  where it fits into the number system
• know by heart addition and subtraction
  facts to 20, multiplication and division
  facts to 10x10, doubles and halves,
  complements to 100, multiply and divide by
  10 and 100
• use what they know to figure out
  answers mentally

5
What can a numerate child do? (cont.)

• calculate accurately and efficiently, both
  mentally and on paper, using a range
  of strategies
• recognise when it is appropriate to use a
  calculator- and when it is not- and be
  able to use one effectively
• explain their methods and reasoning
  using correct mathematical terms
• judge whether their answers are
  reasonable and have strategies for checking
  them where necessary

6
The aim

• The aim is for children to do mathematics in
  their heads, and if the numbers are too
  large, to use pencil and paper to avoid
  losing track. To do this children need to
  learn quick and efficient methods,
  including appropriate written methods.

7
Learning written methods is not the ultimate aim.

• Mathematics is foremost an activity of the
  mind, and written calculations are an aid
  to that mental activity.
• The Numeracy Strategy aims to develop
  childrens mental strategies and then
  written methods that derive from and
  support mental methods.

8
We want children to ask themselves
Can I do this in my head? Can I do this in my
head using drawings or jottings? Do I need to use
an expanded/compact written method? Do I need a
calculator?
9
How do you add and subtract?
61 45 7800 5600 5735 3657 5735 3990 83
68 5002 4996 538 - 295 267 267 2.5
2.7 5.1 - 2.78
10
Mistakes children make
1
16 - 9
11
.and more
643 274 8117

• 803
• 526
• 187

12
Addition

• 76 47

13
Addition
358 473
11
120
700
831
14
Addition
176 147
100 70 6 100 40 7 200
110 13
323
15
Subtraction
Imran has 43 conkers he gives 24 away to his
friends. How many does he have left? 43 24

19 conkers
16
Subtraction
Sam has saved 93p, Amy has 55p. How much more
money does Sam have than Amy? 93 55
38p more
17
Subtraction
8.23 4.55 3.68
0.23
3
0.45
8.23
8.00
4.55
5.00
18
Subtraction
A sports stadium holds 9010 spectators. 5643
people attend a football match. How many empty
seats are there?
57
300
3010
5643
5700
9010
6000
3367 empty seats
19
How do you multiply and divide?
57 x 2 78 2 43 x 50 742 2 36
x 25 700 4 18 x 15 65.5 ?
10 8 x 19 17 5 34 x 7 5.4 6
20
Mistakes children make
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Multiplication
47 x 8 x 40 7 8 320 56 376 37 x 46
x 30 7 40 1200 280
1480 6 180 42 222
1702
22
leading to algebra at KS3
(a b)2
(a b) x (a b)
x a b a a2 ab a2 ab b ab b2 ab
b2
a2 2ab b2
(a b)2 a2 2ab b2
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Division
47 ? 8
24
or chunking
25
First using partitioning 87 7
First we partition the 87 into a convenient
multiple of 7 the rest
87 70 17
Now divide each part by 7 70 7 10 and 17
7 2 remainder 3
Now add the parts to give the answer 12 remainder
3
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Now on a number line 87 7
add 7x10 or 7 ten times
add 7x2 or 7 twice
87
70
84
0
We have added seven 12 times and have 3 left so
87 7 12 r 3
27
Now using repeated subtraction 87 7
A shop notice states that there are 87 shopping
days to Christmas. How many weeks is that?
87
-70 (10 weeks)
17
-14 (2 weeks)
3
So its 12 weeks (and 3 days) of shopping to
Christmas.
28
432 school children are going on an outing. If
each bus takes 15 passengers, how many buses will
be needed?
432
-300 (20 buses)
132
- 90 (6 buses)
42
-30 (2 buses)
12 (people left)
So we need 29 buses or 28 buses and some cars!
29
How can you help?
Talk about how you do maths
Be positive
Ask your child to explain
Give praise and encouragement
Make sure maths is fun!