Transcript Maths workshop

Parents Numeracy
Workshop
Strategies for
Addition & Subtraction
The National Numeracy
Strategy
Good teaching incorporates:
• An oral/ mental starter
• Main teaching focus
• Plenary
• ICT
• Assessment for Learning as well as
Assessment of Learning
Assessment for learning
•
•
•
•
•
Shared learning intention
Planned success criteria
Pupil self-assessment
Talk about and explain maths
Written and oral feedback
Supporting your child
at home
Think about:
• The value of children explaining the task
to their parents
• Ways in which the parent supports the
child’s learning through listening,
encouraging and confirming
• The quality of work – content and
presentation
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
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
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.
Learning written methods is not
the ultimate aim.
 Mathematics is mainly an activity of the
mind, and written calculations are an aid
to that mental activity.
 The Numeracy Strategy aims to develop
children’s mental strategies and then
written methods that derive from and
support mental methods.
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?
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
Mistakes children make:
1
16
-
9
…….and more:
643
6
10
13
803
+ 274
- 526
8117
187
These equations are
carried out horizontally
• which leads to
Addition
76 + 47 =
+10
76
+10
86
+10
96
+10
106
+7
116
+ 40
76
123
+7
116
123
Addition
358 + 473 =
358
358
+ 473
+ 473
11
120
831
700
831
1
1
Subtraction
Imran has 43 conkers; he gives 24 away to his
friends. How many does he have left?
43 – 24 =
19 20
-1
19 conkers
23
-3
33
-10
43
-10
Subtraction
Sam has saved 93p, Amy has 55p. How much
more money does Sam have than Amy?
93 – 55 =
+5
55
+30
60
+3
90
38p more
93
Subtraction
8.23 – 4.55 =
+0.45
4.55
3.68
5.00
+3
+0.23
8.00
8.23
Subtraction
A sports stadium holds 9010 spectators. 5643
people attend a football match. How many
empty seats are there?
+ 57
5643
5700
+300
+3010
6000
9010
5643
3367 empty seats
5700
6000
9010
57
+300
+3010
3367
Parents Numeracy
Workshop
Strategies for
Multiplication & Division
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
Mistakes children make:
76
67
8
x 54
5648
268
x
335
101 r 5
7 847
603
Multiplication
Early stages
• Counting in groups of
• Arrays or repeated addition
• 3x2 or 2 x3
•
•
•
But also 2X 3= 6
3 x 2= 6
x3=6
Multiplication
Later
• Partition 23 x 4
•
20 x 4 = 80
•
3 x 4 = 12
•
92
Multiplication
More formal methods
47 x 8 =
x
8
40
320
7
56
30
1200
180
7
280
42
376
37 x 46 =
x
40
6
1480
222
1702
Multiplying using more
traditional methods
• 27
• X5
• 135
• 3
• 33
• X 24
• 132
• 660
• 932
Division early on
• Groups of and sharing
• But also
•
•
•
6÷3=2
6÷2= 3
÷2= 3
Division
47  8
375  43
8
47
43 375
First on a number line
3
87 ÷ 7
17
87
-14
subtract 7x2 or 7 twice
-70
subtract 7x10 or 7 ten times
We have subtracted seven
12 times and have 3 left
so… 87 ÷ 7 = 12 r 3
A shop notice states that there are 87 shopping
days to Christmas. How many weeks is that?
87
-70
(x10 weeks)
17
-14
(x2 weeks)
3
So it’s 12 weeks (and 3 days) of shopping to
Christmas.
432 school children are going on an outing. If
each bus takes 15 passengers, how many buses
will be needed?
432
-300
132
(x20 buses)
- 90
(x6 buses)
42
-30
(x2 buses)
12
(people left)
So we need 29 buses or 28 buses and some
cars!
Parents Numeracy
Workshop
Division: mental & written methods
Understanding relationships
between multiplication & division
17 x ? = 34
? -:- 5 = 90
? x 4 = 1600
20 x ? = 8000
? x 0.5 = 35
640 -:- ? = 32
What operations did you use?
Using informal pencil and paper
methods to support, record or
explain divisions
Self adhesive stamps come in
sheets of 24.
1. Estimate how many sheets you
would need to buy if you wanted
500 stamps.
2. How would we work it out exactly?
“Chunking” method
Subtracting multiples of 24 from 500.
Answer
How many coaches would be needed
to take 780 people on coaches which
hold 42 people each?
How could we use the chunking
method to answer this question?
Rounding up or down after division,
depending on the context
Calculator activity:
500 -:- 24 =
What does the decimal part mean?
How many CDs at £11.99 each could you
buy with £50?
Estimate?
Use a calculator
What does the decimal part represent?
Is there enough money to buy 5 CDs?
Strategies for problem
solving
• Read the problem
• Understand the problem
• Choose the operation and estimate
the answer
• Solve the problem
• Answer the question
• Check the answer
Identify and use appropriate
operations to solve word problems
involving numbers and quantities
89 children are camping. There are 3
tents that each take 9 children and
the other tents take 4 children.
How many tents taking 4 children are
needed, and how many tents are
needed all together?
Estimate and record working