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### Session 1 Key Features Of Maths Session 2 Approaches To Calculation: Mental and written strategies (this session will run from about 10:00 until lunch at 12:00. – PowerPoint PPT presentation

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Title: Have a go at this puzzle.

1
Have a go at this puzzle.
What would you rather have? 5000 NOW, or 1p
today, 2p tomorrow, 4p the following day, 8p the
day after, doubling every day for 4 weeks?
If you could wait 4 weeks, you would end up with
2,683,355
2
TA Training Day Thursday September 24th 2009
Teacher Ferndown Middle School, (year 5 to year
8) I have a hearing impairment!
3
Outline for the day
Session 1 Key Features Of Maths Session 2
Approaches To Calculation Mental and written
strategies (this session will run from about
1000 until lunch at 1200. We will stop for
coffee at about 1100) Session 3 Language and
Maths Session 4 Role Of The TA In A
Lesson Session 5 Effective Quick
Activities with a planned finish time of 315pm.
cup of tea taken at a convenient moment, maybe
middle of session 4.
4
Course Book
I have altered the order in which the pages in
the coursebook will be used. I will tell you what
page you need and when. This entire PowerPoint
presentation and all accompanying resources are
School website.
5
Session 1 Key Features Of Maths
6
Maths Is Fun!
What makes for a good maths lesson? (discussion)
7
Playing board for the game Crooked Rules
Hundreds
Tens
Ones
Player A Player B Player C Player D
Note die singular, dice plural No die? Why
not number some blank playing cards. Then you
could go 0 to 9. Anyone got Spin To Win? Primary
Games volume 1, (www.primarygames.co.uk)
8
You could do things like this
6
gt
2
3
8
9
Or this
1
lt
2
2
1
10
Or maybe even this
3
x
8

6
x
?
9
-
2

?

3
11
Key features of mathematics within the Primary
National Strategy
• The strategy involves
• 1. A structured, daily mathematics lesson of
4560 minutes, depending on the pupils ages
• 2. An emphasis on mental calculation with oral
and mental work in each lesson
• 3. Direct, interactive teaching of the whole
class, with as many pupils as possible taking
part
• 4. Group work in which pupils in three or four
groups work at different levels on the same topic
• 5. Regular activities for pupils to do out of
class and at home
• 6. The Primary Framework offers teachers guidance
on planning and teaching to help all children to
learn mathematics and make good progress.

12
Key features of mathematics within the Primary
National Strategy
• The strategy involves
• 1. A structured, daily mathematics lesson of
4560 minutes, depending on the pupils ages
• 2. An emphasis on mental calculation with oral
and mental work in each lesson
• 3. Direct, interactive teaching of the whole
class, with as many pupils as possible taking
part
• 4. Group work in which pupils in three or four
groups work at different levels on the same topic
• 5. Regular activities for pupils to do out of
class and at home
• 6. The Primary Framework offers teachers guidance
on planning and teaching to help all children to
learn mathematics and make good progress.

13
Key features of mathematics within the Primary
National Strategy
• The strategy involves
• 1. A structured, daily mathematics lesson of
4560 minutes, depending on the pupils ages
• 2. An emphasis on mental calculation with oral
and mental work in each lesson
• 3. Direct, interactive teaching of the whole
class, with as many pupils as possible taking
part
• 4. Group work in which pupils in three or four
groups work at different levels on the same topic
• 5. Regular activities for pupils to do out of
class and at home
• 6. The Primary Framework offers teachers guidance
on planning and teaching to help all children to
learn mathematics and make good progress.

14
Key features of mathematics within the Primary
National Strategy
• The strategy involves
• 1. A structured, daily mathematics lesson of
4560 minutes, depending on the pupils ages
• 2. An emphasis on mental calculation with oral
and mental work in each lesson
• 3. Direct, interactive teaching of the whole
class, with as many pupils as possible taking
part
• 4. Group work in which pupils in three or four
groups work at different levels on the same topic
• 5. Regular activities for pupils to do out of
class and at home
• 6. The Primary Framework offers teachers guidance
on planning and teaching to help all children to
learn mathematics and make good progress.

15
• Homework
• Mental calculation strategies

16
• Planning the lesson with the teacher
• Assessing pupils progress and difficulties
• Making learning resources and classroom displays
• Getting the class ready to begin work
• Giving out learning materials
• Helping pupils with correct vocabulary

Video clip Newcastle Compare similarities and
differences to your own experience. Discussion.
17
Teaching assistants activities
• Helping pupils use mental, informal or formal
methods of calculation
• Learning new mathematics themselves
• Helping pupils read and understand what is needed
• Asking pupils questions to probe and secure their
learning
• Encouraging pupils in their efforts
• Helping pupils see the links with other learning
• Knowing when to intervene and when to back off.

18
Teaching assistants activities
• Helping pupils use mental, informal or formal
methods of calculation
• Learning new mathematics themselves
• Helping pupils read and understand what is needed
• Asking pupils questions to probe and secure their
learning
• Encouraging pupils in their efforts
• Helping pupils see the links with other learning
• Knowing when to intervene and when to back off.

19
Session 2 Approaches To Calculation Mental And
Written
and God said..
and there was light.
20
How would you tackle these calculations?
• 1). 23 9
• 2). 127 x 6
• 3). 4358 843 276
• 4). 98 6
• 5). 5 8 5
• 6). 4 7 8 6 3
• 7). 24 17 16 12 33
• 8). 2.54 2.67 1.46

21
Considering how you did the calculations
• How did you work out each calculation?
• Who did it another way?
• Which is the easiest way?
• What did you jot down to help you? How did this
help and how might you encourage pupils to use
jottings?

22
Comparing methods
• Were you surprised by any of the methods others
used?
• Were you taught to use any of these methods at
school?
• Why do you think you use them now?
way
any way?

23
Try this one
365 99 ___
365 99
24
Key skills to develop

Rapid recall of bonds and complements. Addition
and subtraction by rounding and adjusting. Rapid
recall of tables facts. Rapid recall of division
facts which correspond to tables facts. Ability
to complete division with remainders using
numbers within the range of the tables
recall. Halving by partitioning and combining
halving of values where the digit itself is odd
including amounts of money. Writing numbers in
digits when read aloud with a focus on zero as
place holder.
25
Written Methods
T.A.s have asked for upskilling on written
methods. We will now take some time to look
at Addition from number line to
columns Subtraction methods number
line expanded subtraction compact
borrowing Written multiplication TU x U to
TU x TU Written division what have you seen
going on?
You can have such an impact by suggesting to a
teacher I saw this bloke called Ed doing this.
26
Subtraction
Subtraction begins by children literally taking
away with objects. This then progresses to
counting backwards on the number line. FIND THE
DIFFERENCE SHOULD BE INTRODUCED HERE! Children
SHOULD then progress to counting FORWARD on the
number line.
27
Subtraction
Using objects.
take away
makes
28
Subtraction
Number Line
What is 23 take away 8?
-1
-1
-1
-1
-1
-1
-1
-1
23
22
21
20
19
18
17
16
15
29
Subtraction
Number Line Stage 2
What is 23 take away 8?
-5
-3
23
22
21
20
19
18
17
16
15
30
Subtraction
Number Line Stage Subtract 8 or 9
What is 23 take away 8?
2
-10
23
22
21
20
19
18
17
16
15
14
13
Subtract 9 strategy often gets confused with
subtract 11 strategy.
31
Subtraction
Number Line Going Forward
What is 572 take away 238?
572
etc
etc
300
290
280
270
260
250
240
238
32
Subtraction
Number Line Going Forward
What is 572 take away 238?
200
72
2
60
572
500
300
240
238
Now add the jumps Its easiest to consider 262
72.
33
Subtraction
Write The Landing Numbers First
What is 5271 take away 2638?
5000
3000
2700
2640
2638
5271
34
Subtraction
Then Write In The Jumps
What is 5271 take away 2638?
2000
271
300
2
60
5000
3000
2700
2640
2638
5271
first 4. This leaves 2362 271
2362
271
35
Subtraction
Expanded Subtraction
What is 5271 take away 2638?
Step 1
Step 2
• 200 70 1
• 2000 600 30 8

Step 3
60
4000
• 200 70 1
• 2000 600 30 8
• 2000 6000 30 3

1
1
Sometimes 4 steps needed. Answer here is 2633
36
Subtraction
The Equals Sign
Children tend to be taught that the answer goes
after the equals sign. They can do this 12 7
But not this 7 12 -
37
Subtraction
Lets Do Some Sums!
We will spend a few moments now doing some
sums. End of Y2 children beginning to work
forwards on the number line From Y3 children
can solve a variety of empty box sums End of
Y4 children can bridge on the number line
values up to 10,000 and also work with
money. End of Y6 children have compact
strategy for subtraction.
38
Multiplication
Multiplication
Begin with rapid tables recall. Then informal
partitioning or use of a grid
To solve 47 x 6
40 7
40 7
6
6
240
42
39
Multiplication
Classic Error
Then when faced with a question like this 37 x
25 Children will do 30 x 20 and 7 x 5 This is
WRONG. (but they often cannot see why) The sum 37
x 25 would need a grid like this
Can you see why this proves 30 x 20 and 7 x 5 is
incorrect?
40
Multiplication
Proof
30
7
20
600
140
150
35
5
It is within this type of question that the add
zero rule can pop up.
41
Multiplication
Errors
Question 1 78 x 96 Question 2 63 x 54 Question
2 will cause more errors than question 1. Why do
you think this is?
42
Multiplication
And now some more sums
We will now spend a few moments doing some
calculations. You choose some questions to
complete. TU x U end of Year 3 TU x TU end of
Year 4 HTU x TU end of Year 6 1 decimal place x
U end of Year 6
43
Division
Sharing Or Grouping
These tend to be the classic early models of
division. They are slightly different. I will
model the difference on the flip chart.
44
Division
Sharing With Objects, Grouping With Cups
It can help for childrens general development to
experience both models of early division. Sharing
can be easily be modelled with counters, sweets
and the like.
45
Division
Sharing With Objects
It can help for childrens general development to
experience both models of early division. Sharing
can be easily be modelled with counters, sweets
and the like. For example 32 6.
46
Division
Grouping With Cups
This involves how many groups of the divisor can
be made. For example 32 6. (This is best done
with a practical model)
47
Division
Old Method v Chunking
This is more top end KS2. Take some time now to
consider some children you work with. Are there
any tips, hints or strategies here you could take
back to the classroom? Is there anything here
which you could share with your teacher(s) or
even the whole staff? If anyone wants to talk
about more formal division I will do this in
small groups or individually.
48
Session 3 Language And Maths
49
Work out the total number of shapes
50
Work out the total
Circle 1 Rectangles 4 Triangles 5 Squares
9 TOTAL 19
51
Work out the total
15
52
Ellies problem
• In your purse you have lots of 5p, 10p and 20p
coins.
• How could you pay for some fruit costing 45p?

53
Eds Classroom
• Danielle working on 428 379
• We were using the number line as our primary
strategy.
said this
• I took the 300 away from 400.
• I then got a bit worried. She carried on.
• She struggled to explain but in the end we
figured out she had turned 428 379 into 128 - 79

54
Maries sum
This is the calculation Marie was asked to do
47 100 She wrote 63 47 100
• Get some coins / a calculator to prove it
• Suggest the child makes up some of their own
what do they notice? (tens values add to 90).

Do you find that sometimes children cannot spot
an error?
55
Closed To Open Shapes
C
A
B
D
E
56
Closed To Open Number
Write down a multiple of 5.
Write down a multiple of 5 that is bigger than 20.
Write down a multiple of 5 that is bigger than 20
and is also a multiple of 7.
Write down a multiple of 5 that is bigger than
20, that is also a multiple of 7 and is even.
Write down a multiple of 5 that is bigger than
20, that is also a multiple of 7, that is even
and is not a multiple of 10.
57
Session 4 The Role Of The T.A part 1
58
The three-part lesson
• Oral and mental activity Oral and mental
calculation for the whole class to rehearse and
sharpen skills
• Main part of the lesson Interactive teaching
input and pupils activities including work as a
whole class, in groups, in pairs or individually
• Review of learning
• All pupils involved Clear up any
misunderstandings and identify progress Summarise
and reinforce the key learning points and what
pupils should remember and discuss next steps

59
Language and mathematics
• Pupils talking and listening to each other and to
• Adults listening to pupils responses
• Different kinds of questioning
• Video clip x 10 x 100

60
Considering the role of the TA in the video
• How was the girl encouraged to test her answers
on the TA?
• Why is it important that she is encouraged to do
this?
• What is the best seating position during
whole-class interactive mental and oral
activities? Why?
• The TA encourages the girl to use the fraction
wall. What problem do you think she might have?
• How does the fraction wall help?
• Do you know of any other resources that could be
used?
• How could the TA have helped the two pupils
before the Follow Me card activity began?
• How do you know the TA used these activities for
assessment for learning purposes?

61
Considering the role of the TA in the video
• How was the girl encouraged to test her answers
on the TA?
• Why is it important that she is encouraged to do
this?
• What is the best seating position during
whole-class interactive mental and oral
activities? Why?
• The TA encourages the girl to use the fraction
wall. What problem do you think she might have?
• How does the fraction wall help?
• Do you know of any other resources that could be
used?
• How could the TA have helped the two pupils
before the Follow Me card activity began?
• How do you know the TA used these activities for
assessment for learning purposes?

62
The role of the TA in the oral and mental
activity (1)
• Being responsible for a small group of pupils to
ensure they take part in the lesson by
• encouraging them to join in counting activities
• encouraging them to sit still and take part
• getting them to repeat in a whisper what they
hear
• having a smaller version of the resource used by
the teacher
• helping pupils to use resources such as fan
cards

63
The role of the TA in the oral and mental
activity (2)
• Being responsible for a small group of pupils to
ensure they take part in the lesson by
• repeating discreetly questions the teacher asks
and helping the pupils find an answer
• asking questions that will help pupils to think
when they are discussing in pairs
• observing pupils and making notes about their
responses to questions

PROMT
64
Four In A Row
• Rules
• Make one of the numbers on the playing board
using the numbers 1, 2, 3, 4 and the symbols ,
x, , -, and brackets. Each number MUST be used
once and once only.

KS1 20 Objects In The Tin Chose 2 numbers which
you can add to make the objects Chose 3
numbers. I have taken 3 objects out. How many
are left? (with then without counting) Teddy
Bear Combinations
65
Session 5 - Role Of The T.A. Part 2
66
Role of the TA in the video Julia Sherlock clip
2
• What are the main differences in the way the TA
supports pupils during whole-class interactive
teaching and during group work?
• Why is it important for the TA to be present
during the direct teaching that takes place
before the group work?
• How do the teacher and the TA help pupils when
they have difficulties without simply telling
them what to do?
• What advantage does the TA have over the teacher
while she is involved in direct teaching?

67
Video clip working with children in the Early
Years clips from foundation session 4
• 1. How do the TAs involve the children?
• 2. What sort of questions do they ask?
• 3. Do they help children to work and play
together in any way?
• 4. How do they develop mathematical vocabulary?
• 5. How successful are they in helping the
children learn new skills?
• 6. What else could they do to help the children
with their learning?

68
Working with a group
• How would you support a group of pupils playing a
game like Fall in the water?
• How would your role differ if pupils were
carrying out a practice exercise or solving
mathematical word problems rather than playing a
game?
• What kind of feedback do you think you might give?

69
The TAs role when working with a group (1)
• When pupils are playing a game
• make sure they all understand the instructions
• reinforce social skills such as taking turns and
not interrupting others
• encourage pupils to describe the mental
strategies they used and help them to refine
these, using jottings on the empty number line
where necessary
• encourage them to work out and consider carefully
any options available to them in the game
• note for the teacher any number facts the pupils
find hard to remember and any observations about
pupils who have found the task difficult or who
have been particularly successful

70
The TAs role when working with a group (2)
• When pupils are carrying out practice exercises
or solving word problems
• ensure they understand what they have to do and
then monitor that they are performing the task
correctly
• ask questions or give them clues when they are
stuck but dont let them become too dependent on
• help to keep them on task and remind them how
much time they have to complete the exercise
• help them to learn, read and use mathematical
words and terms new to them
• make sure that they check answers for
reasonableness
• encourage them to tell you how they tackled
certain examples
• note what pupils have learned or any mathematics
they need more help with so you can share it with
the teacher

71
Giving feedback
• You could
• mention any misunderstandings pupils had in
relation to the work
• state how far pupils got with the activity
• list what they found easy and/or hard
• mention a pupil who has done particularly well or
who has found the work particularly difficult
• discuss support and next steps in learning
with the teacher

72
Notes for the teacher
• Learning objectives for the lesson (year 1, block
B, unit 2)
• Describe simple patterns and relationships
involving numbers or shapes decide whether
examples satisfy given conditions
• Feedback notes
• All can use numbers or shapes to make patterns of
their own
• All can describe their pattern so that others can
make it
• Rupee and Paul can tell each other how to
continue their patterns

73
Sessions 6 Quick Activities
FMS