Title: Have a go at this puzzle.
1Have 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
2TA Training Day Thursday September 24th 2009
Ed Crocombe (crowcome) Advanced Skills
Teacher Ferndown Middle School, (year 5 to year
8) I have a hearing impairment!
3Outline 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.
4Course 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
available for download from the Ferndown Middle
School website.
5Session 1 Key Features Of Maths
6Maths 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)
8You could do things like this
6
gt
2
3
8
9Or this
1
lt
2
2
1
10Or maybe even this
3
x
8
6
x
?
9

2
?
3
11Key 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.
12Key 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.
13Key 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.
14Key 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.
15What do you think about
 Homework
 Mental calculation strategies
16Teaching assistants tasks
 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.
17Teaching 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.
18Teaching 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.
19Session 2 Approaches To Calculation Mental And
Written
and God said..
and there was light.
20How 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
21Considering 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?
22Comparing 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?
 Did having to explain your method help you in any
way  Did hearing any other persons method help you in
any way?
23Try this one
365 99 ___
365 99
24Key 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.
25Written 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.
26Subtraction
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.
27Subtraction
Using objects.
take away
makes
28Subtraction
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
29Subtraction
Number Line Stage 2
What is 23 take away 8?
5
3
23
22
21
20
19
18
17
16
15
30Subtraction
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.
31Subtraction
Number Line Going Forward
What is 572 take away 238?
572
etc
etc
300
290
280
270
260
250
240
238
32Subtraction
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.
33Subtraction
Write The Landing Numbers First
What is 5271 take away 2638?
5000
3000
2700
2640
2638
5271
34Subtraction
Then Write In The Jumps
What is 5271 take away 2638?
2000
271
300
2
60
5000
3000
2700
2640
2638
5271
Now add the jumps. It is quite easy to add the
first 4. This leaves 2362 271
2362
271
35Subtraction
Expanded Subtraction
What is 5271 take away 2638?
Step 1
Step 2
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
36Subtraction
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 
37Subtraction
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.
38Multiplication
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
Answer 282
39Multiplication
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?
40Multiplication
Proof
30
7
20
600
140
Adding these four values gives the answer 925
150
35
5
It is within this type of question that the add
zero rule can pop up.
41Multiplication
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?
42Multiplication
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
43Division
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.
44Division
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.
45Division
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.
46Division
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)
47Division
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.
48Session 3 Language And Maths
49Work out the total number of shapes
50Work out the total
Circle 1 Rectangles 4 Triangles 5 Squares
9 TOTAL 19
51Work out the total
15
52Ellies problem
 In your purse you have lots of 5p, 10p and 20p
coins.  How could you pay for some fruit costing 45p?
53Eds Classroom
 Danielle working on 428 379
 We were using the number line as our primary
strategy.  Danielle had the correct answer. She, however,
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
54Maries 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?
55Closed To Open Shapes
C
A
B
D
E
56Closed 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.
57Session 4 The Role Of The T.A part 1
58The threepart 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
59Language and mathematics
 Pupils talking and listening to each other and to
adults  Adults listening to pupils responses
 Different kinds of questioning
 Video clip x 10 x 100
60Considering 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
wholeclass 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?
61Considering 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
wholeclass 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?
62The 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
63The 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  alerting the teacher if a pupil has 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
64Four 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
65Session 5  Role Of The T.A. Part 2
66Role of the TA in the video Julia Sherlock clip
2
 What are the main differences in the way the TA
supports pupils during wholeclass 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?
67Video 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?
68Working 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?
69The 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
70The 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
adult help  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
71Giving 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
72Notes 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
73Sessions 6 Quick Activities
FMS