have a go at this puzzle. what would you rather have? £5000 now, or 1p today, 2p tomorrow, 4p the...

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 £2,684,354.55

TA Training Day Thursday October 20th 2011

Ed Crocombe (crow-come)

Advanced Skills Teacher

Ferndown Middle School, (year 5 to year 8)

I have a hearing impairment!

Outline for the day

Session 1 – Key Features Of Maths

Session 2 – Approaches To Calculation: Mental and written strategies incorporating activities to support mental and written calculations

(sessions 1 and 2 will run from 9:15 to 12:25 with a pause for coffee at a convenient moment, probably about 10:45)

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 3:00pm.

cup of tea taken at a convenient moment, maybe middle of session 4.

Session 6 – Any questions (optional)

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 available for download from the Ferndown Middle School website.

Session 1 – Key Features Of Maths

Maths Is Fun!

What makes for a good maths lesson?

(discussion)

Player A

Player B

Player C

Player D

Playing board for the game Crooked Rules

Hundreds Tens Ones

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)

Key features of mathematics within the Primary National Strategy

The strategy involves:

1. A structured, daily mathematics lesson of 45–60 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.

Key features of mathematics within the Primary National Strategy

The strategy involves:

1. A structured, daily mathematics lesson of 45–60 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.

Key features of mathematics within the Primary National Strategy

The strategy involves:

1. A structured, daily mathematics lesson of 45–60 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.

Key features of mathematics within the Primary National Strategy

The strategy involves:

1. A structured, daily mathematics lesson of 45–60 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.

Teaching assistant’s tasks

• Planning the lesson with the teacher

• Assessing pupil’s 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.

Teaching assistant’s 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.

Teaching assistant’s 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.

Key Strategies for Mental Calculations

Number Bonds And Compliments

These are essential facts for children to know.

3 4

+

+

=

7=

This is an example of a number bond. If given the number 7 the child needs to identify two numbers which would add to give the target number.Bonds of ALL numbers up to 20 is a key skill to be mastered by the end of Year 2.

Key Strategies for Mental Calculations

Number Bonds And Compliments

3

+

+

=

7=?This is an example of a number compliment. If given the total 7 and one number, state the other which adds to make the targe

total.

Key Strategies for Mental Calculations

+ = 13

+ = 13

Show how many are in one hand; how many must now be in the other? (Consider ‘What’s In The Box’ game

Race To 100

This is a two player game.

The aim is to be the first player to take the running total to 100 or above.

Players take it in turns choosing numbers from 1 to 10.

Here is an example:

Player 1 chooses 7 running total is 7

Player 2 chooses 4 running total is 11

Player 1 chooses 10 running total is 21

Player 2 chooses 3 running total is 24

Lets play this game for a few minutes in small groups.

Shut The Box

Two dice are rolled and added.

Any combination of numbers can be ‘shut’ providing they equal the total of both dice.

Play continues until no further numbers can be ‘shut’.This becomes the player’s score for their first go and play transfers to another player.

This is a negative scoring game. Hence the first player to reach 50 LOSES.

If the box is successfully ‘shut’ then the player who shut the box wins that game irrespective of the scores.

I Am Thinking Of A Number

I am thinking of a number between 0 and 10,000.

Each time you guess I will tell you if you are too high or too low.

You have 14 guesses.

The Kidney Bean Game

There are 35 kidney beans in a pot.

Players take it in turns to take kidney beans out of the pot. You can take 1, 2, 3, 4 or 5 kidney beans at a time.

THE WINNER IS THE PLAYER WHO TAKES THE LAST HANDFUL AND LEAVES THE POT EMPTY.

Lets play this game for a few minutes in small groups.

In The Middle

How would you find the middle number in between 45 and 73?

Most people would find the difference, halve that difference and add it to the lower number.

But this would work and is often quicker:

45 + 73 then halve the result.

Tables Number Lines

Tables recall is very important.

Counting using a number line is a great way to develop tables rapid recall.

This number line shows the 7 times table:

0 1 2 3 4 5 6 7 8 9 10

0 7 14 21 28 35 42 49 56 63 70

Jigsaws

Lets have a go at one….

Session 2 – Approaches To Calculation: Mental And Written

and God said…..

……and there was light.

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

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?

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?

• Did having to explain your method help you in any way

• Did hearing any other person’s method help you in any way?

Try this one…

365

– 99

___

365 – 99

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.

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….’

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.

Subtraction

Using objects.

take away makes

Subtraction

Number Line

“What is 23 take away 8?”

232221201918171615

-1-1-1-1-1-1-1-1

Subtraction

Number Line Stage 2

“What is 23 take away 8?”

232221201918171615

-3-5

Subtraction

Number Line Stage Subtract 8 or 9

“What is 23 take away 8?”

232221201918171615

-10

1413

+2

Subtract 9 strategy often gets confused with subtract 11 strategy.

Subtraction

Number Line Going Forward

“What is 572 take away 238?”

572etcetc300290280270260250240238

Subtraction

Number Line Going Forward

“What is 572 take away 238?”

572500300240238

+2 +60+200 +72

Now add the jumps

It’s easiest to consider 262 + 72.

Subtraction

Write The Landing Numbers First

“What is 5271 take away 2638?”

50003000270026402638 5271

Subtraction

Then Write In The Jumps

“What is 5271 take away 2638?”

50003000270026402638

+2 +60+300 +2000

5271

+271

Now add the jumps. It is quite easy to add the first 4.

This leaves 2362 + 271 2362

+ 271

Now lets do some!

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 -

Have a go at the empty box sum questions.

Multiplication

Multiplication

Begin with rapid tables recall.

Then informal partitioning or use of a grid:

To solve 47 x 6:

6

40 7

6

40 7

240 42

Answer = 282

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?

Multiplication

Proof30 7

20

5

600 140

150 35

Adding these four values gives the answer 925

It is within this type of question that the ‘add zero’ rule can pop up.

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?

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.

Division

Sharing With Objects, Grouping With Cups

It can help for children’s general development to experience both models of early division.

Sharing can be easily be modelled with counters, sweets and the like.

Division

Sharing With Objects

It can help for children’s 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.

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)

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.

Session 3 – Language And Maths

Work out the total number of shapes:

Work out the total

Circle = 1

Rectangles = 4

Triangles = 5

Squares = 9

TOTAL = 19

Work out the total

15

Ellie’s problem

In your purse you have lots of 5p, 10p and 20p coins.

How could you pay for some fruit costing 45p?

Ed’s 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

Marie’s sum

This is the calculation Marie was asked to do:

+ 47 = 100

She wrote: 63 + 47 = 100

1. Get some coins / a calculator to ‘prove’ it

2. 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?

Closed To Open ~ Shapes

A

B

C

D

E

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.

You could do things like this:

6 2 3 8>

Or this…

1 2 2 1<

Or maybe even this…

3 x 8 = 6 x ?

9 - 2 = ? + 3

Language 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

How could the TA have been better briefed and equipped to help?

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.

Fall In The Water

Rules:

Choose what numbers between 1 and 20 (or 30 / 40 / 50 etc) will make you ‘fall in the water’

Take it in turns to roll the die and add to your own running total. If you fall in the water you start again at zero.

Poker Cups

Rules:

Each poker chip is worth a different value (these values can be changed)

Keep a track of the running total in cup A, cup B or BOTH cups if you are really brave!

3 5 7 8

Sessions 6 – Quick Activities

We will have a go at a couple of quick, meaningful ‘time-fillers’. Along with these are some useful websites:

www.online-translator.com/

www.echalk.co.uk/

www.sheppardsoftware.com/math.htm

www.arcademicskillbuilders.com/

www.senteacher.org

www.coolmath-games.com