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Aspiration Respect Endeavour
How do we know what your child is 
capable of? 
• Prior Attainment Predictions 
• Fischer Family Trust data (Band D) 
• 3 and 4 Levels of Progress (Core Subjects) 
• Target Grades 
• Teacher Assessment 
All of these factors are used to make a ‘predicted grade’
Does diet matter? 
• Poor diets have a significant effect on a child’s; 
– behaviour 
– concentration 
– learning ability 
– mood. 
– Children with diets lacking in essential vitamins, minerals and essential fatty 
acids tend to perform worse academically, cannot concentrate and are more 
aggressive.
Diet 
• Children need a healthy, balanced diet, which is rich 
in fruit, vegetables and starchy foods. 
• Five a day (five portions of fruit and vegetables). 
• Breakfast- healthy start to the day. 
• Are they drinking enough water throughout the day? 
• Healthy balanced evening meal.
The figures: 
• 92% of children consume more saturated fat 
than is recommended 
• 86% consume too much sugar 
• 72% consume too much salt 
• 96% do not get enough fruit and vegetables
Sleep patterns 
• Teenagers are under pressure to be increasingly alert in the evenings due 
to their social activities. 
• Students need to be on site by 8.35am. 
• Most teenagers sleep in at the weekend to try and catch up on their sleep 
• 28% of high school students fall asleep in school at least once a week 
• Insufficient sleep correlates strongly with lower grades 
• More than a quarter of teenagers report being too tired to exercise 
• A lack of sleep in teenagers leads to irritability, anxiety and depression
Sleep 
• Bedtime routine and sufficient time for sleep: What can you do?? 
• Teenager's sleep needs to be a priority. 
– Sleep needs to be seen as more important than part time jobs, parties, 
using the PC and telephone late at night & extra-curricular activities. 
• MINIMUM of nine hours in bed every night. 
• In addition, you should have at least an hour before bedtime when use of 
the PC, watching television and talking on the phone are discouraged. 
Instead encourage your teen to enjoy relaxing activities like a warm bath, 
reading for pleasure or listening to (quiet) music. By bedtime your 
teenager should be relaxed and sleepy. 
• Restrict caffeine intake. When did they have their last cup of coffee or 
cola?
Friendship groups 
• The key to success in any school. 
• Friendships for teens are based on 
– Status 
– Common interests 
– Values 
– Personalities. 
– This is an important change for parents to acknowledge. Parents are less 
likely to know their teenage children’s friends. 
– Much of what you may know about their friends is second hand 
information through your teen or their siblings.
Outcomes 
• 2014 Roding Valley High School 
– 68.3% of students achieved 5 or more A* to C 
grades including English and Maths. 
– Best ever results for the school.
Examination success 
• Exercise books - presentation 
• File - dividers 
• Revision notes – throughout the year 
• Coloured highlighter pens 
• Exam question folders 
• Case Study folders 
• Revision techniques
At home 
• Music? 
• TV? 
• Computer? 
• Plan when homework is going to be completed 
• Check their diary 
• Keep on top of deadlines 
• Get them reading (anything)
• Do not underestimate the power of parental influence, 
particularly when this is in partnership with the school 
• Believe in your child’s potential, encourage them and 
make sure they are as prepared as they can be. 
• ‘It’s funny, but the more I practise, the luckier I get.’
End word 
• Ask your son or daughter what they are doing 
in their subjects. 
• Don’t accept the usual response.
Frequently Asked Questions 
• Settling in 
• Friendships / Bullying 
• Homework 
• Attainment 
• Keeping in contact with school
Friendships/Anti-Bullying
Anti-Bullying 
• Bullying is the use of force, threat, 
or coercion to abuse, intimidate, or 
aggressively dominate others. 
• The behaviour is often repeated and habitual.
Info on pages 13 & 14 of school planner
Homework/Planner
How can parents support? 
• Attendance / Punctuality 
• Newsletter / Website 
• Parent Mail 
• Parents Evenings 
• Supervision of Internet 
“Do not overestimate parental support”
E-Safety Awareness 
• Facebook 
• Twitter 
• Instagram 
• Snapchat 
• BBM 
• What’s app 
- A large amount of time spent by young people (and 
adults) on these sites every week 
- As a school we recognise that and want to do all we 
can to keep the students safe
WhatsApp 
This is an internet instant 
messenger. 
You have to be 
connected to the 
internet but you can 
send free 
messages/videos/photos 
You have a contacts list – 
which links with your 
phone contacts and 
Facebook. 
You have to 
accept/decline people 
and you can block 
people. 
IF YOUR SON/DAUGHTER HAS 
THEIR MOBILE NUMBER ON 
FACEBOOK OR TWITTER THEN 
ANYONE CAN ADD THEM ON 
WHATSAPP. THE SITES ARE 
LINKED!
Kik 
A very similar application to 
whatsapp (originally 
whatsapp was made for 
iphones and kik all android) 
It’s an instant chat 
messaging service run via an 
internet connection. 
This is not linked with 
Facebook – you have to add 
contacts and have their 
number. You can block 
people.
Keek is a free online service that 
allows its users to upload video 
status updates, which are called 
"keeks". Users can post keeks to the 
Keek website using a webcam or via 
the Keek mobile apps Users can also 
reply back with text or video 
comments, known as "keekbacks", 
and share content to other major 
social media networks. There is also 
an embed option so users can embed 
their keeks into a blog or website. 
The video is uploaded onto a site that 
allows everyone/anyone to view your 
‘keek’ in a similar way to youtube.
Using the application, users can 
take photos, record videos, add 
text and drawings, and send them 
to a controlled list of recipients. 
These sent photographs and 
videos are known as "Snaps". 
Users set a time limit for how long 
recipients can view their Snaps (as 
of April 2014, the range is from 1 
to 10 seconds), after which they 
will be hidden from the recipient's 
device and deleted from 
Snapchat's servers.
Twitter is an online social networking and 
microblogging service that enables users to 
send and read short 140-character text 
messages, called "tweets". Registered users 
can read and post tweets, but unregistered 
users can only read them…….. 
@RVHSTeam 
#greatschool 
You can make your account private which 
will only allow people you accept to see 
your tweets but young people tend to 
want lots of followers and want to be 
able to interact with everybody…….
Photography social network news feed. 
Users ‘follow’ one another. 
Can be linked to Twitter and Facebook. 
# widely used – was the original purpose supposedly 
Can be made secure, but your followers can see 
what you’ve been ‘liking’ and who you’ve started 
‘following’ and you can see what they have been 
doing…………
Online social networking site. You can make your account private, but you do 
have to keep updating security settings. 
Friends of friends of friends of friends is where the problems can lie. 
‘Checking in’ can be dangerous as it provides a map of where to find you! 
Just as you should for any social media…………..
What the students are told 
• Students are regularly reminded about the dangers of using these sites 
and disclosing personal information 
• Check the privacy settings 
• Do not accept anyone as a “friend” that you do not know 
• Do you know who you are online with? 
• Access these sites in a room where your parent / guardian can monitor 
you 
• If you have any concerns then tell someone straight away
Roding Valley Rewards 
Honours 
Y7 
Passport 
Postcards 
Queue 
Jumper 
Trips 
Clubs 
Pupil 
of the 
week 
Class of 
the 
week/term 
Disco 
Punctuality Attendance
Mathematics Mastery
A belief and a frustration 
ARK Schools wanted a new maths curriculum to ensure that their 
aspirations for every child’s mathematics success becomes reality, 
through significantly raising standards. 
• Success in mathematics for every child 
• Close the attainment gap
The connections 
Schools 
Mathematics Mastery 
Best practice – national and 
international 
Research findings and evidence
Curricular principles 
• Fewer topics in greater depth 
• Mastery for all pupils 
• Number sense and place value come first 
• Problem solving is central
Feedback 
Problem solving and investigations give pupils the 
opportunity to demonstrate an in-depth understanding of 
the topic. 
Since teaching in a mastery style, 
I have really had to think about 
my questioning which has 
improved my subject knowledge.
Why are we here? 
“We know that no child is limited by their background 
and that by working hard all children can become 
excellent mathematicians. ”
Research shows: 
• The gap at age 10 between our strongest and weakest maths performers is 
one of the widest in TIMSS - with fewer of our pupils overall reaching the 
very highest levels 
• The 10% not reaching the expected level at age 7 becomes 20% by age 11 
and, in 2012, almost 40% did not gain grade C at GCSE 
• Girls are less likely than boys to study maths beyond 16 and less confident 
about their ability overall 
• Lower income pupils are falling behind in maths
International Trends 
2009 PISA 
Nationally, what are we 
doing well? What are 
we not doing so well?
Maths is not a measuring tool 
“Mathematics education should be so much more than 
just passing exams and Mathematics Mastery will help 
us achieve this. We want every child to not just pass 
GCSE mathematics but pass with top grades and to leave 
our school with a love of mathematics. ”
Our shared vision 
• Every school leaver to achieve a strong foundation in 
mathematics, with no child left behind 
• A significant proportion of pupils to be in a position to choose 
to study A-level and degree level science, technology, 
engineering and mathematics-related subjects 
What is necessary to make this vision a reality?
Shared 
curriculum 
framework 
Online 
• Task banks 
• Assessments 
• Training 
• Videos 
• Blogs 
Collaborative 
cluster 
workshops 
In-school 
development 
visits 
Lesson 
observation 
tools 
Mathematics 
Mastery 
Training 
• Teachers 
• Leaders
Our approach 
You say: 
“The mathematics team is firmly committed to a problem solving 
approach which will equip our students for later life.” 
Language and 
communication 
Mathematical 
thinking 
Conceptual 
understanding 
Mathematical 
problem 
solving
Our approach: problem solving 
What does it mean to teach through problem solving? 
What does it mean to teach for problem solving?
Potential barrier 1: language and 
communication 
Represent 
Mathematical 
problem 
solving 
Generalise Communicate
Mastering mathematical language 
Mathematics Mastery lessons provide opportunities for pupils to 
communicate and develop mathematical language through: 
• Sharing essential vocabulary at the beginning of every lesson and insisting 
on its use throughout 
• Modelling clear sentence structures using mathematical language 
• Insisting on correct use of language – “I know what you’re trying to say” as 
start not end 
• Talk Tasks 
• Continuous questioning in all segments which give a further opportunity 
to assess understanding through pupil explanations
Potential barrier 2: reasoning 
Represent 
Mathematical 
problem 
solving 
Generalise Communicate
Mastering mathematical thinking 
“Mathematics can be terrific fun; knowing that you can 
enjoy it is psychologically and intellectually empowering.” 
(Watson, 2006) 
We believe that pupils should: 
• Explore, wonder, question and conjecture 
• Compare, classify, sort 
• Experiment, play with possibilities, modify an aspect and 
see what happens 
• Make theories and predictions and act purposefully to see 
what happens, generalise
Mathematical thinking – you say 
“By focusing on fewer topics whilst increasing their skills 
as independent learners (which fits fantastically with our 
whole school policy of collaborative learning) we will 
increase the confidence of a large majority of our 
students in their key mathematical skills.”
Potential barrier 3: conceptual 
understanding 
Represent 
Mathematical 
problem 
solving 
Generalise Communicate
What are manipulatives? 
Language and 
communication 
Bead strings 
Fraction towers 
Mathematical 
thinking 
Conceptual 
understanding 
Mathematical 
problem 
solving 
Bar models 
Dienes blocks 
Cuisenaire rods 
Multilink cubes 
100 grids 
Number lines 
Shapes
Let’s do some maths... 
Problem solving using bar models! 
• Pupils draw a visual representation of a word 
problem. 
• Taught early on in the programme, using 
concrete and pictorial representations, in the 
context of the four operations. 
• Pupils are then expected to use models for 
fractions, decimals, percentages, algebra, pie 
charts....
John 
Solving problems with unknowns 
John’s brother 
John gives his brother three marbles. 
Now his brother has three times as many marbles as John. 
Altogether they now have sixteen marbles. 
How many marbles did John have at the start? 
16 
? 3
Conceptual understanding – you say 
“It is essential that all of our teachers aim for all our 
students to clearly understand a mathematical concept 
rather than simply learning the process.” 
“Our aim is to teach for understanding, but realistically 
this is not happening in all classes all the time.” 
“I feel that the use of concrete manipulatives and a 
constant focus on problem solving will mean that 
students are much more able to understand 
mathematical concepts.”
Lesson structure 
Do Now 
New 
learning 
Talk task 
Develop 
learning 
Independent 
task 
Ofsted outstanding: 
• Planning is astute 
• Time is used very well 
• Every opportunity is used to successfully develop crucial skills (inc. literacy and numeracy) 
• Lessons proceed without interruption 
• Appropriate independent learning tasks are set 
• Pupils are resilient, confident and independent 
• Well judged and often imaginative teaching strategies are used 
Plenary
YOU DON’T ACHIEVE MASTERY BY CLIMBING...YOU 
ACHIEVE MASTERY THROUGH DEPTH 
Generalising 
Modifying Comparing 
MATHEMATICAL THINKING 
Curriculum 
with problem solving at the heart
Maths learning in your school 
What is consistent across the department? 
What happens in every lesson? 
What does ‘students’ work’ look like? 
How are students supported to: 
• use language to reason and communicate with accuracy? 
• represent mathematical concepts and techniques? 
• make connections within mathematics? 
• make connections beyond mathematics? 
• think mathematically and solve problems?
Using data and evidence 
Fine grain detailed data analysis on a question level and by national 
curriculum sub-levels are essential to ensuring that every student is 
successful 
The big picture is what’s important – the focus should be on the best way to 
teach the students, and the best way to teach the concept or technique, with 
their long term success in mind
‘Big picture’ data can tell us… 
1) What the essential concepts and techniques are for 
students to succeed at A-level and beyond. 
2) What the essential concepts and techniques are for 
students who might otherwise fall behind. 
3) That these are the same! 
4) The ‘habits of mind’ that students need to succeed 
a) in maths 
b) in applying their maths
Work scrutiny
Assessment 
Pre- and post-module assessments 
Termly holistic assessments
Expectations
Half term 1 
Number sense 
Half term 2 
Multiplication & division 
Half term 3 
Angle and line 
properties 
Half term 4 
Fractions 
Half term 5 
Algebraic 
representation 
Half term 6 
Percentages & pie 
charts 
Place value  
Addition and subtraction 
Year 7 
KEY 
Half term topic 
Big idea 
Substantial new 
knowledge mastered 
Multiplication and 
division 
Using scales 
Angle and line 
properties 
Area 
Perimeter 
Calculating with fractions 
Algebraic notation 
Fractions, decimals and percentages
Problem Solving 
by 
Bar Modelling
Trey has $248. Evan has $345 more than Trey. Nikki has $145 
less than Evan. 
How much money do they have altogether? 
$248 
$145 
$345 
Trey 
Evan 
Nikki
There are 372 daisies in a field. There are 206 more roses 
than daisies and 122 fewer tulips than roses. 
How many flowers are in the field altogether? 
Daisies 
Roses 
Tulips
Do Now 
1 
The three little pigs went shopping. 
The first little pig spent ÂŁ23 on a bundle of straw and a stack of 
wood. 
The second little pig spent ÂŁ35 on a stack of wood and a pile of 
bricks. 
The third little pig spent ÂŁ42 on a bundle of straw and a pile of 
bricks. 
How much did each item cost (assuming the bundles, stacks and 
piles were the same size for each little pig)? 
Can you represent this using bar modelling?
2 
The three little pigs 
First little pig Second little pig 
ÂŁ23 ÂŁ35 
Third little pig 
ÂŁ42 
How does this help solve the problem? 
Is there more than one way to solve this?
3 
The three little pigs 
ÂŁ23 ÂŁ35 
ÂŁ42 
How could this be redrawn to help solve the problem?
4 
The three little pigs 
ÂŁ23 
ÂŁ35 
ÂŁ42 
How could this be redrawn to help solve the problem?
5 
The three little pigs 
ÂŁ35 ÂŁ42 
ÂŁ23 
How could this be redrawn to help solve the problem?
There are 2000 pet owners at a pet convention. There are 630 
cat owners and 250 more dog owners than cat owners, If the 
rest are rabbit owners, how many more dog owners than 
rabbit owners are there? 
630 
250 
cat 
dog 
rabbit 
2000 
?
Mr Riviera spent $1300 while shopping. He spent $398 on a 
pair of shoes and $352 more on a suit than on the shoes. He 
spent the remaining money on 2 shirts. If the shirts cost the 
same, how much did Mr Riviera spend on each shirt? 
shoes 
suit 
shirts 
?
Mr Lewis bought a dining table and 6 chairs for $1200. The 
table cost $300. What was the cost of 1 chair? 
chair 
chair 
chair 
chair 
chair 
chair 
table 
$300 
$ 1200
A baker packed 180 cereal bars into 1 big box and 5 small 
boxes. If the big box contained 60 cereal bars, how many 
cereal bars did each small box contain? 
small 
small 
small 
small 
small 
Big box
Child Success Factors

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Child Success Factors

  • 2. How do we know what your child is capable of? • Prior Attainment Predictions • Fischer Family Trust data (Band D) • 3 and 4 Levels of Progress (Core Subjects) • Target Grades • Teacher Assessment All of these factors are used to make a ‘predicted grade’
  • 3. Does diet matter? • Poor diets have a significant effect on a child’s; – behaviour – concentration – learning ability – mood. – Children with diets lacking in essential vitamins, minerals and essential fatty acids tend to perform worse academically, cannot concentrate and are more aggressive.
  • 4. Diet • Children need a healthy, balanced diet, which is rich in fruit, vegetables and starchy foods. • Five a day (five portions of fruit and vegetables). • Breakfast- healthy start to the day. • Are they drinking enough water throughout the day? • Healthy balanced evening meal.
  • 5. The figures: • 92% of children consume more saturated fat than is recommended • 86% consume too much sugar • 72% consume too much salt • 96% do not get enough fruit and vegetables
  • 6. Sleep patterns • Teenagers are under pressure to be increasingly alert in the evenings due to their social activities. • Students need to be on site by 8.35am. • Most teenagers sleep in at the weekend to try and catch up on their sleep • 28% of high school students fall asleep in school at least once a week • Insufficient sleep correlates strongly with lower grades • More than a quarter of teenagers report being too tired to exercise • A lack of sleep in teenagers leads to irritability, anxiety and depression
  • 7. Sleep • Bedtime routine and sufficient time for sleep: What can you do?? • Teenager's sleep needs to be a priority. – Sleep needs to be seen as more important than part time jobs, parties, using the PC and telephone late at night & extra-curricular activities. • MINIMUM of nine hours in bed every night. • In addition, you should have at least an hour before bedtime when use of the PC, watching television and talking on the phone are discouraged. Instead encourage your teen to enjoy relaxing activities like a warm bath, reading for pleasure or listening to (quiet) music. By bedtime your teenager should be relaxed and sleepy. • Restrict caffeine intake. When did they have their last cup of coffee or cola?
  • 8. Friendship groups • The key to success in any school. • Friendships for teens are based on – Status – Common interests – Values – Personalities. – This is an important change for parents to acknowledge. Parents are less likely to know their teenage children’s friends. – Much of what you may know about their friends is second hand information through your teen or their siblings.
  • 9. Outcomes • 2014 Roding Valley High School – 68.3% of students achieved 5 or more A* to C grades including English and Maths. – Best ever results for the school.
  • 10. Examination success • Exercise books - presentation • File - dividers • Revision notes – throughout the year • Coloured highlighter pens • Exam question folders • Case Study folders • Revision techniques
  • 11. At home • Music? • TV? • Computer? • Plan when homework is going to be completed • Check their diary • Keep on top of deadlines • Get them reading (anything)
  • 12. • Do not underestimate the power of parental influence, particularly when this is in partnership with the school • Believe in your child’s potential, encourage them and make sure they are as prepared as they can be. • ‘It’s funny, but the more I practise, the luckier I get.’
  • 13. End word • Ask your son or daughter what they are doing in their subjects. • Don’t accept the usual response.
  • 14.
  • 15. Frequently Asked Questions • Settling in • Friendships / Bullying • Homework • Attainment • Keeping in contact with school
  • 16.
  • 18. Anti-Bullying • Bullying is the use of force, threat, or coercion to abuse, intimidate, or aggressively dominate others. • The behaviour is often repeated and habitual.
  • 19. Info on pages 13 & 14 of school planner
  • 21. How can parents support? • Attendance / Punctuality • Newsletter / Website • Parent Mail • Parents Evenings • Supervision of Internet “Do not overestimate parental support”
  • 22. E-Safety Awareness • Facebook • Twitter • Instagram • Snapchat • BBM • What’s app - A large amount of time spent by young people (and adults) on these sites every week - As a school we recognise that and want to do all we can to keep the students safe
  • 23. WhatsApp This is an internet instant messenger. You have to be connected to the internet but you can send free messages/videos/photos You have a contacts list – which links with your phone contacts and Facebook. You have to accept/decline people and you can block people. IF YOUR SON/DAUGHTER HAS THEIR MOBILE NUMBER ON FACEBOOK OR TWITTER THEN ANYONE CAN ADD THEM ON WHATSAPP. THE SITES ARE LINKED!
  • 24. Kik A very similar application to whatsapp (originally whatsapp was made for iphones and kik all android) It’s an instant chat messaging service run via an internet connection. This is not linked with Facebook – you have to add contacts and have their number. You can block people.
  • 25. Keek is a free online service that allows its users to upload video status updates, which are called "keeks". Users can post keeks to the Keek website using a webcam or via the Keek mobile apps Users can also reply back with text or video comments, known as "keekbacks", and share content to other major social media networks. There is also an embed option so users can embed their keeks into a blog or website. The video is uploaded onto a site that allows everyone/anyone to view your ‘keek’ in a similar way to youtube.
  • 26. Using the application, users can take photos, record videos, add text and drawings, and send them to a controlled list of recipients. These sent photographs and videos are known as "Snaps". Users set a time limit for how long recipients can view their Snaps (as of April 2014, the range is from 1 to 10 seconds), after which they will be hidden from the recipient's device and deleted from Snapchat's servers.
  • 27. Twitter is an online social networking and microblogging service that enables users to send and read short 140-character text messages, called "tweets". Registered users can read and post tweets, but unregistered users can only read them…….. @RVHSTeam #greatschool You can make your account private which will only allow people you accept to see your tweets but young people tend to want lots of followers and want to be able to interact with everybody…….
  • 28. Photography social network news feed. Users ‘follow’ one another. Can be linked to Twitter and Facebook. # widely used – was the original purpose supposedly Can be made secure, but your followers can see what you’ve been ‘liking’ and who you’ve started ‘following’ and you can see what they have been doing…………
  • 29. Online social networking site. You can make your account private, but you do have to keep updating security settings. Friends of friends of friends of friends is where the problems can lie. ‘Checking in’ can be dangerous as it provides a map of where to find you! Just as you should for any social media…………..
  • 30. What the students are told • Students are regularly reminded about the dangers of using these sites and disclosing personal information • Check the privacy settings • Do not accept anyone as a “friend” that you do not know • Do you know who you are online with? • Access these sites in a room where your parent / guardian can monitor you • If you have any concerns then tell someone straight away
  • 31. Roding Valley Rewards Honours Y7 Passport Postcards Queue Jumper Trips Clubs Pupil of the week Class of the week/term Disco Punctuality Attendance
  • 32.
  • 34. A belief and a frustration ARK Schools wanted a new maths curriculum to ensure that their aspirations for every child’s mathematics success becomes reality, through significantly raising standards. • Success in mathematics for every child • Close the attainment gap
  • 35. The connections Schools Mathematics Mastery Best practice – national and international Research findings and evidence
  • 36. Curricular principles • Fewer topics in greater depth • Mastery for all pupils • Number sense and place value come first • Problem solving is central
  • 37. Feedback Problem solving and investigations give pupils the opportunity to demonstrate an in-depth understanding of the topic. Since teaching in a mastery style, I have really had to think about my questioning which has improved my subject knowledge.
  • 38. Why are we here? “We know that no child is limited by their background and that by working hard all children can become excellent mathematicians. ”
  • 39. Research shows: • The gap at age 10 between our strongest and weakest maths performers is one of the widest in TIMSS - with fewer of our pupils overall reaching the very highest levels • The 10% not reaching the expected level at age 7 becomes 20% by age 11 and, in 2012, almost 40% did not gain grade C at GCSE • Girls are less likely than boys to study maths beyond 16 and less confident about their ability overall • Lower income pupils are falling behind in maths
  • 40. International Trends 2009 PISA Nationally, what are we doing well? What are we not doing so well?
  • 41. Maths is not a measuring tool “Mathematics education should be so much more than just passing exams and Mathematics Mastery will help us achieve this. We want every child to not just pass GCSE mathematics but pass with top grades and to leave our school with a love of mathematics. ”
  • 42. Our shared vision • Every school leaver to achieve a strong foundation in mathematics, with no child left behind • A significant proportion of pupils to be in a position to choose to study A-level and degree level science, technology, engineering and mathematics-related subjects What is necessary to make this vision a reality?
  • 43. Shared curriculum framework Online • Task banks • Assessments • Training • Videos • Blogs Collaborative cluster workshops In-school development visits Lesson observation tools Mathematics Mastery Training • Teachers • Leaders
  • 44. Our approach You say: “The mathematics team is firmly committed to a problem solving approach which will equip our students for later life.” Language and communication Mathematical thinking Conceptual understanding Mathematical problem solving
  • 45. Our approach: problem solving What does it mean to teach through problem solving? What does it mean to teach for problem solving?
  • 46. Potential barrier 1: language and communication Represent Mathematical problem solving Generalise Communicate
  • 47. Mastering mathematical language Mathematics Mastery lessons provide opportunities for pupils to communicate and develop mathematical language through: • Sharing essential vocabulary at the beginning of every lesson and insisting on its use throughout • Modelling clear sentence structures using mathematical language • Insisting on correct use of language – “I know what you’re trying to say” as start not end • Talk Tasks • Continuous questioning in all segments which give a further opportunity to assess understanding through pupil explanations
  • 48. Potential barrier 2: reasoning Represent Mathematical problem solving Generalise Communicate
  • 49. Mastering mathematical thinking “Mathematics can be terrific fun; knowing that you can enjoy it is psychologically and intellectually empowering.” (Watson, 2006) We believe that pupils should: • Explore, wonder, question and conjecture • Compare, classify, sort • Experiment, play with possibilities, modify an aspect and see what happens • Make theories and predictions and act purposefully to see what happens, generalise
  • 50. Mathematical thinking – you say “By focusing on fewer topics whilst increasing their skills as independent learners (which fits fantastically with our whole school policy of collaborative learning) we will increase the confidence of a large majority of our students in their key mathematical skills.”
  • 51. Potential barrier 3: conceptual understanding Represent Mathematical problem solving Generalise Communicate
  • 52. What are manipulatives? Language and communication Bead strings Fraction towers Mathematical thinking Conceptual understanding Mathematical problem solving Bar models Dienes blocks Cuisenaire rods Multilink cubes 100 grids Number lines Shapes
  • 53. Let’s do some maths... Problem solving using bar models! • Pupils draw a visual representation of a word problem. • Taught early on in the programme, using concrete and pictorial representations, in the context of the four operations. • Pupils are then expected to use models for fractions, decimals, percentages, algebra, pie charts....
  • 54. John Solving problems with unknowns John’s brother John gives his brother three marbles. Now his brother has three times as many marbles as John. Altogether they now have sixteen marbles. How many marbles did John have at the start? 16 ? 3
  • 55. Conceptual understanding – you say “It is essential that all of our teachers aim for all our students to clearly understand a mathematical concept rather than simply learning the process.” “Our aim is to teach for understanding, but realistically this is not happening in all classes all the time.” “I feel that the use of concrete manipulatives and a constant focus on problem solving will mean that students are much more able to understand mathematical concepts.”
  • 56. Lesson structure Do Now New learning Talk task Develop learning Independent task Ofsted outstanding: • Planning is astute • Time is used very well • Every opportunity is used to successfully develop crucial skills (inc. literacy and numeracy) • Lessons proceed without interruption • Appropriate independent learning tasks are set • Pupils are resilient, confident and independent • Well judged and often imaginative teaching strategies are used Plenary
  • 57. YOU DON’T ACHIEVE MASTERY BY CLIMBING...YOU ACHIEVE MASTERY THROUGH DEPTH Generalising Modifying Comparing MATHEMATICAL THINKING Curriculum with problem solving at the heart
  • 58. Maths learning in your school What is consistent across the department? What happens in every lesson? What does ‘students’ work’ look like? How are students supported to: • use language to reason and communicate with accuracy? • represent mathematical concepts and techniques? • make connections within mathematics? • make connections beyond mathematics? • think mathematically and solve problems?
  • 59. Using data and evidence Fine grain detailed data analysis on a question level and by national curriculum sub-levels are essential to ensuring that every student is successful The big picture is what’s important – the focus should be on the best way to teach the students, and the best way to teach the concept or technique, with their long term success in mind
  • 60. ‘Big picture’ data can tell us… 1) What the essential concepts and techniques are for students to succeed at A-level and beyond. 2) What the essential concepts and techniques are for students who might otherwise fall behind. 3) That these are the same! 4) The ‘habits of mind’ that students need to succeed a) in maths b) in applying their maths
  • 62. Assessment Pre- and post-module assessments Termly holistic assessments
  • 64. Half term 1 Number sense Half term 2 Multiplication & division Half term 3 Angle and line properties Half term 4 Fractions Half term 5 Algebraic representation Half term 6 Percentages & pie charts Place value  Addition and subtraction Year 7 KEY Half term topic Big idea Substantial new knowledge mastered Multiplication and division Using scales Angle and line properties Area Perimeter Calculating with fractions Algebraic notation Fractions, decimals and percentages
  • 65. Problem Solving by Bar Modelling
  • 66. Trey has $248. Evan has $345 more than Trey. Nikki has $145 less than Evan. How much money do they have altogether? $248 $145 $345 Trey Evan Nikki
  • 67. There are 372 daisies in a field. There are 206 more roses than daisies and 122 fewer tulips than roses. How many flowers are in the field altogether? Daisies Roses Tulips
  • 68. Do Now 1 The three little pigs went shopping. The first little pig spent ÂŁ23 on a bundle of straw and a stack of wood. The second little pig spent ÂŁ35 on a stack of wood and a pile of bricks. The third little pig spent ÂŁ42 on a bundle of straw and a pile of bricks. How much did each item cost (assuming the bundles, stacks and piles were the same size for each little pig)? Can you represent this using bar modelling?
  • 69. 2 The three little pigs First little pig Second little pig ÂŁ23 ÂŁ35 Third little pig ÂŁ42 How does this help solve the problem? Is there more than one way to solve this?
  • 70. 3 The three little pigs ÂŁ23 ÂŁ35 ÂŁ42 How could this be redrawn to help solve the problem?
  • 71. 4 The three little pigs ÂŁ23 ÂŁ35 ÂŁ42 How could this be redrawn to help solve the problem?
  • 72. 5 The three little pigs ÂŁ35 ÂŁ42 ÂŁ23 How could this be redrawn to help solve the problem?
  • 73. There are 2000 pet owners at a pet convention. There are 630 cat owners and 250 more dog owners than cat owners, If the rest are rabbit owners, how many more dog owners than rabbit owners are there? 630 250 cat dog rabbit 2000 ?
  • 74. Mr Riviera spent $1300 while shopping. He spent $398 on a pair of shoes and $352 more on a suit than on the shoes. He spent the remaining money on 2 shirts. If the shirts cost the same, how much did Mr Riviera spend on each shirt? shoes suit shirts ?
  • 75. Mr Lewis bought a dining table and 6 chairs for $1200. The table cost $300. What was the cost of 1 chair? chair chair chair chair chair chair table $300 $ 1200
  • 76. A baker packed 180 cereal bars into 1 big box and 5 small boxes. If the big box contained 60 cereal bars, how many cereal bars did each small box contain? small small small small small Big box