1. Maths at King William Street
Problem Solving

2. Maths at kws
At King William Street we aim to achieve success in mathematics for every child by developing a ‘can do’ mindset, where positive attitudes and consistent effort are encouraged and rewarded.
Don’t just do maths – think like a mathematician!
Curricular Principles
Develop fluency in the foundations
Ensure mastery by embedding mathematical reasoning and problem solving
Make rich connections across maths and other curriculum areas.

3. Maths in the new curriculum
The key changes:
Problem solving is fully integrated, rather than being a separate strand
All children must work on the national curriculum level designated for their age group
The focus is on breath and depth of learning, not moving on to the next level.
Mastery

4. The foundations
In order for all children to succeed as mathematicians, these skills must not only be secure, but children must be able to work with them rapidly.
We use these to set the children termly targets.
Approximate expectations:
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Number bonds up to 10.
+/- 10
Doubles
Count in 2s/5s/10s
Number bonds up to 20
Near doubles
+/- partitioning
2/5/10 x table
4,8,3,6 x table
½ and double TU
+/- multiples of 10
+/- TU with partitioning
Near doubles to add
All other tables
10x bigger/
Smaller
Half and double U.t
+/- multiples of 0.1, 10s, 100s, 1000s
Partition to ÷
All previous skills
Review all previous skills, apply to larger numbers

5. The Do it, use it, own it approach
In order to assess children on the new curriculum, we have devised three levels of working.
DO IT: I can answer straight forward questions on the objectives
USE IT: I can use and apply my knowledge of the objective to answer questions requiring higher order thinking.
OWN IT: I can not only use my knowledge of the objective, but I can solve open ended problems based around this objective, making choices about how I approach it, reasoning with my answers. If I have worked efficiently and systematically enough for someone else to understand how I got to my solutions, I will have owned the objective.

6. Examples of D.U.O. Year 1
Add and subtract one digit and two digit numbers to 20 including zero
Choose a number from A and number from B and add them together.
Choose a number form A and a number from B and subtract them.
_ + _ = 30
How many ways can you make this true?
Tim has 17 books. Toby gives him 8 more. How many does he have?
Choose a number from A and a number from B. Make the biggest number you can. Now make the smallest. Convince me this is the best way to do it.
If you take a single digit number (from box A) from a double digit number (from box B) the answer always ends in 0. Is this always, sometimes or never true.

7. Examples of d.u.o. year 6
Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
Use flags printed on squared paper.
What fraction of each flag is each colour?
Write down two fractions which have a difference of ½ … and another, … and another, …
Write down 8 pairs of fractions with a total of 3 4/5. Do not use the digit 5 more than once in each.
=1 5
How many ways can you make this true?
Is it possible only using each digit once?

8. Integrating word problems

9. Choral counting
Children will count most days throughout the school, even up to year 6 (sometimes even the teachers do it in staff meetings).
Sometimes the class will count in unison
Other times each group will take a different increment and the counting will switch between groups.
32, 42, 52, 62, 72, 82, 92, 102,
17, 18, 19, 20, 21, 22,

10. Using practical models and resources
Whenever possible teachers use practical resources to model learning and all children should use resources to explore learning and ‘show me’ when reasoning.

11. Explicit problem solving skills
Reasoning
Communicating
Selecting mathematics
Developing own strategies
Discussing to get started
Breaking it down
Rewording the problem
Making connections
Choosing equipment
Trying different approaches
Checking answers
Exploring outcomes
Overcoming difficulties
Looking for patterns
Simplifying
Trial and improvement
Testing statements
Predicting
Making general statements
Justifying answers
Noticing relationships
Asking and responding to ‘what if’ questions
Identifying patterns
Proving hypotheses
Organising work
Explaining thinking
Discussing the maths
Recording
Vocabulary
Use of symbols
Presenting information
Representing thinking

12. Probing questions and scaffolded sentences
What is happening? Why?
If I know…then…
What do you notice?
Convince me that…
Show me that…
It can’t be… because…
As…so…
Find me some more examples where…

13. Working walls

14. Fix-it time Each lesson now starts with fix it time.
This time is where children respond to the feedback marking their teacher has given them the previous day.
After responding to this the they get on with a task that is set for them on the board.
The teacher and teaching assistants check the children’s answers then and there and it is either ticked or stamped when it has been seen.
If a child makes a mistake on their fix-its, the teacher will discuss this with them and stamp their book with a ‘seen and discussed with my teacher’ stamp.

15. Flexible lesson approach
The DUO approach has completely changed how we teach maths here at King William Street.
Once a child is secure in the ‘Do it’ aspect of the objective, they are moved on to the ‘Use it’ stage. You will not find children working on pages and pages of simple calculations.
Once a child has shown they can use and apply their knowledge they will be invited to try an ‘Own it’ challenge.
At this stage of the year, it is rare to find children working on ‘Own it’ challenges, as we all need to start at the beginning and master the basic skills.
In the summer terms, it will not be uncommon to see all three levels of questions being taught at the same time, with children all being moved on at different rates. This certainly keeps us teachers on our toes!

16. Guided maths
Children still take part in guided maths sessions which normally works on a roata system.
Each week children will:
Work with their teacher
Play maths games
Work on securing their foundations
Work on a problem solving activity
Manga High or other ICT based maths activity

17. Maths homework
Each week your children will be set a game based on the secure foundations for their year group, which is recorded in their maths homework book.
In years 4-6 children also have a login for Manga High which
they are encouraged to play on at home (this is
not part of their homework, but offers fun
opportunities for learning basic number skills.

18. Go see it for yourself! Feel free to go visit your children in class…
If you could please make sure you have signed out of school by 10am
(Parents from Blue Whale Class, please go and see what is happening in Tiger (year1)
I am free, for anyone with further questions.