The document summarizes the key points from a maths inset for teachers. It outlines a proposed progression of addition calculation stages from counting all objects to the standard written method. Practical resources like number tracks and base 10 blocks are recommended for the early stages. Ensuring conceptual understanding, problem solving and choosing an appropriate method are emphasized. The next steps are to review calculation policies for other operations and use assessment to track individual progress through the stages.

1. MATHS INSET
12th May 2015
Rachel Cowen

2. Aims of the session
• To give an update from the Better Mathematics
Conference 2015
• To look at addition calculation methods & decide
on a progression of stages across the school

3. Achievement
o Although attainment is generally rising pupils are not made to think hard
enough for themselves. Pupils of all ages do too little problem solving &
application of Mathematics.
o The % of pupils meeting expected standards falls at successive key stages.
This is often due to a focus on meeting thresholds rather than securing
essential foundations for the next stage.
o FSM pupils do worse than their peers at all key stages.
o Low attainers are not helped soon enough to catch up, particularly in the
EYFS & KS1.
o High attainers not challenged enough from EYFS onwards.

4. Made to Measure Report
The report draws attention to serious inequalities in
pupils’ experiences and achievements. It includes
examples of best practice that help avoid or
overcome the inequalities and weaker practice that
exacerbates them.

5. Teaching Findings
• The best teaching develops conceptual
understanding alongside pupils’ fluent recall of
knowledge & confidence in problem solving &
mathematical reasoning
• In highly effective practice, teachers get ‘inside
pupils’ heads’. They find out how pupils think by
observing them closely, listening carefully to what
they say, & asking questions to probe & extend their
understanding, then adapt teaching accordingly.
• Too much teaching concentrates on the acquisition
of disparate skills that enable pupils to pass tests &
exams but do not equip them for the next stage of
education, work & life.

6. Aims of the National
Curriculum 2014
• Become fluent in the fundamentals of mathematics,
so that pupils develop conceptual understanding &
the ability to recall & apply knowledge rapidly &
accurately
• Reason mathematically
• Solve problems

7. National Teaching Key
Concerns
• Conceptual understanding & problem solving are
underemphasised
o Too often teaching approaches focus on how, without understanding
why, so that pupils have insecure foundations on which to build future
learning.
o Many pupils spend too long working on straightforward questions
• Wide in school variation in teaching quality.
• Circulating to check & probe each pupil’s
understanding throughout the lesson & adapting
teaching accordingly are not strong enough.

8. What does ‘Outstanding’
look like?
• Problem solving & Mathematical reasoning are
embedded into all parts of the Maths curriculum & not
viewed as a separate entity.
• Children are discussing Maths & methods & making
connections for themselves.
• Everyone is teaching for understanding.
• Practical resources, visual images & ICT foster pupils’
deeper understanding. All children are encouraged to
use practical equipment, there is evidence this has real
benefits in terms of developing mental imagery.
• Teachers work & plan together to support consistency &
improvement.
• There is timely intervention which overcomes gaps &
builds a firm foundation for future learning.

9. Recommendations for
Primary Schools
• Improve pupils’ progress from the Early Years
Foundation Stage through to Year 2 to increase
attainment of the most able.
• Act early to secure the essential skills & knowledge
of the least able.

10. Questions to consider
• How can we develop consistency in our teaching in
terms of subject knowledge and language
choices?
• How can we ensure our calculation policy reflects
the changes in the New Curriculum and the needs
of the children in our school?
• How can our policy build effectively on prior
learning?
• How can we improve the accuracy of children’s
addition work across the school?
• How can we support the children to effectively
record their mathematical thinking?

11. Concepts of addition
• What do we think these are?
• How would we define addition?

12. The concept of addition
• The combining of 2 or more groups to give a total or
sum
• It is the increasing of an amount.

13. Key principles of addition
• It is the inverse of subtraction
• It is commutative i.e. 5 + 3 = 3 + 5
• It is associative i.e. 5 + 3 + 7 = 5 + (3 + 7)

14. Addition Structures
Aggregation Augmentation
• The key language to
be developed in the
aggregation structure
of addition includes:
o how many altogether?
o How much altogether?
o The total.
• The key language to
be developed in the
augmentation structure
of addition includes:
o start at and count on,
o increase by,
o go up by.

15. Addition Structures
• Children must experience the two addition
structures in a range of relevant contexts, including
money (shopping, bills, wages and salaries) and
various aspects of measurement.
• Then they also have to recognise addition in
situations in the contexts of measurements, such as
length and distance, mass, capacity and liquid
volume, and time. For example,
o Can you calculate the distance for this journey? If I have already travelled
63 miles and then do a further 45 miles?
o Can you find the total time for the journey? If the first stage has taken me
85 minutes and the second stage takes 65 minutes?

16. • Our next step is to think about the policy from the
child’s perspective:
o How would the children show you their learning at each stage?
o What would you see in their books on paper or in photos?
o How do we ensure the progression from practical to written?

17. How do we teach
addition now?
• With your class, what methods do you use?
• What practical equipment do you use?
• What written methods do you use?

18. Stage 1- Combining 2 or
more amounts
• Counting all method
Children begin to develop their
ability to add by using practical
equipment to count out the
correct amount for each number
in the calculation and then
combine them to find the total.
For example, when calculating 4 +
2, they are encouraged to count
out four counters and count out
two counters.

19. Counting all
• To find how many altogether, touch and drag them
into a line one at a time whilst counting.
1 2 3 4 5
6

20. Counting all
Children should be taught that addition is the combining of two or
more amounts. They will begin by counting all of the items in the
groups, then move on to counting on from the largest amount.
They can begin to record addition number sentences such as
2 + 4 = 6 and 8 = 3 + 5 and 3 + 2 + 4 = 9

21. Counting on
4

22. Stage 2- Using Number
Tracks & Base 10
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
11 + 5 = 16
Model of Base 10 equipment

23. KS1 Addition Games
• https://www.tes.co.uk/teaching-resource/teachers-
tv-primary-maths--calculation-6038949

24. What about number lines?
• https://www.ncetm.org.uk/self-
evaluation/browse/topic/883

25. Stage 3
34 + 23 = 57 34 + 23 = ?
The units/ones are
added first 4 + 3 = 7
The tens are added
next
30 + 20 = 50
Both answers are put
together 50 + 7 = 57

26. Stage 4
28 + 36 = ?
The units/ones are added
first
8 + 6 = for 1 ten.
A ring is put around the
units/ones not exchanged –
this is the units part of the
answer. The tens are then
added, including the
exchanged ten, to complete
the sum.

27. Stage 5
TU HTU
67 267
+ 24 + 85
1 1 (7 + 4) 12 (7 + 5)
80 (60 + 20) 140(60+80)
91 200
352
The Base 10 equipment should be used
alongside to model the transition to the
vertical method but this should not be
recorded by the children

28. 65 + 27 =

29. Stage 6
The example top left would be ‘said’ as
follows:
5 + 8 = 13, put 3 down and carry the 10
20 + 40 + 10 that was carried over = 70
(7 written in the tens column)
600 + 0 = 600 (6 written in the hundreds
column)

30. • Children should extend the carrying method to numbers with
at least four digits.
587 3587
+ 475 + 675
1062 4262
1 1 1 1 1
3121 3.20
+ 37 +2.88
+ 148 6.08
3306 1
1 1

31. Important Points
• Children should not be made to go onto the next
stage if:
1) they are not ready.
2) they are not confident.
• Children should be encouraged to consider if a
mental calculation would be appropriate before
using written methods.

32. Our next steps
• Look at the calculation policy for the other
operations, ensure there is a clear progression from
practical to written methods.
• Use the policy in a fluid way, look at where the child
is and what their next steps are.

33. Homework
Look at the results of the Times Tables Club in your
class. Can you track progress & do some analysis
about the overall effectiveness/ impact this is having
on learning and progress?
Please bring this to the next Maths
inset on 16th June.