Transcript Calculation Open Morning

Welcome to our
Calculations
Afternoon
Aims of the session:
• To give you the opportunity
to see the progression in
addition and subtraction from
KS1 to KS2.
• To demonstrate the strategies
and techniques we use in
school to teach addition and
subtraction.
Home-School
Partnership
• Reinforces and consolidates
learning
• Develops confidence and selfesteem
• Encourages children to talk
about mathematics at home
The Curriculum
• Higher expectations in each year
group
• Focus on deepening
understanding
• Strong emphasis on ‘traditional’
formal written methods
• Less emphasis on calculators
• Levels replaced by ‘Age Related
Expectations’
Mental strategies
Objectives – Mental Strategies
Year 1
I can recall, represent and use number bonds and
related subtraction facts within 20
Year 2
I can add and subtract three 1-digit numbers mentally
I can add and subtract two 2-digit numbers in my head
Year 3
I can add and subtract ones, tens and hundreds to
and from any 3-digit number
Year 4
I can add multiples of 10, 100 or 1 000 to any number
up to 9 999 mentally
Year 5
I can add and subtract numbers mentally with
increasingly large numbers
Year 6
I can add, subtract and use negative numbers in
context, and calculate intervals across zero
I can perform mental calculations, including with mixed
operations and large numbers
Counting on or backwards
KS1 counting on and back in 1s and 2s.
KS2 counting on or back in 5s, 10s, fractions and
decimals.
Reordering
Changing the order of numbers.
KS1 e.g. 5 + 13 change order to 13 + 5 and count
on.
KS2 applying knowledge of number bonds e.g. 1.7
+ 0.5 + 2.3 = 2.3 + 1.7 bonded to 4 + 0.5
Partitioning
Partitioning numbers into tens and ones.
KS1 – 30 + 47 = 30 + 40 + 7
KS2 – 4.7 – 3.5 = 4.7 – 3 – 0.5
Bridging
Compensating or adjusting
For numbers that are close to 10
KS1 – 52 + 21 = 50 + 20 + 2 + 3
5 + 9 = 5 + 10 - 1
KS2 – 405 + 399 = 405 + 400 -1
5.7 – 3.9 = 5.7 – 4 - 0.1
Using doubles and near doubles
KS1 5 + 6 = Double 5 + 1
KS2 60 + 70 = Double 60 + 10
1.5 + 1.6 = Double 1.5 + 0.1
Typical mental maths questions:
Objectives – Written Strategies
Year 1
I can read, write and work out questions
involving addition (+), subtraction (-)
Year 2
I can choose if it is best to work out an answer
using a mental method or a written method
Year 3
I can use column addition and column
subtraction to add and subtract 3-digit numbers
Year 4
I can use column addition and column
subtraction to add and subtract numbers with up
to 4-digits
Year 5
I can add and subtract whole numbers with
more than 4 digits, including using efficient
written methods (columnar addition and
subtraction)
altogether
sum
add
minus
difference
take-away
Using the correct terminology with your child is
important as it enables them to ‘talk’ about maths
and therefore develop their understanding.
Recognise
that
addition
can be
done in
any order.
Understand subtraction
as taking away.
7–3=4
Early stages of addition and subtraction focus on:
• Understanding addition as combining two sets
of objects
• Understanding subtraction as taking away
• Recognising the commutative law for addition
• Practical activities
Early Years and Year 1
54 – 15 = 39
8 + 3 = 11
+2
8
+1
10
-5
11
39
-10
44
54
Number lines are used for:
• Bridging across tens boundaries
• Using known number facts
• Partitioning
Hundred squares are also used for these
purposes.
Years 1, 2 and 3
3 6 8
+ 4 9 3
1 1
1 5 0
+ 7 0 0
8 6 1
9 6 8
- 4 5 3
5
1 0
- 5 0 0
5 1 5
Expanded Column Notation:
Year 3
• Uses partitioning
• Allows learners to see what is happening
Breaks column addition down into small steps
• Moves from starting with most significant digit to
least significant digit
4
7
+
7
6
1
2
3
1
1
+
3
6
8
4
9
3
8
6
1
1
1
-
6
8
4
3
2
5
8
-
9
15
6
1
8
3
8
9
5
7
9
Compact Column Notation:
• Allows the flexibility of manipulating increasingly
larger numbers and decimals
Years 3, 4, 5 and 6
Chilli challenges – steps to success!
Over to you!
Try these calculations using the
methods we have discussed:
1. 124 + 365 =
2. 346 + 247=
3. 462 + 459 =
1. 375 + 438 =
2. 569 + 543=
3. 1283 + 637 =
1. 1471 + 849 =
2. 2674 + 1548 =
3. 9853 + 3367 =
4. 643.4 + 578.7=
Over to you!
Try these calculations using the
methods we have discussed:
1. 89 – 34 =
2. 134 – 27 =
3. 156 - 65 =
1. 168 – 79 =
2. 345 – 152 =
3. 684 - 396 =
1. 955 – 489 =
2. 1517 – 638 =
3. 3587 - 1744 =
Objectives – Application
Year 1
Year 2
I can solve simple one step addition and subtraction problems,
including ones where a number is missing
Year 3
Year 4
I can estimate the answer to a calculation and use inverse
operations to check answers
Year 5
I can solve single- and multi-step problems involving a
combination of addition, subtraction, multiplication and division
calculations, including understanding the meaning of the
equals sign
I can explain my choice of calculation when solving single- and
multi-step problems
I can prove that I can add two numbers in any order and get
the same answer
I can prove that changing the order of numbers in a subtraction
calculation makes the answer change
I can solve addition and subtraction two-step problems in
contexts, deciding which operations and methods to use and
explaining why
One-step/multi step problems:
One-step/multi step problems:
Finally…
Please:
• Ask questions…
• Complete an evaluation at the
end and return to me or the
Office.
• Thank you for coming along!