Transcript Four Rules of Maths - Elk River School District

Four Rules of Maths
In seven stages
Four Rules
 Addition
 Subtraction
 Multiplication
 division
Addition Stage 1 (Reception)
 Practical
activities and discussions
 Finding one more than a number
from 1 to 10
 Using vocabulary associated with
addition
Addition Stage 2 (Year 1)
 Begin
to use the + and = sign to
record mental calculations
 Know by heart all number bonds to
10
 Use knowledge to know that addition
can be done in any order to do
mental calculations more efficiently
Addition Stage 3 (Year 2 )
Adding three single digit numbers
mentally
 Know by heart all number bonds to 20
 Use +and = to record mental calculations
 Use number line to make informal jottings
 Use partitioning to reflect mental methods
47 + 78 =40 + 70 + 7 + 8

Addition Stage 4 (Year 3)


Using informal pencil and paper methods
(jottings) and introducing vertical addition
Adding TU and TU, moving into HTU using
jottings (most significant digit first)
83
+ 42
---120
+ 5
---125
Addition Stage 5 (Year 4)

Vertical format least significant digit first extends
to bigger numbers
368
+ 493
----11
150
+ 700
----861
Addition Stage 6 (Year 5)

Children using the compact layout,
involving carrying
368
+ 491
----859

Extending to decimals
Addition Stage 7 (Year 6)
 Compact
addition using carrying for
thousands, hundreds, tens and units,
and decimals
 Consolidation of Stage 6
Subtraction Stage 1 (Reception)
 Practical
activities and discussion
 Finding one less than a number from
1 to 10
 Begin to relate subtraction to “taking
away”
Subtraction Stage 2 (Year 1)
 Begin
to use the - and = sign to
record mental calculations
 Know by heart all subtraction facts to
10
Subtraction Stage 3 (Year 2 )
 Know
20
by heart all subtraction facts to
Subtraction Stage 4 (Year 3)


Using informal pencil and paper
methods (jottings)
Use a number line to record
complimentary addition
84 – 56
+4
56
+20
60
+4
80
84
=28
Subtraction Stage 5 (Year 4)
563 - 248
500 + 60 + 3
- 200 + 40 + 8
--------------500 + 50 + 13
- 200 + 40 + 8
---------------300 + 10 + 5
Subtraction Stage 5 (Year 4)
Cont…….
50
10+
500 + 60 + 3
- 200 + 40 + 8
--------------300 + 10 + 5
Subtraction Stage 6 (Year 5)
Decomposition extended to decimals and
larger numbers
 Contracted recording at decomposition

5
10+
3
10+
6476
-2684
------3792
Subtraction Stage 7 (Year 6)
 Consolidation
of stage 5
 Contracted recording of decimals
Multiplication Stage 1 (Reception)
 Working
at a practical level to gain
experience of doubling and become
familiar with the appropriate
language
Multiplication Stage 2 (Year 1)
 Know
by heart addition doubles to at
least 5
Multiplication Stage 3 (Year 2)
 Understand
multiplication as
repeated addition
 Know by heart the multiplication
facts for the 10 and 2 multiplication
tables
Multiplication Stage 4 (Year 3)
Mental methods using partitioning
38 x 7 = (30 x 7) + (8 x 7)
 Introduction of grid layout to show
expanded working out


x
30
8
7
210
56
266
Know by heart the multiplication facts for
the 10, 2, 5, 3 and 4 times tables
Multiplication Stage 5 (Year 4)

Grid method extended to bigger numbers
56 x 27
x
50
6
20
1000
120
1120
7
350
42
392
1512

Know by heart the multiplication facts up
to 10 x 10
Multiplication Stage 6 (Year 5)

Grid method extended to bigger numbers
and decimals
23.5 x 12
x
20
3
0.5
10 200
30
5
235
2
6
1
47
40
282
Multiplication Stage 6 (Year 5)
Cont…………….

Introduction of vertical format linked to grid method
38
x 7
----210 (30 x 7)
+ 56 ( 8 x 7)
-----266

Vertical format using decimals and larger numbers
Multiplication Stage 7 (Year 6)

Consolidation of stage 6

Contracted vertical multiplication, e.g.
38
X 7
----266
Division Stage 1 (Reception)
 Working
at a practical level to gain
experience of sharing and become
familiar with the appropriate
language
Division Stage 2 (Year 1)
 Separate
a given number of objects
into equal groups and record results
informally
Division Stage 3 (Year 2)
 Understanding
division as grouping,
repeated subtraction or sharing, and
recording informally
Division Stage 4 (Year 3)
 Use
the ÷ and = signs, recording
horizontally
Division Stage 5 (Year 4)

Begin to use standard written methods,
e.g. 96 ÷ 6
96
- 60 (6 x 10)
----36
- 36 (6 x 6) +
--------00
16
Division Stage 6 (Year 5)

Use standard written methods using
multiples of 10, e.g. 196 ÷ 6
196
- 180 (6 x 30)
----16
- 12 (6 x 2) +
-------4
32 remainder 4
Division Stage 7 (Year 6)


Consolidation of stage 6
Contraction of formal method
196
- 180
----16
- 12
----4
30
2+
---32 remainder 4