Download Progression in Mathematics – Division

Progression in Mathematics – Division
Stage
What will division look like?
R
Sharing objects into equal groups and count how many
in each group, such as 10 biscuits on two plates.
Primary Framework for literacy and
mathematics page 92 and 94 and PSRN
(foundation stage)
•
Sharing (and grouping)
Solve practical problems that involve sharing and
grouping “how many lots or groups of”.
Primary Framework for literacy and
mathematics page 92 and 94
•
Counting back in ones, twos, fives and
tens.
•
Sharing and grouping
1
Use of number lines, counting back, repeated
subtraction.
Record using the correct division symbols.
2
Emphasis on grouping.
6÷2=
20 ÷
=2
÷3=8
Use the vocabulary of division.
Solve simple problems, including answers with
remainders by informal methods such as:
Notes
Primary Framework for literacy and
mathematics page 92 and 94
•
Begin to understand division as sharing
and repeated subtraction( grouping )
•
Use practical and informal written methods
and related vocabulary to support division,
including calculations with remainders
•
Related division facts corresponding to the
2 ,5 and 10 times tables
•
Use x and ÷ signs Use knowledge of
number facts and operations to estimate
and check answers
(a) Drawing pictures






12 ÷ 2 = 6
(b) Counting back with equal steps on a number line.
 -10
-10
 -10
-10
-10
-10
60 ÷ 10 = 6
0
10
36 ÷ 4 =
3
30
20

40
50
60
360 ÷ 4 = 
5 x 6 = 30, 30 ÷ 5 = 6, 30 ÷ 6 = 5( inverse relationship)
(a) Repeated subtraction along a number line.
-5
-5
-5
-5
-5
-5
30 ÷ 5 = 6
0
5
10
15
20
25
30
(b) Finding remainders after simple division
Know when to round up or down the remainder,
depending on context of problem
14 ÷ 4
rem 2 -4
0
-4
2
6
Primary Framework for literacy and
mathematics page 92 ad 94
•
Understand division as grouping or
repeated subtraction (or repeated addition)
•
Use practical and informal written methods
to divide a 2-digit number by a 1-digit
number, including calculations with
remainders
•
Understand that division is the inverse of
multiplication and use this to record related
number sentences
•
Related division facts corresponding to the
2, 3,4,5,6 and 10 times tables.
•
Use knowledge of number operations and
corresponding inverse, including doubling
and halving, to estimate and check
answers.
-4
10
14
14 ÷ 4 = 3 r2
(c) It is much harder to count back to solve this problem
than to count on, and some children may prefer this
method
+4
0
+4
4
+4
8
rem 2
12
14
Estimate first
Chunking method using appropriate size of step based
Primary Framework for literacy and
mathematics page 93 and 95
•
Derive and recall multiplication facts up to
10 x 10 and corresponding division facts
4
on table knowledge. Number line leads to vertical
method( use both methods side by side to begin with to
show the links)
•
(a) Number line
•
•
10 x 5
2 left over
•
4x5
0 2
22
72
Divide any integer up to 1000 by 10 and
then 100(whole number answers),
understanding the effect.
Begin to use chunking method for TU by U
division, including remainders
Use knowledge of rounding number
operations and inverse to estimate and
check answers
Use calculator as appropriate, including
carrying out 1 and 2 step calculations and
interpreting the display in the context of
money
(b) Vertical method
72 ÷ 5 = 14 r 2
10x5
4x5
72
50
22
20
2
Recognise that division is non-commutative.
i.e. 10 ÷ 2 is not equal to 2 ÷ 10
A number cannot be divided by 0.
5
Estimate first, some children may still prefer to use a
number line.
(a) Numberline
256 ÷ 7
Rem 2
0
6x7
4
Primary Framework for literacy and
mathematics page 93 and 95
•
Recall quickly all multiplication facts to10 x
10 and derive quickly corresponding
division facts
•
Use understanding of place value to divide
whole numbers and decimals by 10, 100
and 1000
•
Refine and use efficient written method to
include HTU by U, with a remainder.
•
Use knowledge of rounding, place value,
number facts and inverse operations to
estimate and check answers
•
Use calculator to solve problems (also
involving decimals) as appropriate
30 x 7
46
256
(b) Vertical method
256 ÷ 7
256 ÷ 7 = 36 r 4
256
30x7 - 210
46
6x7 - 42
4
36 r 4
7) 256
210
46
42
4
Check answer with inverse.
Estimate first, some children may still prefer to use a
number line.
6
977 ÷ 36 = 27 r 5
(a) 977
20x36 -720
257
5x36 -180
77
2x36 -72
5
Check answer with inverse
(b)
27 r 5
36)977
720
257
180
77
72
5
Primary Framework for literacy and
mathematics page 93 and 95
•
Use knowledge of place value and
multiplication facts to 10 x 10 to derive
related division facts involving decimals
e.g. 4.8 ÷ 6
•
Use efficient written method to divide
integers and decimals by a 1-digit integer
and HTU by TU
•
Use approximations, inverse operations
and tests o divisibility to estimate and
check results
•
Appropriate use of a calculator, including
solving multi step problems