Download Counting and Part-whole Strategies HNP_NZ_MR Comparison

Counting Strategies
HNP
Example
Maths
Recovery
NZMaths
Pupils are unable to consistently count a given number
of objects because they lack the knowledge of
counting sequences and/or the ability to match things
one-to-one.
I could not collect 7 counters.
Emergent
Stage 0
Emergent
Stage 0
Early **
Pupils can count up to ten but cannot solve simple
problems that involve joining and separating sets like 4
+ 3.
I collected 4 counters and
collected another 3 counters but
then I did not know what to do. ‘I
have 4 and 3’.
Or says - it makes 10
N/A
One-to-one
Counting
Stage 1
Early ***
When solving joining or separating of sets problems,
pupils first rely heavily on counting physical materials,
like their fingers. They count all the objects in both sets
to find the answer. (They start their count at one).
I used my fingers. 8 + 5 =
1, 2, 3, 4, 5, 6, 7, 8,
9, 10, 11, 12, 13
Perceptual
Counting
Stage 1
Counting from One
using Materials
Stage 2
Early ***
When solving joining or separating of sets problems,
they can move away from using materials and are able
to image visual patterns of the objects in their minds
and count them. They count all the objects in both sets
to find the answer. (They start their count at one).
First *
Pupils can solve number problems by counting on, or
back. They keep track of the count using materials (e.g.
fingers) or by imaging (in their heads). They understand
that the end number in a counting sequence measures
the whole set and can relate addition and subtraction
of objects to the forward and backward number
sequence by ones and tens etc.
Early *
Description of Stages of Thinking
Pupils at this stage use a skip-counting strategy to solve
multiplication problem.
1, 2, 4, 5, 10
I pictured the 8 and 5 counters in
my head and counted: 8 + 5 =
1, 2, 3, 4, 5, 6, 7, 8,
9, 10, 11, 12, 13
I thought 9 and then
counted on:
9 + 4 = 9, 10,11, 12, 13
Or
32 + 21 = 32, 42, 52, 53
7 x 3 = I counted in 3s like this: 3, 6,
9, 12 …but I didn’t know the next
numbers so I had to count like this:
13, 14, 15, 16, 17, 18,19, 20, 21
Figurative Counting Counting from One
Stage 2
by Imaging
Stage 3
Counting On
Stage 3
Counting Down
Stage 4
Advanced
Counting
(Counting
on/back)
Stage 4
Part-Part Whole Strategies
HNP
First **
First ***
Second *
Second **
Second
***
Description of Stages of Thinking
Pupils at this stage have begun to recognise that
numbers can be split into parts and recombined in
different ways. This is called part-whole thinking.
Pupils use a limited range of mental strategies to
estimate answers and solve addition and subtraction
problems. Strategies used at this stage are most often
based on a group of five or ten or use a known fact,
such as a double.
Pupils are familiar with a range of part-whole strategies
and are learning to choose appropriately between
these. They have well developed strategies for solving
addition and subtraction problems. They see numbers
as whole units but also understand that they can be
‘nested’ within these units.
Pupils are able to solve multiplication answers from
known facts. These pupils are also able to solve
problems using a combination of multiplication and
addition- based strategies.
Pupils at this stage choose appropriately from a range
of part-whole strategies to solve and estimate problems
with whole numbers and decimals to one place. They
are able to choose a multiplicative strategy to solve an
addition problem where appropriate.
Pupils are learning to manipulate factors mentally to
solve multiplication and division problems. They move
from partitioning additively to using a halving and
doubling strategy. A key strategy of this stage is
reversibility, solving division problems using
multiplication.
Example
Maths
Recovery
NZMaths
48 + 7 as (48 + 2) + 5
Facile
Stage 5
Early Additive
Stage 5
N/A
Advanced Additive
Part Whole
Stage 6
N/A
Advanced
Multiplicative
Part Whole
Stage 7
26 – 9 = (26 – 10) + 1 = 17
8 + 9 = (8 + 8) + 1
367 + 260 as
(300 + 200) + (60 + 60) + 7
135 – 68 = 135 – 70 + 2
604 – 598 as 598 + ? = 604
6 x 3 = (5 x 3 ) + 3 = 15 + 3 = 18
6.5 + 7.7 = 6.5 + 8 = 14.5 – 0.3 = 14.2
55 + 44 + 33 =
(5 x 11)+ (4 x 11) + (3 x 11) = 12 x 11
Understand that 5 x 12 can be
partitioned into (5 x 10) + ( 5 x 2)
Begins to understand how
5 x 12 is the same as 10 x 6