National Standards and Maths @ TKP
Reference /
Resource
National
Standard
TKP2012
After 1 year at school
(A1)
After one year at school, students
will be achieving at early level 1 in
the mathematics and statistics
learning area of the NZC
In contexts that require them to
solve problems or model situations,
students will be able to:

Apply counting-all strategies

Continue sequential patterns
and number patterns based on
ones.
After 2 years at school
(A2)
After two years at school, students
will be achieving at level 1 in the
mathematics and statistics learning
area of the NZC
In contexts that require them to
solve problems or model situations,
students will be able to:



Number and
Algebra





Geometry and
Measurement
compare the lengths, areas and
volumes or capacities, and
weights of objects directly
sort objects and shapes by a
single features and describe the
feature, using everyday
language
represent reflections and
translations by creating patterns
describe personal locations and
give directions, using everyday
language




apply counting-on, countingback, skip-counting, and simple
grouping strategies to combine
or partition whole numbers
use equal sharing and symmetry
to find fractions of sets, shapes,
and quantities
create and continue sequential
patterns by identifying the unit
of repeat
continue number patterns
based on ones, twos, fives, and
tens.
compare the lengths, areas,
volumes or capacities, and
weights of objects and the
durations of events, using selfchosen units of measurement
sort objects and shapes by
different features and describe
the features, using
mathematical language
represent reflections and
translations by creating and
describing patterns
describe personal locations and
give directions, using steps and
half- or quarter-turns.
After 3 years at school
(A3)
By the end of year 4
(Y4)
By the end of year 5
(Y5)
By the end of year 6
(Y6)
After three years at school, students
will be achieving at early level 2 in
the mathematics and statistics
learning area of the NZC
In contexts that require them to
solve problems or model situations,
students will be able to
By the end of year 4, students will be
achieving at level 2 in the
mathematics and statistics learning
area of the NZC
In contexts that require them to
solve problems or model situations,
students will be able to:
By the end of year 5, students will be
achieving at early level 3 in the
mathematics and statistics learning
area of the NZC
In contexts that require them to
solve problems or model situations,
students will be able to:
By the end of year 6, students will be
achieving at level 3 in the
mathematics and statistics learning
area of the NZC
In contexts that require them to
solve problems or model situations,
students will be able to:

apply basic addition facts and
knowledge of place value and
symmetry to:
- combine or partition whole
numbers
- find fractions of sets, shapes,
and quantities
create and continue sequential
patterns with one or two
variables by identifying the unit
of repeat
continue spatial patterns and
number patterns based on
simple addition or subtraction.

apply basic addition and
subtraction facts, simple
multiplication facts, and
knowledge of place value and
symmetry to:
- combine or partition whole
numbers
- find fractions of sets, shapes,
and quantities
create, continue, and give the
rule for sequential patterns with
two variables
create and continue spatial
patterns and number patterns
based on repeated addition or
subtraction.

apply additive and simple
multiplicative strategies and
knowledge of symmetry to:
- combine or partition whole
numbers
- find fractions of sets, shapes,
and quantities
create, continue, and predict
further members of sequential
patterns with two variables
describe spatial and number
patterns, using rules that involve
spatial features, repeated
addition or subtraction, and
simple multiplication

measure the lengths, areas,
volumes or capacities, and
weights of objects and the
duration of events, using linear
whole-number scales and
applying basic addition facts to
standard units
sort objects and two- and threedimensional shapes by their
features, identifying categories
within categories
represent reflections,
translations, and rotations by
creating and describing
patterns
describe personal locations and
give directions, using wholenumber measures and half- or
quarter-turns.

measure the lengths, areas,
volumes or capacities, weights,
and temperatures of objects
and the duration of events,
reading scales to the nearest
whole number and applying
addition, subtraction, and
simple multiplication to standard
units
sort objects and two- and threedimensional shapes by two
features simultaneously
represent and describe the
symmetries of a shape
create nets for cubes
describe personal locations and
give directions, using simple
maps.

measure time and the attributes
of objects, choosing
appropriate standard units and
working with them to the
nearest tenth
sort two- and three-dimensional
shapes, considering the
presence and/or absence of
features simultaneously and
justifying the decisions made
represent and describe the
results of reflection, rotation,
and translation on shapes
create nets for rectangular
prisms
draw plan, front, and side views
of objects
describe locations and give
directions, using grid references
and points of the compass.

investigate summary and
comparison questions by using
the statistical enquiry cycle:
- gather, display, and identify
patterns in category and wholenumber data
- interpret results in context
order the likelihoods of
outcomes for simple situations








investigate questions by using
the statistical enquiry cycle (with
support), gathering, displaying,
and/or counting category data

Statistics

investigate questions by using
the statistical enquiry cycle (with
support), gathering, displaying,
and/or identifying similarities
and differences in category
data
describe the likelihoods of
outcomes for a simple situation
involving chance, using

investigate questions by using
the statistical enquiry cycle (with
support):
- gather and display category
and simple whole-number data
- interpret displays in context









compare and explain the
likelihoods of outcomes for
investigate questions by using
the statistical enquiry cycle
independently:
- gather and display category
and simple whole-number data
- interpret displays in context
compare and explain the
likelihoods of outcomes for a
simple situation involving

















apply additive and simple
multiplicative strategies flexibly
to:
- combine or partition whole
numbers, including performing
mixed operations and using
addition and subtraction as
inverse operations
- find fractions of sets, shapes,
and quantities
determine members of
sequential patterns, given their
ordinal positions
describe spatial and number
patterns, using:
- tables and graphs
- rules that involve spatial
features, repeated addition or
subtraction, and simple
multiplication.
measure time and the attributes
of objects, choosing
appropriate standard units
use arrays to find the areas of
rectangles and the volumes of
cuboids, given whole-number
dimensions
sort two- and three-dimensional
shapes (including prisms),
considering given properties
simultaneously and justifying the
decisions made
represent and describe the
results of reflection, rotation, and
translation on shapes or patterns
identify nets for rectangular
prisms
draw or make objects, given
their plan, front, and side views
describe locations and give
directions, using grid references,
turns, and points of the
compass.
investigate summary and
comparison questions by using
the statistical enquiry cycle:
- gather or access multivariate
category and whole-number
data
- sort data into categories or
intervals, display it in different
ways, and identify patterns
everyday language.
a simple situation involving
chance.
chance, acknowledging
uncertainty.
JAM (Junior Assessment in Maths)
Additive
Strategies
Forwards and
backwards
sequences
knowledge
Multiplicative
and Fraction
Strategies
Stages 2 and 3
Applying ‘Counting all’ strategies
Stages 2 and 3
Says forward and backward
sequences and the number before
or after in range 0-20
Stages 2 and 3
Applying ‘Counting all’ strategies
Fraction
Knowledge
Grouping and
Place Value
Stages 2 and 3
Knows grouping within 5, with 5, and
within 10
Recognises patterns and doubles to
10
Basic Facts
Stages 2 and 3
Recalls facts to 5, doubles to 10, and
groupings within 10
Early Stage 5
Apply basic addition facts and
knowledge of place value and
symmetry to combine or partition
whole numbers
Early Stage 5
Says forward and backward
sequences and the number before
or after in the range 0-1000
Stage 4
Advanced counting
Applying counting on, counting
back, skip-counting, and simple
grouping strategies, and,
Use equal sharing to find fractions of
sets
Identifies symbols for halves,
quarters, thirds and fifths
Early Stage 5
Apply basic addition facts and
knowledge of place value and
symmetry to combine or partition
whole numbers, and find fractions of
sets, and quantities
Algebra
(patterns)
Continue sequential patterns
Geometry
(shapes)
Sort objects and shapes by a single
feature and describe the feature,
using everyday language
Sort objects and shapes by different
features and describe the features,
using mathematical language
Measurement
(length)
Compare the lengths of objects
directly
Compare the lengths of objects
using self-chosen units of
measurement
Can sort objects (eg. animals) into
categories, using a set grouping or
pictograph
Can answer simple questions about
results
Can make comparisons between
groups of objects
Can identify two possible outcomes
(probability)
Statistics

- interpret results in context,
accepting that samples vary
order the likelihoods of
outcomes for situations involving
chance, considering
experimental results and models
of all possible outcomes.
GLoSS
Stage 4
Advanced counting
Applying counting on, counting
back, skip-counting, and simple
grouping strategies
Stage 4
Says forward and backward
sequences and the number before
or after in range 0-100
Stage 4
Knows groupings with 10 and the
pattern of –teens
Knows groupings within 20
Knows the number of tens in
decades
Stage 4
Recall facts to 10, doubles to 20,
and corresponding halves and –
teen facts
Create and continue sequential
patterns by identifying unit of repeat
involving chance,
experimenting or listing all
possible outcomes.
Early Stage 5
Identifies the symbols for the most
common fractions, including halves,
quarters, thirds, fifths and tenths
Early Stage 5
Knows groupings within 100 and
multiples of 5
Knows groupings of 10 in a 3-digit
number
Early Stage 5
Recall addition facts to 20 and
subtraction facts to 10
Create and continue sequential
patterns with one or two variables
by identifying the unit of repeat
Sort objects and two and threedimensional shapes by their
features, identifying categories
within categories
Measure the lengths of objects,
using linear, whole-number scales
and applying basic addition facts to
standard units
Sort whole-number data into groups
Display data in enclosed groupings
or organised displays eg. bar graph
Make comparison statements about
data displayed
Can classify probability eg. use likely
and least likely; use fractions to
describe likelihood
Stage 5:Early Additive / Part
whole (End of year 4 – achieving
Stage 5)
Stage 6: Advanced Additive / Early Multiplicative
(End of year 5 – working within Stage 6: End of year 6 – achieving
Stage 6)
Addition and Subtraction
Solve subtraction problems (separating, change/start unknown, or comparing)
by going back through tens.
Solve addition problems by forming tens from ones and forming hundreds from
tens.
Solve subtraction problems by operating on place values while “parking” ones,
tens (hundreds).
Solve subtraction problems using standard place value partitioning, e.g. 73 – 46
=␣as73–40 =33, 33– 6 =␣.
Solve addition and subtraction
problems by working from doubles.
Solve addition and subtraction
problems by using groupings with
five.
Solve addition problems by looking
for compatible numbers that add to
ten, other decades or one hundred.
Solve addition problems by going
up through tens.
Solve addition and subtraction
problems by combining and
separating tens and ones.
Solve addition problems by compensating with tidy numbers.
Solve addition problems by looking for compatible numbers.
Solve addition and subtraction problems by compensating with tidy numbers
(including equal additions).
Solve comparison and difference problems by reversing (adding instead of
subtracting),
e.g. 72 – 45 =␣as 45 +␣= 72. Solve addition and subtraction
problems by exchanging ones for tens, and tens for hundreds (decomposition),
leading to a written algorithm.
Choose critically from a range of mental strategies to solve addition and
subtraction problems.
Multiplication and Division
Solve multiplication problems using
repeated addition
Solve five times tables by doubling
and halving (and learn them)
Use the commutative property,
e.g. 4 × 6 = 6 × 4
Dividing by sharing using addition to
predict
Dividing by making equal sets
Proportions and Ratios
Find a unit fraction of a set using
addition facts, particularly doubles,
e.g. 1 of16is4using 1 of 42
16 is 8.
Find unit fractions of a continuous
region, like a length or area, using
halving.
Order unit fractions and fractions
with the same denominator and
explain why they are larger or
smaller
Order fractions visually using
materials, including improper
fractions like 5/3 and 7/4 and
explain what the numerator and
denominator mean
Use times five facts to work out times six, seven, and four facts (using the
distributive property)
Use times ten facts to work out times nine facts (using the distributive
property)
Change the order of the factors to make a multiplication problem easier,
e.g. 26 x 3 = 3 x 26
Find out how many ones, tens, hundreds and thousands are in all of a whole
number,
Use two times facts to work out three, four, six, and eight times facts (using
doubling and the distributive property)
Multiply by tens, hundreds, thousands, and other multiples of ten
Solve sharing problems by reversing multiplication facts
Solve “How many equal sets of ?” problems by reversing multiplication facts
Solve problems using a combination of addition, subtraction, multiplication
and division mental strategies
Find fractions of a set using multiplication and division
Use symmetry to find fractions of continuous shapes like lengths, circles, and
rectangles.
Solve division problems that have fraction answers using halving.
Create equivalent ratios by repeated copying.
Measure how many times a unit fraction goes into a whole number, e.g.
How many quarters are in five?
Rename improper fractions as mixed numbers using materials with
multiplication, and position improper fractions on a number-line
Stage 5:Early Additive / Part
whole (End of year 4 – achieving
Stage 5)
Addition and Subtraction
IKAN
Identify all of the numbers in the
range 0-1000
Say the forwards and backwards
number word sequences by ones,
tens, and hundreds in the range 01000.
Say the number 1, 10, or 100 more or
less than a given number in the
range 0-1000.
Order numbers in the range 0-1000.
Recalls groupings within 100, e.g. 49
and 51 (particularly multiples of 5
e.g. 25 & 75)
Recall the number of groupings of
tens that can be made from a
three-digit number
Recall addition and subtraction
facts to 20
Recall the number of tens and
hundreds in centuries and
thousands.
Round three-digit whole numbers to
the nearest 10, or hundred
Recall the multiples of 100 that add
to 1000, e.g. 400 and 600.
Record the results of addition
calculations, using equations and
diagrams.
Multiplication and Division
Say the forwards and backwards
skip-counting sequences in the
range 0- 100 for twos, threes, fives,
and tens at least.
Recall groupings of two in numbers
to 20, groupings of five in numbers to
50, and groupings of 10 in numbers
to 100.
Automatically recall the
multiplication and division facts for
the multiples of 2, 5, and 10.
Record the results of mental
multiplication calculations using
equations and diagrams
Proportions and Ratios
Identify the symbols for halves,
quarters, thirds, fifths, and tenths
including fractions greater than 1.
Order fractions with like
denominators, e.g. 1/4. and 2/4.
PAT Maths
Stage 6: Advanced Additive / Early Multiplicative
(End of year 5 – working within Stage 6: End of year 6 – achieving
Stage 6)
Identify all of the numbers in the range 0 - 1 000 000.
Say the forwards and backwards whole number word sequences by ones,
tens, hundreds, and thousands in the range 0 – 1 000 000, including finding
numbers that are 10, 100, and 1 000 more or less than a given number
Order whole numbers in the range 0-1 000 000.
Read decimals with tenths, count forwards and backwards in tenths, order
decimals with tenths.
Recall groupings within 1000, e.g., 240 + 760.
Recall addition and subtraction facts to 20.
Recall how many tens and hundreds there are in four- digit numbers.
Record the results of mental calculation using addition and subtraction
equations and diagrams
Round whole numbers to the nearest ten, hundred, or thousand
Carry out column addition and subtraction with whole numbers of up to
four digits
Recall groupings of twos, threes, fives, and tens that are in numbers to 100
and the resulting remainders
Recall all the multiplication and division facts for 2, 3, 5, 10 x tables
Recall groupings of 10 and 100 that can be made from a four-digit number
Recall multiplication facts for squares to 100
Record the results of mental calculation using multiplication and division
equations and diagrams
Identify decimals to three places
Identify symbols for any fraction, including tenths, hundredths, thousandths,
and those greater than 1
Say the forwards and backwards word sequences for halves, quarters,
thirds, fifths, and tenths
Say the decimal number word sequences, forwards and backwards, in
tenths and hundredths
Order unit fractions for halves, quarters, thirds, fifths, and tenths
Recall the number of tenths and hundredths in decimals to two places
Round decimals with up to two places to the nearest whole number
Students achieving at Stanine 5 or 6 are considered to be ‘meeting’ the standard
References and Resources:
NZC, JAM Assessment kit; Mathematics Standards, Numeracy Framework and texts. Teachers should refer to these for more detailed explanations and examples and also the National
Standard Illustrations http://www.nzmaths.co.nz/national-standards-illustrations?parent_node=