Draft
Maths
Mathematics Milestones - Problem Solving
Adventures
NZC 1
1
5 - 6 years old
2
NZC 2
3
6 - 7 years old
7 - 8 years old
4
8 - 9 years old
9 - 10 years old
Students are able to solve problems* involving addition, subtraction, multiplication and division of whole numbers
Counting
groups of
objects
up to 10
Joining and
separating
groups
up to 20
Joining groups the same size
and sharing equally up to 10
with physical objects
NZC 3
5
Joining and separating
groups of objects
(2 digit ± 1 digit)
using counting on or back,
and skip counting in tens
Addition and subtraction
(2 digit ± 1 digit)
not using counting
one step problems
Addition and subtraction
(3 digit ± 1 digit)
with renaming, and
(3 digit ± 3 digit)
with no renaming
Joining groups of objects the
same size and sharing equally
Multiplication and division
using counting, addition,
subtraction & equal sharing
Multiplication and division
groups of two, groups of five,
and groups of ten
6
10 - 11 years old
Stage 2
Using count on, count back
Stage 4
Early Stage 5
Students are able to solve problems* involving fractions and decimals
Doubling and halving
groups of objects up to 20,
areas and lengths
Stage 5
9
12 - 13 years old
NZC 5
13 - 14 years old
* In problem solving contexts, e.g. word problems, students get the correct answer independently. No help on day of testing, no warm up and no support except to read question if needed.
Addition and subtraction
(2 digit ± 2 digit)
with renaming
Addition and subtraction
(3 digit ± 2 digit)
with renaming
Using two different efficient strategies, based on problem and numbers involved.
Multiplication and division
(1 digit x/÷ 1 digit)
one step problems with
answers matching x/÷ facts
Multiplication x 1 digit
with answers up to 100
Division (up to 100 ÷ 1 digit)
with remainder
Addition and subtraction of
any whole numbers
Addition with answers
less than zero
Add and subtract integers
Multiplication and division
(2 digit x/÷ 1 digit)
÷ with remainder as fraction
Multiplication and division
(3 digit x/÷ 1 digit)
÷ with remainder as fraction
Using two different efficient strategies, based on problem and numbers involved.
Add, subtract,
multiply & divide
integers
X/÷
(3 digt x/÷ 1 digt)
÷ with remainder
as a decimal
Language of problem is less obvious, more complex
Using advanced additive and early multiplicative thinking
Using any non counting strategy / using part-whole thinking
8
11 - 12 years old
Language of problem is a guide with operator to use obvious
Using counting from one
NZC 4
7
Early Stage 6
Using advanced multiplicative and early proportional thinking
Stage 6
Early Stage 7
Advanced proportional
Stage 7
Stage 8
* In problem solving contexts, e.g. word problems, students get the correct answer independently. No help on day of testing, no warm up and no support except to read question if needed.
Addition and subtraction
halves and quarters
incl. fractions more than one
Add, subtract, order fractions
with the same denominator
incl. fractions more than one
Addition and subtraction
halves, quarters and eights
incl. fractions more than one
Addition and subtraction
(thirds, sixths and twelfths) &
(fifths, tenths and hundredths)
Addition and subtraction
halves, thirds and quarters
Addition and subtraction
halves, thirds, quarters, fifths
sixths, eighths and tenths
Finding ½ and ¼
of groups, areas and lengths
easily divided by 2 and 4
Finding halves and quarters
of groups up to 100,
areas and lengths
incl. fractions more than one
Finding halves, thirds
quarters, fifths and tenths
of whole numbers with the
denominator a multiple
Finding any fraction of
whole numbers with the
denominator a multiple
Finding halves, thirds
quarters, fifths, sixths,
eighths and tenths of any
whole number
Finding fractions
of any whole number
Order unit fractions
Order halves, thirds
and quarters
Order halves, thirds,
quarters, fifths and tenths
Order any fraction
Multiply any fraction by a half
incl. fractions more than one
Multiply any fraction by
a unit fraction
Multiply fraction
by halves, thirds
and quarters
Divide any fraction by half
Divide fractions
by unit fractions
Add and subtract any decimal
Multiply and divide tenths
and hundredths
Multiply and
divide any
decimal
Add and subtract tenths
Add and subtract tenths
and hundredths
Multiply and divide tenths
Find common percentages
10%, 25%, 50%, 75%, 90%,
100%, 110% ...
Addition &
subtraction
of any
fractions
Find percentage of any
number
of any number up to 1,000
Convert 25%, 50%, 75%,
100%, 125% 150% .. into
halves, quarters and fractions
with the denominator 100
Convert common fractions into
decimals and percentages
10%, 25%, 50%, 75%, 90%,
100%, 110% ...
Double and halve rates
Convert between fractions,
decimals and percentages
Comparing rates and ratio
by repeated replication
Rates and ratios