Nrich F-6 curriculum mapping document - Primary Learning

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Nrich F-6 curriculum mapping document
Mapping to the Australian Curriculum - Number and Algebra
Many Australian teachers access the problems, games and investigations from the website www.nrich.maths.org to use with their
students either as launch activities or as longer investigations during mathematics lessons. This resource maps the Nrich tasks to the
Australian Curriculum descriptors (ACARA) for Number and Algebra. The Nrich primary site provides links to other countries’ curriculum
documents (e.g. England’s curriculum) and these have been a guide for the production of this resource. In this resource, the tasks have
been linked to the Australian curriculum content descriptors only. All of these tasks potentially link to the proficiencies of understanding,
fluency, problem solving and reasoning however, it is more how the individual teacher utilises the tasks, and how the students interact
with them, that determine the links to these processes.
This resource maps task to the Number and Algebra strand, two other resources have been developed that link to Measurement and
Geometry and Statistics and Probability. The links here are not an exhaustive list of the many ways the tasks can be utilised or
connected to concepts across the curriculum. The tasks have been linked to the content descriptor they mainly focus on, other
connections can be made to other areas as well. As more tasks are added to the Nrich site this document will be updated.
Nrich also have a Primary Live Problems site where schools and their students can access problems and then send their solutions to
Nrich who will publish a section of them.

References
Australian Curriculum, Assessment and Reporting Authority (ACARA) mathematics curriculum content descriptors are all © Australian
Curriculum, Assessment and Reporting Authority accessed via https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics
Nrich website www.nrich.maths.org all tasks © University of Cambridge

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                                                                       Number and place value

Foundation content descriptors

Establish understanding of the            Connect number names, numerals              Subitise small collections of objects   Compare, order and make
language and processes of counting        and quantities, including zero, initially   (ACMNA003)                              correspondences between collections,
by naming numbers in sequences,           up to 10 and then beyond                                                            initially to 20, and explain reasoning
initially to and from 20, moving from     (ACMNA002)                                  Number talks                            (ACMNA289)
any starting point (ACMNA001)                                                         Hidden jewels
                                          Number talks                                Show me                                 The voting station
The estimation station                    The estimation station                                                              Show me
Using books: Maisie goes camping          Golden beans                                                                        Dice
Number book                               Number rhymes                                                                       Number match
Owl’s packing list                        Dice                                                                                Using books: The doorbell rang
Tidying                                   The box game                                                                        Maths story time

Represent practical situations to model
addition and sharing (ACMNA004)

Using books: Maisie goes camping
Double trouble
Maths story time
Playing Incey Wincey spider

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                                                                    Number and place value

Year 1 content descriptors

Develop confidence with number            Recognise, model, read, write and       Count collections to 100 by partitioning Represent and solve simple addition
sequences to and from 100 by ones         order numbers to at least 100; locate   numbers using place value                and subtraction problems using a
from any starting point. Skip count by    these numbers on a number line          (ACMNA014)                               range of strategies, including counting
twos, fives and tens starting from zero   (ACMNA013)                                                                       on, partitioning and rearranging parts
(ACMNA012)                                                                        Snail one hundred                        (ACMNA015)
                                          Writing digits                          Six beads
Buzzy bee                                 Shut the box                            How would we count?                      Shut the box
Dotty Six                                 Snail one hundred                       Count the crayons                        Two dice
100 square jigsaw                         Six beads                                                                        Same length trains
That number square                        How would we count?                                                              Snail one hundred
Five steps to 50                          Tug of war                                                                       Noah
Noah                                      The eightness of eight                                                           Robot monsters
Making sticks                             Count the digits                                                                 All change
I like…                                   Two spinners                                                                     Largest even
Heads and feet                            Number match                                                                     Eggs in baskets
Lots of biscuits!                                                                                                          Cuisenaire counting
Clapping times                                                                                                             Pairs of numbers
                                                                                                                           Weighted numbers
                                                                                                                           Ladybirds in the garden
                                                                                                                           Unit differences
                                                                                                                           Sealed solution
                                                                                                                           Roll these dice
                                                                                                                           Finding fifteen
                                                                                                                           Six numbered cubes

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                                                                  Number and place value

Year 2 content descriptors

Investigate number sequences, initially   Recognise, model, represent and    Group, partition and rearrange           Explore the connection between
those increasing and decreasing by        order numbers to at least 1000     collections of up to 1000 in hundreds,   addition and subtraction (ACMNA029)
twos, threes, fives and tens from any     (ACMNA027)                         tens and ones to facilitate more
starting point, then moving to other                                         efficient counting (ACMNA028)            Tug of war
sequences (ACMNA026)                      Count the crayons                                                           How do you see it?
                                                                             Snail one hundred                        2, 4, 6, 8
Five steps to 50                                                             Two-digit targets                        Getting the balance right
Biscuit decorations                                                          Six beads                                Number balance
Same length trains                                                           Count the crayons                        Number lines
                                                                             Two spinners                             Strike it out
                                                                             Which is quicker?                        Sort them out (1)
                                                                                                                      Find the difference
                                                                                                                      The add and take-away path
                                                                                                                      How many?
                                                                                                                      Secret number

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                                                                 Number and place value

Solve simple addition and subtraction   Recognise and represent multiplication Recognise and represent division as
problems using a range of efficient     as repeated addition, groups and       grouping into equal sets (ACMNA032)
mental and written strategies           arrays (ACMNA031)
(ACMNA030)                                                                     Sitting round the party tables
                                        Same length trains                     Lots of biscuits!
I’m eight                               Grouping goodies                       Share bears
Two-digit targets                       Making sticks                          Birthday sharing
Tug of war                              Heads and feet                         Let us divide!
Robot monsters                          The Brown family                       Remainders
Dotty Six                               Doubling fives                         Sweets in a box
Making sticks                           Catrina’s cards
Round the two dice                      Sweets in a box
How do you see it?                      I’m eight
What could it be?                       Sitting round the party tables
2, 4, 6, 8                              Lots of biscuits!
Heads and feet
One big triangle
Strike it out
Number round up
Dicey addition
Dice in a corner
Maze 100
Six numbered cubes

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                                                                   Number and place value

Year 3 content descriptors

Investigate the conditions required for   Recognise, model, represent and     Apply place value to partition,           Recognise and explain the connection
a number to be even or odd and            order numbers to at least 10 000    rearrange and regroup numbers to at       between addition and subtraction
identify even and odd numbers             (ACMNA052)                          least 10 000 to assist calculations and   (ACMNA054)
(ACMNA051)                                                                    solve problems (ACMNA053)
                                          How would we count?                                                           Strike it out
Grouping goodies                          Coded hundred square                Coded hundred square                      Sort them out (1)
Largest even                              Which scripts?                      Which scripts?                            Find the difference
Light the lights                          Nice or nasty                       Space distances                           The add and take-away path
Domino sorting                            Four-digit targets                  Round the four dice                       How many?
Even and odd                              Ordering journeys                                                             Which distance?
Ring a ring of numbers                    Representing numbers                                                          Number lines in disguise
Always, sometimes or never?               Which is quicker?                                                             Build it up
How odd                                                                                                                 Number balance
Two numbers under the microscope
More numbers in the ring
Number differences
Light the lights again

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                                                                       Number and place value

Recall addition facts for single-digit     Recall multiplication facts of two,        Represent and solve problems
numbers and related subtraction facts      three, five and ten and related division   involving multiplication using efficient
to develop increasingly efficient mental   facts (ACMNA056)                           mental and written strategies and
strategies for computation                                                            appropriate digital technologies
(ACMNA055)                                 Double or halve                            (ACMNA057)
                                           Odd times even
Number lines                               Count me in                                Doing and undoing
Butterfly facts                            The deca tree                              Secret number
Strike it out                              Representing numbers                       Number detectives
Number round up                            Multiples grid                             Our numbers
4 Dom                                      Times table shifts                         Dicey operations
Jumping squares                            Table patterns go wild!                    The deca tree
Sometimes, always, never? KS1              Multiplication squares                     Four-digit targets
Double or halve                            Round and round the circle                 Sitting round the party tables
Two numbers under the microscope                                                      Six ten total
Number detectives                                                                     Sweets in a box
Our numbers
Number lines in disguise
A mixed-up clock
Magic V
Fifteen cards
Amy’s dominoes
Sealed solution
Roll these dice
Play to 37
Finding fifteen
Domino square
Make 37
Dice in a corner
Maze 100
Six ten total
Six numbered cubes

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                                                                   Number and place value

Year 4 content descriptors

Investigate and use the properties of   Recognise, represent and order          Apply place value to partition,       Investigate number sequences
even and odd numbers (ACMNA071)         numbers to at least tens of thousands   rearrange and regroup numbers to at   involving multiples of 3, 4, 6, 7, 8 and
                                        (ACMNA072)                              least tens of thousands to assist     9 (ACMNA074)
What could it be?                                                               calculations and solve problems
Domino sorting                          Which distance?                         (ACMNA073)                            Odd times even
Number round up                         Space distances                                                               Number lines in disguise
Lots of biscuits!                       Nice or nasty                           Coded hundred square                  Music to my ears
Even and odd                            Four-digit targets                      Which scripts?                        Carrying cards
Ring a ring of numbers                  Ordering journeys                       Which distance?                       Multiples grid
Always, sometimes or never?             Which is quicker?                       Space distances                       Times table shifts
How odd                                 Nice or nasty                           Tug harder!                           Table patterns go wild!
Two numbers under the microscope        Four-digit targets                      Dicey operations                      Follow the numbers
More numbers in the ring                Number lines in disguise                Dicey operations in line              Round and round the circle
Number detectives                       Ordering journeys                       Round the four dice
Four-digit targets                                                              Got it
Take three numbers                                                              Make 37
Number differences                                                              Twenty divided into six
Play to 37                                                                      Reach 100
Consecutive numbers                                                             Subtraction surprise
Subtraction surprise

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                                                                     Number and place value

Recall multiplication facts up to 10 ×   Develop efficient mental and written
10 and related division facts            strategies, and use appropriate digital
(ACMNA075)                               technologies, for multiplication and for
                                         division where there is no remainder
I’m eight                                (ACMNA076)
Double or halve
Odd times even                           Double or halve
Count me in                              Our numbers
Multiplication square jigsaw             Lots of lollies
Multiples grid                           Dicey operations
Times table shifts                       Four-digit targets
Table patterns go wild!                  A mixed-up clock
Multiplication squares                   Twenty divided into six
Round and round the circle               Six ten total
                                         Multiplication square jigsaw
                                         Shape times shape
                                         Let us divide!
                                         Carrying cards
                                         Zios and Zepts
                                         What do you need?
                                         Mystery matrix
                                         Make 100

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                                                                Number and place value

Year 5 content descriptors

Identify and describe factors and    Use estimation and rounding to check     Solve problems involving multiplication   Solve problems involving division by a
multiples of whole numbers and use   the reasonableness of answers to         of large numbers by one- or two-digit     one-digit number, including those that
them to solve problems (ACMNA098)    calculations (ACMNA099)                  numbers using efficient mental and        result in a remainder (ACMNA101)
                                                                              written strategies and appropriate
The deca tree                        Round the four dice                      digital technologies (ACMNA100)           Dicey operations
Four-digit targets                   Reasoned rounding                                                                  Dicey operations in line
Satisfying four statements                                                    Dicey operations                          Remainders
Flashing lights                                                               The deca tree                             Remainders game
Abundant numbers                                                              Four-digit targets                        Division rules
Factors and multiples game                                                    Dicey operations in line                  Grouping goodies
Three dice                                                                    A square of numbers                       Lots of lollies
Factor track                         Use efficient mental and written         All the digits                            Growing garlic
What do you need?                    strategies and apply appropriate digital Trebling
Factor lines                         technologies to solve problems           Curious number
Factor-multiple chains               (ACMNA291)                               Four go
Counting cogs                                                                 Highest and lowest
                                     Tug harder!                              Make 100
                                     Swimming pool
                                     Sea level
                                     First connect three
                                     Dicey operations
                                     Dicey operations in line
                                     Round the four dice
                                     Number lines in disguise
                                     Fifteen cards
                                     Domino square
                                     Got it

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                                                                 Number and place value

Year 6 content descriptors

Identify and describe properties of   Select and apply efficient mental and     Select and apply efficient mental and     Investigate everyday situations that
prime, composite, square and          written strategies and appropriate        written strategies and appropriate        use integers; locate and represent
triangular numbers (ACMNA122)         digital technologies to solve problems    digital technologies to solve problems    these numbers on a number line
                                      involving addition and subtraction with   involving addition and subtraction with   (ACMNA124)
Square subtraction                    whole numbers (ACMNA123)                  whole numbers (ACMNA123)
Satisfying four statements                                                      continued …                               Tug harder!
Two primes make one square            Tug harder!                                                                         Swimming pool
Up and down staircases                First connect three                       A square of numbers                       Sea level
One wasn’t square                     Dicey operations                          This Pied Piper of Hamlin                 First connect three
Cycling squares                       Dicey operations in line                  All the digits
Picture a pyramid …                   Round the four dice                       Trebling
Always, sometimes or never? Number    Amy’s dominoes                            Mystery matrix
Odd squares                           Build it up                               Division rules
Cubes within cubes                    Dice in a corner                          Highest and lowest
                                      Twenty divided into six                   Make 100
                                      Reach 100                                 Four goodness sake
                                      Subtraction surprise                      Orange drink
                                      How do you do it?                         Pumpkin pie problem
                                      Four-digit targets                        Finding 3D stacks
                                      Remainders game

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                                                                   Fractions and decimals

Year 1 content descriptor               Year 2 content descriptor                Year 3 content descriptor

Recognise and describe one-half as      Recognise and interpret common uses Model and represent unit fractions,
one of two equal parts of a whole       of halves, quarters and eighths of  including 1/2, 1/4, 1/3 and 1/5 and
(ACMNA016)                              shapes and collections (ACMNA033)   their multiples, to a complete whole
                                                                            (ACMNA058)
Fair feast                              Fair feast
Halving                                 Halving                             Halving
Using books: The doorbell rang          Happy halving                       Happy halving
Two halves                              Fractional wall                     Chocolate
                                        Matching fractions                  Fractional wall
                                                                            Fractional triangles
                                                                            Bryony’s triangle
                                                                            Fraction match
                                                                            Balance of halves

Year 4 content descriptors

Investigate equivalent fractions used in Count by quarters, halves and thirds,   Recognise that the place value system
contexts (ACMNA077)                      including with mixed numerals; locate   can be extended to tenths and
                                         and represent these fractions on a      hundredths, and make connections
Fractional wall                          number line (ACMNA078)                  between fractions and decimal
Fraction match                                                                   notation (ACMNA079)
Tumbling down                            Chocolate
More fraction bars                       Fractional triangles                    Greater than or less than?
Extending fraction bars                  Fraction match
Fraction lengths                         Tumbling down
Rectangle tangle                         Balance of halves
                                         Matching fractions

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                                                                Fractions and decimals

Year 5 content descriptors

Compare and order common unit        Investigate strategies to solve          Recognise that the place value system Compare, order and represent
fractions and locate and represent   problems involving addition and          can be extended beyond hundredths     decimals (ACMNA105)
them on a number line (ACMNA102)     subtraction of fractions with the same   (ACMNA104)
                                     denominator (ACMNA103)                                                         Greater than or less than?
                                                                              Greater than or less than?            Spiralling decimals
                                     Chocolate                                Spiralling decimals
                                     Fractional triangles
                                     More fraction bars
                                     Extending fraction bars
                                     Balance of halves
                                     Fraction lengths
                                     A4 fraction addition
                                     A4 fraction subtraction
                                     Linked chains

Year 6 content descriptors

Compare fractions with related       Solve problems involving addition and    Find a simple fraction of a quantity   Add and subtract decimals, with and
denominators and locate and          subtraction of fractions with the same   where the result is a whole number,    without the use of digital technologies,
represent them on a number line      or related denominators (ACMNA126)       with and without the use of digital    and use estimation and rounding to
(ACMNA125)                                                                    technologies (ACMNA127)                check the reasonableness of answers
                                     More fraction bars                                                              (ACMNA128)
Rectangle tangle                     Extending fraction bars                  How do you do it?
                                     Fraction lengths                         Andy’s marbles                         Round the dice decimals 1
                                     A4 fraction addition                     Fractions in a box                     Round the dice decimals 2
                                     A4 fraction subtraction                                                         Jumping
                                     Linked chains
                                     Fraction fascination

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                                                                    Fractions and decimals

Multiply decimals by whole numbers       Multiply and divide decimals by       Make connections between equivalent
and perform divisions by non-zero        powers of 10 (ACMNA130)               fractions, decimals and percentages
whole numbers where the results are                                            (ACMNA131)
terminating decimals, with and without
the use of digital technologies                                                Doughnut percents
(ACMNA129)                                                                     Matching fractions, decimals and
                                                                               percentages
How do you do it?
Route product
Forgot the numbers

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                                                             Money and financial mathematics

Year 1 content descriptor              Year 2 content descriptor                 Year 3 content descriptor                 Year 4 content descriptor

Recognise, describe and order          Count and order small collections of      Represent money values in multiple        Solves problems involving purchases
Australian coins according to their    Australian coins and notes according      ways and count the change required        and the calculation of change to the
value (ACMNA017)                       to their value (ACMNA034)                 for simple transactions to the nearest    nearest fie cents with and without
                                                                                 five cents (ACMNA059)                     digital technologies (ACMNA080)
Shopping - Pirate Poundland (note:     Shopping - Pirate Poundland (note:
use of UK pounds, will need to adapt   need to adapt to cents)                   How do you see it?                        How do you see it?
to cents)                                                                        Money bags (note: use of UK pence,        Planning a school trip
                                                                                 will need to adapt to Australian cents)   Money bags (note: use of UK pence,
                                                                                 Price match (note: use of UK pounds/      will need to adapt to Australian cents)
                                                                                 pence, will need to adapt to Australian   Buying a balloon
                                                                                 cents)                                    Plenty of pens (note: use of UK
                                                                                                                           pounds/pence, will need to adapt to
                                                                                                                           Australian cents)
                                                                                                                           Price match (note: use of UK pounds/
                                                                                                                           pence, will need to adapt to Australian
                                                                                                                           cents)

Year 5 content descriptor              Year 6 content descriptor

Create simple financial plans          Investigate and calculate percentage
(ACMNA106)                             discounts of 10%, 25% and 50% on
                                       sale items, with and without the use of
Planning a school trip                 digital technologies (ACMNA132)

                                       Would you rather? (Note: This task
                                       needs to be modified to reference
                                       Australian notes/ coins)

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                                                                     Patterns and Algebra

Foundation content descriptor            Year 1 content descriptor              Year 2 content descriptors

Sort and classify familiar objects and   Investigate and describe number        Describe patterns with numbers and   Solve problems by using number
explain the basis for these              patterns formed by skip counting and   identify missing elements            sentences for addition or subtraction
classifications. Copy, continue and      patterns with objects (ACMNA018)       (ACMNA035)                           (ACMNA036)
create patterns with objects and                                                                                     Same length trains
drawings (ACMNA005)                      Five steps to 50                       Buzzy bee                            Birthday cakes
                                         Biscuit decorations                    Writing digits                       4 Dom
Double trouble                           Noah                                   Domino sequences                     Unit differences
                                         Domino sequences                       Domino number patterns               Dicey addition
                                         I like…                                What could it be?                    Jumping squares
                                         Light the lights                       Half time                            The add and take-away path
                                         Light the lights again                 Eggs in baskets                      What was in the box?
                                                                                The tall tower                       Super shapes

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                                                                    Patterns and Algebra

Year 3 content descriptor              Year 4 content descriptors

Describe, continue and create number   Explore and describe number patterns Solve word problems by using number         Use equivalent number sentences
patterns resulting from performing     resulting from performing multiplication sentences involving multiplication or   involving addition and subtraction to
addition or subtraction (ACMNA060)     (ACMNA081)                               division where there is no remainder    find unknown quantities (ACMNA083)
                                                                                (ACMNA082)
Writing digits                         Doubling fives                                                                   Getting the balance right
Eggs in baskets                        Double or halve                          Are you well balanced?                  Number balance
Birthday cakes                         Odd times even                           Pebbles                                 Which symbol?
What was in the box?                   Ordering cards                           Multiply multiples 1                    Super shapes
Doing and undoing                      Which symbol?                            Multiply multiples 2                    Shape times shape
Secret number                          Magic plant                              Multiply multiples 3                    Follow the numbers
Ordering cards                         The amazing splitting plant                                                      Two and two
Which symbol?                          The tomato and the bean
Ip Dip                                 The deca tree
The tomato and the bean                Table patterns go wild!
Number lines in disguise               Flashing lights
A mixed-up clock                       Pebbles
Three neighbours                       Round and round the circle
Magic V                                Holes
Build it up
Diagonal sums

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                                                                     Patterns and Algebra

Year 5 content descriptors                                                        Year 6 content descriptors

Describe, continue and create patterns Use equivalent number sentences            Continue and create sequences          Explore the use of brackets and the
with fractions, decimals and whole     involving multiplication and division to   involving whole numbers, fractions and order of operations to write number
numbers resulting from addition and    find unknown quantities (ACMNA121)         decimals; describe the rule used to    sentences (ACMNA134)
subtraction (ACMNA107)                                                            create the sequence (ACMNA133)
                                       A square of numbers
Number lines in disguise               Trebling                                   Consecutive numbers
Three neighbours                       Becoming maths detectives                  Music to my ears
Magic V                                Exploring number patterns you make         Pebbles
Diagonal sums                          Multiply multiples 1                       Becoming maths detectives
Domino sets                            Multiply multiples 2                       Exploring number patterns you make
Break it up!                           Multiply multiples 3                       The moons of Vuvv
Holes                                                                             Up and down staircases
Two and two                                                                       Domino sets
                                                                                  Break it up!
                                                                                  Holes
                                                                                  Button up
                                                                                  Button up some more

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