
Choose Your Mathematics
Working like a mathematician begins with an interesting problem

Welcome
We suggest you bookmark this page.
This is a library of activities and investigations to help you
learn to work like a mathematician.
 Click this link. Print and keep the page.
 Use it like you have a mathematician sitting beside you.
Mmm, I wonder what my mathematician would do now?
 Lots of other kids have found these challenges interesting.
 For each challenge we tell you the school years
where they have been used.
 Your teacher or parent might tell you which one to choose.
 Or choose your own mathematics.

Be Prepared
You will need...
 a webconnected device that opens PDF and is connected to a printer.
 a maths journal.
 other stuff from around the house.
 help sometimes  ask for it.
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Maths at Home Activity Library
74 activities so far...

Name 
Year Levels
(K = 5 y.o.) 
Content
(Depends on age and experience) 

Calculator Walk

K, 1, (2) 
1:1 correspondence, counting, mathematical conversation, numeral recognition, ordering, recording  calculator, visual and kinaesthetic representation of number, writing (and making) numerals


Counting Frames

K, 1, (2) 
1:1 correspondence, counting, estimating/predicting number, exploring large numbers, group (or skip) counting, making/recording groups of 10, mathematical conversation, multiplication  array model, number line  ordering, operations, pattern recognition, recording  calculator, visual and kinaesthetic representation of number


Kites and Kite Tails

K, 1, (2) 
1:1 correspondence, addition facts up to and beyond 10, counting, counting on, estimating number, making groups of 5 & 10, multiplication (informal  equal rows), pattern  visual and number, recording  calculator, visual & kinaesthetic representation of number


Ten Friends

K, 1, (2) 
1:1 correspondence, addition facts up to and beyond 10, making groups of 10, place value, recording  calculator, visual & kinaesthetic representation of number


Seats on a Bus

K, 1, (2) 
arrays, commutative law of multiplication (informal), factors (informal), maths in context, multiplication experiences, times tables (informal), repeated addition


Two Dollar Shop

K, 1, 2, 3 
addition facts up to and beyond 10, complementary addition, making change, mathematical conversation, operations  money, operations  whole number, recording  calculator, recording  written


Fill The Board

K, 1, 2, 3, 4, 5, 6 
1:1 correspondence, addition facts beyond 10, addition facts to 10, complimentary addition, counting, data: collecting, recording, displaying, data: describing & comparing with statistics, data: interpretation, estimating number, likely, less likely and unlikely events, mathematical conversation, pattern generalisation, pattern interpretation, pattern recognition, probability, subtraction, recording  written, tallying


Six Plus

K, 1, 2, 3, 4, 5, 6 
addition facts up to and beyond 10, developing number sense, equations (creating & solving), estimating number, multiplication, operations  whole number, problem solving


What Can You Do With The Sunday Paper?

K, 1, 2, 3, 4, 5, 6, 7, 8 
constructing 2D and 3D shapes and objects, exploring rigidity, mathematical language of shapes and objects, spatial and numerical patterns leading to algebra, tables of values, value relations  if this is worth ..., what is that worth?


Capturing Mathematics
You need a mixed collection of at least fifty plastic screw caps to
begin this activity.

K, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 
1:1 correspondence, basic arithmetic, counting, equations, estimating number & measures, graphing, measurement, memory games, odd & even numbers, pattern generalisation, patterns  visual & number, probability experiences, rectangle, square & triangle numbers, sorting & classifying


Crazy Animals

K, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 
average, collecting & recording data, combination theory, informal probability experiences, more or less likely events, probability  long run frequency, shortterm variability versus long term average, tree diagrams, Venn diagrams


Dice Footy

K, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 
addition, average, mathematical modelling, mental arithmetic, multiplication, calculations / times tables, probability calculations, probability, expected number, probability experiences, statistics  analysing data, statistics  collecting & organising data


Ten Tens

(K), 1, 2, 3 (4, 5, 6) 
1:1 correspondence, addition facts up to and beyond 10, complementary addition, estimating number, mathematical conversation, recording  calculator, recording  written, visual & kinaesthetic representation of number


Number Shapes

1, 2, 3, 4, 5, 6, 7, 8 
arithmetic of whole number, place value, arithmetic of decimals (and fractions), problem solving, recognising, interpreting and creating patterns, creating and recording equations


Highest Number

(K), 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 
basic arithmetic skills  especially addition, basic place value skills, counting in 1s, 2s, 5s, & 10s, informal chance experiences, probability  including calculating chances of simple events / long run expectation / probability distribution patterns, statistics  including data collection in stem and leaf form and potential to introduce or revise statistical measures in the context of first hand data


Predict A Count

(1), 2, 3, 4, 5, 6, 7, 8 
addition facts beyond 10, estimating/predicting number, group counting, pattern interpretation, pattern recognition, recording  calculator, recording  written, subtraction


Toss Up

(1), 2, 3, 4, 5, 6 
addition, group counting, mental arithmetic, multiplication, pattern interpretation, pattern recognition, place value (base 10 and other bases informally), times tables


Domino Trails

2, 3, 4, 5, 6 
1:1 correspondence, addition and subtraction, counting, creating equations, multiplication and division, number recognition, problem solving strategies, sorting


Pattern Charts

2, 3, 4, 5, 6 
addition, basic arithmetic skills, odd & even numbers, number patterns, pattern interpretation, pattern recognition, skip counting, square numbers, problem creation, problem solving


Please May I Have

2, 3, 4, 5, 6 
addition facts beyond 10, mathematical conversation, numeral recognition, whole number operations, place value, subtraction


13 Away

2, 3, 4, 5, 6, 7 
calculator game, generalisation, logic and reasoning, number patterns, problem solving strategies, simple addition and subtraction, visual and kinaesthetic representation of number, working like a mathematician


Making & Breaking Rectangles

2, 3, 4, 5, 6, 7 
conservation of number, factors & primes, graphing number pairs, multiplication  array model, recording  calculator, recording  written, times tables, visual and kinaesthetic representation of number


Calculator Slido

2, 3, 4, 5, 6, 7, 8 
decimal calculations, decimal interpretation, division, exploring large numbers, multiplication, numeral recognition, operations  whole number, pattern interpretation, pattern recognition, place value, properties of number, properties of zero, recording  calculator, recording  written, writing numerals


Exploring Times Tables

2, 3, 4, 5, 6, 7, 8 
basic arithmetic, group (or skip) counting, mathematical conversation, multiplication  array model, square numbers, times tables, visual and kinaesthetic representation of number


Four Odd Numbers

2, 3, 4, 5, 6, 7, 8 
visual & concrete representation of number, odd & even numbers, addition, multiplication, times tables, pattern recognition and interpretation, working backwards, generalisation 

Five Cards

2, 3, 4, 5, 6, 7, 8 
addition facts up to and beyond 10, division, equations: creating/solving, mathematical conversation, multiplication, whole number operations, order of operations, subtraction, times tables, using brackets


Money Charts

2, 3, 4, 5, 6, 7, 8 
arithmetic  addition / subtraction, arithmetic  money, equations  creating / solving, mental arithmetic, reasoning  ifthen / working backwards


The Big One

2, 3, 4, 5, 6, 7, 8 
decimal interpretation, division, estimating number, multiplication, pattern generalisation, pattern interpretation, pattern recognition, problem solving, recording  calculator


Truth Tiles 1

2, 3, 4, 5, 6, 7, 8 
basic arithmetic skills, connection between addition and subtraction, fundamental laws of arithmetic  identity, commutative, inverse operations, problem solving strategies


Cars In A Garage

2, 3, 4, 5, 6, 7, 8, 9, 10 
1:1 correspondence, counting, large numbers logical reasoning, mathematical language of position and order, multiplication, multiplication principle of counting, multiplicative thinking, permutations & combinations, problem posing and solving, recording mathematics, standard form, visual patterns including colour patterns


Coloured Squares

2, 3, 4, 5, 6, 7, 8, 9, 10 
logical reasoning and problem solving strategies, visual patterns, reflection, rotation, mathematical conversation 

Cube Nets

2, 3, 4, 5, 6, 7, 8, 9, 10 
2D representation of 3D objects, cube nets, nets of other objects, sorting & classifying, problem solving strategies  particularly try every possible case


Farmyard Friends

2, 3, 4, 5, 6, 7, 8, 9, 10 
mathematical language related to space and order, reasoning and communication in mathematics, spatial facts and relationships, problem solving strategies, combination theory


Sphinx Shapes

2, 3, 4, 5, 6, 7, 8, 9, 10 
shape recognition, measurement, perimeter and area experiences, experience with similar shapes, spatial perception, spatial problem solving, reasoning to find every possible case, tessellations (tiling patterns).
Note: 'Similar' in mathematics means lengths are connected by a scaling factor. 

Steps

2, 3, 4, 5, 6, 7, 8, 9, 10 
arithmetic (addition / subtraction, multiplication / division), combination theory / ordered arrangements, concept of proof, mental arithmetic. number patterns, recording mathematics


Time Together

2, 3, 4, 5, 6, 7, 8, 9, 10 
applying understanding of the interconnectedness of the hands of a clock, clockwise & anticlockwise, counting patterns, division of time into hours/minutes/(seconds), fractions related to elevenths and twelfths, graphical representation of simultaneous linear equations, proportional reasoning, visualising angles, visualising passing of time


Tricubes

2, 3, 4, 5, 6, 7, 8, 9, 10 
length measurement, estimating number, mental arithmetic, 3D spatial perception, isometric drawing, spatial problem solving, informal introduction of area, perimeter, base area and surface area


Truth Tiles 2

2, 3, 4, 5, 6, 7, 8, 9, 10 
basic arithmetic skills, addition, subtraction, multiplication, division, problem solving strategies


Colour Spots on a Number Line

3, 4, 5, 6, 7 
basic number skills, counting in groups, equations  substitution and solution, finding rules in tables, generalising patterns in words and symbols, making and continuing patterns visually and with numbers, plotting and interpreting ordered pairs on a graph, times tables  especially 3s & 7s


Letters & Numbers

3, 4, 5, 6, 7 
basic number skills, addition up 3 digit totals, counting groups / multiplication, difference between numbers, estimating number, strategies for totalling lists of numbers, strategy of checking an answer another way, strategy of seeking implied or consequential extra information in a problem


Wipe Out

3, 4, 5, 6, 7 
addition, complementary addition, equations  creating & solving, mental arithmetic, place value, recording  calculator, recording  written, subtraction


Ainsley and the Planting Problem

3, 4, 5, 6, 7, 8, 9 
mental arithmetic, learning to work like a mathematician, problem solving strategies  particularly breaking a problem into parts and trying every possible case


Sphinx Sizes

3, 4, 5, 6, 7, 8, 9, 10 
logic & reasoning, powers of 2, prime and composite numbers, problem solving, proportion, spatial perception, square numbers, tessellation


Symmetric Shapes

3, 4, 5, 6, 7, 8, 9, 10 
2D spatial perception, line symmetry, reflection, rotational symmetry, problem solving


Bob's Buttons

4, 5, 6, 7, 8 
division with remainders  sharing, making, counting & arranging groups, factors, multiples, multiplication, prime numbers, seeking & seeing number pattern, times tables, working like a mathematician


Crosses

4, 5, 6, 7, 8 
basic arithmetic skills, number patterns, probability opportunity, problem solving strategies, properties of odd and even numbers, working like a mathematician


Decimals With A Tape

4, 5, 6, 7, 8 
arithmetic  addition / subtraction, arithmetic  multiplication / division, decimals  calculations, decimals  number line, estimating number, fractions  whole & parts, measurement  length, mental arithmetic, number line, place value, recording mathematics


Doug's Tablecloth

4, 5, 6, 7, 8 
counting, division, fractions, length measurement, number facts, number patterns, spatial perception, whole and parts


Networks

4, 5, 6, 7, 8 
game analysis, mathematics in design, problem solving, reasoning, tessellation, transformation geometry  translation, rotation, reflection


Plate Triangles

4, 5, 6, 7, 8 
spatial and number patterns, consecutive numbers, natural numbers, triangle numbers, mental arithmetic, connections with algebra including generalisation of patterns, problem solving strategies


Rectangle Fractions

4, 5, 6, 7, 8 
adding and subtracting fractions, basic number skills, concept of a fraction, equivalent fractions, visualisation of common denominator


Rectangle Fractions Game

4, 5, 6, 7, 8 
adding and subtracting fractions, basic number skills, concept of a fraction, equivalent fractions, visualisation of common denominator


Rows, Rectangles and Multiplication

4, 5, 6, 7, 8 
array model of multiplication, basic arithmetic, counting patterns, distributive law, informal algebra, 'long' multiplication, multiplication algorithm, times tables, visual and kinaesthetic representation of number


Tricube Constructions A

4, 5, 6, 7, 8 
length measurement, estimating number, mental arithmetic, 3D spatial perception, front & side (elevation) views, isometric drawing, plan (or aerial) view, problem solving


Wallpaper Patterns

4, 5, 6, 7, 8 
language of space, position and order, recording mathematics, spatial perception, symmetry  line, symmetry  rotation, tessellation, transformations (reflection, rotation, translation), visual patterns


Target Range

4, 5, 6, 7, 8, 9 
decimal calculations, decimal interpretation, division, estimating number, exploring large number, mental arithmetic, multiplication, operations  whole number, recording  calculator, times tables


Garden Beds

4, 5, 6, 7, 8, 9, 10 
algebra (including: concept of a variable, generalisation, substitution, solving linear functions, domain and range, equivalent algebraic expressions), basic arithmetic, equations (substitution & solution), graphical representation, multiplication (array concept, calculations, times tables, patterns (visual & number)


In Between Time

4, 5, 6, 7, 8, 9, 10 
before and after a given time, clockwise & anticlockwise, division of time into hours, minutes & seconds, fractions, proportional reasoning, time difference, understanding and applying interconnectedness of clock hands, visualising angles, visualising the passing of time


Less Than Fractions

4, 5, 6, 7, 8, 9, 10 
addition, fractions (calculations, comparing, denominator, equivalence, greater than, less than, multiplication, numerator, whole & parts), measurement, mental arithmetic, number line, number patterns, times tables, triangle numbers, problem solving strategies, reasoning and justification


Mushroom Hunt

4, 5, 6, 7, 8, 9, 10 
addition, doubling, powers of 2, binary numbers, index notation, multiplicative (exponential) growth, nonlinear graphs, problem solving strategies, reasoning and justification


Number Tiles

4, 5, 6, 7, 8, 9, 10 
basic arithmetic skills, concept of proof, connection between addition and subtraction, number patterns, place value, problem solving strategies, symbolic representation, symmetry and combination theory properties


Princess Catharina's Gold Rings

4, 5, 6, 7, 8, 9, 10 
addition / subtraction, breaking a problem into parts, combination theory / ordered arrangements, concept of proof, considering every possible case, mental arithmetic, multiplication / division. numbers / odd & even, numbers / properties & laws, recording mathematics, tree diagrams


Protons & AntiProtons

4, 5, 6, 7, 8, 9, 10 
basic number skills, addition/subtraction of zero, arithmetic of positive and negative numbers, concept of positive and negative numbers, ifthen reasoning, integer arithmetic, negative as the additive inverse of positive, working backwards, zero as the identity element of addition


Red To Blue

4, 5, 6, 7, 8, 9, 10 
algebraic notation, generalisation, odd and even numbers, problem solving strategies, recording and communicating mathematics, tree diagrams and flow charts


Square Numbers

4, 5, 6, 7, 8, 9, 10 
square numbers; odd numbers; square numbers as the sum of odd numbers; properties of odd and even numbers; number patterns; algebraic generalisation


The Farmer's Puzzle

4, 5, 6, 7, 8, 9, 10 
addition, multiplication, basic arithmetic, learning to work like a mathematician, relative money values, number sense, number patterns, using a table to organise and explore data


Training For Maths

4, 5, 6, 7, 8, 9, 10 
breaking a problem into parts, combination theory, counting all possiblities, Fibonacci Numbers, pattern, recording in a table, working mathematically process


ThirtyOne

5, 6, 7, 8 
basic arithmetic practice, mental arithmetic, recognition and interpretation of number patterns, generalisation and representing of number patterns in words & symbols, problem solving


Monkeys & Bananas

5, 6, 7, 8, 9, 10 
basic arithmetic skills, creating & solving equations, flow diagrams, fractions of a set of objects, linear algebra, multiplicative thinking, problem solving strategies, spreadsheets as a problem solving tool, tracking & backtracking


Square Pairs

5, 6, 7, 8, 9, 10 
concept of proof, modern history of mathematics (circa 1999), odd & even numbers, square numbers, reasoning, recording & communicating mathematics


Jumping Kangaroos

6, 7, 8, 9, 10 
problem solving including examining all possibilities and trying a simpler problem, seeking & seeing patterns, arithmetic, especially addition, multiplication and times tables, quadratic expressions, tables of values, graphing parabolas


Pythagoras 1

6, 7, 8, 9, 10 
2D spatial perception, concept of proof, history of mathematics, measurement (length & area), Pythagoras Theorem, square numbers, transformations (rotation & translation)


Working Mathematically
with Viruses

8, 9, 10, 11, 12 
building tables and plotting graphs from a concrete model, extending the model through a suite of 5 Excel spreadsheets, formulas and their representation in graphs, words and symbols, exponential growth, mathematical modelling, multiplication patterns, powers and indices, reading and interpreting computer generated graphs, recognising, reading and writing large numbers, using real data

Maths At Home is a division of Mathematics Centre
