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 web-connected device that opens PDF and is connected to a printer. a maths journal. other stuff from around the house. help sometimes - ask for it. You can use digital technology to partner with someone else. Have you registered your email address?

Maths at Home Activity Library

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?

Cap-turing 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, short-term 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 - if-then / 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

Times Tables Torture

2, 3, 4, 5, 6, 7, 8, 9, 10

times tables, multiplication

Time Together

2, 3, 4, 5, 6, 7, 8, 9, 10

applying understanding of the interconnectedness of the hands of a clock, clockwise & anti-clockwise, 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 & anti-clockwise, 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, non-linear 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 & Anti-Protons

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, if-then 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

Thirty-One

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