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.
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Maths at Home Activity Library

Click a Name to open the activity.
Activities are listed in the order of the first school year shown.
Click our logo at the top of an activity page to return here.
Sources
Calculating Changes
Professor Morris Puzzles
Mathematics Task Centre
Working Mathematically with Infants

 

50 activities so far...

Name

Year Levels
(K = 5 y.o.)

Content
(Depends on age and experience)

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

Maths At Home is a division of Mathematics Centre