Enhancing Maths With Attitude This page is for teachers and schools that already have Maths With Attitude kits. (Use the link above to explore Maths With Attitude if this is your first experience with the resource.) MWA kits are built around the attitude that all students can learn to work like a mathematician. Kits resource teachers to: model how a mathematician works invite students to apply the model independently practise the skills of a mathematician in context.

Creating a balanced Working Mathematically curriculum.

The set of 4 MWA kits for a Year level provides 25 weeks of hands-on, investigative learning, deliberately leaving the rest of the year free for teachers and schools to include the best of their past practice. Since the suite of kits (Years 3 - 10) were completed we have added more Tasks and Lessons to our resources. This page details what they are, and to which kits they could be added.

Working Mathematically with Infants (WMI) has been designed to integrate with Maths With Attitude. By using WMI in Years K, 1 & 2 and following with MWA in other primary (and secondary) years you will build a connected curriculum centred on all students learning to work like a mathematician in best practice classrooms.

Maths With Attitude Code

Tasks

No.	Name	Description	Content	Add To...
12	Matching Cards	The initial challenge is to correctly match given pieces, then to order the correct matches. But how many not-matches are possible? Originally designed as an example of what a task card for Infants (Years K - 2) might look like, this one simple question opens the task to much older students - even students in senior high school.	recognition of attributes and of left and right sides, sorting, classifying and ordering, recording data, informal experience with probability, combinatorial mathematics, sample space and theoretical probability.	S & L, Years 3 & 4 C & M, Years 9 & 10
19	Cookie Count	Place any number of cookies on a plate ready to offer equal shares to guests. The problem is: If I tell you any number of guests can you tell me the share they each receive?	1:1 correspondence, counting, sharing and grouping, partitioning wholes, times tables facts, multiples and factors, fractions of a whole	N & C, Years 3 & 4
21	Tactical	A logic game with clear rules and a spatial dimension. The aim is to force your opponent to take the last counter.	2D spatial perception, logical reasoning, in particular 'if...then' reasoning and working backwards	S & L, Years 5 & 6 S & L, Years 9 & 10
22	Time Together	A task to help students explore the passing of time. The focus is on those moments in a 12 hour cycle when the hands are 'on top of each other'. The task encourages manipulation of the clock hands, estimation and, for the more mathematically mature, precise calculation. The task also offers experience with the meaning of clockwise and opportunity for informal learning related to counting, angles and fractions.	division of time into hours, minutes and seconds, visualising the passing of time, applying understanding of the interconnectedness of the hands of a clock, visualising angles, clockwise & anti-clockwise, counting patterns, proportional reasoning, fractions related to elevenths and twelfths, graphical representation of simultaneous linear equations	C & M, Years 3 & 4 N & C, Years 9 & 10
25	In Between Time	As time passes, both the minute hand and the hour hand move. This task first uses a thirty minute difference (embodying the idea of half of the hourly minute hand journey) to establish that students understand: (a) Time difference can be clockwise or anti-clockwise, and (b) If the minute hand moves half an hour, then the hour hand has moved half of its journey towards the next (or previous) hour. From this basis the students are challenged to set a position for one of the hands and explore where the other hand must, or sometimes could, be.	division of time into hours and minutes, visualising the passing of time, applying understanding of the interconnectedness of the hands of a clock, visualising angles, clockwise & anti-clockwise, before and after a given time, time difference, fractions, proportional reasoning	C & M, Years 3 & 4 C & M, Years 7 & 8
32	Tetrahedron Nets	By making a tetrahedron and unfolding it to make its net, students discover its symmetric properties. The challenge is extended to looking for an alternative net and to discovering that 3D objects can be reflected.	2D representation of 3D objects, nets, axis of symmetry (3D), reflection in 3D, problem solving strategies	See Note below.
50	Flight Departures	An observer gives clues about the take off order of four planes at an airport. The challenge is to decide the actual order in which the planes took off.	logical reasoning, problem solving strategies, combination theory	S & L, Years 3 & 4 S & L, Years 7 & 8
59	13 Away	This is a game situation that has an underlying strategy waiting to be discovered. It is easy to state and easy to start, which is one feature that makes it suitable for younger as well as older students. The starting point is a pile of 13 counters. The person who takes the last one loses. Players take turns to take either 1, 2 or 3 counters on any move. The unwritten challenge is to find a way to always win.	reasoning skills, patterns in number, generalisation, algebraic representation	P & A, Years 3 & 4 P & A, Years 7 & 8
69	Tricubes	A set of tricubes is used to construct a 'building' in a specific order. Each stage is shown as an isometric drawing. The (apparently) simple challenge is to reconstruct the construction sequence.	2D representation of 3D objects, isometric drawing, problem solving strategies	See Note below.
72	Farmyard	A spatial challenge with aspects of area. A farmer wants to divide a field shaped like an L into smaller areas which are all the same size and shape. This task relates to Task 237, Trisquares (see below) and to Task 115, Dividing Shapes which is in S & L, Years 7 & 8.	spatial problem solving, perimeter, area	C & M, Years 5 & 6 P & A, Years 7 & 8
74	Button Sort	A logical challenge that draws attention to the attributes of buttons to sort and classify them. The task informally introduces significant ideas in mathematical logic such as the connectives 'and', 'or' and 'not' and introduces diagrams similar to flow charts as a way of sorting and making decisions.	sorting & classifying, attributes & properties, logic	S & L, Years 5 & 6
88	Rice, Rice, Rice	Set in a story shell, the challenge is to estimate grains of rice without actually counting their number. This is equivalent to the problems faced by many people in practical employment - for example a bricklayer estimating the number of bricks to order to clad a house. Such problems are often guided by 'rules of thumb'. In this task students are experimenting with possibilities so there is no right or wrong answer.	counting, mass, basic arithmetic, volume	C & M, Years 5 & 6
90	Tricube Constructions B	Students are provided with four Tricubes and cards with isometric drawings showing only the outer edges of 'buildings' made from them. The challenge in each case is to discover how the object was made.	3D spatial perception, isometric drawing, representing 3D objects in 2D, problem solving strategies	See Note below.
96	Networks	A game with laminated cardboard tiles which encourages thinking ahead in a spatial situation that is complicated by a growing network of lines. A player can either win by placing the piece which reaches the Finish square, or by placing a piece that forces their opponent to lose.	logical thinking, designing networks	S & L, Years 5 & 6 S & L, Years 7 & 8
104	Building Views	Another task which investigates the link between 3D objects and their 2D representations. Presented with front and side views of a building made from cubes, students have to reconstruct the building and ensure that they have done so with the minimum number of cubes.	3D spatial perception, elevation drawings, representing 3D objects in 2D, problem solving strategies	See Note below.
139	Squound	A square and a circle intersect to form a 'Squound'. The total number of counters is known as is the total in the square and circle. But how many in the Squound? Students must realise that the number in the intersection can't be counted twice and are led to this by an Investigation Guide. Symbolic representation is also encouraged.	addition and subtraction, pattern, generalisation in words and symbols	N & C, Years 3 & 4 P & A, Years 7 & 8
153	Knight Protectors	A famous chess-based puzzle requiring significant patience that results in a beautiful rotationally symmetric solution. The challenge is to place the minimum number of knights on a chess board so that every square is either occupied or attacked.	problem solving skills, spatial perception	S & L, Years 5 & 6 S & L, Years 7 & 8
164	Symmetric Tiles	Using two designs of laminated cardboard tiles, the task encourages exploration of symmetry, where the line of symmetry will most likely be seen as diagonal. One of the shapes is the key to finding many solutions easily, and even when this is realised, the final challenge on the card is not easy to resolve.	line symmetry, problem solving skills	S & L, Years 5 & 6
170	Equilateral Triangles	Designed to invite younger students to think 'outside the square' this task hints at both algebraic pattern and the idea that three dimensional objects are made from flat surfaces which have familiar names.	constructing triangles, pattern	S & L, Years 3 & 4
185	Coloured Cubes	This is a classic puzzle requiring a great deal of thought to solve without hint. The four cubes supplied have their faces coloured with four different colours. But each cube has its faces coloured in a different way. The challenge is to place the cubes in a line so that all four colours show down each long surface of the 'square-section rod' that is created.	nets of cubes, problem solving strategies	S & L, Years 5 & 6 S & L, Years 9 & 10
195	Stop At 4	The task is presented as a set of instructions which appear to be a card trick. Indeed, although the procedure could be memorised and used to surprise an audience, further analysis shows that is actually an ingenious device to arrange that the number of cards left in a pile reveal the number on a particular card. Full analysis requires symbolic representation of the instructions.	pattern, number, algebraic representation	N & C, Years 7 & 8
213	Chains	The board is six squares in a line and the equipment is six cubes. The arrangement in which cubes are placed scores points. What is the lowest possible score? The highest? Try boards of different lengths.	number, logical thinking	N & C, Years 5 & 6 N & C, Years 7 & 8
229	Animal Farm	Arithmagon problems (Tasks 188 & 194) are recreated in this task in a more visual way and embedded in a simple story shell. This allows younger and less experienced students to enter the family of problems. In essence the problems are based around three known numbers say a, b & c and three unknown numbers x, y & z. It is also known that x + y = a, y + z = b and x + z = c. The unknown numbers have to be found - but it is not necessary to use algebra to do so.	counting, addition, subtraction, pattern	P & A, Years 3 & 4
230	Pack Up Your Bears	Simply and sweetly this task, which was designed for infants, has children exploring sums of three numbers that add to six (or seven, or eight, or...).	counting, addition, pattern	N & C, Years 3 & 4
231	Flowers In The Field	Also designed for infants, but with a twist that lifts it right up through the school. There are many problems on the card, including ones the students decide for themselves, but they all revolve around having a known number of different flowers and asking how many bunches of a different size can be made.	counting, pattern, combinatoric mathematics	N & C, Years 3 & 4 N & C, Years 7 & 8
234	Growing Tricubes	A Tricube is an L-shape made of three cubes. The task explores different objects that can be made with various numbers of Tricubes and asks for calculations related to their base area, surface area and volume. The greater challenge is making Tricubes from Tricubes and developing a pattern.	3D spatial reasoning, area, surface area, volume, visual and number patterns, algebraic generalisation	Originally designed for: C & M, Years 9 & 10 This task could also be used to enhance: C & M, Years 5 & 6
235	Tables for 25	The familiar context of sitting in table groups in the classroom leads to problems with multiple solutions when the teacher adds conditions related to the size of the table group and the least number of boys (or girls) allowed to be in a group.	multiples, factors, primes, reasoning skills, problem solving strategies - particularly trying every possible case	N & C, Years 3 & 4 N & C, Years 7 & 8
236	Star Numbers	Star Numbers are constructed by adding Triangle Numbers to each side of a Square Number. In this sense, they have to be made as shapes to be understood. As the size of the Star Number increases, so does the number of plugs needed to make it. Students can explore particular cases, thereby applying number skills, or can generalise for any size Star Number.	square and triangle numbers, patterns, arithmetic, generalisation, graphing, substitution & solution of equations, quadratic equations.	N & C, Years 5 & 6 P & A, Years 9 & 10
237	Trisquares	Students explore the creation of new shapes from this simple shape made of three squares joined as an L. This leads to the problem of finding all the new shapes that can be made with just 2 Trisquares and to an investigation of area and perimeter.	concept and measurement of area and perimeter, reasoning skills	C & M, Years 3 & 4 C & M, Years 7 & 8
238	Growing Trisquares	The crux of this problem is that 4 Trisquares can be joined to make a new, scaled up, Trisquare. This provides a 'template' for constructing the next size, and the next, and the next... The visual pattern can also be represented as a number pattern and this leads to graphing, equation work and scale factors.	growth pattern, squares, powers of 2, multiples, scale factors, graphing, length/area relationship under enlargement	P & A, Years 5 & 6 P & A, Years 9 & 10
239	Money Charts	Text book exercises on adding and subtracting money come to life in this hands-on logic challenge that is most effectively completed by patient application of if-then reasoning and working backwards. In effect there is a little equation solving going on too.	Australian coin recognition, addition & subtraction of money, making change, concept of minimum, if-then reasoning, working backwards	N & C, Years 3 & 4 N & C, Years 7 & 8
240	Less Than Fractions	Number tiles (1 - 9) allow students to experiment with fractions less than 1 in a non-threatening, open-ended way. Early success is guaranteed because there are 36 possible answers and the obvious one is 1/2. But the greater challenge is to add two fractions (each tile can be used only once) and still get an answer less than one. How many solutions are there? How do you know when you have found them all?	concept of a fraction - especially meaning of numerator and denominator, fractions less than 1, addition of fractions, breaking a problem into smaller parts	N & C, Years 5 & 6 N & C, Years 9 & 10

Note

• These tasks are best used within the separate kit Points of View which would enhance the Space curriculum in Years 5/6 or 7/8. This kit is an example of the Mixed Media Model. It explores the topic of representing 3D objects in 2D. It has also been used successfully in Year 11 non-academic courses. Further, Points of View includes Maths300 Lesson 163, Building Views and its software. The kit is available to both members and non-members of Maths300.

Maths300

Note: The first lesson you click on below will open in a new window. The second will (most likely) open in the same window, thereby replacing the first. So, if you think a link doesn't work, look again at the second window. The Back button in this window will lead you to the first lesson window.