1. Introduction to maths python
simulating a simple random walk
manipulating sets of numbers using a given rule, for example, if a number is even, halve it; or if a number is odd, subtract 1 then halve it
creating algorithms that use multiplication and division facts to determine if a number is a multiple or factor of another number; for example, using a flow chart that determines whether numbers are factors or multiples of other numbers using branching, such as yes/no decisions
identifying lowest common multiples and highest common factors of pairs or triples of natural numbers; for example, the lowest common multiple of {6, 9} is 18, and the highest common factor is 3, and the lowest common multiple of {3, 4, 5} is 60 and the highest common factor is 1
using the ‘fill down’ function of a spreadsheet and a multiplication formula to generate a sequence of numbers that represent the multiples of any number you enter into the cell, and describing and explaining the emerging patterns
using an algorithm to create extended number sequences involving rational numbers, using a rule and digital tools, and explaining any emerging patterns
designing an algorithm to model operations, using the concept of input and output, describing and explaining relationships and any emerging patterns; for example, using function machines to model operations and recognising and comparing additive and multiplicative relationships
designing an algorithm or writing a simple program to generate a sequence of numbers based on the user’s input and a chosen operation, discussing any emerging patterns; for example, generating a sequence of numbers and comparing how quickly the sequences are growing in comparison to each other using the rule ‘add 2 to the input number’ compared to multiplying the input number by 2
devising flowcharts to represent algorithms for a common processes such as adding two fractions
creating a classification scheme for triangles based on sides and angles, using a flow chart that uses sequences and decisions
creating a flow chart or hierarchy for quadrilaterals that shows the relationships between trapeziums, parallelograms, rhombuses, rectangles, squares and kites
creating a classification scheme for regular, irregular, concave or convex polygons that are sorted according to the number of sides
modelling additive situations involving positive and negative quantities; for example, a lift travelling up and down floors in a high-rise apartment where the ground floor is interpreted as zero, or in geography when determining altitude above and below sea level
modelling contexts involving proportion, such as the proportion of students attending the school disco, proportion of the bottle cost to the recycling refund, proportion of the school site that is green space, 55% of Year 7 students attended the end of term function or 23% of the school population voted ‘yes’ to a change of school uniform; and interpreting and communicating answers in terms of the context of the situation
modelling financial problems involving profit and loss, credits and debits, gains and losses; for example, holding a fundraising sausage sizzle and determining whether the event made a percentage profit or loss
finding the sum of a set of consecutive numbers using a loop structure
constructing geometric patterns such as a honeycomb, using dynamic geometry functionality
using mathematical modelling to investigate the proportion of land mass/area of Aboriginal Peoples’ traditional grain belt compared with Australia’s current grain belt
Debugging search-and-sort programs
Testing a number for divisibility
creating an algorithm using pseudocode or flow charts to apply the triangle inequality, or an algorithm to generate Pythagorean triples
creating and testing algorithms designed to construct or bisect angles, using pseudocode or flow charts
developing an algorithm for an animation of a geometric construction, or a visual proof, evaluating the algorithm using test cases
Using two-dimensional arrays such as matrices to represent and implement sequences of transformations of sets of points in the plane
Using pointers in algorithms
Applying a systematic guess-check-and-refine algorithm to identify an approximate value for the root of an equation in an interval
Developing simulations for counterintuitive problems in probability such as the Monty Hall problem or derangements
1.1. Previous curricula
Using a sort algorithm to determine the median of a set of numbers
Exploring variation in proportion and means of random samples, drawn from a population