The resources on this page were used in YuMi Deadly Maths accelerated learning projects. These projects developed teaching and learning modules of vertically sequenced mathematics activities to accelerate the learning of mathematically under-performing students.

Spending time on the foundations of topics enables later work with symbols to be more quickly learnt, accelerating normal progress and closing the gap between students’ ability level in mathematics and their age level.

The YDM accelerated learning approach was originally developed across 2010 to 2013 for the Accelerated Indigenous Mathematics (AIM) project funded under the Australian Government’s *Closing the Gap: Expansion of Intensive Literacy and Numeracy* program for Indigenous students. This was later renamed the Accelerated Inclusive Mathematics project.

The accelerated learning approach was adapted to the early years in the AIM Early Understandings project, which was a collaboration with Victoria Park State School in Mackay, a YDM Centre for Excellence school.

Further resources were developed through funding from an Australian Research Council (ARC) Linkage project – LP120200591 *Accelerating the mathematics learning of low socio-economic status junior secondary students*, shortened to XLR8 Mathematics.

## Accelerated Inclusive Mathematics (AIM) resources

### AIM overview and module scope and sequence

We strongly recommend that teachers read the AIM Overview book and refer to the AIM Module Scope and Sequence before attempting to teach units using the 24 AIM modules. The modules are designed to accelerate student learning from Year 3 level to Year 9 level during the first three years of secondary school (Years 7 to 9). They were developed in three parts as follows:

- The mathematics content for the AIM modules was divided using the strands from the Australian Mathematics Curriculum but with Operations separated from Number and Algebra, and Statistics and Probability considered as one strand. This gave six topic areas of Number, Operations, Algebra, Geometry, Measurement, and Statistics and Probability.
- The length of time for a module was set at half a school term (i.e. normally 5 weeks) which, in three years, means at most 24 modules. Each of the topic areas was therefore divided into modules that could be completed in half a term, based on a sub-topic or a collection of connected sub-topics that cover the same mathematics big ideas.
- The modules were collected into three year levels (called Years A, B and C) so that (a) each year covers an important cross-section of mathematics, (b) there is a sequence across the years, and (c) there are connections made within each year (to get chunking across as well as within modules).

The years were based on the uses of mathematics and how mathematics changes from Years 3 to 9:

**Year A**. Basic mathematics necessary for employment in a trade (whole and decimal numbers, measurement, operations, shape, and tables and graphs) – enables connections between metrics and place value, and operations to be applied in measurement situations.**Year B**. Multiplicative approaches to mathematics (fractions; percent, rate and ratio; probability; and equations and equivalence), and completion of Year A ideas (measurement and flips-slides-turns geometry) – also completes the coverage of all mathematics necessary for an apprenticeship.**Year C**. Generalisation to algebra (patterns, functions, principles, and algebraic computation) and advanced topics (negatives and indices, projections-topology, statistical inference, and financial mathematics) – extends understandings to the topics that underlie the Years 10–12 mathematics subjects that lead to university and STEM careers (e.g. engineering, accountancy).

This led to a scope and sequence for AIM of 24 modules that teach mathematics content from Year 3 to Year 9 and cover the three years with two modules each term. These 24 modules were written and, where possible, trialled in classrooms with low-performing students. The modules were refined as a result of these trials. Each module is signified by a letter (giving topic area) and a number which gives order.

### AIM Year A modules

Early grouping, big ideas for H-T-O; pattern of threes; extension to large numbers and number system.

Fraction to decimal; whole number to decimal; big ideas for decimals; tenths, hundredths and thousandths; extension to decimal number system.

**O1: Addition and Subtraction for Whole Numbers **

Concepts; strategies; basic facts; computation; problem solving; extension to algebra.

**M1: Basic Measurement (Length, Mass and Capacity) **

Measurement attribute; direct and indirect comparison; non-standard units; standard units; applications.

**O2: Multiplication and Division for Whole Numbers **

Concepts; strategies; basic facts; computation; problem solving; extension to algebra.

**M2: Relationship Measurement (Perimeter, Area and Volume) **

Measurement attribute; direct and indirect comparison; non-standard units; standard units; applications and formulas.

**G1: Shape (3D, 2D, Line and Angle) **

3-dimensional and 2-dimensional shapes; lines, angles, diagonals, rigidity and properties; Pythagoras; teaching approaches.

Different tables and charts; bar, line, circle, stem and leaf, and scatter graphs; use and construction.

### AIM Year B modules

**M3: Extension Measurement (Time, Money, Angle and Temperature) **

Measurement attribute; direct and indirect comparison; non-standard units; standard units; applications and formulas.

Concepts and models of common fractions; mixed numbers; equivalent fractions; relationship to percent, ratio and probability.

**G2: Euclidean Transformations (Flips, Slides and Turns) **

Line-rotation symmetry; flips-slides-turns; tessellations; dissections; congruence; properties and relationships.

**O3: Common and Decimal Fraction Operations **

Addition, subtraction, multiplication and division of common and decimal fractions; models, concepts and computation.

Definition of equals; equivalence principles; equations; balance rule; solutions for unknowns; changing subject

Concepts and models for percent, rate and ratio; proportion; applications, models and problems.

Definition and language; listing outcomes; likely outcomes; desired outcomes; calculating (fractions); experiments; relation to inference.

Polar and Cartesian coordinates; line graphs; slope and y-intercept; distance and midpoints; graphical solutions; nonlinear graphs.

### AIM Year C modules

**A2: Patterns and Linear Relationships **

Repeating and growing patterns; position rules, visual and table methods; application to linear and nonlinear relations and graphs.

**N5: Directed Number, Indices and Systems **

Concept and operations for negative numbers; concept, patterns and operations for indices; scientific notation and number systems.

Function machine; input-output tables; arrowmath notation, inverse and backtracking; solutions for unknowns; model for applications to percent, rate and ratio.

Visualisation; divergent and affine projections; perspective; similarity and trigonometry; topology and networks.

**O4: Arithmetic and Algebra Principles **

Number-size, field and equivalence principles for arithmetic; application to estimation; extension to algebra; simplification, expansion and factorisation.

Gathering and analysing data; mean, mode, median, range and deviation; box and whisker graphs; large data sets, investigations and inferences.

Arithmetic to algebra computation; modelling-solving for unknowns; simultaneous equations, quadratics.

Applications of percent, rate and ratio to money; simple and compound interest; best buys; budgeting and planning activities.

## AIM Early Understandings (AIM EU) modules

The 9 AIM EU modules combine mathematics learning for Foundation to Year 2 with the understandings normally provided prior to school. They are particularly suited to schools where students start school with little cultural capital to excel in schoolwork.

The modules are designed to improve teacher capacity through use of diagnostic tools to identify barriers to early understanding and to accelerate learning so all students attain satisfactory or higher levels of mathematical knowledge by Year 3, giving a solid foundation on which to build primary maths.

The sequence below is recommended for the modules.

Sorting/correspondence, subitising, rote, rational, symbol recognition, models, counting competencies.

Repeating patterns, growing patterns, visuals/tables, number patterns.

**3. Algebra A2: Functions and Equations **

Functions: change, function machine, inverse/backtracking.

Equations: equals, balance.

Concepts: place value, additive structure, odometer, multiplicative structure, equivalence.

Processes: role of zero, reading/writing, counting sequences, seriation, renaming.

Concepts: number line, rank.

Processes: comparing/ordering, rounding/estimating.

Relationship to place value.

**6. Operations O1: Thinking and Solving **

Early thinking skills, planning, strategies, problem types, metacognition.

**7. Operations O2: Meaning and Operating **

Addition and subtraction, multiplication and division, word problems, models.

Computation/calculating, recording, estimating.

Concepts: fractions as part of a whole, fractions as part of a group/set, fractions as a number or quantity, fraction as a continuous quantity/number line.

Processes: representing, reading and writing, comparing and ordering, renaming.

## XLR8 Mathematics resources

The XLR8 Mathematics resources comprise a teacher guide book and 15 units covering concepts from early understandings to Year 9 that can be taught as a two- or three-year mathematics program across Years 7 to 9. They draw on real contexts found in measurement, geometry, statistics and probability and provide opportunities to demonstrate the connectedness of mathematical ideas across strands within the curriculum.

Additional resources include sample Reality–Abstraction–Mathematics–Reflection (RAMR) lessons, some sample worksheets with accompanying notes for teaching, templates, portfolio tasks, and assessment and recording tools. Please contact Dr David Nutchey in the School of Teacher Education and Leadership at QUT to request the additional resources to accompany each unit.

**Unit 01: Comparing, counting and representing quantity **

**Unit 02: Additive change of quantities **

**Unit 03: Multiplicative change of quantities **

**Unit 04: Investigating, measuring and changing shapes **

**Unit 05: Dealing with remainders **

**Unit 06: Operations with fractions and decimals **

**Unit 09: Measuring and maintaining ratios of quantities **

**Unit 10: Summarising data with statistics **

**Unit 11: Describing location and movement **

**Unit 12: Enlarging maps and plans **

**Unit 13: Modelling with linear relationships **

Resources developed by the YuMi Deadly Centre, Queensland University of Technology are distributed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International (CC BY-NC-SA) Licence.

©YuMi Deadly Centre, Queensland University of Technology