What is here
Six maths courses so far, written against the Australian Curriculum (version 9) for Years 7 and 8. Each lesson teaches one step of the curriculum's own learning progression, and says which earlier steps it relies on.
- Algebra Foundations: expressions and formulas, equations (try and check, backtracking, the balance method), brackets (expanding, factorising, changing the subject), harder equations and inequalities.
- Linear relations: patterns to tables to graphs, changing one variable in a formula, gradient and intercept, lines and regions, solving and modelling with lines.
- Number Foundations: integers (comparing, adding and subtracting, multiplying and dividing), squares and square roots, powers, prime factors, HCF and LCM, equivalent fractions, fractions, decimals and percentages, the number line, the four operations with fractions, percentages of amounts, choosing a strategy, negative fractions and decimals, place value and powers of 10, rounding and estimating, ratios, and modelling with money and ratios; for Year 8, rates, ratio and rate models (and checking them), percentage change and money models (pay and income tax).
- Irrational numbers and index laws (Year 8): recurring decimals and which fractions terminate, irrational numbers and where they sit on the number line, and the index laws.
- Angles and shapes: angles at parallel lines, reasoning with angles, angle sums of triangles and polygons, unknown angles in shapes, classifying triangles, quadrilaterals and polygons, nets and views of solids, translations, reflections and rotations, and algorithms that classify shapes; for Year 8, congruent and similar triangles, proving and using quadrilateral properties, algorithms for congruence, and coordinates in 3D.
- Area, volume, circles and Pythagoras: why the area formulas for parallelograms and triangles work, area problems with units and composite shapes, volume as layers of the base, prisms and capacity, the parts of a circle, discovering π by rolling circles, circumference, and Pythagoras' theorem (finding sides, and testing for a right angle); for Year 8, composite and irregular shapes, capacity and prism problems, the area of a circle and circle problems, and time zones.
- Data and chance: counting and measuring, mean, median, mode and range, choosing a measure, stem-and-leaf plots, comparing data sets, statistical investigations, sample spaces and probability, experiments and the law of large numbers; for Year 8, complementary events, Venn diagrams and two-way tables, grids and tree diagrams, and, or and not, and simulating compound events; samples: census and sample, bias, sampling methods, describing a sample, sampling variation, and investigations with samples.
More is on the way; tell us what you would use.
How a lesson runs
Every lesson has the same six steps, and takes about 40 to 50 minutes.
- Predict. Students commit to an answer before they see anything, which brings their current idea into the open.
- Try. An interactive board (algebra tiles, a number line, fraction bars, a factor tree, parallel lines, a shape you cut and rearrange, a circle you roll out, a graph, a dot plot, a spinner) lets them test the prediction.
- Worked example. One new move, set out step by step, then a planted mistake to find: a common misconception, met after the method.
- Vary. The same idea, changing one thing at a time, ending with an edge case.
- Practise. Mixed questions, with a review question from an earlier lesson.
- Make. Students work backwards: build a problem that has a given answer.
Answers are marked kindly. An equal answer in an unexpected form is accepted, or told what is left to do ("collect the like terms", "simplify"). In reasoning tasks, students write their working their own way and it is never marked; the answer and the reason at the key step are, and then students compare their working with a model solution.
Each lesson has an Explain it to me drawer with a short voiced clip and a summary, opened from the step bar once a student has made their first prediction.
For you
At the bottom of each course page there is a Teacher guide link. It opens:
- a teacher guide for each lesson: goals, timing, what to say at each step, the misconceptions and what to do about them, stretch and support, and an exit ticket;
- a unit primer ("in 5 minutes") for each unit;
- printable cheat sheets and a slide deck and worksheet for each lesson, which load into Prepare.
There is nothing to install and no accounts. Progress is kept in each student's own browser; we do not track anyone.
A ten-minute tour
Try these as if you were a student, then open the teacher guide for one of them.
- Reasoning with angles (Year 7): the parallel-lines board, a planted mistake, and a reasoning task where students write their own working.
- Expanding brackets (Year 8): algebra tiles, answers marked by form, and working checked one line at a time.
- Fractions, decimals and percentages (Year 7): fraction bars and a hundred grid.
- Inequalities (Year 8): building a solution on the number line.
- Many trials (Year 7): thousands of coin flips, and a mystery bag to estimate.
Tell us what you think
These lessons are new and have not yet been used with a class. We would especially like to know:
- whether the mathematics and the language match how you teach it;
- where a lesson is too fast, too slow, or assumes something your students do not have;
- whether you would use it in class, for homework, for revision or not at all, and why.
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