Programs from KG to Grade 8
One continuous sequence of Math skills, taught with Montessori materials. The diagnostic places your child on it at exactly the right step, whatever their school grade.
Kindergarten
Children build a true sense of quantity before symbols: counting with meaning, matching numerals to amounts, and meeting the decimal system with their hands.
- Number
- Quantities and numerals to 10, teens and tens, the decimal system to 1,000 with golden beads.
- Algebra and patterns
- Sorting, matching and continuing simple repeating patterns.
- Fractions and proportion
- Whole and half with real objects and shapes.
- Measurement
- Longer, shorter, heavier, lighter; ordering by size; the days of the week.
- Geometry
- Naming and matching plane shapes and solids.
- Data and probability
- Sorting objects into groups and comparing which has more.
- Financial literacy
- Recognizing coins and the idea of paying for things.
Montessori materials
- Number rods
- Sandpaper numerals
- Spindle box
- Cards and counters
- Golden beads
- Teen and ten boards
- Geometric cabinet
Example skills
- Counts out a quantity to 10 and matches it to its numeral
- Builds teen numbers with a ten bar and a coloured bead bar
- Recognizes and continues an AB pattern
Lower Primary
Place value becomes solid, and the four operations are understood with materials before they become fast on paper.
- Number
- Place value to 1,000; addition and subtraction with exchanging; the meaning of multiplication and division.
- Algebra and patterns
- Number patterns, skip counting and missing numbers in equations.
- Fractions and proportion
- Halves, thirds and quarters of shapes and amounts.
- Measurement
- Length in centimetres and metres, time to the quarter hour, mass and capacity.
- Geometry
- Properties of 2D and 3D shapes, symmetry and position.
- Data and probability
- Tallies, pictographs and simple bar charts.
- Financial literacy
- Counting money, giving change and saving towards a goal.
Montessori materials
- Stamp game
- Golden beads
- Bead bars and short chains
- Hundred board
- Addition and subtraction strip boards
- Fraction circles
- Teaching clock
Example skills
- Adds three-digit numbers with exchanging on the stamp game, then on paper
- Explains multiplication as equal groups using bead bars
- Tells the time to the quarter hour
Upper Primary
The big operations become fluent and understood. Fractions and decimals stop being rules to memorize and start making sense.
- Number
- Multi-digit multiplication and long division, factors, multiples and place value to millions and thousandths.
- Algebra and patterns
- Order of operations, simple expressions and input–output rules.
- Fractions and proportion
- Equivalent fractions, all four operations with fractions, decimals and first percentages.
- Measurement
- Perimeter, area, volume, converting units and elapsed time.
- Geometry
- Angles, triangles and quadrilaterals, coordinates and transformations.
- Data and probability
- Bar and line graphs, mean, and the language of chance.
- Financial literacy
- Budgets, unit prices and comparing value.
Montessori materials
- Checkerboard
- Large bead frame
- Racks and tubes
- Fraction circles
- Decimal board
- Protractor and geometry sticks
Example skills
- Multiplies two-digit by two-digit numbers on the checkerboard, then on paper
- Finds equivalent fractions with fraction circles and explains why they are equal
- Calculates the area of rectangles and composite shapes
Middle School
Abstract thinking grows from concrete foundations. Students reason, explain and connect, ready for higher Math.
- Number
- Integers, powers and roots, scientific notation and rational numbers.
- Algebra and patterns
- Expressions, linear equations and inequalities, sequences and graphs of relationships.
- Fractions and proportion
- Ratio, rates, percentages and proportional reasoning.
- Measurement
- Area of circles, surface area and volume of prisms and cylinders.
- Geometry
- Angle relationships, constructions, Pythagoras and transformations on the coordinate plane.
- Data and probability
- Statistics, sampling, and probability of compound events.
- Financial literacy
- Percent change, discounts, VAT, simple interest and planning a budget.
Montessori materials
- Binomial and trinomial cubes
- Pegboard for squares and roots
- Fraction and decimal materials
- Algebra tiles
- Geometry instruments
Example skills
- Solves two-step linear equations and checks the solution
- Uses ratio tables to solve proportion problems
- Explains (a + b)² with the binomial square
Not sure where your child fits?
That is what the diagnostic is for. It places your child skill by skill, so nothing is repeated without reason and nothing is skipped.