Porirua Montessori Primary School

39 Cleat St, Whitby, Porirua Call – 021 08427 037

## Mathematics - The Montessori Way

Montessori maths equipment is unique in its well thought out hands on equipment that introduces ideas to students systematically and helps them see the big picture. A key feature of Montessori maths is colour coding. Hands on beads for the number four are made of four interlocking yellow beads. The colour for five is light blue. Place value is also colour co-ordinated for example units are always represented with green, tens with blue and hundreds with red. This colour coding system helps give students a visual reminder of what they are learning about and helps them internalise ideas.

Montessori maths equipment includes hands on materials for teaching about angles, algebra, geometry, number, fractions, decimals and basic facts.

Montessori uses the Montessori Great Stories to look at how maths has been used across cultures and time to help humans, being in New Zealand we take a particular interest in how Māori have used number and math through concepts as vast as  kowhaiwhai to building.

## Our Approach to Mathematics

We have a thorough knowledge of the New Zealand maths curriculum used in state schools. By the end of year 8 our students will have covered the same concepts as their peers in state schools but using a different curriculum. It is our aim for all our students to go onto succeed well with maths at secondary school

We use the Montessori maths equipment and montessori inspired ideas to help our students learn the same concepts they would at a normal skill but with lots of hands on tools. The tools are always present in the room which allows for students to use them whenever they need them or want to explore a concept.

We encourage individual and group learning in maths.

## Numbers

• Whole numbers from 1 to 1,000 (ordering numbers and learning place value)
• Number lines
• Positive and negative numbers
• Odd and even numbers
• Commutative and associative properties
• Skip counting (by a number to its cube)
• What zero does
• Hierarchies (formation, reading, and writing of numbers to 1,000,000)
• Rounding to the nearest ten, hundred, orthousand
• Estimation e.g. 290 + 789 is close to 1000
• Expanded notation

## Whole Number Operations

• Memorization of basic facts through using a variety of hands on equipment
• Number sentences with missing addends, etc.
• Static and dynamic addition and subtraction
• Addition and subtraction of decimals (money)
• Multiplication with one-, two-, and three-digit multipliers
• Division with one- and two-digit divisors (with remainders)
• Distributive and group division; long division algorithm
• Negative numbers
• Fractions and decimals
• Comparing fractions (>, <, =) including finding equivalent fractions.
• Adding and subtracting fractions with like denominators
• Mixed numbers and improper fractions
• Adding and subtracting fractions with unlike denominators
• Reducing fractions to lowest terms
• Adding and subtracting mixed numbers
• Introduction to fraction multiplication and division
• Decimals from the unit to millionths (quantity and symbol)
• Comparing and ordering decimals (>, <, =)
• Multiplication and division of decimals by whole numbers
• Ratios and percentages (proportions of a fraction and decimal, finding percentage of an amount)
• Multiples and factors
• Tables of multiples
• Common multiples and the search for the LCM
• The decanomial (geometric and numerical)
• Common factors and the search for the GCF
• Divisibility
• Order of operations
• Memorization of basic facts through using a variety of hands on equipment
• Number sentences with missing addends, etc.
• Static and dynamic addition and subtraction
• Addition and subtraction of decimals (money)
• Multiplication with one-, two-, and three-digit multipliers
• Division with one- and two-digit divisors (with remainders)
• Distributive and group division; long division algorithm
• Negative numbers
• Fractions and decimals
• Comparing fractions (>, <, =) including finding equivalent fractions.
• Adding and subtracting fractions with like denominators
• Mixed numbers and improper fractions
• Adding and subtracting fractions with unlike denominators
• Reducing fractions to lowest terms
• Adding and subtracting mixed numbers
• Introduction to fraction multiplication and division
• Decimals from the unit to millionths (quantity and symbol)
• Comparing fractions (>, <, =) including finding equivalent fractions.
• Adding and subtracting fractions with like denominators
• Mixed numbers and improper fractions
• Adding and subtracting fractions with unlike denominators
• Reducing fractions to lowest terms
• Adding and subtracting mixed numbers
• Introduction to fraction multiplication and division
• Decimals from the unit to millionths (quantity and symbol)
• Comparing and ordering decimals (>, <, =)
• Multiplication and division of decimals by whole numbers
• Ratios and percentages (proportions of a fraction and decimal, finding percentage of an amount)
• Multiples and factors
• Tables of multiples
• Common multiples and the search for the LCM
• The decanomial (geometric and numerical)
• Common factors and the search for the GCF
• Divisibility
• Order of operations
• Prime numbers
• Powers of numbers
• Squares and cubes of numbers from 1 to 10 (using montessori bead material)
• Notation of powers (exponents)
• Square roots of numbers less than 100
• Squares of binomials and trinomials
• Square of the decanomial
• Square roots of numbers greater than 100
• Powers of two/three
• Integers

## Measurement/Strand

• History of measurement
• Measurement of time, temperature, length, liquid, volume, and weight
• Money
• Probability
• Statistics and Data (types of graph, data collection, mean/median/mode, analysis of data)

## Geometry

• History of Geometry (Maori, Babylonian, Egyptian, Greek contributions, etc.)
• Design elements (metal insets, the geometric cabinet, etc.)
• Use of tools (straight edge, ruler, compass, protractor)
• Symmetry
• Geometry in art and architecture
•  2d and 3d shapes
• Point, line, surface, and solid

## Study of lines

• Study of angles
• Study of shapes (triangles, quadrilaterals, regular and irregular polygons, closed curved figures)
• Perimeter of shapes
• Congruence, equivalence, and similarity
• Concept of area
• Working out area of different shapes

## Problem-solving

• One- and two-step problems, involving all four operations
• Mental math – influenced by the work of Jo Boaler
• Problems using whole numbers, fractions, and decimals
• Problems applying time, money, and measurement
• Writing original problems