Fractions

The recommended sequence for learning fractional knowledge : students
• talk about a fractional amount in quantities where the whole is perceptually defined .
• use terms such as "two thirds" or "three quarters" in mathematically correct ways;
• describe parts of quantities divided into 2, 3, 4, 5, 6 and 10 equal parts,
• say the number of parts that make a whole when told the name of each part
• divide wholes into halves, thirds, quarters, fifths, sixths, eighths and tenths.
• write or select the number for a fractional quantity, match quantity with a number
• describe the meaning provided by the numerator and the denominator
• compare two fractions in size, where both have either the same numerator or denominator
• write the numbers in order, beginning with the first number in the sequence.
• automatize what a written fractional numeral means;
• rapidly recall what the numerator and denominator mean,
• visualise the essential features of the fraction
• decide whether it is larger / smaller than another fraction
• explain how a fractional numeral is different from a whole number.
• describe a fractional quantity in different ways, eg., 3 quarters in eights, twelfths ....
• use a procedure for producing equivalent fractions
• simplify fractions by producing equivalent fractions
• calculate fractional portions of a set of items
• find the lowest common denominator for two or more fractions and compare two fractions.
• describe a fractional quantity in different ways, for example, 7 fourths
• convert improper fractions to mixed numbers and vice versa.
• estimate the value of fractions and mixed numbers.
• add or subtract two or more fractions with the same denominator
• add or subtract two or more fractions with different denominators
• multiply two or more fractions.
• multiply two or more fractions and mixed numbers, cancelling where necessary.
• divide whole numbers, fractions and mixed numbers by fractions cancelling where necessary.

Part-whole relationships : Decimals and percentages

Teach decimal knowledge in three areas or strands; a comprehension of
• the tenth-whole relationship in quantities and the symbolism used to specify individual
fraction quantities,
• the sequencing-counting properties of decimals, sequencing and relating decimals numbers
to each other, arranging decimal numbers in order and
• the algorithms associated with fractions; develop these for
• addition of decimals
• subtraction of decimals
• multiplication of decimal by whole numbers
• division of decimal by whole numbers
• multiplication of decimal by decimal numbers
• conversion of decimals to fractions and vice versa.
Develop this for the following types of quantities
• quantities of < a whole divided into tenths
• quantities comprising wholes and tenths
• quantities of < a whole divided into twentieths, thirtieths, ... hundredths
• quantities of < a whole comprising tenths and hundredths
• quantities comprising wholes, tenths and hundredths
For each area
• introduce the idea to be learnt as problems to be solved
• introduce the operations as physical actions that pupils gradually internalize
• have pupils draw pictures of the ideas they are learning and act on these.
• provide activities for pupils to look for patterns and to generalize from specific instances .
• have pupils share ideas, work co-operatively on problems
• have students talk about ideas
• have pupils express new ideas first in familiar language formats and later to learn
conventional, abstract formats
• present ideas in 'learner-friendly' with concrete or pictorial referents.