Greenvale Primary School

Year 5 and 6 Maths Information Session

Fractions, Decimals and Percentages

Partitioning

Victorian Curriculum in brief

• Foundation - Learning everything about the numbers 0 – 10 (Trust the count)

• Year 1 - students learn about numbers to 99 (Place Value)

• Year 2 – addition and subtraction (Mental strategies)

• Year 3 and 4 – multiplication and division (multiplicative thinking)

• Year 5 and 6 – fractions and decimal (partitioning)

• http://victoriancurriculum.vcaa.vic.edu.au/mathematics/curriculum/f-10

The Learning sequence for fractions, decimals and percentages

• Make, model or visualise – picture

• Name and record

• Compare, order and sequence

• Rename

• Link together eg 1/5 = 0.2 = 20%

• Operations – addition and subtraction

• Only decimals are multiplied at this stage!!

Fractions Make or model

• Very difficult concepts to understand as it is abstract

• Parts are too small to manipulate

• Today much focus is on decimals and percentages, fractions are rarely used but an understanding of fractions needs to be developed fully use decimals and percentages

• Forms the basis of majority of secondary school maths

• Sometimes referred to as artificial numbers as ¾ is 3 parts out of 4 but that 3 is very different to the number 3 eg it is not 3 + 1 = 4

Fractions – Name

• Fractions is a very difficult language to learn, a lot of conflicting vocabulary

• Come from ancient Egyptians. If a loaf of bread was divided between 8 workers, the last worker – the eighth worker received the last piece or the eighth. The seventh worker received the seventh piece. This is why fractions are named after the ordinal number eg, third, fourth, fifth, sixth

• ½ is known as half, not one second. ¼ is one quarter, only occasionally referred to as one fourth

Fractions - record

• The numerator comes from the latin word numere meaning ‘to number’ and the denominator is from the word de nomen meaning name.

• Can be greater than 1, even though we teach that fractions is dividing a whole into smaller parts.

• Fractions words – common fraction, improper fraction and mixed numbers are all fractions in different forms.

Fractions - Renaming

• Begins with equivalence ½ = 2/4 = 5/10

• Improper fractions 5/4 The numerator is larger than the denominator or the fraction is greater than 1

• Mixed numbers are fractions with a whole number and a fraction eg 1 ¼

• Students need to visualise these fractions as the same

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Fractions - Ordering

• Need to find common lowest denominator

• Which is bigger 2/5 or 3/8?

• Need to find common multiple (5 x 8 ) = 40

• Work out the equivalent fraction (16/40 and 15/40)

• Compare the numerators (16 > 15)

• Then can easily see which is bigger

• However need to be able to visualise this and make an approx. guess

• Same process for addition and subtraction

Fractions - Applying

• Need all knowledge of making, naming, ordering, renaming to then solve the problems of addition and subtraction

Fractions Applying

Decimals - Naming

• Difficult language – tens, tenths, hundreds and hundredths

• When writing decimals a zero is used in the ones place eg 0.36, but in whole numbers the zero is left off eg 36 is not written 036.

• Reading decimals is 6.1 is six and one tenth gives it meaning and a visual picture opposed to six point one.

• 3 and 47 hundredths is written 3.47

• However in real life the common way to say decimals is 6 point 1 and 3 point 4 7

Decimals - ordering

• Need to build on place value knowledge

• Builds on knowledge of base 10 system• 1 hundred is the same as 10 tens,

• 1 ten is the same as 10 ones,

• 1 one is the same as 10 tenths

• 1 tenth is the same as 10 hundredths

• Understand that 3.7 is larger than 3.42. Students may see that 7 is larger than 42 if they are not visualising tenths and hundredths

Decimals - Renaming

• 10 ones is the same as 1 ten ( multiplying by 10)

• So 10 tenths is the same as 1

• And 10 hundredths is the same as 1 tenth

• Because of the names becomes confusing

• Need this to be able to add, subtract and multiply decimals

• 0.6 is the same as 600 hundredths

• 0.37 is the same as 370 thousandths

Fractions to decimals

Percentages

• Most common form of fractions used today

• Percent is out of each hundred.

• Needs to be linked to decimal hundredths

• 17% is fairly straightforward, it is 17 out of 100 or 0.17

• When decimals are added it becomes confusing 17.5%, so it is 17.5 hundredths or 175 thousandths or 0.175

• Percentages greater than 100 tests understanding as % is out of 100. How can it be 300% increase in petrol??

Decimals to Fractions to Percentages and back again

• Fluently, efficiently convert between the two

• Common amounts need to be memorised eg ½, ¼, 1/3,

• Apply to real problems eg money, length

• Apply to chance – probability

• Apply to graphs and tables – statistics

• Shapes and angles become geometry

• Algebra 4x + 2 = 10, 4x = 10 – 2, 4x = 8, 4x /4 = 8/4 x = 2

Assistance at home

• Ask them to explain the problem

• Ask them to draw it or make a diagram

• Encourage them to tell you what they have learnt in maths, keep a maths journal at home

• Notice and tell your child when you are dealing with fractions, decimals and percentages eg recipes, shopping, money

• Google it or you tube

• Khan academy https://www.khanacademy.org/

• Mathletics

Further help

• See your child’s teacher

• Email Mr Rovetto rovetto.robert.j@edumail.vic.gov.au

• Ms Elicia Briggs briggs.elicia.k@edumail.vic.gov.au

• Ms Robyn White white.robyn.r@edumail.vic.gov.au