YEAR 6 MATHS FOCUS
NUMBERS AND ALGEBRA
Fractions & Decimals
Learning Experiences
Fractions & Decimals
FRACTIONS & DECIMALS
OUTCOME
A student:
MA3-7NA:
compares, orders and calculates with fractions, decimals and percentages
TEACHING POINTS | In Stage 3 Fractions and Decimals, students study fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12 and 100. A unit fraction is any proper fraction in which the numerator is 1, eg 12, 13, 14, 15, … |
| The process of writing a fraction in its ‘simplest form’ involves reducing the fraction to its lowest equivalent form. In Stage 4, this is referred to as ‘simplifying’ a fraction. | |
| When subtracting mixed numerals, working with the whole-number parts separately from the fractional parts can lead to difficulties, particularly where the subtraction of the fractional parts results in a negative value, e.g. in the calculation of 2 1/3−1 5/6, 1/3−5/6 results in a negative value. |
LANGUAGE | Students should be able to communicate using the following language: whole, equal parts, half, quarter, eighth, third, sixth, twelfth, fifth, tenth, hundredth, thousandth, fraction, numerator, denominator, mixed numeral, whole number, number line, proper fraction, improper fraction, is equal to, equivalent, ascending order, descending order, simplest form, decimal, decimal point, digit, round to, decimal places, dollars, cents, best buy, percent, percentage, discount, sale price. |
| The decimal 1.12 is read as ‘one point one two’ and not ‘one point twelve’. | |
| The word ‘cent’ is derived from the Latin word centum, meaning ‘one hundred’. ‘Percent’ means ‘out of one hundred’ or ‘hundredths’. | |
| A ‘terminating’ decimal has a finite number of decimal places, eg 3.25 (2 decimal places), 18.421 (3 decimal places). |
Expectations of Attainment
Compare fractions with related denominators and locate and represent them on a number line (ACMNA125) | model, compare and represent fractions with denominator of 2, 3, 4, 5, 6, 8, 10, 12 and 100 of a whole object, a whole shape and a collection of objects |
compare the relative size of fractions drawn on the same diagram, e.g.
{Reasoning, Critical and creative thinking} | |
| compare and order simple fractions with related denominators using strategies such as diagrams, the number line, or equivalent fractions, e.g. write 3/5, 3/10, 1 1/10, 4/5 and 7/10 in ascending order | |
find equivalent fractions by re-dividing the whole, using diagrams and number lines, e.g. | |
| record equivalent fractions using diagrams and numerals | |
| develop mental strategies for generating equivalent fractions, such as multiplying or dividing the numerator and the denominator by the same number, e.g. 1/4=(1×2)/(4×2)=(1×3)/(4×3)=(1×4)/(4×4)= …, i.e. 1/4=2/8=3/12=4/16= … | |
| – explain or demonstrate why two fractions are or are not equivalent {Communicating, Reasoning, Critical and creative thinking} | |
| write fractions in their ‘simplest form’ by dividing the numerator and the denominator by a common factor, e.g. 4/16=(4÷4)/(16÷4)=1/4 | |
| – recognise that a fraction in its simplest form represents the same value as the original fraction {Reasoning} | |
| – apply knowledge of equivalent fractions to convert between units of time, e.g. 15 minutes is the same as 15/60 of an hour, which is the same as 1/4 of an hour (Problem Solving) |
Solve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126) | add and subtract fractions, including mixed numerals, where one denominator is the same as, or a multiple of, the other, e.g. 2/3+1/6, 2 3/8−1 1/2, 2 3/8−3/4 |
| – convert an answer that is an improper fraction to a mixed numeral {Communicating} | |
| – use knowledge of equivalence to simplify answers when adding and subtracting fractions {Communicating, Reasoning} | |
| – recognise that improper fractions may sometimes make calculations involving mixed numerals easier {Communicating} | |
| solve word problems involving the addition and subtraction of fractions where one denominator is the same as, or a multiple of, the other, eg ‘I ate 1/8 of a cake and my friend ate 1/4 of the cake. What fraction of the cake remains?’ {Literacy Critical and creative thinking} | |
| multiply simple fractions by whole numbers using repeated addition, leading to a rule, e.g. 2/5×3=2/5+2/5+2/5=6/5=1 1/5 leading to 2/5×3=(2×3)/5=6/5=1 1/5 {Critical and creative thinking} |
Find a simple fraction of a quantity where the result is a whole number, with and without the use of digital technologies (ACMNA127) | calculate unit fractions of collections, with and without the use of digital technologies, e.g. calculate 1/5 of 30 {Information and communication technology capability} |
| – describe the connection between finding a unit fraction of a collection and the operation of division {Communicating, Problem Solving, Critical and creative thinking} | |
| calculate a simple fraction of a collection/quantity, with and without the use of digital technologies, e.g. calculate 2/5 of 30 {Information and communication technology capability} | |
| – explain how unit fractions can be used in the calculation of simple fractions of collections/quantities, e.g. ‘To calculate 3/8 of a quantity, I found 1/8 of the collection first and then multiplied by 3’ {Communicating, Reasoning, Critical and creative thinking} | |
| solve word problems involving a fraction of a collection/quantity {Literacy} |
Add and subtract decimals, with and without the use of digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128) | add and subtract decimals with the same number of decimal places, with and without the use of digital technologies {Information and communication technology capability} |
| add and subtract decimals with a different number of decimal places, with and without the use of digital technologies {Information and communication technology capability} | |
| – relate decimals to fractions to aid mental strategies {Communicating} | |
| round a number of up to three decimal places to the nearest whole number | |
| use estimation and rounding to check the reasonableness of answers when adding and subtracting decimals {Critical and creative thinking} | |
| – describe situations where the estimation of calculations with decimals may be useful, eg to check the total cost of multiple items when shopping {Communicating, Problem Solving} | |
| solve word problems involving the addition and subtraction of decimals, with and without the use of digital technologies, including those involving money {Personal and social capability, Work and enterprise} | |
| – use selected words to describe each step of the solution process {Communicating, Problem Solving, Literacy} | |
| – interpret a calculator display in the context of the problem, e.g. 2.6 means $2.60 {Communicating} |
Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without the use of digital technologies (ACMNA129) | use mental strategies to multiply simple decimals by single-digit numbers, e.g. 3.5 × 2 |
| multiply decimals of up to three decimal places by whole numbers of up to two digits, with and without the use of digital technologies, e.g. ‘I measured three desks. Each desk was 1.25 m in length, so the total length is 3 × 1.25 = 3.75 m’ {Information and communication technology capability} | |
| divide decimals by a one-digit whole number where the result is a terminating decimal, e.g. 5.25 ÷ 5 = 1.05 | |
| solve word problems involving the multiplication and division of decimals, including those involving money, eg determine the ‘best buy’ for different-sized cartons of cans of soft drink {Personal and social capability, Work and enterprise, Critical and creative thinking} |
Multiply and divide decimals by powers of 10 (ACMNA130) | recognise the number patterns formed when decimals are multiplied and divided by 10, 100 and 1000 {Critical and creative thinking} |
| multiply and divide decimals by 10, 100 and 1000 | |
| – use a calculator to explore the effect of multiplying and dividing decimals by multiples of 10 {Reasoning} |
Learning Experiences
To be added