Decimals, percentages and ratio: maths lessons by year

What's taught, year by year

The steps in decimals, percentages and ratio, in the order children usually meet them. Years are named as in Australia; the ages are a guide.

Tenths as fractions. Split a whole into ten equal parts and count in tenths.

Write tenths as decimals. Write tenths with a decimal point, such as 3/10 = 0.3 and 1 7/10 = 1.7.
Hundredths as fractions and decimals. Show hundredths on a hundred grid and write them as 0.01 to 0.99.
Decimal place value: ones, tenths and hundredths. Say the value of each digit in a number like 4.67 and write it in expanded form.
Decimals on a number line. Place tenths and hundredths on a number line between whole numbers.
Compare and order decimals to two places. Use place value to compare decimals like 0.4 and 0.38.
Decimal equivalents of halves and quarters. Know that 1/2 = 0.5, 1/4 = 0.25 and 3/4 = 0.75.
Divide by 10 and 100 to make decimals. See digits move right when a whole number is divided by 10 or 100.
Round a decimal to the nearest whole number. Round numbers with one or two decimal places to the nearest whole.
Add and subtract decimals with one decimal place. Add and subtract numbers like 1.3 + 0.8 using place value.

Thousandths and decimals to three places. Read, write and show decimals with three decimal places.
Compare and order decimals to three places. Order decimals with different numbers of places, such as 0.5, 0.45 and 0.405.
Round decimals to one or two places. Round decimals to the nearest tenth or hundredth.
Add and subtract decimals to two places. Line up decimal points to add and subtract in columns, with regrouping.
Multiply and divide decimals by 10, 100 and 1000. Move digits left or right to multiply or divide a decimal by a power of ten.
Multiply a decimal by a whole number. Work out products like 2.35 x 4 using known facts or a written method.
Divide a decimal by a whole number. Share a decimal amount like 7.2 equally into 3 using short division.
Division answers as decimals. Continue a division past the decimal point instead of leaving a remainder.
Percent means out of 100. Shade a hundred grid to show a percentage and write it as a fraction out of 100.
Fraction, decimal and percentage equivalents. Match common values such as 1/4 = 0.25 = 25% and 1/5 = 0.2 = 20%.
Scale a quantity up or down. Double, halve or multiply all amounts in a recipe for more or fewer people.

Compare and order fractions, decimals and percentages. Convert to one form to order a mix like 3/5, 0.55 and 58%.
Convert fractions to decimals by dividing. Divide the numerator by the denominator, for example 3/8 = 0.375.
Multiply decimals by decimals. Multiply numbers like 0.3 x 1.2 and place the decimal point correctly.
Divide by a decimal. Rename a division like 4.8 / 0.6 as 48 / 6 and solve it.
Percentage of an amount. Find 10%, 25%, 50% and then any percentage of a quantity.
Find the whole from a percentage. Work out the total when a percentage of it is known, like 25% is 40.
Percentage increase and decrease. Increase or decrease an amount by a given percentage.
Ratio language: for every. Describe a relationship like 2 red for every 3 blue and write it as 2:3.
Equivalent ratios and ratio tables. Use a table to find equivalent ratios and simplify a ratio.
Share an amount in a given ratio. Split a quantity unequally, for example 30 sweets in the ratio 2:3.
Unit rates and best value. Find the amount for one unit, such as cost per item, to compare deals.
Scale factors with similar shapes. Find a missing length when a shape is enlarged by a scale factor.
Speed as a rate. Use distance and time to find speed, and speed to find distance.