Working with Decimals

Ordering Decimal Numbers

Adding and Subtracting with Decimals

Long Multiplication

Long Division

Product of Decimal Numbers

Division with Decimal Numbers

Prerequisite Knowledge

• read and write decimal numbers as fractions [for example, 0.71 = 71/100 ]
• recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents
• round decimals with two decimal places to the nearest whole number and to one decimal place
• read, write, order and compare numbers with up to three decimal places

Success Criteria

• order positive and negative decimals
• use the symbols =, ≠, <, >, ≤, ≥
• apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper and improper), and mixed numbers – all both positive and negative;
• understand and use place value
• recognise and use relationships between operations
• estimate answers; check calculations using approximation and estimation, including answers obtained using technology

Key Concepts

• Use the place value table to teach the column method of addition and subtraction of decimal numbers. This helps students to align the digits to the decimal place.
• When calculating with decimal numbers encourage students to estimate the solution as means to check their working.
• Students may need to recap multiplying and diving by powers of ten when calculating the product of decimal numbers.
• Use equivalent fractions when performing long division. Simplifying the fractions help to break down the calculation.

Common Misconceptions

• Students incorrectly consider multiplications to always increase a number and divisions to decrease.
• Students fail to spot incorrect calculations due to not estimating solutions.