Working with Decimals

Students learn how to use a range of written methods to calculate and order decimal numbers.  As learning progresses they use equivalent fractions to solve problems involving long division.

This unit takes place in Term 5 of Year 9 and is followed by working with fractions and mixed numbers.


Working with Decimals Lessons
Revision Lessons


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.

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Mr Mathematics Blog

Mathematics OFSTED Inspection – The Deep Dive

Earlier this week, my school took part in a trial OFSTED inspection as part of getting ready for the new inspection framework in September 2019. This involved three Lead Inspectors visiting our school over the course of two days. The first day involved a ‘deep dive’ by each of the Lead Inspectors into Mathematics, English […]

How to Solve Quadratics by Factorising

The method of how to solve quadratics by factorising is now part of the foundational knowledge students aiming for higher exam grades are expected to have.   Here is an example of such a question. Solve x2 + 7x – 18 = 0 In my experience of teaching and marking exam papers students often struggle with […]

How Write 3 Part Ratios

When learning how to write 3-part ratios students need to understand how ratios can be made equivalent. The start of the lesson reminds students by asking which of six ratios is the odd one out.  This is presented to the class as they come into the lesson.    Writing Equivalent Ratios  A few students immediately go […]