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Your email address will not be published.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

Angles in Polygons

There are two key learning points when solving problems with angles in polygons.  The first is to understand why all the exterior angles of a polygon have a sum of 360°.  The second is to understand the interior and exterior angles appear on the same straight line. Students can be told these two facts and […]

Getting Ready for a New School Year

When getting ready for a new school year I have a list of priorities to work through. Knowing my team have all the information and resources they need to teach their students gives me confidence we will start the term in the best possible way.  Mathematics Teaching and Learning Folder All teachers receive a folder […]

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 […]