Your Basket 0 items - £0.00

Fractions, decimals and percentages are ways of showing a proportion of something. Any fraction can be written as a decimal, and any decimal can be written as a percentage. In this blog I discuss how to use the place value table and equivalent fractions to illustrate how fractions, decimals and percentages are connected.

In the starter I want to remind students how to work with equivalent fractions, especially those that have denominators which are factors of one hundred. Later in the lesson they will use this to convert a percentage to a simplified fraction.

I include the factors of one hundred as a reminder. This way students focus on matching the equivalent fractions rather than trying to calculate how many times the denominator goes into one hundred.

*Click to view the video on converting between fractions, decimals and percentage using place value.*

I work through questions a) to c) for the students then ask them to attempt d) to j) one at a time on mini-whiteboards. Each time I feedback to address any misconceptions.

When I ask the class to convert 1.25 to a fraction and percentage students follow the same method but some question the validity of their final outcome commenting “a percentage cannot be greater than one hundred”. To address this common misconception, we discuss how percentages can be used to show growth. For instance, when something increases by 5% in value, we take 100% as the original and 105% as the new value. Hence, the need for percentages greater than 100.

So far, as a class, we have only considered fractions with a denominator of one hundred. We now progress on to converting a decimal to a percentage and simplified fraction. We know 0.50, or 0.5, is equal to 50/100. 50/100 can be simplified by dividing the numerator and denominator by the highest common factor of each. Therefore 50/100 is equivalent to 1/2. We work through a few more examples with students presenting their processing on their mini-whiteboards.

To write a fraction in the place value table we discuss the need for the denominator to be a power of ten. For instance, converting 4/10 to a percentage is easier than 3/5. Next, we discuss how to convert fractions such as 3/5 to 6/10 using equivalent fractions.

When converting between fractions, decimals and percentages I may provide the factor pairs of one hundred for the less able students as well as a laminated place value table. I challenge the more able students by asking them to convert fractions such as 1/40, and 3/8 to percentages.

October 16, 2019

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 […]

August 22, 2019

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 […]

July 6, 2019

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 […]