There are three common methods for sharing an amount to a given ratio. Depending on the age group and ability range I am teaching I would choose one approach over the other two.
The three methods are:
In this blog I will demonstrate each of the three methods for the same problem.
Nikki and Gemma share £36 in the ratio 4 : 5.
Work out how much Nikki and Gemma each receive.
Change the shares for each person in to a fraction.
Nikki’s Share = 4/(4+5) = 4/9
Gemma’s Share = 5/(4+5) = 5/9
Calculate each fraction of the total amount.
Nikki receives £36 × 4/9 = £16. Gemma receives £35 × 5/9 = £20.
I use this approach when teaching more able students as it reinforces the link between ratio and proportion. The fractions are seen as proportions of the total amount.
The unitary method emphasises the need to find the value of one share by dividing the total amount by the total number of shares. This can be taught illustratively or with clear writing frames.
The illustrative approach represents each share as a box. Each box contains an equal proportion of the total amount. Illustrating the shares as boxes helps the younger and less able students to visualise the importance of finding one share and using that to split the amount correctly.
Unitary method using writing frames to find the value of a single share
Unitary Method using Writing Frames
Step 1: Find the total number of shares: 4 + 5 = 9.
Step 2: Find the value of one share: £36 ÷ 9 = £4 per share
Step 3: Multiply each part of the ratio by the value of one share.
Nikki = 4 shares × £4 = £16, Gemma = 5 shares × £4 = £20
The written unitary method is my most common approach for teaching how to share an amount to a ratio as it breaks the problem down into three intuitive stages.
The first column of the table uses the ratio given in the question. Subsequent columns are multiples of the first column. This method works well when the total shares is a factor of the amount.
I use this method for lower ability students and those in key stage 3. It reinforces multiples and patterns while providing a visual representation of the increasing shares.
When calculating instantaneous rates of change students need to visualise the properties of the gradient for a straight line graph. I use the starter activity to see if they can match four graphs with their corresponding equations. The only clue is the direction and steepness of the red lines in relation to the blue line […]
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. You can […]
In my experience, students, in general, find the concept of a mean straightforward to calculate and understand. However, the mean alone does not provide a complete picture of a set of data. To achieve this, a measure of spread is also required. The range is the simplest measure that can be used for this. Not […]