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.
In this blog I will share some practical tips for using mini-whiteboards in a mathematics lesson. I use mini-whiteboards nearly every lesson because they help the students show me the progress they are making. When I understand what the misconceptions are I am able to address them in subsequent examples as part of my feedback. […]
Demonstrating student progression during a mathematics lesson is about understanding the learning objective and breaking that down into explicit success criteria. Using Success Criteria Take, for example, a lesson on calculating the area of compound rectilinear shapes. The intended learning objective was written on the main whiteboard. Success criteria were used to break down the individual […]
Plotting and interpreting conversion graphs requires linking together several mathematical techniques. Recent U.K. examiner reports indicate there are several common misconceptions when plotting and interpreting conversion graphs. These include: drawing non-linear scales on the x or y axis, using the incorrect units when converting between imperial and metric measurements, taking inaccurate readings from either axis not […]