Many pupils find fractions, decimals, and percentages daunting, often perceiving them as complex and anxiety-inducing topics. However, with the right tools and models, and a positive attitude, these concepts can be simplified and effectively taught in maths lessons, enhancing pupil understanding and making connections across different areas of maths.
A beadstring is a visual and tactile tool, perfect for introducing and exploring percentages in upper key stage 2 and beyond.
If you are new to using beadstrings, it would be worthwhile reading the Step-by-step guide to using the 0-100 bead string from Year 1 to Year 6.
Teaching percentages with beadstrings
Simply put, a percent is a way of expressing a number as a fraction of 100 and so 0-100 beadstrings are great manipulatives to use in maths lessons when exploring percentages.
If the whole beadstring represents 100% (100 beads = all the beads in the whole), then each bead represents 1% (1 out of 100 equal parts).
Connecting fractions and percentages with beadstrings
The beadstring can be used to draw out relationships with familiar fractions, visually linking them to percentages.
For example, the beadsting can be divided into 2 halves to connect:
- 50 out of 100
- 50/100
- 1/2
- 50%
Connections between benchmark fractions and percentages may also include:
- 1/10 and 10%
- 1/4 and 25%
- 3/4 and 75%
Understanding these relationships will enable pupils to visualise the proportional comparison when calculating percentages of amounts.
How to use beadstrings to link fractions, decimals and percentages
Beadstrings can be an excellent tool for linking fractions, decimals, and percentages, helping pupils to grasp these concepts more clearly. By incorporating decimals into these representations, we can further reinforce pupils' understanding of decimal fractions.
Using a speaking frame can aid this process by offering a structured approach for pupils to express their thoughts and reasoning, thereby enhancing their comprehension and confidence in maths lessons.
Calculating percentages of amounts with beadstrings
Once pupils understand that a percent represents a part of 100, the next step is to apply this knowledge to finding percentages of amounts where the whole is a different number. It's important to emphasise the connection between fractions and percentages, as pupils will have prior experience with finding fractions of an amount.
The images above demonstrate how to find 50% of 400 by understanding that 50% is the same as one-half, and half of 400 is 200.
Using this model, we can also determine what each bead represents by considering the relationship between the whole and the number of parts. If the whole is 400 and there are 100 equal parts, each bead represents 4.
This model and speaking frame can be used to find 50% of other numbers and adapted to calculate different percentages, such as 25% of 400, 10% of 400, or 20% of 400.
Teaching efficient strategies using the beadstring
This model can be revisited for finding more challenging percentages of amounts. Different strategies can be explored, encouraging pupils to use their known and familiar facts.
For example, to find 27% of 300:
- Use knowledge of finding 25% and 1% (and use 1% to find 2%)
- Or, find 10% (and double this to find 20%), 5% (by halving 10%), and 1% (and then double)
This approach helps pupils regroup percentages using strategies they are comfortable with.
Rehearsal opportunities
Regular use of practice scaffolds supports pupil understanding by providing a structured approach to translating between different models and here, making links to multiplication and division. This helps pupils build confidence and develop a deeper understanding of mathematical concepts.
Practice scaffolds also allow pupils to make connections between different strategies and apply their knowledge in various contexts.
In the example scaffold below, the story is used as the starting point and then connections drawn from there.
Alternatively, the information originally provided could be the calculation, or the bar model, or even the ‘calculate it’ section. Starting points could be varied across the class depending on the children’s confidence with the concept.
When could rehearsal take place?
- Early morning maths warm-up: Start the day with a quick practice session using beadstrings to find percentages of different amounts.
- Maths lessons: Integrate scaffolded practice into your main teaching activities, allowing pupils to apply new strategies in a guided setting.
- Independent practice: Provide scaffolded worksheets for pupils to complete independently, reinforcing the strategies learned during lessons.
- Group work: Encourage pupils to work in pairs or small groups to solve percentage problems using beadstrings, discussing their strategies and reasoning.
To read more about practice scaffolds: Making times tables stick: how to use a practice scaffold for learning multiplication facts
How to solve The 1% Club’s ‘1% question’ using a beadstring
Before Christmas, I watched an episode of the 1% Club on ITV with my family. This quiz show features increasingly difficult questions, culminating in the 1% question, which only 1% of the people originally asked answered correctly.
Spoiler alert: I’m sharing the 1% question from this episode because it brilliantly illustrates how a beadstring can reveal the mathematical structure behind the answer.
When solving it, I visualised and manipulated the beadstring model in my head!
The question: In a room of 100 people, 99% are left-handed. How many left-handed people need to leave to reduce that percentage to 98%?
Before reading on, try:
- Using a beadstring to solve the problem.
- Using a beadstring to prove your answer if you solved it differently.
Finding the solution to this percentage question on a beadstring
We know that there are 100 people in the room and 99% are left-handed.
Now what if the percentage of left-handed people changes to 98%?
If we stick to each bead representing 1 person, there would now be 98 left-handed people. However, this would also mean that there are now 2 right-handed people.
The question asks how many left-handed people leave the room. It doesn’t say any right-handed people enter.
We know there is 1 right-handed person. If 98% of people are left-handed, this must mean that 2% are right-handed.
2 out of 100 beads represents the 1 right-handed person so each group of 2 beads on our beadstring must now represent 1 person.
If each group of 2 beads represents 1 person, we must put the remaining 98 beads into groups of 2.
This makes 49 equal groups, meaning there must be 49 left-handed people still in the room.
At first, there were 99 left-handed people (99% of the original total) and now there are 49 left-handed people (98% of the new total).
This must mean that 50 left-handed people left the room.
Year 6 teachers, this could be a great scenario to present to your classes! We would love to hear how they get on.
Please share your experiences with us at laura.dell@hfleducation.org or on X @hertsmaths.
Are you looking to enhance the way your primary school pupils learn and engage with mathematics? Our dedicated primary maths teaching and learning advisory team is here for you.
Laura Dell
