29 October 2025

The Mathematics of Music – Ratios and Frequencies

Mathematics and music share a deep connection — both rely on patterns, structure, and proportion. When students explore musical notes and harmonies through ratios and frequencies, they see how simple numbers shape the sounds we hear every day.

The Concept

Musical notes are based on frequency, the number of vibrations per second (measured in hertz, Hz). When two notes are played together, the ratio of their frequencies determines how harmonious they sound.

For example:

Octave: 2:1 ratio (e.g., 440 Hz and 880 Hz)
Perfect fifth: 3:2 ratio (e.g., 440 Hz and 660 Hz)
Perfect fourth: 4:3 ratio
Major third: 5:4 ratio

These simple ratios create consonance — pleasant, stable sounds. More complex ratios produce dissonance, which gives tension and colour to music.

The Experiment

Students can use tuning forks, keyboard apps, or digital synthesiser tools to measure and compare frequencies. By analysing waveforms or using PASCO sound sensors, they can see how frequencies combine to form interference patterns and beats.

Plotting these waves shows visually why harmonious intervals have simple repeating patterns, while dissonant ones do not.

The Maths

If the frequency of a note is $f$ , then an octave above is $2f$ , and a fifth above is $\frac{3}{2}f$ .
Modern tuning (equal temperament) divides the octave into twelve semitones, where each note is $f \times 2^{1/12}$ times the frequency of the previous one — a perfect example of exponential growth in sound.

Skills Highlight

Exploring ratios and proportional reasoning in a musical context
Applying logarithmic and exponential relationships to real data
Visualising wave patterns and frequency combinations
Linking mathematical precision with creative expression

Why It Works in Teaching

This topic shows students that mathematics isn’t just abstract — it creates harmony, melody, and rhythm. Linking sound, frequency, and ratios provides a powerful and engaging way to explore number patterns and scientific thinking together.

28 October 2025

Investigating Friction with an Inclined Plane

Friction is one of the most familiar yet misunderstood forces in physics. Using an inclined plane, students can measure and understand how friction opposes motion, how it depends on surface type, and how it relates to the angle of the slope.

The Experiment

A small wooden or metal ramp is set up so that its angle can be adjusted gradually. A block or PASCO dynamics cart is placed on the surface.

Students:

Increase the angle slowly until the block just begins to slide — this angle is used to calculate the coefficient of static friction. My inclined plane has a measurement scale on it, but it is not very accurate, so we use a mobile phone with an inclinometer app on it
Use a force sensor to measure the force needed to keep the block moving at constant speed, showing the kinetic friction.
Compare how different surfaces — wood, plastic, felt, sandpaper — affect results.

The Science

The key relationship for the coefficient of static friction is:

$\mu_s = \tan(\theta)$

where $\theta$ is the angle at which the object begins to slide.

The higher the angle, the greater the coefficient of friction. Students can compare static friction (force needed to start motion) with kinetic friction (force needed to maintain motion).

This experiment links to Newton’s laws and the balance of forces acting parallel and perpendicular to the surface.

Skills Highlight

Measuring forces using sensors and interpreting vector components
Calculating coefficients of friction from experimental data
Understanding the difference between static and kinetic friction
Relating experimental results to everyday examples — tyres, shoes, and machinery

Why It Works in Teaching

The inclined plane turns an abstract force diagram into something real and measurable. Students can see the transition from rest to motion, test different materials, and understand why friction is sometimes helpful and sometimes a hindrance.

27 October 2025

Food Tests – Starch, Reducing and Non-Reducing Sugars, Proteins and Lipids

Testing foods for biological molecules is a core practical in GCSE Biology. By applying simple chemical tests, students can identify the main nutrients present — starch, sugars, proteins, and lipids — and see how each type of food contributes to a balanced diet.

The Core Tests

Test	Reagent / Method	Positive Result	Negative Result
Starch Test	Add a few drops of iodine solution	Blue-black colour	Yellow-brown
Reducing Sugar Test	Add Benedict’s reagent and heat in a water bath	Green → orange → brick-red (depending on sugar concentration)	Blue
Non-Reducing Sugar Test	After a negative Benedict’s test, boil sample with dilute hydrochloric acid, neutralise with sodium hydrogencarbonate, then re-test with Benedict’s	Brick-red colour	Blue
Protein Test (Biuret Test)	Add Biuret solution (sodium hydroxide + copper sulfate)	Lilac or purple colour	Blue
Lipid Test (Emulsion Test)	Mix with ethanol, then add water	Milky white emulsion	Clear

Example Food Results

Food Sample	Starch	Reducing Sugars	Non-Reducing Sugars	Protein	Lipid
Cheese	–	–	–	+	+
Biscuits	+	+	+	–	+
Carrot	+	+ (glucose)	–	–	–
Crisps	+	–	–	–	+
Potato	+	+ (maltose)	–	–	–
Egg white	–	–	–	+	–
Egg yolk	–	–	–	+	+

(+ = positive result, – = negative result)

The Science

Each test targets a different biological molecule:

Iodine binds with starch helices.
Benedict’s detects aldehyde groups in reducing sugars.
Biuret reacts with peptide bonds in proteins.
Ethanol–water emulsifies lipids for visibility.

These reactions demonstrate the molecular diversity of foods and how chemical testing can reveal their composition.

Skills Highlight

Using chemical reagents safely and accurately
Recording qualitative results systematically
Interpreting results in terms of macronutrient content
Linking observations to biological function and diet

Why It Works in Teaching

Food testing is colourful, visual, and immediately meaningful. Students connect lab results with the food they eat every day, reinforcing their understanding of macromolecules and experimental design.

26 October 2025

Business Studies Market Segmentation – Identifying Your Target Customer

In business, not every product suits every person. Market segmentation helps companies divide a broad market into smaller groups with shared characteristics so they can focus their marketing, design, and pricing more effectively. Understanding segmentation gives students insight into why products, adverts, and messages look so different even within the same industry.

The Concept

Market segmentation means dividing customers into categories that share similar traits or needs.
The four main types are:

Demographic: age, gender, income, education
Geographic: location, climate, region
Psychographic: attitudes, interests, lifestyles
Behavioural: spending habits, brand loyalty, product use

By analysing these segments, businesses can tailor their approach — from the design of a product to the tone of its advertising.

The Example

A sportswear company might use:

Demographic segmentation to target 16–25-year-olds,
Psychographic segmentation to focus on active lifestyles, and
Behavioural segmentation to reward loyal customers through fitness apps and discounts.

Students can apply the same logic to real-world case studies such as phone contracts, fashion brands, or subscription services.

Skills Highlight

Identifying target markets using segmentation data
Linking consumer characteristics to product design and pricing
Analysing how marketing messages vary between customer groups
Understanding the balance between niche and mass marketing

Why It Works in Teaching

Segmentation connects theory to everyday experience. Students quickly see that every advert or product choice is deliberate — based on data and psychology rather than guesswork. It develops analytical and commercial thinking, key skills for business and marketing studies.

25 October 2025

Building a Basic Webpage with HTML and CSS – Why It Still Matters

In an age of website builders and AI design tools, it’s easy to wonder whether there’s any point in learning HTML and CSS from scratch. Yet understanding how to build a webpage manually remains one of the most valuable digital skills a student can gain. It teaches the logic, structure, and design principles that underpin everything from professional web development to app design and digital communication.

The Experiment in Code

Students start with a blank text editor and create a simple webpage:


<!DOCTYPE html>
<html>
  <head>
    <title>My First Webpage</title>
    <style>
      body { font-family: Arial; background-color: #f2f2f2; text-align: center; }
      h1 { color: #333; }
    </style>
  </head>
  <body>
    <h1>Hello World</h1>
    <p>This is my first HTML and CSS page built from scratch.</p>
  </body>
</html>

Within minutes, they produce a page that displays correctly in any browser — something they’ve constructed entirely themselves.

Why Learn It?

Modern drag-and-drop tools are convenient, but they hide how web pages work. Learning the basics gives students:

Control: You can edit, fix, and improve what others can’t.
Understanding: Knowing HTML and CSS helps debug layout problems even when using automated tools.
Transferable Skills: The same concepts of structure, syntax, and logic appear in programming and app development.
Confidence: Building something from scratch provides a foundation for learning JavaScript, Python Flask, or other web technologies later.

Adding a Database to a Webpage – Bringing Data to Life

Once students understand how to build a static webpage using HTML and CSS, the next step is to make it interactive — to allow the site to store and retrieve information. This is where databases come in. Adding a database transforms a webpage from a simple display into a dynamic, data-driven application.

From Static to Dynamic

A static page always looks the same: the text and images are written directly into the code.
A dynamic page, by contrast, changes based on data — for example, a login page that checks usernames, a form that saves results, or a shop page that lists products from a database.

Using technologies such as Python with SQLite, PHP with MySQL, or JavaScript with Firebase, even beginners can now connect a webpage to a simple database.

The Basic Idea

A database stores information in tables — just like a spreadsheet, but faster and smarter.
A simple student project might include:

Table: Students
ID
1
2

When a webpage connects to this table, it can:

Display stored data (e.g. a list of grades)
Add new records through a form
Search or filter existing data
Update or delete entries as needed

The Example

Using Python Flask and SQLite, students can create a small web app:

The HTML form collects input (name and grade).
Flask connects to the SQLite database.
Submitting the form stores the new record.
A second page lists all entries from the table.

This simple project introduces concepts used across all major websites — from social media platforms to online stores.

Skills Highlight

Writing and editing basic HTML and CSS code
Understanding webpage structure: head, body, and styles
Linking code to visible design changes
Recognising how automation tools build on fundamental web technologies

Understanding how webpages communicate with databases
Using SQL commands to create, read, update, and delete records
Building simple web apps that store and display data
Linking coding and database design into one functional project

Why It Works in Teaching

Writing your own webpage demystifies the web. Students move from being passive users of technology to active creators. They understand what’s happening behind the page and learn the logic that every digital system builds upon. Adding a database makes programming feel purposeful. Students see how real websites function — collecting input, storing it, and producing useful output. It’s where theory meets practice, providing learners with a strong foundation in data handling and web development.

24 October 2025

Investigating Reaction Order with Sodium Thiosulfate and a PASCO Colorimeter

The reaction between sodium thiosulfate and hydrochloric acid is a classic way to study rates of reaction. As the reaction proceeds, a yellow sulfur precipitate forms, turning the solution opaque. Using a PASCO colorimeter, students can now measure this change quantitatively and determine the reaction order with precision.

The Experiment

The reaction is:

\text{Na}_2\text{S}_2\text{O}_3(aq) + 2\text{HCl}(aq) \rightarrow 2\text{NaCl}(aq) + \text{SO}_2(g) + \text{S}(s) + \text{H}_2\text{O}(l)

Traditionally, students time how long it takes for a cross beneath the flask to disappear. With a PASCO colourimeter, the reaction becomes measurable in real time: the sensor tracks light transmission as the solution becomes cloudy.

Students run several experiments, varying:

Sodium thiosulfate concentration while keeping acid constant, or
Acid concentration while keeping thiosulfate constant.

The colorimeter records transmittance vs. time, which can be converted into reaction rate data for analysis.

The Science

As the sulfur precipitate forms, light transmission decreases. The rate of this change is directly related to how fast the reaction occurs.

By plotting 1/transmittance (or absorbance) against time and comparing runs with different concentrations, students can determine how rate depends on concentration.

If rate ∝ [thiosulfate]¹, the reaction is first order in thiosulfate; if rate ∝ [thiosulfate]², it is second order. The slope of the initial rate graph provides quantitative evidence of reaction order.

Skills Highlight

Using a PASCO colorimeter to collect quantitative reaction data
Calculating initial reaction rates and plotting rate–concentration graphs
Determining reaction order from experimental evidence
Understanding how kinetics connects to chemical mechanism

Why It Works in Teaching

The colorimeter replaces guesswork with real data. Students see how a qualitative “disappearing cross” experiment becomes a precise kinetic analysis, linking visible changes to concentration and time. It’s a perfect example of chemistry moving from observation to quantification.

23 October 2025

Exploring Standing Waves – Using a Strobe to See the Pattern

Standing waves are a perfect example of physics that you can both see and measure. When a vibrating string is viewed under a strobe light, the motion appears frozen, revealing the hidden structure of the wave — the nodes, antinodes, and harmonics that define resonance.

The Experiment

Using a string is stretched under tension and driven by a variable-frequency signal generator.
A strobe light flashes at adjustable frequency to make the oscillating string appear stationary.

As the driving frequency changes, students observe:

No stable pattern at most frequencies.
Clear standing waves at resonant frequencies — the string divides into distinct loops separated by nodes.

By synchronising the strobe frequency to match the wave’s motion, students can slow or freeze the pattern, making it easy to count loops and measure wavelength.

The Science

Standing waves form when two waves of the same frequency and amplitude travel in opposite directions, interfering to create stationary nodes and vibrating antinodes.

The condition for resonance is:

f = \frac{n}{2L}\sqrt{\frac{T}{\mu}}

where $n$ is the harmonic number, $L$ is string length, $T$ is tension, and $\mu$ is mass per unit length.

The strobe effectively samples the motion at discrete times, creating the illusion of a stationary or slowly moving pattern — allowing students to measure details that are otherwise too fast for the eye to follow.

Skills Highlight

Using a strobe to visualise rapid oscillations
Measuring wavelength, frequency, and tension relationships
Identifying harmonics and verifying wave equations
Relating resonance to real-world systems such as strings, bridges, and air columns

Why It Works in Teaching

A strobe light turns invisible vibration into visible form. Students can pause motion, count nodes, and verify equations that describe wave behaviour. It’s one of the most satisfying demonstrations of resonance, combining precision measurement with a memorable visual experience.