Normal Distributions – How Understanding Them Helps Shops Order the Right Number of Clothes

The normal distribution appears everywhere in statistics — from exam results and human height to machine tolerances and weather data. But it’s not just for maths lessons. Businesses use normal distributions every day to make smart, data-driven decisions — including something as simple (and important) as deciding how many of each clothing size to stock.

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The Concept

A normal distribution is the classic bell-shaped curve where most values cluster around the mean, and fewer appear at the extremes.
For example, if the average chest size for men is 100 cm with a standard deviation of 8 cm, the distribution of sizes will look like this:

• Around 68% of people fall within one standard deviation (92–108 cm).

• Around 95% fall within two standard deviations (84–116 cm).

That means most customers will need sizes around the middle — not the smallest or largest options.

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The Real-World Application

Shops use this kind of data to avoid overstocking or understocking certain sizes.
If a retailer orders the same quantity of every size, they’ll run out of mediums while being left with piles of XS and XXL shirts.

By analysing customer data, they can order according to the normal curve:

• Fewer extreme sizes

• More of the average

• Enough variation to meet most demand without waste

Understanding the mean, standard deviation, and percentiles helps businesses match supply to real customer needs — saving money and reducing unsold inventory.

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Example

If data show:

Size	% of Customers	Recommended Stock per 100 Items
XS	5%	5
S	15%	15
M	40%	40
L	30%	30
XL	10%	10

Then a retailer ordering 100 shirts would stock more mediums and larges — exactly what the normal distribution predicts.

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Skills Highlight

• Interpreting and applying the normal distribution

• Understanding mean, standard deviation, and probability

• Linking mathematical models to real business data

• Seeing how statistics drive practical decision-making

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Why It Works in Teaching

When students see how a mathematical curve can shape real commercial decisions, statistics stops being abstract. The normal distribution becomes a story about prediction, planning, and efficient use of resources — connecting classroom maths to everyday economics.

 

Investigating Pressure Using Fizzy Drinks Bottles and Water

Understanding pressure is key to both physics and everyday life — from hydraulics and weather systems to the way submarines, pumps, and aircraft work. With a few empty fizzy drinks bottles and some water, students can explore how pressure changes with depth and how fluids behave under force, all with simple, recycled materials.

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The Experiment

Equipment:

• 1 L or 2 L clear plastic fizzy drinks bottles

• Water

• Nail or small pin

• Blu-Tack or waterproof tape

• Measuring cylinder or ruler

Method:

1. Fill the bottle with water and seal the top with the lid.

2. Use a pin to make small holes at different heights along the side of the bottle — near the top, middle, and bottom.

3. Cover the holes with Blu-Tack until you’re ready to test.

4. Remove the lid, then release the Blu-Tack and observe the jets of water emerging from the holes.

Students will see that the lower holes produce stronger, faster jets — showing that pressure increases with depth.

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The Science

The deeper the point in a liquid, the greater the pressure due to the weight of the water above it:

$$P = \rho g h$$

where:

• $P$ = pressure (Pa)

• $\rho$ = density of the liquid (kg/m³)

• $g$ = acceleration due to gravity (9.8 m/s²)

• $h$ = depth (m)

The jets from the lower holes travel further because the pressure — and therefore the force on the water — is greater. This same principle applies to dams, deep-sea diving, and how submarines must be engineered to withstand immense forces.

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Extensions

• Quantify the results by measuring how far each jet travels horizontally.

• Compare liquids (e.g. salt water vs fresh water) to see the effect of density.

• Discuss real-world examples such as hydraulics, atmospheric pressure, and Pascal’s Principle.

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Skills Highlight

• Designing and conducting a fair experiment using recycled materials

• Measuring and comparing qualitative pressure effects

• Linking observed patterns to mathematical relationships

• Understanding applications of pressure in science and engineering

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Why It Works in Teaching

This experiment is safe, inexpensive, and visually dramatic. Students can see immediately how depth affects pressure, reinforcing theoretical formulas with real, observable data — and all from an everyday object they recognise.

Diffusion Using Agar Blocks and Bromothymol Blue

Diffusion — the movement of particles from a region of high concentration to one of low concentration — is a fundamental concept in biology and chemistry. Demonstrating diffusion visually helps students understand how size, surface area, and concentration affect the rate of movement. A simple but effective classroom experiment uses agar blocks and bromothymol blue to make diffusion visible and measurable.

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The Experiment

Equipment:

• Agar mixed with bromothymol blue indicator (slightly alkaline)

• Dilute hydrochloric acid

• Scalpel or knife

• Ruler

• Timer

Method:

1. Prepare a block of indicator agar by mixing bromothymol blue into an alkaline agar solution and allowing it to set.

2. Cut cubes of different sizes — e.g. 1 cm³, 2 cm³, and 3 cm³.

3. Place each cube into a beaker of dilute hydrochloric acid.

4. As acid diffuses into the cube, it neutralises the indicator, changing its colour from blue to yellow.

5. Time how long it takes for the colour to change completely in each cube.

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The Science

The smaller the cube, the faster it changes colour because it has a larger surface area-to-volume ratio.
Diffusion occurs across the agar surface, so smaller blocks allow molecules to reach the centre more quickly.

This simple model mirrors what happens in biological systems: cells rely on diffusion to absorb nutrients and release waste, which limits how large a single cell can grow.

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Typical Results

Cube Size (cm)	Surface Area (cm²)	Volume (cm³)	SA:V Ratio	Time to Fully Change (min)
1	6	1	6.0	3
2	24	8	3.0	7
3	54	27	2.0	12

Smaller cubes diffuse faster — a clear demonstration that surface area to volume ratio directly affects diffusion rate.

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Skills Highlight

• Designing fair tests and measuring reaction times

• Observing and recording qualitative colour changes

• Calculating and comparing SA:V ratios

• Linking diffusion principles to cell biology and transport systems

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Why It Works in Teaching

This experiment turns an invisible process into something colourful and measurable. Students can easily see how size influences diffusion and understand why biological structures — from cells to alveoli — are adapted for maximum surface area.

 

 

Classical Conditioning – Pavlov’s Dogs in the Modern World

The image of Pavlov’s dogs salivating at the sound of a bell is one of psychology’s most famous experiments — but classical conditioning isn’t just history. It remains a foundation for understanding human and animal behaviour today, shaping everything from advertising to education and even our digital habits.

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The Experiment That Started It All

In the early 1900s, Ivan Pavlov, a Russian physiologist, noticed that his dogs began to salivate not only when food was presented but also when they heard the footsteps of the assistant who fed them.

To study this formally, Pavlov paired a neutral stimulus (a bell) with an unconditioned stimulus (food). After several repetitions, the dogs began to salivate at the sound of the bell alone — demonstrating classical conditioning.

Key terms:

• Unconditioned stimulus (UCS): food

• Unconditioned response (UCR): salivation

• Conditioned stimulus (CS): bell

• Conditioned response (CR): salivation to the bell

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How It Applies Today

Classical conditioning still influences behaviour in many modern contexts:

• Advertising: Products are paired with positive imagery or music to evoke emotional responses.

• Education: Students may associate success or anxiety with particular environments, teachers, or subjects.

• Everyday life: Notifications and alerts on phones create conditioned responses — a sound or vibration can trigger anticipation or stress.

• Therapy: Techniques such as systematic desensitisation use conditioning to help individuals overcome phobias.

The principle remains the same — linking two stimuli so that one triggers a learned response to the other.

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Skills Highlight

• Understanding the principles of associative learning

• Applying psychological theory to real-world contexts

• Evaluating classical conditioning in contrast to operant conditioning

• Analysing modern examples of conditioned behaviour

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Why It Works in Teaching

Pavlov’s research is both historical and highly relatable. Students can easily recognise conditioned responses in daily life — from craving certain foods to checking their phones — helping them connect classic experiments to modern psychology.

 

Understanding Algorithms Through Flowcharts

Before writing a single line of code, good programmers learn to think logically — breaking problems down into clear, ordered steps. Flowcharts are one of the best ways to visualise this process. They turn abstract algorithms into simple, visual maps that show exactly how data moves and decisions are made.

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The Concept

An algorithm is a set of instructions that solves a problem or completes a task.
A flowchart represents that algorithm visually, using standard symbols to describe processes, decisions, and flow of control.

Common flowchart symbols:

• Oval: Start or End

• Parallelogram: Input or Output (data entry or display)

• Rectangle: Process (a calculation or action)

• Diamond: Decision (yes/no or true/false)

• Arrows: Direction of flow

Example problem:
Find the largest of two numbers.

The algorithm can be shown as a flowchart:

1. Start

2. Input numbers A and B

3. If A > B, output A

4. Else, output B

5. End

This visual approach makes logic clear even before coding begins.

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The Classroom Application

Students can draw flowcharts on paper or use software such as Lucidchart, draw.io, or Python’s Turtle/Flowgorithm. They then convert their flowcharts into real code — seeing how structured logic translates into Python’s if, while, and for statements.

Typical student tasks include:

• Calculating averages

• Testing divisibility

• Simulating decisions in games or apps

• Building sorting or counting routines

Flowcharts encourage stepwise refinement — simplifying complex problems into smaller, testable parts.

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Skills Highlight

• Understanding algorithm structure and logical sequence

• Translating flowcharts into executable code

• Debugging by tracing flow and decision paths

• Linking computing logic with mathematical reasoning

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Why It Works in Teaching

Flowcharts make computational thinking visible. Students can plan, predict, and debug before touching code, developing a stronger understanding of how algorithms control software, games, and devices in everyday life.

 

Rates of Reaction – The Effect of Concentration Using the PASCO Colourimeter

The rate of a chemical reaction depends on how frequently particles collide with enough energy to react. One of the easiest ways to explore this relationship is with the reaction between sodium thiosulfate and hydrochloric acid, which produces a cloudy sulfur precipitate. Using a PASCO colourimeter, students can measure this change precisely, transforming a classic “disappearing cross” experiment into a fully quantitative study of reaction kinetics.

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The Experiment

Reaction:

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

Traditional method:
Students mix sodium thiosulfate and hydrochloric acid, and time how long it takes for a printed cross beneath the flask to disappear as sulfur forms.

With the PASCO colourimeter:

• The colourimeter measures light transmission through the solution at regular intervals.

• As sulfur forms, the solution becomes cloudy, reducing the amount of transmitted light.

• The data are recorded automatically in PASCO Capstone, producing a transmission vs time graph.

By repeating the experiment with different thiosulfate concentrations, students can plot reaction rate against concentration and determine the order of reaction with respect to thiosulfate.

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The Science

As concentration increases, more particles occupy the same volume, leading to more frequent collisions and a faster rate of reaction.

The colourimeter allows students to calculate initial reaction rates objectively, avoiding human error and giving a clear quantitative link between concentration and rate.

$$\text{Rate} = k [\text{Na}_2\text{S}_2\text{O}_3]^n$$

The graph of rate versus concentration reveals whether the reaction is first, second, or zero order with respect to thiosulfate.

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Skills Highlight

• Using PASCO colourimeters for real-time quantitative data

• Measuring reaction rate from absorbance or transmission curves

• Controlling variables: temperature, volume, and acid concentration

• Analysing graphs to interpret reaction order and rate laws

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Why It Works in Teaching

The experiment connects a familiar reaction with advanced data analysis. Students see the transition from a qualitative observation to precise measurement and mathematical modelling — exactly the kind of scientific thinking needed at GCSE and A-Level.

 

Demonstrating and Visualising Electric Fields

Electric fields are often described in theory, but they can also be made visible in the lab. With a simple setup using castor oil, semolina, and electrodes, students can see how invisible forces act between charges — a striking and memorable demonstration of field lines in physics.

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The Experiment

Equipment:

• 90 mm petri dish

• Castor oil (enough to cover the base)

• A pinch of semolina grains

• Two metal electrodes (pins, rods, or plates)

• High-voltage DC power supply (around 1–5 kV, current-limited for safety). We find that a Wimshurst machine works best as we can turn the handle a few times to see the effect

Method:

1. Pour a thin layer of castor oil into the petri dish — this acts as an insulating medium that allows particles to move freely without conducting electricity directly.

2. Sprinkle a light dusting of semolina grains evenly over the surface.

3. Insert the two electrodes in the oil — start with parallel plates for a uniform field.

4. Apply voltage gently and observe the movement of semolina grains.

   • The grains align themselves along the electric field lines, forming a visual map of the field.

Repeat the demonstration with different configurations:

• Parallel plates: uniform straight lines.

• Point and plate: radial pattern showing divergence from a point charge.

• Two points: curved lines showing attraction or repulsion.

• Parallel wires: more complex patterns with symmetrical curves.

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The Science

The semolina grains become polarised in the electric field. One side becomes slightly positively charged, the other negatively charged, so each grain aligns with the direction of the field. The castor oil slows the motion, allowing the pattern to form clearly and remain stable.

This visualisation shows how electric field lines represent direction and strength:

• Lines are closer together where the field is stronger.

• Lines curve smoothly, never crossing.

• The pattern changes shape with each electrode configuration, matching textbook diagrams almost perfectly.

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Skills Highlight

• Constructing experimental setups safely for electrostatics

• Observing and recording field patterns qualitatively

• Linking visual evidence to theoretical field diagrams

• Understanding polarity, potential difference, and charge interaction

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Why It Works in Teaching

Seeing the invisible is always powerful in physics. The semolina-in-oil demonstration makes electric fields concrete, a vivid link between diagrams on the board and the real behaviour of charges in space. Students grasp the geometry and symmetry of electric fields far more effectively when they can see them form before their eyes.