18 July 2026

Building an A Level Platform Game Project — Part 3: Adding Gravity and Jumping

  


Building an A Level Platform Game Project — Part 3: Adding Gravity and Jumping

In Part 1, we planned the platform game and set realistic success criteria.

In Part 2, we created the first working prototype: a game window, a visible player, left and right movement, frame rate control and screen boundary checks.

At that point, the game was visible and interactive, but it was not really a platform game yet.

A player sliding left and right across the screen is a start. But a platform game needs vertical movement. It needs the player to fall, jump, land and respond to gravity.

This is where the project starts to become much more interesting technically.

Adding gravity and jumping introduces some important programming ideas:

  • velocity
  • acceleration
  • game physics
  • state checking
  • keyboard input
  • conditions
  • testing awkward cases
  • preventing repeated jumping in mid-air

It also gives students a proper programming problem to solve, not just a drawing exercise.

Why Gravity Makes the Game Feel Real

In a simple game, the player’s position is controlled by x and y coordinates.

In Part 2, we changed the x-coordinate to move the player left and right.

Now we need to change the y-coordinate as well.

This is where students often meet one of the first confusing ideas in game programming: screen coordinates do not behave like a normal maths graph.

On most screens:

  • x increases as you move right
  • y increases as you move down
  • y decreases as you move up

So when the player falls, the y-coordinate increases.

When the player jumps, the y-coordinate decreases.

This feels backwards at first, but students soon get used to it.

The Aim for Part 3

The target for this stage is:

Add gravity so the player falls downwards, add jumping so the player can move upwards, and prevent the player from jumping again while already in the air.

By the end of this stage, the player should be able to:

  • move left and right
  • stand on the ground
  • jump when the space bar is pressed
  • rise into the air
  • slow down
  • fall back down
  • land on the ground
  • avoid repeated jumping while in the air

This is a major step forward.

The game will still not have platforms yet. That comes in Part 4.

For now, we will use the bottom of the screen as the ground.

Thinking About Vertical Velocity

In Part 2, movement was simple.

If the right arrow was pressed:

player_x += player_speed

If the left arrow was pressed:

player_x -= player_speed

Jumping is more complicated because it changes over time.

When the player first jumps, they move upwards quickly. Then gravity slows them down. Eventually they stop rising and begin to fall.

This means we need a vertical velocity.

A velocity is a speed in a particular direction.

For the player, we can create a variable:

player_y_velocity = 0

This will control how much the player’s y-position changes each frame.

If the vertical velocity is positive, the player moves down.

If the vertical velocity is negative, the player moves up.

That is because screen y-coordinates increase as you move down.

Adding Gravity

Gravity can be represented by increasing the vertical velocity each frame.

For example:

gravity = 0.5
player_y_velocity += gravity
player_y += player_y_velocity

This means the player falls faster and faster.

At first, the vertical velocity may be 0.

After one frame, it becomes 0.5.
Then 1.0.
Then 1.5.
Then 2.0.

This creates acceleration.

The player does not simply fall at one fixed speed. The fall becomes faster over time, which feels more natural.

This is a very useful teaching point because it connects programming with physics.

Creating a Ground Level

Before we add platforms, we need somewhere for the player to land.

A simple approach is to define the ground as a y-coordinate near the bottom of the screen.

For example:

GROUND_LEVEL = 540

If the player is 60 pixels tall, and the screen height is 600 pixels, then placing the player’s top-left y-coordinate at 540 means the bottom of the player is at 600.

So the player stands exactly on the bottom of the screen.

We can check if the player has fallen below the ground:

if player_y > GROUND_LEVEL:
    player_y = GROUND_LEVEL
    player_y_velocity = 0

This prevents the player falling forever.

It also resets the vertical velocity when the player lands.

Adding the Jump

To make the player jump, we give the vertical velocity a negative value.

For example:

player_y_velocity = -12

This moves the player upwards because it reduces the y-coordinate.

The number controls the strength of the jump.

A larger negative number makes the player jump higher.
A smaller negative number makes the player jump lower.

For example:

jump_strength = -12

Then, when the player presses space:

if keys[pygame.K_SPACE]:
    player_y_velocity = jump_strength

This seems simple, but it creates a problem.

The Infinite Jump Problem

If we use the code above, the player may be able to jump again and again while already in the air.

This is sometimes called infinite jumping.

The player can keep pressing space and fly upwards forever.

That might be useful in a different type of game, but it is not what we want in a normal platform game.

We need the program to know whether the player is on the ground.

We can use a Boolean variable:

on_ground = True

A Boolean can only be True or False.

The player should only be allowed to jump if on_ground is True.

For example:

if keys[pygame.K_SPACE] and on_ground:
    player_y_velocity = jump_strength
    on_ground = False

Then, when the player lands:

if player_y > GROUND_LEVEL:
    player_y = GROUND_LEVEL
    player_y_velocity = 0
    on_ground = True

This is an important moment in the project.

The student is no longer just moving a shape. They are managing the state of the player.

The Updated Prototype Code

At the end of Part 3, the prototype might look like this:

import pygame

pygame.init()

SCREEN_WIDTH = 800
SCREEN_HEIGHT = 600
GROUND_LEVEL = 540

screen = pygame.display.set_mode((SCREEN_WIDTH, SCREEN_HEIGHT))
pygame.display.set_caption("Escape the Platforms")

clock = pygame.time.Clock()

player_x = 100
player_y = GROUND_LEVEL
player_width = 40
player_height = 60
player_speed = 5

player_y_velocity = 0
gravity = 0.5
jump_strength = -12
on_ground = True

running = True

while running:
    clock.tick(60)

    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            running = False

    keys = pygame.key.get_pressed()

    # Horizontal movement
    if keys[pygame.K_LEFT]:
        player_x -= player_speed

    if keys[pygame.K_RIGHT]:
        player_x += player_speed

    # Jumping
    if keys[pygame.K_SPACE] and on_ground:
        player_y_velocity = jump_strength
        on_ground = False

    # Apply gravity
    player_y_velocity += gravity
    player_y += player_y_velocity

    # Ground collision
    if player_y > GROUND_LEVEL:
        player_y = GROUND_LEVEL
        player_y_velocity = 0
        on_ground = True

    # Screen boundary checks
    if player_x < 0:
        player_x = 0

    if player_x + player_width > SCREEN_WIDTH:
        player_x = SCREEN_WIDTH - player_width

    # Draw everything
    screen.fill((255, 255, 255))

    pygame.draw.rect(
        screen,
        (0, 0, 255),
        (player_x, player_y, player_width, player_height)
    )

    pygame.draw.line(
        screen,
        (0, 0, 0),
        (0, GROUND_LEVEL + player_height),
        (SCREEN_WIDTH, GROUND_LEVEL + player_height),
        3
    )

    pygame.display.update()

pygame.quit()

This is still a simple prototype, but it now behaves much more like a game.

The player can move.
The player can jump.
The player falls because of gravity.
The player lands on the ground.
The player cannot repeatedly jump in mid-air.

That is a very important development stage.

Why We Draw a Ground Line

In the example code, a black line is drawn at the bottom of the screen:

pygame.draw.line(
    screen,
    (0, 0, 0),
    (0, GROUND_LEVEL + player_height),
    (SCREEN_WIDTH, GROUND_LEVEL + player_height),
    3
)

This is mainly for visual clarity.

It helps the student see where the ground is.

At this stage, the ground is not a proper platform. It is simply a boundary that stops the player falling off the screen.

In Part 4, we will replace this simple ground idea with proper platforms.

Testing Gravity and Jumping

This stage needs proper testing.

Students should not simply say “jumping works”.

They should test specific behaviours.

Test NumberTestExpected ResultActual ResultPass/Fail
1Run the programPlayer appears standing on the groundPlayer appears on the groundPass
2Press left arrowPlayer moves leftPlayer moves leftPass
3Press right arrowPlayer moves rightPlayer moves rightPass
4Press space while on groundPlayer jumps upwardsPlayer jumps upwardsPass
5Release space after jumpingPlayer continues moving according to velocity and gravityPlayer rises then fallsPass
6Press space repeatedly in the airPlayer does not keep jumping upwardsPlayer cannot double jumpPass
7Player falls back to groundPlayer lands and stops fallingPlayer lands correctlyPass
8Hold left arrow while jumpingPlayer moves left in the airPlayer moves left while airbornePass
9Hold right arrow while jumpingPlayer moves right in the airPlayer moves right while airbornePass
10Move to screen edge while jumpingPlayer stays within the screenPlayer remains inside screenPass

This table creates useful evidence for the project.

It also shows that the student has thought about normal tests and more awkward cases.

Linking Back to Success Criteria

In Part 1, we created success criteria for the project.

This stage helps meet several of them:

  • The player falls when not standing on a platform.
  • The player can jump from the ground.
  • The player cannot repeatedly jump while already in the air.
  • The player lands without falling through the ground.
  • The player can move left and right while jumping.
  • The player cannot move beyond the edge of the game screen.

This is why success criteria are so valuable.

They allow the student to show measurable progress.

A development log could say:

This stage successfully added gravity and jumping. Testing showed that the player could jump from the ground, fall back down and land correctly. A Boolean variable was added to prevent the player from repeatedly jumping while in the air.

That is much stronger than simply writing:

I added jumping.

Common Bugs Students May Meet

This stage often produces interesting bugs.

That is good.

A Level projects need evidence of problems being found and solved.

Bug 1: The Player Falls Through the Ground

This may happen if the ground check is missing or incorrect.

For example, if the program checks:

if player_y == GROUND_LEVEL:

this may fail because the player might move from just above the ground to just below the ground in one frame.

It is safer to check:

if player_y > GROUND_LEVEL:

or sometimes:

if player_y >= GROUND_LEVEL:

This is a useful programming lesson.

Exact equality is not always the best test when movement is changing every frame.

Bug 2: The Player Can Jump Forever

This usually happens if the program does not check whether the player is on the ground.

The solution is to use a variable such as:

on_ground

and only allow jumping when this is True.

Bug 3: The Jump Is Too High or Too Low

This is controlled by the jump strength and gravity.

For example:

gravity = 0.5
jump_strength = -12

Students can experiment with these values.

A smaller gravity value makes the player float for longer.
A larger gravity value pulls the player down faster.
A more negative jump strength creates a higher jump.
A less negative jump strength creates a smaller jump.

This gives a good opportunity for testing and user feedback.

The student could ask a user:

Does the jump feel too high, too low or about right?

Then they can adjust the values and record the improvement.

Bug 4: The Player Appears to Sink Into the Ground

This may happen if the ground level has been calculated incorrectly.

The important question is:

Does player_y represent the top of the player or the bottom of the player?

In our example, player_y represents the top-left corner of the player rectangle.

That means the bottom of the player is:

player_y + player_height

This distinction becomes very important when we add platforms.

Why This Is Good Evidence for A Level

Gravity and jumping create a strong section for the project write-up because the student can explain the algorithm.

They can describe:

  • why a vertical velocity variable was needed
  • how gravity changes the velocity each frame
  • why a negative velocity moves the player upwards
  • how the program detects landing
  • why a Boolean variable prevents repeated jumping
  • how the values for gravity and jump strength were tested

This is exactly the kind of thinking that should appear in a strong programming project.

The final program matters, but the explanation of the development process matters too.

Improving the Code Structure

At this stage, the code is still manageable.

However, we can already see that it is becoming more complex.

The player now has:

  • x-position
  • y-position
  • width
  • height
  • horizontal speed
  • vertical velocity
  • jump strength
  • ground state

Later, the player may also have:

  • lives
  • score
  • direction
  • animation state
  • collision rectangle
  • health
  • current level

This is a good point to discuss whether a class may eventually be useful.

A Player class could store the player’s data and methods in one place.

For example, it might eventually include:

class Player:
    def __init__(self, x, y):
        self.x = x
        self.y = y
        self.width = 40
        self.height = 60
        self.speed = 5
        self.y_velocity = 0
        self.on_ground = True

    def move(self, keys):
        pass

    def jump(self):
        pass

    def apply_gravity(self):
        pass

    def draw(self, screen):
        pass

Students do not need to do this immediately, but they should be aware of why it might help.

A strong project can show how the code was improved as complexity increased.

Should the Player Be Able to Move in the Air?

In the current version, the player can move left and right while jumping.

That is common in many platform games.

However, it is a design decision.

Some games give the player a lot of control in the air. Others make jumping more rigid and realistic.

Students can think about this as part of their evaluation.

Questions to consider:

  • Should the player be able to change direction while in the air?
  • Should air movement be slower than ground movement?
  • Should the game feel realistic or arcade-like?
  • What does the target user prefer?

This is a nice example of how programming choices connect to user experience.

Adding Debug Information

During development, it can be useful to display values on the screen or print them to the console.

For example, students might print:

print(player_y, player_y_velocity, on_ground)

This helps them see what is happening when the player jumps and lands.

However, debug output should usually be removed or hidden in the final version.

Students can mention this in their documentation:

I used printed debug values to check the player’s y-coordinate, vertical velocity and ground state while testing the jump algorithm. This helped identify when the player was landing and when the on_ground variable changed.

That is useful evidence of debugging.

Practical Task for Students

Before moving on to platforms, students should complete this task.

Part 3 Student Task

Add gravity and jumping to your platform game prototype.

Your program should include:

  1. A vertical velocity variable.
  2. A gravity value.
  3. A jump strength value.
  4. A ground level.
  5. A Boolean variable to record whether the player is on the ground.
  6. A jump controlled by the space bar or another chosen key.
  7. A check to stop the player falling through the ground.
  8. A check to stop repeated jumping in mid-air.
  9. A test table for gravity and jumping.
  10. Screenshots or short video evidence of the player jumping and landing.

Extension Task

Improve the jumping system by adding one of the following:

  • a different jump height
  • a maximum falling speed
  • a double jump as an intentional feature
  • a smoother jump animation
  • reduced air control
  • a sound effect when jumping
  • a debug display showing vertical velocity

Students should only attempt the extension once the basic jump works correctly.

Development Log Example

A good development log entry for this stage might look like this:

Development Stage

Adding gravity and jumping.

Aim

To make the player fall under gravity, jump when the space bar is pressed and land correctly on the ground.

What Was Added

  • vertical velocity variable
  • gravity variable
  • jump strength variable
  • ground level
  • on_ground Boolean variable
  • jump input using the space bar
  • landing check
  • testing for repeated jumping

Problems Found

  • The player initially kept jumping while already in the air.
  • The player sometimes moved slightly below the ground before being reset.
  • The jump height needed adjusting to feel natural.

Changes Made

  • Added an on_ground variable to prevent repeated jumping.
  • Reset the player’s y-position to the ground level after landing.
  • Adjusted gravity and jump strength values after testing.

Evidence Collected

  • screenshot of the player standing on the ground
  • screenshot of the player in the air
  • test table showing jump behaviour
  • code section showing gravity and jump logic
  • notes explaining how the infinite jump bug was fixed

This kind of evidence is valuable because it shows a real development process.

Final Thoughts: The Game Is Starting to Behave

At the end of Part 3, the game still looks simple.

The player may still be just a rectangle.
There may be no platforms yet.
There may be no enemies, collectables or levels.

But something important has changed.

The game now has behaviour.

The player can move, jump, fall and land. The program now includes a simple physics system. It uses velocity, gravity and state checking. It has already produced bugs that need proper solutions.

That is exactly what makes it a useful A Level project.

A platform game becomes interesting not because of the graphics, but because of the rules underneath.

In the next article, we will add one of the most important and challenging parts of the project: platforms and collision detection.

That is where the player stops jumping on an imaginary ground and starts interacting with the world of the game.

17 July 2026

Why Does Reactivity Increase Down One Side of the Periodic Table but Decrease Down the Other?

 


Why Does Reactivity Increase Down One Side of the Periodic Table but Decrease Down the Other?

One of the most interesting features of the periodic table is that its patterns are not always as simple as students first expect.

We often teach that elements in the same group have similar chemical properties because they have the same number of electrons in their outer shell. That sounds straightforward enough. However, when we investigate how reactivity changes down different groups, an apparent contradiction appears.

In Group 1, the alkali metals become more reactive as we move down the group.

In Group 7, the halogens become less reactive as we move down the group.

How can moving down the periodic table produce completely opposite effects?

This is a particularly useful question because it forces students to move beyond memorising trends. They must think about what is happening to the electrons during a chemical reaction.

Starting with the Alkali Metals

The alkali metals include:

Lithium
Sodium
Potassium
Rubidium
Caesium

They all have one electron in their outer shell.

During a chemical reaction, a Group 1 atom loses this outer electron and forms a positive ion with a charge of +1.

For example:

Na → Na⁺ + e⁻

The easier it is for the atom to lose this electron, the more reactive the metal will be.

Observing Group 1 Metals Reacting with Water

The trend becomes much easier to understand when students see the reactions rather than simply reading about them.

Lithium and water

Lithium floats on the surface and moves slowly. It fizzes as hydrogen gas is produced, but the reaction is relatively gentle.

Sodium and water

Sodium reacts more rapidly. The heat produced melts the metal into a silvery ball, which moves quickly across the surface of the water.

Potassium and water

Potassium reacts much more vigorously. The hydrogen produced often ignites, producing the characteristic lilac flame associated with potassium compounds.

The overall reaction can be represented by:

2Na + 2H₂O → 2NaOH + H₂

Similar equations can be written for lithium and potassium.

The important observation is clear:

Lithium reacts steadily.
Sodium reacts rapidly.
Potassium reacts very rapidly.

Therefore, reactivity increases as we move down Group 1.

These demonstrations must, of course, be carried out with very small pieces of metal, suitable eye protection and appropriate safety precautions. Rubidium and caesium are far too reactive for an ordinary classroom demonstration.

Why Does Group 1 Become More Reactive?

As we move down Group 1, each element has an additional occupied electron shell.

Lithium has two occupied shells.
Sodium has three.
Potassium has four.

This produces two important effects.

The outer electron is farther from the nucleus

The negatively charged outer electron is attracted to the positively charged nucleus. However, the greater the distance between them, the weaker this attraction becomes.

In potassium, the outer electron is farther from the nucleus than it is in sodium or lithium.

There is more electron shielding

The inner shells of electrons lie between the nucleus and the outer electron.

These inner electrons reduce the full attractive effect of the nucleus on the outer electron. This is known as shielding.

Although the number of protons in the nucleus increases as we move down the group, the increased distance and shielding have a greater effect.

The outer electron is therefore held less strongly.

It is easier to remove.

The atom reacts more readily.

A Useful Way to Think About Group 1

Imagine holding an object using a piece of elastic.

When the object is close to your hand, it is held firmly. As it moves farther away, your control becomes weaker.

The outer electron in a larger Group 1 atom is rather like the object at the end of a longer piece of elastic. It is farther from the nucleus and more easily removed.

This is why potassium loses its outer electron more easily than sodium, and sodium loses it more easily than lithium.

The first ionisation energy therefore decreases down Group 1.

As a result, reactivity increases.

Moving Across to the Halogens

The halogens are found in Group 7 of the traditional school numbering system, or Group 17 in modern IUPAC numbering.

They include:

Fluorine
Chlorine
Bromine
Iodine

Halogen atoms have seven electrons in their outer shell.

Instead of losing an electron, as the alkali metals do, a halogen atom gains one electron to complete its outer shell.

For example:

Cl + e⁻ → Cl⁻

The ability to attract and gain an electron is central to halogen reactivity.

Investigating Halogen Displacement Reactions

A good way to compare the reactivity of the halogens is to use halogen water and potassium halide solutions.

The halogen waters commonly used are:

Chlorine water
Bromine water
Iodine solution

The potassium halide solutions might include:

Potassium chloride, KCl
Potassium bromide, KBr
Potassium iodide, KI

A more reactive halogen will displace a less reactive halogen from one of its compounds.

For example:

Cl₂ + 2KBr → 2KCl + Br₂

Chlorine displaces bromine from potassium bromide because chlorine is more reactive than bromine.

Chlorine can also displace iodine:

Cl₂ + 2KI → 2KCl + I₂

Bromine can displace iodine:

Br₂ + 2KI → 2KBr + I₂

However, bromine cannot displace chlorine from potassium chloride, and iodine cannot displace either chlorine or bromine from their compounds.

Building the Halogen Reactivity Order

The displacement results allow students to construct the reactivity series:

Chlorine > Bromine > Iodine

Fluorine would be placed above chlorine, although it is not normally used in these classroom experiments because it is extremely dangerous and difficult to handle.

Therefore, the full trend is:

Fluorine > Chlorine > Bromine > Iodine

The reactivity of the halogens decreases as we move down Group 7.

At first, this seems to be the opposite of what happens in Group 1.

However, the same changes in atomic structure are responsible.

Why Does Group 7 Become Less Reactive?

As we move down Group 7, atoms again gain additional occupied electron shells.

The atomic radius increases, and there is more shielding from the inner electrons.

However, a halogen atom needs to gain an electron rather than lose one.

For a reaction to occur, the nucleus must attract an additional electron into the outer shell.

In chlorine, the incoming electron is attracted into a relatively small atom.

In bromine, the outer shell is farther from the nucleus and more strongly shielded.

In iodine, the incoming electron must enter an even larger atom with still more shielding.

The attraction between the nucleus and the incoming electron therefore becomes weaker as we move down the group.

The atom becomes less able to gain an electron.

Its reactivity decreases.

The Same Cause Produces Opposite Trends

This is the key idea that students need to understand.

Moving down either group produces:

A larger atomic radius
More occupied electron shells
More shielding
A weaker attraction between the nucleus and outer electrons

However, the elements on the two sides of the periodic table react differently.

Group 1 metals

Group 1 atoms react by losing an electron.

A weaker attraction makes the electron easier to lose.

Therefore, reactivity increases down the group.

Group 7 halogens

Group 7 atoms react by gaining an electron.

A weaker attraction makes the incoming electron harder to attract.

Therefore, reactivity decreases down the group.

The structural trend is the same, but the chemical process is different.

That is why the changes in reactivity appear to run in opposite directions.

An Electron-Transfer View of the Reaction

The relationship becomes even clearer when we consider a reaction between an alkali metal and a halogen.

Sodium reacts with chlorine to form sodium chloride:

2Na + Cl₂ → 2NaCl

During this reaction, each sodium atom loses an electron:

Na → Na⁺ + e⁻

Each chlorine atom gains an electron:

Cl + e⁻ → Cl⁻

The sodium and chloride ions then attract one another because they have opposite charges.

Group 1 metals are effective electron donors.

Group 7 halogens are effective electron acceptors.

Moving down Group 1 makes electron donation easier.

Moving down Group 7 makes electron acceptance more difficult.

This provides a much more satisfying explanation than simply memorising two apparently unrelated trends.

Why Practical Work Makes This Easier to Understand

Students can learn the reactivity trends from a textbook, but practical work gives the ideas meaning.

Watching potassium react much more vigorously than lithium provides immediate evidence that something is changing down Group 1.

Similarly, the halogen displacement reactions allow students to infer a pattern from evidence.

Instead of being told that chlorine is more reactive than bromine, they can observe chlorine producing bromine from a bromide solution.

They are then able to ask the scientific question:

What must chlorine have done to the bromide ions?

The ionic equation gives the answer:

Cl₂ + 2Br⁻ → 2Cl⁻ + Br₂

Chlorine molecules gain electrons from bromide ions. Chlorine is reduced, while bromide ions are oxidised.

This links the topic not only to periodicity, but also to oxidation, reduction and electron transfer.

Avoiding a Common Misconception

Students sometimes say that atoms lower down a group are more reactive simply because they are larger.

Size alone is not a complete explanation.

The important question is:

Does the atom need to lose an electron or gain one?

A larger atom holds its outer electrons less strongly. That makes losing an electron easier but attracting an additional electron harder.

Students should also be careful with the phrase “the nucleus becomes weaker”. The nucleus does not lose its positive charge. In fact, atoms lower down the group contain more protons.

The effective attraction at the outer shell becomes weaker because the distance from the nucleus increases and the inner electrons provide more shielding.

That distinction is important when writing a full examination answer.

A Strong Examination Explanation

A good answer explaining the increase in Group 1 reactivity might say:

“Down Group 1, the atoms have more occupied electron shells. The outer electron is farther from the nucleus and experiences more shielding. The attraction between the nucleus and the outer electron is therefore weaker, so the electron is lost more easily. Reactivity increases.”

A good answer explaining the decrease in Group 7 reactivity might say:

“Down Group 7, the atoms have more occupied electron shells. An incoming electron is farther from the nucleus and experiences more shielding. The attraction between the nucleus and the incoming electron is therefore weaker, so the atom gains an electron less easily. Reactivity decreases.”

The explanations are almost mirror images of one another.

A Personal Reflection from Teaching This Topic

I have always found this one of the most satisfying periodic table patterns to teach.

At first, students often treat the two trends as separate facts:

Group 1 gets more reactive.
Group 7 gets less reactive.

Once they begin thinking about the movement of electrons, the apparent contradiction disappears.

The alkali metal experiments provide the drama. Lithium fizzes, sodium races across the water and potassium may ignite.

The halogen displacement reactions are less dramatic, but they require more careful observation and reasoning. Students must compare colours, interpret the results and decide which element has displaced which.

Together, the two sets of experiments show why chemistry is not simply a collection of facts. It is a logical subject in which the visible behaviour of substances can be explained by particles, forces and electrons that we cannot see directly.

Conclusion: Look at What the Electron Is Doing

The periodic table is not merely a chart of elements. It is a map of repeating patterns in atomic structure and chemical behaviour.

Down both Group 1 and Group 7:

Atoms become larger.
The number of occupied shells increases.
Electron shielding increases.
The attraction between the nucleus and the outer shell becomes weaker.

For Group 1, this makes an electron easier to lose, so reactivity increases.

For Group 7, this makes an additional electron harder to gain, so reactivity decreases.

The next time two periodic trends appear to contradict one another, the best question to ask is not simply, “What happens down the group?”

It is:

“What does the atom need to do with its electrons in order to react?”

Once that question is answered, the strange pattern on the periodic table becomes a logical and elegant consequence of atomic structure.

16 July 2026

Is It a Liquid or a Solid? The Strange Science of Non-Newtonian Fluids


 Is It a Liquid or a Solid? The Strange Science of Non-Newtonian Fluids

Most students learn that matter can be divided into three familiar states: solids, liquids and gases.

A solid keeps its shape. A liquid flows and takes the shape of its container. A gas expands to fill the available space.

That classification is useful, but nature is rarely quite so tidy.

Some materials appear to behave like liquids when they are handled gently, yet become surprisingly solid when they are struck, squeezed or moved rapidly. A simple mixture of cornflour and water can flow through your fingers one moment and resist a sharp impact the next.

It raises a fascinating question:

How can the same material behave like a liquid and a solid without changing temperature or chemical composition?

The answer introduces us to the strange world of non-Newtonian fluids.

A Liquid That Does Not Follow the Normal Rules

Water, cooking oil and many other familiar liquids are described as Newtonian fluids.

In a Newtonian fluid, the viscosity remains approximately constant at a particular temperature.

Viscosity is a measure of how strongly a fluid resists flowing. Water has a relatively low viscosity, so it flows easily. Glycerol and golden syrup have much higher viscosities, so they flow much more slowly.

However, although glycerol is considerably more viscous than water, its viscosity does not suddenly change simply because we stir it faster or apply a greater force.

Cornflour mixed with water behaves differently.

When it is moved slowly, it flows. When it experiences a sudden force, it becomes much more resistant to movement. Its apparent viscosity increases.

This makes it a non-Newtonian fluid.

More precisely, a cornflour-and-water mixture is an example of a shear-thickening suspension. The faster we try to deform it, the more strongly it resists.

What Is Actually Inside the Mixture?

Cornflour does not dissolve in water in the same way that sugar or salt does. Instead, tiny solid particles remain suspended throughout the liquid.

When the mixture is handled gently, the particles have time to move around one another. Water acts as a lubricant between them, allowing the mixture to flow.

A sudden impact changes the situation.

The particles are forced together so quickly that they cannot rearrange themselves easily. They form temporary networks and become jammed against one another. The mixture then strongly resists further movement.

It can feel solid, but it has not undergone a permanent change of state. The effect only continues while the force is being applied.

Release the pressure, and the particles can begin moving again. The material returns to its flowing, liquid-like behaviour.

This is why a ball made from cornflour mixture appears solid while it is being squeezed but collapses into a puddle as soon as it is left alone.

Making a Non-Newtonian Fluid

The experiment is remarkably simple.

You will need:

Cornflour

Water

A large bowl or tray

A spoon

Food colouring, if required

Begin with approximately two parts cornflour to one part water. Add the water gradually because different brands of cornflour may require slightly different quantities.

Mix slowly until the material flows when gently tilted but strongly resists rapid stirring.

The mixture should not be watery. If it splashes easily, add more cornflour. If it remains dry and crumbly, add a small amount of water.

Once the consistency is correct, the investigation can begin.

Demonstration One: Slow Finger, Fast Finger

Place a finger gently onto the surface of the mixture and push down slowly.

Your finger should gradually sink into it.

Remove your finger and then strike the surface quickly with the flat of your hand or tap it sharply with one finger. The surface suddenly feels firm.

The mixture has not had time to flow away from the force. Its particles have become temporarily jammed together.

This is one of the clearest demonstrations because the only variable being changed is the rate at which the force is applied.

The hand is the same. The mixture is the same. The temperature is the same.

Only the speed of the movement has changed.

Yet the behaviour of the material is completely different.

Demonstration Two: Make a Temporary Solid Ball

Pick up some of the mixture and roll it rapidly between your hands.

While you continue applying pressure, it can be shaped into a surprisingly firm ball.

Now stop rolling and open your hands.

The ball immediately loses its shape and flows between your fingers.

Students often find this especially memorable because they can feel the transformation. It is not simply something they are being told about or shown on a diagram.

They experience the change directly.

The material has not chemically reacted, frozen or dried. It appears solid only because continuous force keeps the particles jammed together.

Demonstration Three: Can You Pull Your Hand Out?

Place your fingers into a deeper container of the mixture and try to remove them quickly.

The mixture grips surprisingly firmly.

Now relax and withdraw your fingers slowly. They come out much more easily.

This helps explain why panicking and making rapid movements in mud or other dense suspensions can sometimes make movement more difficult. Slow, controlled movement gives particles and liquid time to rearrange.

However, it is important not to suggest that all mud and quicksand behave exactly like cornflour mixture. Non-Newtonian fluids form a broad family, and different materials respond to force in different ways.

Some become thicker when moved rapidly. Others become thinner.

Demonstration Four: Dancing Cornflour

One of the most spectacular demonstrations involves placing the mixture above a loudspeaker.

The loudspeaker must first be protected with a secure waterproof membrane or covered tray. The mixture should never be poured directly onto the speaker cone.

When a low-frequency sound is played, the speaker vibrates rapidly. These vibrations continually accelerate and compress parts of the mixture.

At suitable frequencies and amplitudes, strange moving columns, folds and finger-like shapes can appear. The material seems to crawl or dance across the surface.

The sound waves are supplying repeated forces. Where the force is greatest, the mixture temporarily stiffens. As the force changes, it begins to flow again.

The resulting patterns can look almost alive.

This demonstration links several areas of science:

sound waves;

frequency;

vibration;

forces;

particle behaviour;

energy transfer;

properties of materials.

It is a particularly good example of how topics normally taught separately are actually connected.

Comparing Different Fluids

A useful investigation is to compare cornflour mixture with water, cooking oil and glycerol.

Pour equal amounts into separate transparent containers and observe how they behave when tilted, stirred or allowed to flow down a ramp.

Water flows quickly because it has a low viscosity.

Cooking oil usually flows more slowly.

Glycerol flows much more slowly because it has a higher viscosity.

However, these liquids do not suddenly become solid when struck. Their viscosities remain relatively predictable under normal classroom conditions.

The cornflour mixture is different because its resistance depends strongly on how rapidly the force is applied.

Students could investigate:

how long each fluid takes to travel down a ramp;

how quickly a ball bearing falls through each fluid;

how stirring speed affects resistance;

how changing the cornflour-to-water ratio affects behaviour;

whether temperature changes the results.

This turns a dramatic demonstration into a genuine scientific investigation involving variables, measurements and evidence.

Not All Non-Newtonian Fluids Become Thicker

The term “non-Newtonian” does not simply mean “a liquid that becomes solid when struck”.

It refers to any fluid whose viscosity does not remain constant under different flow conditions.

Cornflour and water are shear-thickening: they become more resistant when moved rapidly.

Other materials are shear-thinning. Their apparent viscosity decreases when they are stirred, spread or squeezed.

Paint is a familiar example. It needs to be thick enough not to run down the wall after application, but it must also spread easily under a brush or roller.

Tomato ketchup can also become easier to pour after it has been shaken. Toothpaste flows when squeezed but remains on the toothbrush when the pressure is removed.

Some materials require a minimum force before they begin to flow at all. This is why toothpaste can stay inside an open tube until it is squeezed.

The behaviour of non-Newtonian fluids is therefore much broader than the cornflour experiment suggests.

Why Does This Matter Outside the Classroom?

Non-Newtonian fluids are not simply scientific curiosities. Their behaviour is important in engineering, medicine, manufacturing, geology and product design.

Impact-Resistant Materials

Shear-thickening fluids have been investigated for use in protective equipment.

A flexible material is usually more comfortable to wear than a rigid plate. However, a material that temporarily stiffens during an impact could combine flexibility with additional protection.

Researchers have therefore studied fabrics containing shear-thickening fluids for possible use in protective clothing, sports equipment and body-armour systems.

The principle is similar to the cornflour experiment: flexible during ordinary movement, but much more resistant during a sudden impact.

Paints and Printing Inks

Paint needs carefully controlled flow properties.

It must move easily under a brush, roller or spray nozzle, but it should resist dripping once it reaches the wall.

Printing inks must also flow through machinery in a controlled way and then remain in position on the paper or packaging.

Understanding non-Newtonian behaviour allows manufacturers to design products that are easy to apply but remain stable afterwards.

Food Manufacturing

Many foods are non-Newtonian.

Yoghurt, sauces, chocolate, mayonnaise, cream, dough and ketchup all have complicated flow properties.

Manufacturers need to know how these materials will behave while being mixed, pumped, poured, transported and packaged.

A sauce may need to move easily through a factory pipe but remain thick enough to stay on the food when served.

Cosmetics

Shampoo, moisturiser, toothpaste, foundation and other cosmetics need very specific textures.

A cream should spread smoothly across the skin but should not run out of its container. Toothpaste should flow when squeezed but hold its shape on the toothbrush.

These properties are created by controlling the material’s non-Newtonian behaviour.

Geology and Natural Flows

Mud, wet sediment, lava and debris flows can behave in complex ways.

Their movement depends on particle size, water content, pressure, temperature and the forces acting on them.

Understanding these flows is important when studying landslides, volcanic eruptions, river sediment and unstable ground.

However, geological materials do not all behave like cornflour. Some become easier to move once they start flowing, while others can stiffen or jam under particular conditions.

Blood and Biological Fluids

Blood is also non-Newtonian.

It is not simply water with red colouring. It contains cells, proteins and many dissolved substances. Its apparent viscosity changes depending on the size of the blood vessel and the rate of flow.

This has important consequences for circulation and for the design of medical equipment such as pumps, artificial heart valves and blood-flow monitoring systems.

The mucus found in the respiratory and digestive systems also has specialised flow properties. It must be able to move while remaining thick enough to trap particles and protect delicate tissues.

What Looks Like a Simple Mess Is Actually Serious Science

Cornflour and water can easily be dismissed as a messy classroom activity.

In reality, it introduces some profound scientific ideas.

It shows that matter cannot always be placed into simple categories. It demonstrates that the properties of a material may depend not only on what it is made from, but also on how forces are applied to it.

It also encourages students to question the language they use.

Is the mixture really becoming a solid?

Not quite.

It is behaving like a solid for a short period because its internal particles have become jammed together. Once the force disappears, the structure breaks down and the material flows again.

That distinction is important. Scientific explanations should describe what is happening rather than merely repeat what something looks like.

Learning Through Touch, Movement and Surprise

In my experience, students remember science particularly well when an experiment challenges something they thought they already understood.

Most students believe they know the difference between a liquid and a solid. They have used both since early childhood.

Then they meet a substance that refuses to fit neatly into either category.

They press it gently and their finger sinks.

They strike it and it feels hard.

They squeeze it into a ball and then watch it melt through their hands without any change in temperature.

That moment of surprise creates curiosity. Curiosity creates questions, and those questions provide an opportunity for deeper scientific thinking.

At Philip M Russell Ltd, practical demonstrations are not treated as decorations added to a lesson. They are used to create the experience that the explanation must account for.

The student sees something unexpected, proposes an idea, tests it and then improves the explanation.

That is much closer to the way science actually works than simply copying a definition from a worksheet.

Practical Safety and Clearing Up

Cornflour mixture is generally straightforward to handle, but sensible precautions are still needed.

Use a tray to contain spills and protect nearby electrical equipment.

Do not pour large quantities down a sink. The particles can settle and contribute to blockages. Allow the mixture to dry before placing it in household waste, or scrape it into a suitable container for disposal.

If food colouring is used, remember that it may stain clothing and surfaces.

For the loudspeaker demonstration, keep the mixture completely separated from the electrical components by using a strong waterproof membrane or shallow sealed tray. Begin with a low volume and increase it gradually.

The Strangeness Is the Point

Non-Newtonian fluids show us that scientific categories are models rather than unbreakable rules.

Water behaves in a familiar and predictable way, so it is tempting to assume that every liquid must behave similarly.

Cornflour and water demonstrate that this is not true.

A material can flow gently through our fingers, resist a sudden blow and then collapse back into a puddle. Its behaviour depends on the forces acting upon its microscopic particles.

The experiment is inexpensive, memorable and easy to perform, but the ideas behind it connect to advanced materials, medicine, food production, cosmetics, engineering and geology.

The next time someone asks whether cornflour mixture is a liquid or a solid, perhaps the best scientific answer is:

It depends on what you do to it.

That may sound like an evasive answer, but it captures an important truth about science.

The natural world is often far more interesting than the simple categories we first use to describe it.

15 July 2026

Dividing a Line in a Ratio: When Common Sense Works Better Than a Formula

 


Dividing a Line in a Ratio: When Common Sense Works Better Than a Formula

Some mathematical problems look complicated because students are introduced to the formula before they have understood the idea.

Dividing a line in a given ratio is a good example.

Recently, some of my GCSE Further Mathematics students were faced with a coordinate geometry question in which they had to find the point that divided a line in a particular ratio. They knew that there was a formula somewhere in their notes, but they could not remember exactly how it worked.

Which coordinates had to be multiplied by which number?

Did the larger part of the ratio go with the first point or the second point?

Should they add the coordinates before dividing?

The formula had become another piece of information to memorise rather than a useful mathematical tool.

The problem initially stumped them.

However, when we ignored the formula and looked at what the question was actually asking, the solution became surprisingly simple.

What Does It Mean to Divide a Line in a Ratio?

Suppose a point P lies somewhere on the straight line between points A and B.

We are told that:

AP : PB = 2 : 3

This means that the whole line has been divided into five equal parts:

2 + 3 = 5

The distance from A to P represents two of those parts, while the distance from P to B represents the remaining three parts.

Therefore, starting at A, point P must be two-fifths of the way towards B.

That is the key idea.

We do not initially need a special formula. We simply need to:

  1. Find the change from A to B.
  2. Divide that change into the required number of parts.
  3. Move the correct number of parts from the starting point.

This is very similar to following directions on a map.

A Simple Coordinate Example

Suppose:

A = (2, 3)

B = (12, 8)

Point P divides the line AB in the ratio:

AP : PB = 2 : 3

We can solve this using common sense.

Step 1: Find the total number of parts

2 + 3 = 5

The complete journey from A to B has been divided into five equal parts.

Step 2: Find the horizontal change

The x-coordinate changes from 2 to 12.

Horizontal change:

12 − 2 = 10

Divide this change into five equal parts:

10 ÷ 5 = 2

Each ratio part represents a horizontal movement of 2.

To travel two parts from A:

2 × 2 = 4

Starting from the x-coordinate of A:

2 + 4 = 6

Therefore, the x-coordinate of P is 6.

Step 3: Find the vertical change

The y-coordinate changes from 3 to 8.

Vertical change:

8 − 3 = 5

Divide this into five equal parts:

5 ÷ 5 = 1

Each ratio part represents a vertical movement of 1.

To travel two parts from A:

2 × 1 = 2

Starting from the y-coordinate of A:

3 + 2 = 5

Therefore:

P = (6, 5)

No mysterious formula was required. We simply moved two-fifths of the way from A to B.

Seeing the Movement as a Vector

There is another way of presenting exactly the same reasoning.

The movement from A to B is:

(12 − 2, 8 − 3)

= (10, 5)

Point P is two-fifths of the way along this movement.

Therefore:

²⁄₅ × (10, 5) = (4, 2)

Now add this movement to point A:

(2, 3) + (4, 2) = (6, 5)

Again:

P = (6, 5)

This method is particularly useful because it links coordinate geometry with vectors. It helps students see that coordinates are not merely numbers written in brackets. They describe position and movement.

Why the Ratio Order Matters

One common mistake is to see the ratio 2 : 3 and automatically use three-fifths.

The wording must be read carefully:

AP : PB = 2 : 3

The first part, AP, tells us how far we move from A to reach P.

Since AP represents two of the five parts, we move two-fifths of the way from A towards B.

If the ratio were reversed:

AP : PB = 3 : 2

then P would be three-fifths of the way from A to B.

It would therefore be closer to B.

A quick sketch is often enough to prevent this mistake.

A —— —— P —— —— —— B

Here, there are two equal sections between A and P and three between P and B.

The diagram does not need to be accurate. Its purpose is to make the relationship clear.

What Happens When the Coordinates Decrease?

Students sometimes think that the method only works when the coordinates increase.

Consider:

A = (10, 12)

B = (2, 4)

Suppose P divides AB in the ratio:

AP : PB = 3 : 1

There are four parts altogether, and P is three-quarters of the way from A to B.

The change from A to B is:

(2 − 10, 4 − 12)

= (−8, −8)

Three-quarters of this movement is:

¾ × (−8, −8)

= (−6, −6)

Add this to A:

(10, 12) + (−6, −6)

= (4, 6)

Therefore:

P = (4, 6)

The negative values simply tell us that we are moving left and down.

The reasoning remains exactly the same.

A Practical Way to Think About It

Imagine travelling from one town to another.

Town A is 50 kilometres from Town B. A service station divides the journey in the ratio 2 : 3.

The total journey contains five equal parts:

50 ÷ 5 = 10 kilometres per part

The service station is two parts from Town A:

2 × 10 = 20 kilometres

The remaining distance is:

3 × 10 = 30 kilometres

Coordinate geometry uses the same idea, except that we must divide both the horizontal and vertical movements.

This is why practical comparisons can be so useful. They turn an abstract-looking calculation into something familiar.

Why Starting With the Formula Can Cause Problems

The section formula is often written in a form similar to:

P = ((nx₁ + mx₂) ÷ (m + n), (ny₁ + my₂) ÷ (m + n))

where:

AP : PB = m : n

The formula is correct, but it can cause difficulties.

The ratio numbers appear to be attached to the “opposite” coordinates. Students may remember the general shape of the formula but apply the numbers the wrong way around.

They may also complete the calculation successfully without understanding where the point should lie.

A student might obtain an answer outside the line segment and fail to notice that something has gone wrong.

The common-sense method provides a built-in check.

If AP : PB = 2 : 3, then P should:

  • lie between A and B;
  • be closer to A than to B;
  • be two-fifths of the way from A to B.

If the calculated point does not satisfy those conditions, the calculation needs to be reconsidered.

The Formula Should Come From the Reasoning

Once the idea is understood, the formula becomes much easier to explain.

Suppose:

A = (x₁, y₁)

B = (x₂, y₂)

and:

AP : PB = m : n

The total number of parts is:

m + n

Point P is m⁄(m + n) of the way from A to B.

The change from A to B is:

(x₂ − x₁, y₂ − y₁)

Therefore:

P = (x₁, y₁) + m⁄(m + n)(x₂ − x₁, y₂ − y₁)

This is not a separate trick. It is simply the common-sense method written algebraically.

The usual section formula can then be produced by expanding and simplifying this expression.

The formula now has meaning because it has been built from an idea the students already understand.

A Reliable Method for Students

For any question involving the division of a line in a ratio, students can use the following approach.

1. Draw a simple sketch

Mark the two endpoints and show which part of the ratio belongs to each section.

2. Add the ratio numbers

For a ratio of 2 : 3, there are five parts altogether.

3. Decide how far to move

If AP : PB = 2 : 3, move two-fifths of the way from A towards B.

4. Find the change in each coordinate

Calculate:

x₂ − x₁

and:

y₂ − y₁

5. Take the required fraction of each change

For two-fifths of the journey, multiply both changes by ²⁄₅.

6. Add the movement to the starting point

This gives the coordinates of the required point.

7. Check that the answer is sensible

The point should lie between the two endpoints and in the correct relative position.

Why This Matters Beyond One GCSE Question

This small problem illustrates a much wider lesson about mathematics.

Students are often tempted to search immediately for a formula. They ask:

“What equation do I use?”

A more valuable first question is:

“What is actually happening?”

Dividing a line in a ratio connects several important mathematical ideas:

  • fractions;
  • proportion;
  • coordinates;
  • gradients;
  • vectors;
  • interpolation;
  • transformations;
  • movement between points.

It also appears in practical applications such as computer graphics, animation, engineering design, mapping and game development.

For example, a computer game may need to place an object 30% of the way between two positions. An animation may need to calculate an intermediate frame between a starting point and a finishing point. A designer may need to position a support at a particular proportion along a beam.

All these problems use the same underlying principle.

My Reflection as a Teacher

What struck me about this lesson was not that the students lacked the ability to complete the calculation.

They were perfectly capable of working with fractions, coordinates and vectors.

The difficulty was that the problem had been presented as a formula to remember rather than a situation to understand.

Once we stopped searching for the formula and drew a simple line divided into equal parts, the atmosphere changed. The students could see where the point had to be. The arithmetic then became straightforward.

This is something I see repeatedly in mathematics teaching.

A formula can make a solution shorter, but introducing it too early can make the idea harder.

Understanding should come first. The formula should then summarise the understanding.

Conclusion: Draw the Line Before Reaching for the Formula

Dividing a line in a ratio may initially look like a specialised coordinate geometry problem.

In reality, it is simply a journey divided into equal parts.

Find the complete movement.

Divide it into the total number of ratio parts.

Move the required number of parts from the starting point.

Once students see this, the method becomes logical rather than mysterious.

The most useful lesson was not merely how to divide a line in a ratio. It was that when a mathematical formula feels confusing, it is often worth stepping back, drawing a picture and applying some common sense.

Sometimes the simplest route through a Further Mathematics problem is to stop looking for the formula and work out what the numbers actually mean.

#GCSEMaths #FurtherMaths #CoordinateGeometry #MathsTeaching #MathsTutor #MathematicalThinking #Vectors #ProblemSolving #STEMEducation #HemelPrivateTuition

Building an A Level Platform Game Project — Part 3: Adding Gravity and Jumping

    Building an A Level Platform Game Project — Part 3: Adding Gravity and Jumping In Part 1, we planned the platform game and set realistic...