Protons & Anti-Protons
Years 4 - 10


  • About thirty (30) identical small objects in each of two (2) colours. Discs from a game like Connect Four are perfect.
  • If you can't find any counters, print this Protons & Anti-Protons collection and follow the cutting instructions.
  • Print this Playing Board.
  • Write the title of this challenge and today's date on a fresh page in your maths journal.

Getting Started

Protons and Anti-Protons are real.
Scientists know that when equal numbers of Protons and Anti-Protons meet they destroy each other.
Zero remains where the meeting used to be.

Here is an example of a meeting:

  • Make it with your objects.
  • Work out the total value of the collection.
  • Copy the meeting into your journal and explain your answer.
Have fun exploring Protons & Anti-Protons.
The answer to the picture above is explained in the Answers section below.
Don't look until you have tried to work it out.

Make a collection of about twelve (12) Protons on one side of your work table and about twelve (12) Anti-Protons on the other side.
Clear a space between them to make collections.

  • Close your eyes. Drag some from the Protons pile and some from the Anti-Protons pile into the meeting place.
  • Make zeros and push them to the top of your table.
  • Calculate the value of the collection.
  • Record in your journal. You can use pictures, equations or both.
Do this activity five (5) times.

Digging Deeper

Protons & Anti-Protons on the table

  • Chin made a meeting and wrote it in her journal like this: 5A + 3P = 2A
  • Draw Chin's collection and explain her answer.
Here are Chin's other four (4) meetings.

13A + 7P ... A + 4P ... 3A + 3P ... 4A + 9P

Draw them and calculate her answers.

One of Chin's collections totals zero.
  • Draw or write three (3) more collections of Protons and Anti-Protons that total zero.
  • Write a sentence explaining how many ways there are of making a zero total.

Protons & Anti-Protons on a chart

  • Open this Protons & Anti-Protons Starter. You can read it on screen or print it.
  • You will also need the Playing Board you printed before.
  • Follow the instructions on the card.
  • It also tells you how you to check your answers when you have finished.

Working Backwards

  • Any collection with the same number of Protons and Anti-Protons equals zero.
  • Sometimes you might need to add in a collection worth zero to help work something out.
  • Just choose the collection you need.

Make this table in your journal.
In each column do a drawing of the collection and write an equation.

3P + 2P



3P + 2A 3P - 2P 3P - 2A

  • Hint: The last column is not so easy. Can you make it work if you add in a collection worth zero?
  • Answer: Look at the bottom of this page after you try to figure it out for yourself.
Try these four:
3A + 2A    ...    3A + 2P    ...    3A - 2A    ...    3A - 2P

More Practice

  • Choose your own starting number of Ps or As.
  • Make up and solve four questions like the ones you just did.
Akbar chose to start with 5P. Then he wrote:
5P + 7P =
5P + 7A =
5P - 7P =
5P - 7A =
What were Akbar's answers?

Now do five sets like this. Use your objects to check your work.

Try a long one
Mathematicians often have to check their own work by doing the same problem two ways.
If they get the same answer two (2) different ways they are probably right.
Try to work this out in two different ways:

  • 2A + 2P - 3P + 7P - 5A - 7P + P + 6A = ...
Two strategies are listed in the Answer section below.
After you try to find your own ways, you can have a look.
  • Make up a really long one of your own and work it out two ways

One More Thing

One more thing scientists know about Protons and Anti-Protons is that they have equal, but opposite electric charges.
Each Proton is one positive charge and each Anti-Proton is one negative charge.
  • Chin wrote 5A + 3P = 2A.
  • She could also write this as   -5 + +3 = -2
  • Which means 5 negative charges plus 3 positive charges = 2 negative charges
Go back to Akbar's answers.
Write each of them again with their answers, but use positive and negative charges instead of protons and anti-protons.

Just Before You Finish

  • In your journal, finish this paragraph:
    This is what I have learnt by investigating Protons and Anti-Protons...
  • Draw a cartoon of your face that shows how you feel about your learning. Add a speech bubble if you wish.


Answers & Discussion

These notes were originally written for teachers.
We have included them to support parents to help their child learn from Protons & Anti-Protons.
The answer to the first meeting above is shown in this picture. ----->


Below is how you can add in zero to work out

      3P - 2A

Strategies for long ones

  1. Do them in the order they are written. Start with the first two then continue the calculation one term at a time.
  2. Rewrite the equation with all the additions first, then all the subtractions. Do all the additions in order, then take away from that answer one at a time.
The answer to the one in the activity is 3A.

Send any comments or photos about this activity
and we can start a gallery here.


Maths At Home is a division of Mathematics Centre