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Pre-Kindergarten algebra · Ages 3–4

The Hiding Game

Algebra starts long before numbers — with a toy under a cup and a pattern that clap-clap-claps.

❓the unknown

The one idea

Something can be hiding, and we can work out what it is by looking at what is around it.

Nothing here needs reading, writing or counting past five. Everything is said out loud and pointed at. The lessons below are written for you; the practice is pictures your child taps.

📚 The 4 lessons✏️ Practice

This page is the right one if they can already…

  • Can point to the same picture twice in a row
  • Can say “more” and “the same” about two small piles
  • Enjoys peekaboo and hiding games

The four Pre-Kindergarten algebra lessons

In order — each one leans on the last. Every example is broken into single moves and ends by checking itself.

1

What comes next?

Patterns repeat. If you know the beat, you can say what is hiding at the end.

Worked example

🍎 🍌 🍎 🍌 🍎 ❓

  1. 1

    Point at each one and say it out loud.

    apple, banana, apple, banana, apple…

  2. 2

    Say it again like a song and listen for the beat.

    apple-banana, apple-banana, apple-…

  3. 3

    Let the song finish itself.

    banana!

Answer: 🍌

Check: Sing the whole row with the banana in it — it sounds right all the way through.

⚠️ The usual mistake

Picks their favourite fruit instead of the next one.

At three, “what comes next?” sounds a lot like “what do you want?”.

Fix: Clap and chant the row first. The rhythm gives the answer away before they have time to choose a favourite.

💬 Say this

“Let’s sing the row. Apple, banana, apple, banana, apple… what does the song say next?”

🏠 Try it at home

Line up spoon, fork, spoon, fork on the table. Stop, hand them both, and let them put the next one down.

2

The same, or not the same?

“The same” means both sides have just as many. That is what the = sign will mean for the rest of their life.

🧸🧸
🧸🧸

Worked example

One plate has 🍪🍪. The other has 🍪🍪. Is that fair?

  1. 1

    Touch one cookie on each plate at the same time.

    one here, one here

  2. 2

    Touch the next pair.

    one here, one here

  3. 3

    Nothing is left over on either plate.

    same!

Answer: Yes — the same.

Check: Swap the plates round. Still the same — swapping does not change how many.

⚠️ The usual mistake

Says the plate with the cookies spread out has “more”.

Young children judge amount by how much space things take up, not by how many there are.

Fix: Match them up one to one with a finger on each. If every cookie has a partner, it is the same.

💬 Say this

“Does every cookie have a friend on the other plate? Then it’s the same — it’s fair.”

🏠 Try it at home

At snack time, give two plates. Put pieces on one and ask them to make the other plate “the same”.

3

What’s under the cup?

If you know what was there before, you can work out what is hiding now.

Worked example

There were 🚗 🦆 ⭐. Now there is 🚗 ❓ ⭐.

  1. 1

    Name the ones you can still see.

    car… star…

  2. 2

    Remember the three from before.

    car, duck, star

  3. 3

    Which one did we not say?

    duck!

Answer: 🦆

Check: Lift the cup. There’s the duck.

⚠️ The usual mistake

Guesses something that was never there — “a dinosaur!”.

Guessing is fun, and they have not yet linked the hidden thing to what they saw before.

Fix: Start with two toys, not three, and name them both out loud before you hide one.

💬 Say this

“We had car, duck, star. I can see car and star. Who’s hiding?”

🏠 Try it at home

Three toys, one tea towel. Hide one while they close their eyes. Then swap — they hide, you guess.

4

Make it fair

If one side has fewer, the hiding spot has to fill the gap.

❓

Worked example

This plate has 🍇🍇🍇. That plate has 🍇 and a cup. How many grapes are under the cup?

  1. 1

    Match grapes one to one.

    🍇—🍇

  2. 2

    Two grapes on the first plate have no partner.

    🍇 🍇 left over

  3. 3

    The cup must be hiding that many.

    two!

Answer: 2

Check: Lift the cup: 🍇🍇. Now every grape has a partner.

⚠️ The usual mistake

Says “three” — the number of grapes on the other plate.

They answer “how many on the big plate” instead of “how many are missing”.

Fix: Do it with real grapes. Let them add grapes to the short plate until it matches, then count what they added.

💬 Say this

“This plate needs to be the same as that one. How many more does it need?”

🏠 Try it at home

Two cups of blocks. Put 3 in one and 1 in the other. “Make them the same” — then count how many they added.

✏️ Practice that never runs out

Your child taps — no reading needed. Say the question out loud together.

What comes next?

Read nothing — just tap the picture that comes next. Say the row out loud together first.

🐸🐶🐸🐶🐸🐶❓

Make it fair

The gift box is hiding some dots. Tap how many it needs so both sides are the same.

🎁

The words, in plain English

Same
Just as many on both sides.
🍪🍪 and 🍪🍪 are the same.
More
One side has extra.
🍪🍪🍪 is more than 🍪.
Pattern
Something that repeats.
red, blue, red, blue…
Hiding
There, but we can’t see it yet.
The duck is under the cup.

🌍 Algebra in an ordinary day

  • Setting the table: one plate, one cup, one plate, one cup…
  • Sharing snack so both of you have the same
  • Spotting which toy is missing from the bath

🏁 By the end of Pre-Kindergarten

  • Copies and continues an AB pattern (red, blue, red, blue)
  • Says whether two small groups are the same
  • Works out which of three toys is hidden
  • Adds to a small group to make it match another

Where this fits

One idea, twelve rungs. The hiding spot just gets cleverer.

  1. Pre-K❓The Hiding Game
  2. K🎁Make It Fair
  3. 1□The Same As
  4. 2?Number Machines
  5. 3nLetters Are Boxes
  6. 4nNumber Recipes
  7. 5xUndo It
  8. 6xBalance and Tip
  9. 7xTwo Steps Back
  10. 8y = mx + bLines and Slope
  11. 9xAlgebra 1
  12. 10f(x)Curves and Functions

One rung up →

Kindergarten: Make It Fair

All 12 gradesMore maths, grade by grade →

Frequently Asked Questions

What algebra should a Pre-Kindergarten child learn?

Something can be hiding, and we can work out what it is by looking at what is around it. By the end of the year they should be able to: copies and continues an AB pattern (red, blue, red, blue); says whether two small groups are the same; works out which of three toys is hidden; adds to a small group to make it match another.

Isn’t Pre-Kindergarten too early for algebra?

Not the way it is taught here. Algebra is finding a number that is hiding, and at this age the hiding spot is ❓ — something a child can point at. There are no letters, and the ideas match what pre-kindergarten maths already covers.

What is the most common Pre-Kindergarten algebra mistake?

Says the plate with the cookies spread out has “more”. Young children judge amount by how much space things take up, not by how many there are. The fix: Match them up one to one with a finger on each. If every cookie has a partner, it is the same.

Does my child need to read?

No. The lessons are written for you to say out loud, and the practice is pictures and dots your child taps. Nothing needs reading, writing or typing.

Is it free?

Yes. All 4 lessons, the pictures, the worked examples, the balance scale and the practice questions are free with no signup. The practice never runs out — every question is generated fresh and checked.

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