3rd Grade algebra · Ages 8–9
Letters Are Boxes
The first letter shows up in a maths problem this year. It is not scary — it is a box with a name on it.
The one idea
A letter like n is a box with a name on it. It stands for a number we haven’t found yet.
Ready?
3rd Grade algebra · Letters Are Boxes
The first letter shows up in a maths problem this year. It is not scary — it is a box with a name on it.
Full screen — no distractions
For grown-ups: 3rd Grade algebra
Children often freeze the first time they see a letter in maths. Tell them the truth: it is exactly the same as the empty box they have used for years. This year also brings multiplication, so the hidden number can now be a missing factor.
This page is the right one if they can already…
- Finds a missing number in a + or − equation
- Knows what a number machine is
- Understands multiplication as equal groups
Not yet? Start at 2nd Grade: Number Machines — algebra only works one rung at a time.
🏠 Try it at home
Swap the box for a letter
Write puzzles on sticky notes using your initials as the unknown: T + 3 = 8. Let them make one for you.
The missing factor
Deal 20 cards into 4 piles, one at a time like a card dealer. How many in each pile? You just solved 4 × n = 20.
Multiplication machines
Wheels: 1 car has 4 wheels, 2 cars have 8. How many for 5 cars? How many cars have 28 wheels?
Turn a story into a number sentence
Make up a story from your day for them to turn into n + __ = __. Then they make one for you.
The words, in plain English
- Unknown
- The number we need to find.
- In n + 6 = 10, n is the unknown.
- Variable
- A letter standing for a number.
- n, x, or any letter.
- Factor
- A number you multiply.
- 4 and 5 are factors of 20.
- Equation
- A number sentence with an = sign.
- 4 × n = 20
- Inverse
- The opposite operation that undoes it.
- ÷ is the inverse of ×.
🌍 Algebra in an ordinary day
- “Tickets are $4 each and we paid $20. How many tickets?”
- Sharing a bag of 24 sweets between 3 friends
- A recipe for 2 people that needs doubling
🏁 By the end of 3rd Grade
- Uses a letter for an unknown without fuss
- Solves missing-factor equations like 4 × n = 20
- Finds × and ÷ rules from tables
- Writes a word story as an equation and solves it
Where this fits
One idea, twelve rungs. The hiding spot just gets cleverer.
Frequently Asked Questions
What algebra should a 3rd Grade child learn?
A letter like n is a box with a name on it. It stands for a number we haven’t found yet. By the end of the year they should be able to: uses a letter for an unknown without fuss; solves missing-factor equations like 4 × n = 20; finds × and ÷ rules from tables; writes a word story as an equation and solves it.
Isn’t 3rd Grade 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 n — something a child can point at. There are no letters until this year, and the ideas match what 3rd grade maths already covers.
What is the most common 3rd Grade algebra mistake?
Writes 80. They see a × sign and multiply the numbers they can see. The fix: Put it back in: is 4 × 80 equal to 20? Way too big. The groups must be smaller than the total.
What if my child is stuck?
Go down one rung. Every lesson here builds on the 2nd Grade page, and the “ready for this page if” list at the top tells you exactly what they need first. In practice, a wrong answer gives a hint, and a second wrong answer shows the full worked solution.
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.