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4th Grade algebra · Ages 9–10

Number Recipes

An expression is a recipe for a number. This year children learn to read recipes, follow them, and get them in the right order.

nthe unknown

The one idea

An expression is a recipe: it tells you what to do to a number, and in what order.

The order of operations is not a random rule to memorise — it is how mathematicians agreed to read a recipe so everyone gets the same answer. Keep connecting n back to the box: “3n + 2 when n is 6” just means “put 6 in the box and follow the recipe”.

📚 The 4 lessons⚖️ Balance scale✏️ Practice

This page is the right one if they can already…

  • Knows the times tables to 10 × 10
  • Solves 4 × n = 20
  • Finds the rule in a number machine

Not yet? Start at 3rd Grade: Letters Are Boxes — algebra only works one rung at a time.

The four 4th Grade algebra lessons

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

1

Recipe words to symbols

Maths words translate into symbols. “More than” is +, “times” is ×, “shared by” is ÷.

In wordsIn symbols
5 more than nn + 5
3 times n3 × n
n shared by 2n ÷ 2
4 less than n?

Worked example

Write “4 less than n” as an expression.

  1. 1

    Start with n — that is the number we are changing.

    n

  2. 2

    “Less than” means take away.

    n − 4

  3. 3

    Test it with a number, say n = 10.

    10 − 4 = 6, which is 4 less than 10 ✓

Answer: n − 4

Check: Not 4 − n: that would be 4 − 10, which is not “4 less than 10”.

⚠️ The usual mistake

Writes 4 − n.

The words say “4” first, so they write 4 first.

Fix: Always test an expression with a real number. If n is 10, “4 less than n” must be 6.

💬 Say this

“What are we starting with? What’s happening to it?”

🏠 Try it at home

Say “3 more than your age”, “twice your age”, “half your age” — they write each as a recipe and work it out.

2

Follow the recipe

To evaluate an expression, put the number in for the letter, then do the maths.

Worked example

Find 3 × n + 2 when n = 6.

  1. 1

    Swap n for 6.

    3 × 6 + 2

  2. 2

    Multiplication first.

    18 + 2

  3. 3

    Then add.

    20

Answer: 20

Check: Recipe: triple it, then add 2. Triple 6 is 18, add 2 is 20 ✓

⚠️ The usual mistake

Gets 24.

They add first: 6 + 2 = 8, then 3 × 8.

Fix: Multiplication and division come before + and −. Circle the × part and do it first.

💬 Say this

“Put the number in the box first. Then — what does the recipe say to do first?”

🏠 Try it at home

Use cups: “2 cups for each person, plus 1 extra.” How many cups for 4 people? For 7?

3

Brackets go first

Brackets say “do me first”. Without them, × and ÷ go before + and −.

ExpressionValue
2 + 3 × 414
(2 + 3) × 420
10 − 6 ÷ 27
(10 − 6) ÷ 2?

Worked example

(n + 4) × 3 when n = 5

  1. 1

    Swap n for 5.

    (5 + 4) × 3

  2. 2

    Brackets first.

    9 × 3

  3. 3

    Then multiply.

    27

Answer: 27

Check: Without brackets, 5 + 4 × 3 would be 17 — a different recipe.

⚠️ The usual mistake

Works left to right and gets 20 for 2 + 3 × 4.

Reading left to right is what they do with words.

Fix: Think of it as a recipe card: the brackets are a step you must finish before starting the rest.

💬 Say this

“Is there anything in brackets? That goes first. Then × and ÷, then + and −.”

🏠 Try it at home

Give them 2 + 3 × 4 and let them argue for 20. Then show them a calculator says 14. Why?

4

Two-step rules

Some machines do two things. Find both steps and you can predict any output — even the 100th.

nOut
13
25
37
10?

Worked example

1 → 3, 2 → 5, 3 → 7. What does 10 make?

  1. 1

    The outputs go up by 2 each time. That suggests × 2.

    1 × 2 = 2, but we need 3

  2. 2

    What else is needed to get from 2 to 3?

    + 1

  3. 3

    Test the rule n × 2 + 1 on every row.

    2 × 2 + 1 = 5 ✓ 3 × 2 + 1 = 7 ✓

Answer: 10 × 2 + 1 = 21

Check: The rule works for every row, so it is safe to use on 10.

⚠️ The usual mistake

Says 10 makes 9 by counting on in twos from 7 (7, 9…).

Counting on works for the next row only. It does not jump to row 10.

Fix: A rule turns any input into its output. Find the rule, then you can skip straight to n = 10 or n = 100.

💬 Say this

“How much does it go up by? Now what extra bit is needed?”

🏠 Try it at home

Build squares from matchsticks in a row: 1 square uses 4, 2 squares use 7, 3 use 10. How many for 10 squares?

⚖️ Keep it fair

Get n on its own using only fair moves. This is exactly how equations are solved at every grade, right up to Grade 10. Try the wrong button too — see what happens.

Puzzle: n + 2 = 5

n

n + 2 = 5

✏️ Practice that never runs out

Every question is new. A wrong answer gets a hint; a second one shows the worked solution, so no one stays stuck.

Follow the recipe

Put the number in for n. Brackets first, then × and ÷, then + and −.

Work it out when n = 1.

7 × n + 4

Find n

Keep the times tables sharp: find the hidden factor.

Find n.

n × 6 = 42

The words, in plain English

Expression
A maths recipe with no = sign.
3n + 2
Evaluate
Put a number in and work it out.
3n + 2 when n = 6 is 20.
Order of operations
The agreed order: brackets, × and ÷, then + and −.
2 + 3 × 4 = 14
Brackets
A part you must do first.
(2 + 3) × 4 = 20
3n
Short for 3 × n.
If n = 5, 3n = 15.

🌍 Algebra in an ordinary day

  • A taxi ride: $3 to get in, plus $2 for every mile
  • Party bags: 3 sweets each for n friends, plus 5 spare
  • Sticker charts that give 2 stars a day plus a bonus star

🏁 By the end of 4th Grade

  • Writes word phrases as expressions, testing with a real number
  • Evaluates expressions like 3n + 2
  • Uses brackets and the order of operations correctly
  • Finds two-step rules and uses them to jump ahead

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 down

3rd Grade: Letters Are Boxes

One rung up →

5th Grade: Undo It

All 12 gradesMore maths, grade by grade →

Frequently Asked Questions

What algebra should a 4th Grade child learn?

An expression is a recipe: it tells you what to do to a number, and in what order. By the end of the year they should be able to: writes word phrases as expressions, testing with a real number; evaluates expressions like 3n + 2; uses brackets and the order of operations correctly; finds two-step rules and uses them to jump ahead.

Isn’t 4th Grade too early for algebra?

No — number recipes is standard 4th Grade maths in most curricula. This page breaks it into single moves so it never feels like a jump.

What is the most common 4th Grade algebra mistake?

Gets 24. They add first: 6 + 2 = 8, then 3 × 8. The fix: Multiplication and division come before + and −. Circle the × part and do it first.

What if my child is stuck?

Go down one rung. Every lesson here builds on the 3rd 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.

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