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5th Grade algebra · Ages 10–11

Undo It

Grade 5 is where children learn the one move that solves almost everything: do the opposite, to both sides.

xthe unknown

The one idea

To find a hidden number, undo what was done to it — with the opposite operation, on both sides.

x is just this year’s name for the box. The new skill is solving x + 9 = 23 by undoing, rather than by guessing. Guessing works for small numbers and fails later, so praise the undoing even when guessing would have been faster.

📚 The 4 lessons⚖️ Balance scale✏️ Practice

This page is the right one if they can already…

  • Evaluates expressions like 3n + 2
  • Knows the order of operations
  • Knows multiplication and division facts to 10 × 10

Not yet? Start at 4th Grade: Number Recipes — algebra only works one rung at a time.

The four 5th Grade algebra lessons

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

1

Opposites undo each other

Adding and subtracting undo each other. So do multiplying and dividing. That pair is the key to every equation.

Worked example

Something went into a + 7 machine and 15 came out. What went in?

  1. 1

    Name the unknown.

    x + 7 = 15

  2. 2

    The opposite of + 7 is − 7.

    15 − 7

  3. 3

    Work it out.

    x = 8

Answer: x = 8

Check: 8 + 7 = 15 ✓

⚠️ The usual mistake

Thinks the opposite of × 3 is − 3.

They pair the operations by “the other one in the list” rather than by what undoes what.

Fix: Test it: 5 × 3 = 15, and 15 − 3 = 12, not 5. Only ÷ 3 gets you back to 5.

💬 Say this

“What was done to x? What undoes that?”

🏠 Try it at home

Put on socks, then shoes. To undo: shoes off first, then socks. Undoing goes in reverse — and uses the opposite move.

2

Solve one-step equations

Do the opposite operation to both sides. The x is left on its own, and the answer is on the other side.

xxxxxx
42

Worked example

6x = 42

  1. 1

    6x means 6 × x. What undoes × 6?

    ÷ 6

  2. 2

    Divide both sides by 6.

    6x ÷ 6 = 42 ÷ 6

  3. 3

    Work it out.

    x = 7

Answer: x = 7

Check: 6 × 7 = 42 ✓

⚠️ The usual mistake

Solves x + 9 = 23 as x = 32.

They do the same operation again instead of the opposite one.

Fix: Ask before calculating: should x be bigger or smaller than 23? x plus something is 23, so x must be smaller.

💬 Say this

“Whatever we do to one side, we do to the other. What do we do to get x by itself?”

🏠 Try it at home

Use the interactive scale below on the hardest setting. Can they get the box alone in the fewest moves?

3

2x means 2 times x

A number stuck to a letter means multiply. 2x is 2 × x, so if x is 4 then 2x is 8 — not 24.

x2x + 5
17
29
413
10?

Worked example

Find 2x + 5 when x = 4.

  1. 1

    Write the hidden ×.

    2 × x + 5

  2. 2

    Put 4 in for x.

    2 × 4 + 5

  3. 3

    Multiply, then add.

    8 + 5 = 13

Answer: 13

Check: 2x + 5 means double it and add 5. Double 4 is 8, add 5 is 13 ✓

⚠️ The usual mistake

Writes 2x as 24 when x = 4.

Sticking digits side by side is how place value works, so 2 and 4 become 24.

Fix: Always write the × in for the first few weeks: 2 × x. Then put the number in.

💬 Say this

“What is hiding between the 2 and the x?”

🏠 Try it at home

Pocket money: “You get 2x + 5 dollars, where x is the number of chores.” What do 3 chores earn?

4

Rules make pictures

Every rule makes pairs of numbers. Plot the pairs as points and a rule like “double it” draws a straight line.

−5−555xy
  • y = 2x
  • (1, 2) (2, 4) (3, 6)

Worked example

Plot the rule y = 2x for x = 1, 2 and 3.

  1. 1

    Make the pairs.

    (1, 2), (2, 4), (3, 6)

  2. 2

    First number: go across. Second number: go up.

    (1, 2) is 1 across, 2 up

  3. 3

    Join the dots.

    a straight line through (0, 0)

Answer: A straight line going up 2 for every 1 across.

Check: Any point on the line follows the rule — (2.5, 5) does too.

⚠️ The usual mistake

Plots (1, 2) at 2 across, 1 up.

Nothing about the brackets says which number goes which way.

Fix: “Along the corridor, then up the stairs.” Across first, always.

💬 Say this

“Across the corridor first, then up the stairs.”

🏠 Try it at home

Play battleships on squared paper using (across, up) coordinates.

⚖️ Keep it fair

Get x 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: x + 2 = 5

x

x + 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.

One-step equations

Do the opposite to both sides. Check by putting your answer back in.

Solve for x.

x + 4 = 12

Evaluate it

Remember: 2x means 2 × x.

Work it out when x = 45.

x ÷ 5 + 1

The words, in plain English

x
The most common letter for an unknown.
x + 9 = 23
Inverse operation
The move that undoes another.
÷ 6 undoes × 6.
Solve
Find the number that makes the equation true.
x + 9 = 23, so x = 14.
Coefficient
The number stuck to a letter.
In 6x, the coefficient is 6.
Coordinates
A pair (across, up) giving a point’s place.
(3, 6)

🌍 Algebra in an ordinary day

  • “The bill was $42 split between 6 people — how much each?”
  • Working out how many weeks of saving $5 gets you to $35
  • Reading a map grid: B4, then coordinates

🏁 By the end of 5th Grade

  • Names the inverse of each operation
  • Solves one-step equations by undoing, on both sides
  • Evaluates expressions with coefficients like 2x + 5
  • Plots points from a rule and sees the line

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

4th Grade: Number Recipes

One rung up →

6th Grade: Balance and Tip

All 12 gradesMore maths, grade by grade →

Frequently Asked Questions

What algebra should a 5th Grade child learn?

To find a hidden number, undo what was done to it — with the opposite operation, on both sides. By the end of the year they should be able to: names the inverse of each operation; solves one-step equations by undoing, on both sides; evaluates expressions with coefficients like 2x + 5; plots points from a rule and sees the line.

Isn’t 5th Grade too early for algebra?

No — undo it is standard 5th Grade maths in most curricula. This page breaks it into single moves so it never feels like a jump.

What is the most common 5th Grade algebra mistake?

Solves x + 9 = 23 as x = 32. They do the same operation again instead of the opposite one. The fix: Ask before calculating: should x be bigger or smaller than 23? x plus something is 23, so x must be smaller.

What if my child is stuck?

Go down one rung. Every lesson here builds on the 4th 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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