🧱 See It

Picture a balance scale. On the left side sits a mystery bag (it holds some number of blocks, but you can't see how many) plus 3 loose blocks. On the right side sit 7 loose blocks. The scale is perfectly level — both sides weigh exactly the same.

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Mystery bag + 3 blocks = 7 blocks. What's in the bag?

✏️ Draw It

To find the mystery bag's weight without opening it, remove the same number of blocks from both sides. The scale stays balanced no matter what, as long as you do the exact same thing on each side.

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Take 3 blocks off each side — the mystery bag is left alone on the left, and 4 blocks remain on the right.

The bag weighs 4.

🔢 Write It

The mystery bag is written as a letter, usually x. The picture above becomes:

x + 3 = 7

Subtract 3 from both sides — same move as taking 3 blocks off each pan:

x + 3 − 3 = 7 − 3

x = 4

Whatever you do to one side of the equal sign, you must do to the other side too.

💡 Worked Examples

Example 1 — Addition: x + 5 = 12

  1. Goal: get x alone.
  2. Subtract 5 from both sides: x + 5 − 5 = 12 − 5
  3. Answer: x = 7

Example 2 — Multiplication: 4x = 20

Here 4x means "4 mystery bags." All 4 bags together weigh 20, so each bag weighs a quarter of that.

  1. Goal: get one x alone.
  2. Divide both sides by 4: 4x ÷ 4 = 20 ÷ 4
  3. Answer: x = 5

🧠 Quick Reference

If the equation has…Undo it with…
x + a = bSubtract a from both sides
x − a = bAdd a to both sides
a·x = bDivide both sides by a
x ÷ a = bMultiply both sides by a

Addition and subtraction undo each other. Multiplication and division undo each other.

👪 For Parents & Tutors

BC Curriculum (Level 1 / Grade 6, Patterns & Relations): "One-step equations with whole-number coefficients and solutions."

Why this method: The balance-scale model is the same one used in Polypad's algebra tiles and is the model his Zoom tutor should already be using — staying consistent with it here matters more than the specific wording (see the parent/tutor terminology-consistency rule).

Watch for: The working-memory trap isn't the arithmetic here (it's simple), it's remembering to apply the same operation to both sides — mid-solve, working memory can drop the second half of "subtract 3 from both sides" and only subtract it from one. Have him physically write the operation under both sides of the equation every time, not just think it.

Comes up again: This is the direct foundation for Level 2's two-step equations, Level 3's equations with integer coefficients, and Level 4's multi-step equations with variables on both sides — same balance principle, just more steps stacked on top.