L3 · Unknown values and the balance model

Learning goal

“I can model an equation with a balance: the pans are level when both sides hold the same amount. I can find the unknown value that keeps the balance level, whether the unknown is on the left pan or the right pan.”

Unknown value — an amount we do not know yet. In □ + 4 = 11, the unknown is how much is hiding in the box.

Symbol — a mark that stands for the unknown value. This unit uses a box, □. (A letter can do the same job.)

Balance — a scale with two pans. It sits level only when both pans hold the same amount - exactly like an equation.

Level — flat and even. A balance is level when the two sides are equal; it tips toward the heavier side when they are not.

Worked example

Model □ + 4 = 11 on a balance. The left pan holds a covered box and 4 loose blocks. The right pan holds 11 blocks. The balance is level, so the pans hold the same amount: □ + 4 = 11. Step 1: Take 4 blocks off the LEFT pan - the box is now alone. Step 2: A balance only stays level if you do the same to both pans, so take 4 blocks off the RIGHT pan too: 11 - 4 = 7 blocks remain. Step 3: The box alone balances 7 blocks: □ = 7. Check by putting it back: 7 + 4 = 11 - the balance is level again.

Check yourself — explain it

Why must we take blocks off BOTH pans, not just the pan with the box?

Paired problem — example still visible

A balance is level: left pan □ + 5, right pan 13. Find □ -> □ = 8 (take 5 off both pans: 13 - 5 = 8)

Faded completion — last step is yours

"□ + 6 = 14: take 6 off both pans, so □ = 14 - 6 = ___" -> 8

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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