
Here is a puzzle on the scales: 2x + 3 = 11. Two bags of the same size, plus three loose cubes, balance eleven cubes on the other side. Two things have happened to the bag: it was doubled, and three were added. Which one would you undo first to find what is in a single bag?
Take two or three hands-up answers, not open call-outs. Do not settle which step goes first yet — that is the whole lesson. Listen for a pupil who says take the 3 off first and hold their idea for Watch and Notice.
Three balanced puzzles on the scales, each still in its starting state. For each one, the loose cubes need to come off both pans first, and then the bags are shared out. Work out what a single bag is worth each time.
Look hard at the first puzzle before we solve it. The three loose cubes are still sitting on the pan. If we tried to share out the bags with those cubes still there, could we even tell what one bag holds? Why not?
The last one takes away instead of adds. The missing cubes need to go back on both sides first.
On the first puzzle, ask the class the wrong-order question before you solve it: what if we shared out the two bags while the 3 loose cubes are still on the pan? Let a pupil explain that you cannot read a clean bag value while extra cubes are mixed in — the loose cubes get in the way. Then talk through peeling the loose cubes off first and finish it properly on the board. Hold this reasoning; the class points back to it in the reflection.
Now we solve one together on the scales: 2x + 5 = 13. First we take the loose cubes off both pans. Then we share out the bags. Say what you will do to both pans before anyone touches the slider.
Talk this one through together — a pupil comes to the board and the class agrees or corrects out loud.
Insist on the plan before the action: which loose cubes come off first, then divide by what? Revoice a strong answer: so we peel the number off before we share out the bags. Two more equations of this kind come up in the copybook and the Class Challenge, so keep this one crisp.
We just solved 2x + 5 = 13 on the scales. Now look at how that same work is written in two lines in your copy.
First line (peel the loose number off both sides): 2x = 8
Second line (share out the bags): x = 4
Box the final value of the letter.
In your maths copy, solve each two-step equation the same way: show both steps on separate lines, then box the final value of the letter.
Write the first line (what you did to both sides), the second line (dividing to find the letter), then box your answer.
On the board, write the worked bridge from Try It Together before anyone opens a copy:
Point: first line undoes the add or subtract, second line divides by the multiplier. Leave it up while they work.
Walk the room glancing for two separate working lines, not just an answer. This is whole-class copybook practice, not marking. Watch the take-away case (3x − 1 = 14): pupils often divide before adding the 1 back.
Now we take turns solving these on the scales. First 2x + 5 = 13. Then 5x − 4 = 21. Then 3x + 2 = 20. Then 4x + 6 = 12, and that last one lands on an answer that is not a whole number. Peel off the number first, then divide. Predict where the beam will level before we check.
This is the practice round — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.
The last one, 4x + 6 = 12, gives 4x = 6, so x = 1.5 — hold out until a pupil realises the bag can hold half a cube. Use the ✓ as your confirm: yes, the beam is level, so that is it.
You're previewing this lesson. Get full access to this lesson and hundreds more — each one ready to teach, with interactive activities, printable resources and pupil progress tracking built in.