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A friendly flat-vector scene of two bars drawn exactly the same length with different labelled pieces inside, beside an equals sign, in IllumiTutor navy and amber on an off-white background.

The Equal-Stage Method

Drawing equal-length bars at the moment two quantities are the same, then solving for one unit.

⏱ 5 min · 🎯 4 things to master

Some problems hand you a golden clue: at some moment, two people have the same amount. Whenever you read "the same number", "equal", or "they then had the same", draw the two bars exactly the same length at that stage. Lining them up turns the hidden pieces inside into something you can compare — and the answer falls out.

Parents: let your child draw the two bars equal before revealing. The "Method tip" boxes name the move a marker rewards — starting from the equal stage.

By the end you'll be able to use an "equal amount" clue to draw equal bars and solve. Let's line them up.

Draw the equal moment

The clue is the word (or "the same"). At that stage, the two bars must be drawn the same length. Anything different inside them — extra boxes, extra dollars — must therefore balance out. That balance is what you solve.

🤔 Predict first: Aisha and Bina end up with the same amount of money. On a bar model, how should their two bars look?

Match the pieces inside

Suppose at the end Aisha and Bina have the same amount. Aisha has 3 identical boxes plus $5. Bina has 2 identical boxes plus $25. Because the totals are equal, draw both bars the same length:

3 boxes + 5 = 2 boxes + 25.

Take 2 boxes off each side: 1 box + 5 = 25, so 1 box = $20. The equal stage let you cancel the matching boxes and find one box.

🤔 Predict first: 3 boxes + $5 equals 2 boxes + $25. Taking 2 boxes from each side leaves…

Equal at the start or the end

The equal moment can be at the start ("they had the same to begin with") or at the end ("they then had the same"). Either way, draw the bars equal at that stage and work outwards from it.

🤔 Predict first: Two boys START with the same number of marbles. Where do you draw the equal-length bars?

Watch out — these are easily mixed up

Quick recap

🎯 Mastery check

Answer all 6 — your progress is saved on this device.

  1. A problem says two children end up with the same amount. What does that tell you to draw?

  2. 3 boxes + $5 equals 2 boxes + $25. After cancelling 2 boxes from each side, what is left?

  3. From "1 box + $5 = $25", what is one box worth?

  4. Which phrase signals the equal-stage method?

  5. 4 boxes + $3 equals 1 box + $18 (equal amounts). What is one box?

  6. The equal stage in a problem can be…