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Grade 7 · Percent change

Ticket model: Track the percent reference base

Ticket model investigation: track the percent reference base. Change the quantities, follow the motion, and explain the result using the displayed mathematical relationship.

Predict what will happen, press Play, then pause and explain what changed. Every control also works without playback.

Watch the relationship

Paused
Ticket model: Track the percent reference base. Original whole: 70. Signed percent: -10%. Current changed amount: 70. Final answer: 63Percentage change keeps the original baseOriginal whole: 70Changed amount: 70Chosen final percentage: -10%
The percentage is between −50% and +100%, so every displayed amount is positive. There is one change, not repeated compound growth. Bars share a common numerical scale.

Starts paused. Play once, pause anywhere, or use Step to inspect the mathematics. Playback stops when this panel leaves the screen.

Make it your experiment

Change one value. Notice what follows.

The controls adjust the model. Numbers below describe the current frame. Decimals are rounded.

Original whole
70
Signed percent
-10%
Current changed amount
70
Final answer
63

HD animation studio

From experiment to screen.

Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.

Understand what you are seeing

The idea behind the motion.

A percentage change is calculated from a specified original amount. An increase adds a positive part and a decrease adds a negative part. Applying the same percentage to the new amount generally does not undo the first change because the reference whole has changed. This investigation begins with original amount = 70; signed percent change = -10. Treat the named setting as a constructed classroom model, then explain which relationships would still hold if its numbers changed.

A relationship to keep

new = original × (1 + percent/100)

Read the symbols alongside the explanation. A diagram shows the relationship; the assumptions tell you when it applies.

  1. STEP 1

    Represent the given quantities

    Keep the original amount visible as the reference for the requested signed percentage.

  2. STEP 2

    Follow the changing model

    Watch the second bar extend for an increase or shorten for a decrease; the change is original×percent/100.

  3. STEP 3

    Check and explain the relationship

    Compare the new and old amounts. To reverse the process, divide by the multiplier instead of simply changing the percent sign.

Your turn to explain

Make a prediction. Test your reasoning.

Ticket model: Change 70 by -10%. What is the new amount?

Use the values specified in the question. Reset restores the initial values for this investigation.

Compare your explanation

63; the signed change is -7, calculated from the original 70.

Work through a full lesson

Connect the animation to a worked example and practice questions.

Grade 7 · Algebra

Choose the base of a percentage change

A percentage change compares a difference with the original value, so reversing a change uses a different base.