Math With AmarA C A D E M Y
All math animations

Primary · Number sense

Count once, even when the arrangement changes

Follow one object at a time and discover why moving objects does not change how many there are.

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

Watch the relationship

Paused
Count once, even when the arrangement changes. Counted: 0. Still to count: 12. Total objects: 12One object. One counting word.Counted0of 12
Each circle represents one distinct object. The total and row length are whole numbers. Coloring records which objects have been counted; it does not create new objects.

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.

Counted
0
Still to count
12
Total objects
12

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 counting word belongs to exactly one object. The final counting word tells the size of the whole collection. Arrange the same collection in shorter or longer rows, then count again: the layout changes, but the total does not.

A relationship to keep

Counted objects + objects still to count = total objects

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

  1. STEP 1

    Choose the collection

    Set the number of objects. Each pale circle is one object, including those in an incomplete final row.

  2. STEP 2

    Pair a word with an object

    Move the timeline forward. Each newly colored circle receives the next counting number, so no object is skipped or counted twice.

  3. STEP 3

    Rearrange and check

    Change the row length while keeping the total fixed. Finish counting again and compare the result. Zero means that there are no objects to count.

Your turn to explain

Make a prediction. Test your reasoning.

Twelve objects are arranged first in rows of four and then in rows of three. How many objects are there after the rearrangement?

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

Compare your explanation

Still 12. Rearranging changes the rows, not the number of objects.

Work through a full lesson

Connect the animation to a worked example and practice questions.

Grade 1 · Algebra

Count every object once

Match one counting word to each object.

Grade 2 · Algebra

Read an array by rows and columns

Represent equal rows as repeated addition.